2018 - 4 - 16_GS on Vol

PORTFOLIO STRATEGY RESEARCH | April 16, 2018 | 11: 20PM BST

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A taste of the high (vol) life Drivers and asset allocation implications of changing volatility regimes Christian Mueller-Glissmann, CFA +44 20 7774-1714 [email protected] Goldman Sachs International

M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

Alessio Rizzi +44 20 7552-3976 [email protected] Goldman Sachs International

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The S&P 500 vol spike in February has snapped markets out of the low vol regime that dominated 2017. The speed and size of the vol spike has been extreme, especially as it came from very low levels - it has also been exacerbated by technical factors. With volatility an important driver of asset allocation and portfolio risk, the key question is if we have entered a genuinely new regime and whether high vol will remain. The S&P 500 has moved through 15 low and 14 high vol regimes in the past 100 years. While we find the macro backdrop tends to condition vol regi mes, regime shifts have often been difficult to pin on macro alone. In addition vol of vol has increased since the 90s, resulting in faster regime shifts. We We identify macro and market drivers for S&P 500 volatility to assess the probability of regimes. We find a lower probability of a continued low vol regime, but a sustained high vol regime still appears unlikely based on current macro and market indicators. Low vol regimes tend to be 'risk on' and carry-friendly, which usually means rising valuations across assets. The The opposite is true in high vol regimes, somewhat unsurprisingly. Higher volatility means lower risk-adjusted returns, both for equities and for multi-asset portfolios broadly. High vol regimes can also result in 'buying the dip' being a less good strategy, as drawdowns can last longer and be deeper. With rising volatility, somewhat counter-intuitively, counter -intuitively, option selling strategies st rategies have performed better: we find that call overwriting and put writing is more attractive outside low vol regimes.

Ian Wright +44 20 7774-2600 [email protected] Goldman Sachs International

WHAT’S INSIDE Return of risk? 2018 had a volatile start after the low vol in 2017 (p.3) A brief history of vol regimes from cyclical drivers to structural shifts (p.9) Probable cause potential macro and market drivers of vol regimes (p.17) From the low to the high (vol) life asset allocation implications (p.23)

This report is intended for distribution to GS institutional clients only. only. Goldman Sachs does and seeks to do business with companies covered in its research reports. As a result, investors should be aware that the firm may have a conflict of interest that could affect the objectivity of this report. Investors should consider this report as only a single factor in making their investment decision. For Reg AC certification and other important disclosures, see the Disclosure Appendix, or go to www.gs.com/research/hedge.html. www.gs.com/research/hedge.html. Analysts employed by non-US affiliates are not registered/qualified as research research analysts with FINRA in the U.S. This report is intended for distribution to GS institutional clients only. The Goldman Sachs Group, Inc.

Goldman Sachs

GOAL - Global Strategy Paper

Summary �

The S&P 500 50 0 vol spike in February has snapped mark markets ets out of the low vol regime that dominated 2017. The speed and size of the vol spike has been extreme, especially coming from very low levels - it has most l ikely been exacerbated by technical factors. Also, the contagion to volatility across assets has been limited. Since 1928 there have been 34 cases when vol has spiked more 20% (10 (1 0 cases with a peak below bel ow 30%) - those usually normalise in 2-3 months. With volatility an important driver of asset allocation and portfolio risk, the key question is if we have entered a genuinely new regime and whether high vol will remain.

�

The S&P 500 has moved through 15 low and 14 high vol regimes in the past 100 years. While we find the macro backdrop tends to condition vol regimes, regime shifts have have often been difficult to pin on macro alone. Especially since the Great Moderation, vol has often disconnected and led macro, in part due to the unwind of financial imbalances. We find the predictive power of current volatility for the


future, the vol clustering effect, has become less strong as vol of vol has picked up since the 1990s. Also, longer periods of low volatility increase risk of higher volatility in the medium term as they can result in financial and market imbalances. �

We identify macro and market drivers for S&P 500 volatility to assess the probability of shifts between regimes. We find that the probability of a continued low vol

regime has declined but a sustained high vol regime still appears unlikely unlikely.. That said, anticipating vol regime shifts has been difficult and vol often leads the indicators we identified. Low vol vol regimes can be more easily forecast, as these might be more related to the macro, whereas high vol regimes may may,, at least initially, be less linked to fundamentals. Hi gh vol regimes regularly come with extremes in the indicators. The probability of being i n a low vol regime is often highest when indicators are favourable – but not at extremes, as that could signal a turning point. �

Low vol regimes tend to be ‘risk on’ and carry-friendly, which usually means rising valuations across assets. The opposite is true in high vol regimes, somewhat unsurprisingly. unsurprisingly. S&P 500 risk-adjusted returns tend to be highest during low vol regimes regi mes and the same was true in 201 2 017 7, when the S&P S& P 500 had ha d a 12m return / volatility ratio of 4.2x. Similarly for multi-asset portfolios, portfolios, changing changing vol regimes are important as equity/bond correlations have been more positive; in addition, high S&P 500 volatility often coincides with high volatility across assets.

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As volatility increases, so does the probabili ty of larger moves, in both directions.

This also means that ‘buying the dip’ tends to be a less good strategy at those times, as drawdowns can last longer and be deeper. That said, large vol spikes can increase the medium-term asymmetry of equit y returns. With rising volatility, somewhat counter-intuitively, option selling strategies have performed better: we find that call overwriting and put writing is more attractive outside low vol regimes. Many thanks to Peter Oppenheimer, Sharon Bell, Kathy Matsui and Rocky Fishman for their helpful comments. For our index options research and more details on the VIX, covered by Rocky Fishman, see here .

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Return of risk? 2018 had a volatile start after the low vol in 2017 A volatile start to 2018, led by higher equity volatility For most of 2017 2017 S&P 50 0 volatility was very ver y low, both relative to its history and relative to other equity markets. A long-term perspective reveals that S&P 500 1-month realised volatility was close to 100-year lows, despite perceived high political and policy uncertainty. As we wrote in the middle of last year, such ‘boring’ markets can last a long time; they are more common than investors think and have been closely linked to ‘Goldilocks’’ periods, with accelerating growth and anchored inflation (see GOAL - Global ‘Goldilocks Strategy Paper: The upside of boring, boring , June 20, 2017).

Now, after more than 19 months of very low equity volatility globally, the equity drawdown drawdo wn that started at the end of January has been followed by more lasting high volatility. The shift to higher vol was initially triggered by higher rates vol (see M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

GOAL Post: Post: ‘Tis the season to be vol-ly vol-ly,, October 13, 2017) and the unwind of short VIX ETFs. But recently it has moved into a broader worries, including a gl obal growth slowdown, monetary policy uncertaint y, ‘trade wars’ wars’ and headwinds for the US tech sector.. While the recent S&P 500 realised vol spike is well below those seen during the sector Global Financial Crisis and when the Tech Bubble burst, it has been close to some of the larger vol spikes in the last 100 years, similar to the 2015/16 2015/16 EM/oil crisis. Also, the VIX had a large spike to levels l evels close to those during the Asian Financial Crisis in 1998 and the invasion of Kuwait in 1990 (Exhibit 1). Exhibit 1: The vol spike in February was comparable to some of the larger ones in the last 100 years S&P 500 1-month volatility history (since 1928) and VIX (since 1990) 90

VI X

Great Depression

S &P &P 5 00 00 1 -m -m on on th th r ea ea lili se se d

Black Monday

80 Industrial production plunge WW II begins

70 60

Start of Cold War Post war inventory crisis

50 40

Eisenhower recession

Suez Crisis

Escalation Cold War

John F. Kennedy assassinated Cuban Missile Crisis

Vietnam war & monetary tightening

Iran oil production cut

First Oil price shock

Volcker monetary tightening

Invasion of Kuwait

Asian financial crisis

Global Financial Crisis

Tech bubble burst LTCM/ Russian Crisis

May flash crash

US debt downgrade & Euro area crisis EM/ oil crisis

9/11

30 20 10 0 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18

Source: Bloomberg, Datastream, Goldman Sachs Global Investment Research

During the ensuing global equity draw drawdown, down, volatility across assets increased as well, although equity volatility picked up most. During the low vol regime, equity volatility was particularly low compared with history and with other assets. Now Now,, several weeks after the initial spike, S&P 500 1-month volatility remains well above the lows from 2017 2017. US equity equit y volatility volatili ty had the largest lar gest spike out ou t of the different equity equit y markets, and in the recent volatility normalisation S&P 500 volatility has lagged, with non-US

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volatility declining much faster (Exhibit 2 and 3). In part this is due to the continued volatility in the US tech sector, sector, which has a large weight in the S&P 500. Also, volatility

across assets has settled again at below average average levels (Exhibit 4). Exhibit 2: While equity vol was particularly low during the low vol regime, it also rebounded most

Exhibit 3: Volatility has increased most for the S&P 500, which was also particularly low compared with history

Percentile of 1-month realised volatility across assets (since 1970)

Percentile of 1-month realised volatility across equity markets (since 1970)

100%

Bond

TOPIX 80%

Commodity Credit

70%

60%

50%

50%

40%

40%

30%

30%

20%

20%

10%

10%

AprApr-16 16

JulJul-16 16

OctOct-16 16

JanJan-17 17

AprApr-17 17

JulJul-17 17

OctOct-17 17

MSCI EM

70%

60%

0% JanJan-16 16

S&P 500 MSCI Europe

90%

FX

80%


100%

Equity

90%

JanJan-18 18

Apr-1 Apr-18 8

Sour So urce ce:: Blo Bloom ombe berg rg,, Dat Datas astr trea eam, m, Go Gold ldma mann Sach Sachss Glob Global al In Inve vest stme ment nt Re Rese sear arch ch

0% J an an -1 -1 6

A pr pr -1 -1 6

J ul ul -1 -1 6

O ct ct -1 -1 6

J an an -1 -1 7

A pr pr -1 -1 7

J ul ul -1 -1 7

O ct ct -1 -1 7

J an an -1 -1 8

A pr pr -1 -1 8

Sour So urce ce:: Blo Bloom ombe berg rg,, Dat Datas astr trea eam, m, Go Gold ldma mann Sac Sachs hs Gl Glob obal al In Inve vest stme ment nt Res Resea earc rchh

Exhibit 4: Recent volatility has been mostly an equity story - volatility across assets has settled again, while S&P 500 remains elevated 1-month realised volatility (daily changes) 1-month Volatility Data since: Current: 1m Change: Percentile: Since 1990: Average: Median: 75th: 25th: Max: Min:

S&P 500 Jan-28 23.0 8.1 86% 87% 15.4 12.4 17.7 9.2 103.8 2.6

Equities MSCI MSCI TOPIX Europe EM Dec-71 May-49 Jan-70 13.7 18.3 13.5 1.4 0.6 -1.6 69% 75% 53% 54% 55% 49% 12.9 14.9 14.8 10.4 12.9 13.1 15.3 18.4 17.3 7.8 9.0 10.1 78.3 102.7 97.1 3.6 2.8 3.4

B on d s German US 10Y US 30Y 10Y Jan-62 Feb-77 Mar-77 4.8 10.6 2.9 -0.4 -0.7 -0.9 33% 45% 16% 14% 42% 7% 6.3 12.0 4.8 5.9 11.0 4.4 7.8 14.3 5.9 4.2 8.9 3.4 23.9 35.3 15.6 0.5 1.8 0.6

Japan 10Y Jul-86 1.2 0.0 3% 3% 4.3 3.8 5.2 2.6 17.8 0.8

Credit DJ US HY Credit Jan-16 Jan-90 3.7 2.1 0.2 -1.2 69% 48% 38% 48% 3.3 3.0 2.5 2.2 4.3 3.5 1.5 1.5 23.2 25.0 0.4 0.1

C o m m o d i ti e s Gold

Oi l

GSCI

Dec-68 Jan-83 Dec-69 13.4 26.5 15.9 2.1 2.8 1.8 47% 38% 51% 54% 32% 40% 16.9 33.8 17.2 14.0 30.0 15.6 19.9 40.6 21.1 10.0 21 2 1.6 11 1 1.2 105.4 16 160.2 73.8 0.6 2.1 4.4

FX EUR

J PY

GBP

Aug-71 Sep-71 Aug-71 6.1 6.7 6.2 -1.1 -2.8 -0.6 21% 22% 24% 12% 14% 19% 8.9 9.7 8.7 8.6 9.1 8.2 11.0 11.9 10.4 6.5 7.0 6.3 27.9 34.8 35.7 0.7 1.2 0.3

Source: Bloomberg, Datastream, Goldman Sachs Global Investment Research

S&P 500 vol spike was large but the peak level was low relative to history Nevertheless, compared with historical S&P 500 1-month vol spikes above 20%, the peak level was relatively low (Exhibit 5). There have been 34 instances when S&P 500 50 0 1-month 1month vol spiked about 20% since 1928: the average peak was around 40%. Usually a S&P 500 vol spike normalises within 3 months, often even faster, faster, towards an average level of 15%, whereas so far S&P 500 1-month realised vol is tracking at the lower end of historical levels after a large vol increase.

That said, it was unusual to have such a large vol spike originate from such low levels of volatility: realised realised S&P 500 50 0 1-month vol spiked from levels close to 5% in Q4 2017 to more than 25%. On average, vol spikes above 20% have historically come from levels above 10%: of the 34 vol spikes above 20%, only four came from levels l evels below 10%, which which were during the low vol regimes of the 1950s and 1960s. But this vol spike has come from the lowest levels ever. ever. We We think this is to a large extent due to technical factors, as we discuss in the grey box below. below.

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Exhibit 5: S&P 500 vol spike is large compared to history but the peak is relatively low S&P 500 1-month realised volatility around volatility spikes above 20 (34 instances since 1928) 45

25th/75th Percentile Average

40

Current

35 30 25 20 15 10 5 -9m 0


-6m

-3m

+3m

1 year before

+9m

+6m

1 year after

Vol spike

Source: Bloomberg, Goldman Sachs Global Investment Research

Looking at S&P 500 vol spikes above 20% but below 30%, similar to this one, confirms it is unusual to have such a large vol spike from such low vol levels of volatility; i.e., the normalisation of vol after the spike tracks history closely. Based on history after a vol spike above 20% but below 30%, S&P 500 vol should settle after 2-3 months at an average level around 10%. This suggests that S&P 500 vol should continue to decline from here, although clearly this also depends on many other factors (Exhibit 6).

The correction around the vol spike was small compared with history but faster (Exhibit 7). It was roughly in line with corrections during spikes below 30% and with historical bull market corrections. Drawdowns within bull markets of 10% or more (but less than 20%) are not uncommon (we find 22 since 1945): the average correction is 13% and lasts four months (with the recovery also lasting four months). With the continued correction, the S&P 500 is tracking slightly below the ‘normal’ recovery. Exhibit 6: But the vol spike has come from much lower levels than historically would be the case

Exhibit 7: S&P 500 is tracking slightly below the ‘no rmal’ recovery Based on 34 vol spikes above 20% for the S&P 500 since 1928

S&P 500 1-month realised volatility around vol spikes above 20 but with a peak below 30 (10 instances since 1928) 30

25

115

25th/75th Percentile Average Current

110

105 20 100 15 95 10 90 5

0

Average Average for spikes below 30 Average for bull market corrections Current

85 -9m

1 year before

-6m

-3m

+3m

Vol spike


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+6m

+9m

1 year after

80

-9m

1 year before

-6m

-3m

+3m

Vol spike

+6m

+9m

1 year after


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VIX fallout and technical factors have likely exacerbated the vol spike The S&P 500 vol spike and drawdown have likely been exacerbated by the VIX fallout. The VIX spike in February was one of the largest on record and was exacerbated by technical factors (Exhibit 8, see Global Markets Daily: A Technical Sell-off, February 6, 2018). Positioning in short vol strategies was large at the beginning of the year. VIX futures positioning was very short and our Options team highlighted aggregate net short vega position across VIX ETPs at the beginning of the year (see VIX Positioning: VIX ETPs Are Now Net Short Vega - Should We Worry?, January 11, 2018). As our Options team pointed out, there was considerable evidence of distress vol buying from those ETPs. If some of the investors selling VIX futures to ETP issuers simultaneously sold S&P 500 futures as a hedge against the market risk inherent in their short VIX future positions, their positioning could potentially have weighed on equities and increased realised vol. Exhibit 8: Compared with history, the VIX spike ha s been large and from unusually low levels Historical VIX spikes above 20 (19 instances since 1990) M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

40


35

30

25

20

15

10 -9m

-6m

-3m

+3m

+6m

+9m

5

1 year before

VIX spike

1 year after

Source: Datastream, Goldman Sachs Global Investment Research

The VIX had the largest 1-day move in histor y, jumping from 17.31 to 37.32, a move of 20 VIX points. It was larger than during the Lehman failure in October 20 08 or on September 11, 2011 (Exhibit 9). It has only increased >50% on four other occasions (8/8/2011, 2/27/2007, 11/15/1991, 7/23/1990). That said, the drawdown was smaller compared with the VIX spike based on the historical spot/vol relationship (Exhibit 10). Owing to the unwind of short VIX strategies, the spike has been larger and faster but the same has been true for the normalisation: the VIX declined sharply in the days after, alongside realised volatility, before picking up again more recently. But the recent increase is unlikely to be driven by the same VIX ETP trading dynamics, as the AuM in those strategies is lower and the level of the VIX is still elevated (see VIX: Q&A on the Trading Dynamics of ETPs, February 7, 2018). Besides the VIX fallout, other technical factors have likely driven higher vol of vol during the recent vol spike (see GOAL Post: Correction dissection - drivers and implications of the equity drawdown, February 7, 2018). It is likely the equity drawdown has also been exacerbated by a reversal of bullish positioning from investors via upside calls, CTAs, vol target and risk parity funds after a strong, low vol Q4 2017.

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Exhibit 9: February 8, 2018 saw the largest 1-day VIX move in history 25

Lehman bankruptcy

20

US rating downgrade

September 11, 2001

15

Exhibit 10: The VIX spike was much larger than the move in the S&P 500 would imply 25

Brexit

20

CNY devaluation

October 2008

15

R² = 0.62

February 2018

August 2011

X I 10 V n i 5 e g n a 0 h c y l i a -5 D

10 5 0 -5

-10

-10

-15

VIX 1-day moves February 5, 2018

-15

-20 -10%

-20 90

92

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S ou rc e: D at as tr eam , Go ld ma n S ac hs Gl oba l I nv es tme nt R es ea rc h


12

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18

-8%

-6%

-4%

-2%

0%

2%

4%

6%

8%

10%

12%

Daily S&P 500 return

S ou rc e: D at as tr ea m, Go ld ma n S ac hs G lob al I nv es tme nt R es ear ch

Higher portfolio risk YTD with little diversification across assets The S&P 500 vol spike has snapped markets out of the low vol regime that dominated 2017. Long periods of low volatility can increase risks of higher equity volatility in the medium term as they might boost risk appetite from proyclical investors. Very low volatility usually signals stable or improving macro conditions which are supporting risk appetite. Of course, such a backdrop also attracts systematic, procyclical investors such as vol target funds, CTAs and risk parity investors, and encourages them to use leverage, short vol strategies and take illiquidit y risk. On the flipside, breaking out of the low vol cluster might have contributed to the ongoing fragility and higher vol more recently as risk appetite from investors has waned due to concerns over a new vol regime with higher levels of volatility.

With the shift towards higher equity volatility, portfolio risk as a whole has also increased due to positive equity/bond correlations and bonds not being good hedges during the equity drawdown. We have highlighted this risk before: the ‘bull market in everything’ has resulted in a valuation frustration, with bonds, equities and credit somewhat expensive at the same time, limiting potential for diversification ( Global Strategy Paper: The Balanced Bear Part 1: Low(er) returns and latent drawdown risk , November 28, 2017). In Q1, the classic ‘safe havens’, which usually outperform when the VIX spikes, have not provided protection during the recent sell-off (Exhibit 11, GOAL Kickstart: Is anything “safe” anymore?, March 12, 2018).

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This has also increased concerns about the ‘central bank put’, which has historically helped buffer volatility. Central banks appear less able or willing to ease, with inflation likely to move higher and because they may feel that imbalances and excesses are starting to build. In addition, current easing options are more limited for central banks as rates are still low and QE purchases have only just been reduced. While in the recent period of volatility global bond yields have declined to YTD lows, the scope for further decline may be more limited. With equity volatility the key driver of portfolio risk, investors could be forced to reduce risk further in case of continued high equity volatility. Exhibit 11: In the last correction, no assets were positively correlated with VIX Correlation with VIX (weekly changes) 0.3

Correlation with VIX since 1990 Correlation with VIX in Q1 2018

0.1


-0.1

-0.3

-0.5

-0.7

-0.9

0 0 5 P & S

e p o r u E I C S M

M E I C S M

X I P O T

Y H S U

I C S G

l i O

P B G

R U E

d l o G

t i d e r C J D

Y 0 1 n a p a J

Y 0 1 y n a m r e G

Y P J

Y 0 1 S U

Y 0 3 S U

Source: Datastream, Haver Analytics, Goldman Sachs Global Investment Research

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A brief history of vol regimes — from cyclical drivers to structural shifts S&P 500 volatility tends to be countercyclical but there are other drivers Volatility tends to be countercyclical: as the cycle matures, inflation tends to pick up and recession risk increases, both of which can drive increased volatility (see also Options Research: Equity volatility and the business cycle, May 20, 2009). Of course, recessions usually result in bear markets, during which volatility tends to be higher. However, volatility tends to lead the macro and markets can be more volatile for longer than macro. Since 1929, equity volatility has tended to increase before recessions: when growth starts to slow down there is usually a shift to a higher vol regime, especially since the 1990s (Exhibit 12). Volatility tends to fall as the second derivative, or macro momentum, turns positive even if business activity is still contracting. However, the recent vol spike has happened without a US recession or S&P M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

500 bear market.

Not every vol spike is driven by the US business cycle or macro risks. There have been several periods when S&P 500 volatility shifted higher without a US recession or even without a bear market. Examples include corrections such as ‘Black Monday’ in 1987, when volatility spiked primarily due to technical factors. Also, with economies and markets becoming more global, correlations across equity markets (and assets) have increased and, as a result, the global macro backdrop can also drive S&P 500 volatility (see Global Strategy Paper: Correlation Dislocation; Drivers and & Implications , June 28, 2012); for example, S&P 500 volatility increased sharply in the the late 1990s around the Asian Financial Crisis and Russian Default, coupled with the collapse of LTCM and the EM/oil crisis of 2015-16. Exhibit 12: S&P 500 volatility usually spikes around recessions and du ring bear markets, but not only at such times S&P 500 1-month volatility (blue shading = bear market, orange shading = US recession, grey shading = both). Dashed lines represent 25/75th percentile. 70

60

50

40

30

20

10

0 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18

Source: NBER, Bloomberg, Goldman Sachs Global Investment Research

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Switching gears - markets regularly switch between vol regimes... Temporary vol spikes can always happen, even in low vol regimes. However, if volatility does not decline but is settling at higher levels it signals a new vol regime. Markets have regularly moved through different vol regimes in the past 100 years (Exhibit 13). We define high and low vol regimes as those periods during which S&P 500 volatility has clustered for prolonged periods of time (at least six months) in the bottom (<10%) and top (>18%) quartile based on histor y since 1928. The start and end are defined as the point when 1-month volatility drops below 10% / increases above 18% for the first time, and when it increases above 10% / falls below 18% respectively (and 6-month volatility follows). Exhibit 13: The past 100 years have been roughly split equally between high, low and normal vol regimes S&P 500 realised volatility history (green shading = low vol regime, orange shading = high vol regime) 70

60


50

40

30

20

10

0 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18 1-month 6-month 75th percentile 25th percentile

Source: Bloomberg, Goldman Sachs Global Investment Research.

...although their characteristics have varied in the last 100 years Including the most recent one, there have been 15 low vol regimes and 14 high vol regimes since 1928 (see Appendix 1 for an overview and comparison of the periods). The average length of a low vol regime has been 22 months (median 16 months) and the average length of a high vol regime has been 25 months (median 11 months). However, high and low vol regimes have differed materially in the last 100 years. We subdivide further into three distinct periods (Exhibit 14):

1. From 1928 up to and including World War II , which was generally very volatile due to the Great Depression and WW2. As a result, S&P 500 volatility was above the long-term average of 15% for more than a decade, and there were mostly high vol regimes.

2. 1950-90, which had frequent and prolonged low vol regimes, supported by the ‘Golden’ 1950s and the Bretton Woods agreement anchoring FX and rate volatility. Outside of the stagflation periods of the 1970s, there were few high vol regimes: most of this time saw volatility of between 10% and 18%. And, of course, there was ‘Black Monday’ in 1987, which resulted in an extreme high vol regime.

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3. Since 1990, with the ‘Great Moderation’, both low and high vol regimes seem to have become longer (the average length has been more than two years) and to some extent more extreme, with higher vol spikes. Also, there has been less time spent in neither high or low vol regimes since the 1990s. Exhibit 14: S&P 500 high and low vol regimes have changed over the last 100 years Period

1928-2018

1928-1950

1950-1990


1990-2018

Regime Low vol (<10%) Neither High vol (>18%) Overall Low vol (<10%) Neither High vol (>18%) Overall Low vol (<10%) Neither High vol (>18%) Overall Low vol (<10%) Neither High vol (>18%) Overall

Time spent 30% 38% 33%

Length (months) 22 14 25

8% 29% 63%

13 14 41

36% 52% 12%

19 17 11

38% 24% 38%

32 9 26

S&P 500 1-month volatility Average Median 75th 25th Max 9.0 8.7 10.5 7.2 20 12.5 12.2 14.5 10.0 32 24.4 20.6 28.4 16.1 108 15.3 12.4 17.6 9.2 108 9.1 9.0 10.4 7.7 14 15.3 12.4 14.3 10.5 29 26.9 22.9 33.4 16.5 108 21.4 16.5 25.9 12.0 108 8.4 8.3 9.9 6.9 16 12.3 11.9 14.4 9.6 32 20.8 18.3 23.6 14.4 100 11.9 10.7 13.8 8.2 100 9.7 9.5 11.3 7.6 20 12.9 12.8 15.2 10.4 27 22.8 20.2 25.6 16.6 90 15.5 13.2 18.4 9.7 90

Min 2.6 3.2 6.2 2.6 5.2 6.8 6.2 5.2 2.6 3.2 6.9 2.6 3.5 5.0 7.1 3.5

S&P 500 6-month volatility Average Median 75th 25th Max 9.7 9.6 10.7 8.5 18 13.0 12.7 14.8 11.3 30 25.0 21.1 27.2 17.7 59 15.9 13.1 18.1 10.2 59 9.9 9.5 11.0 8.9 13 13.6 13.7 15.0 11.9 18 28.1 24.7 34.4 18.2 59 22.5 17.9 26.8 14.0 59 9.2 9.3 10.1 8.1 18 12.5 12.3 14.5 10.9 22 21.3 18.6 22.2 16.2 46 12.4 11.4 14.4 9.3 46 10.2 10.2 11.5 9.0 18 14.0 12.9 15.4 11.8 30 22.6 20.5 24.3 18.0 58 15.9 13.3 19.6 10.7 58

Min 4.9 4.8 7.2 4.8 7.9 8.9 10.8 7.9 4.9 4.8 7.2 4.8 6.4 7.0 10.9 6.4


With the ‘Great Moderation’ since the mid-1980s, macro volatility and inflation have trended down. Inflation has been a key ingredient for a recession since WW2 as it leads to central bank tightening (see US Economics Analyst: The Next Recession: Lessons from History, June 23, 2017); the lack of inflation has allowed central banks to err on the side of caution and buffer the business cycle. This saw the advent of the ‘central bank put’ since the 1990s, which has driven generally negative equity/bond correlations during ‘risk off’ episodes and thus has helped buffer market shocks as well.

As a result, expansions have become longer and, with them, so have low vol regimes (Exhibit 15 and 16). Exhibit 15: Since the Great Moderation there has been more volatility during expansions

Exhibit 16: Since the 1990s, both high and low vol regimes have been longer

Length of expansion phases and months spent in different vol regimes

Length of S&P 500 vol regimes (dark blue = high vol, light blue = low vol)

140

Months in high vol regime

100

Months in low vol regime

90

120

Neither

80

100

70 60

80

50 60

40 30

40

20 20 10 0

0 1927 1933 1938 1945 1949 1954 1958 1961 1970 1975 1980 1982 1991 2001 2009

S ou rc e: N BE R, B lo omb er g, G old ma n S ac hs G lo ba l In ve st me nt Re se ar ch

28 37 43 46 48 49 50 51 53 58 62 63 66 70 71 73 77 82 85 87 90 92 97 03 07 11 12 15 16

So ur ce: B lo om be rg , Go ld ma n S ac hs Gl ob al I nv es tme nt R es ea rc h

The longest expansion was in the 90s, when the S&P 50 0 increased for nearly a decade without major setbacks , driven by a combination of strong earnings growth, falling bond yields and low inflation. Also, as a result of lower inflation risk, real bond

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yields have trended down, which has contributed to low volatility by boosting the search for yield, supporting asset valuations and reducing pressure to deleverage. They have also boosted US share buybacks since then, which helped buffer equity volatility.

But this has also driven concerns about the so-called ‘volatility paradox’, which suggests that prolonged periods of low volatility can result in excessive risk-taking and releveraging, which then increases the latent risks on a longer horizon. Indeed, at the same time, high vol regimes have become longer and more volatile since recessions have often been accompanied by an unwind of financial and market imbalances that have built up previously (see US Economics Analyst: Monitoring Macro Risk from Financial Excess in the US Economy, March 11, 2018).

Thus, although equity volatility has been lower on average when it is low (<15%) since the 1990s, it has been higher when high (>15%), such as during the Tech Bubble burst and the GFC (Exhibit 17). Indeed, it has been a while since the US had a post-WW2 textbook recession, in which overheating led to high inflation, in turn leading M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

the Fed to tighten; as Fed Chair Powell noted earlier this year: “More recently, with inflation under control, overheating has shown up in the form of financial excess”. The two low vol regimes since the GFC, 2012-14 and 2016-18, were interrupted by external shocks (the Euro area crisis and the EM/oil crisis) - this might have helped prevent a build up of large imbalances during this cycle. The average S&P 500 1-month volatility during expansions still tends to be much lower than during recessions, and the same is true during bull markets relative to bear markets (Exhibit 18). Similarly, the proportion of time spent with S&P 500 1-month vol below 10% is unsurprisingly lower in recessions than in expansions. The difference in volatility has varied: up to and including WW2, the gap was very large. It narrowed for the 1950-90 periods, supported by Bretton Woods, and it has increased again since 1990.

The time spent with S&P 500 volatility above 18% during expansions or bull markets has also increased since the 1990s, suggesting markets have become more volatile due to reasons other than the macro. Exhibit 17: When vol is high, it is higher on average since the 1990s Comparison of 10-year average of S&P 500 1-month volatility 33

Exhibit 18: Gap between vol in ‘good’ and ‘bad’ macro phases has widened since the 1990s Average

10-year average of S&P 500 1-month volatility ...when below 15%

30

...when above 15%

27 24 21 18 15 12 9 6 38

43

48

53

58

63

68

73

78

83

88


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93

98

03

08

13

18

S&P 500 1-month volatility Median 75th 25th Vol >18%

Vol <10%

1928-50 Expansions Recessions Difference Bull markets Bear market Difference

17.9 29.5 -11.6 19.8 23.3 -3.5

14.9 25.8 -10.9 14.7 19.0 -4.3

20.9 39.2 -18.3 22.4 29.8 -7.4

11.5 14.3 -2.8 10.8 13.3 -2.5

36% 67% -30% 38% 54% -16%

14% 7% 7% 19% 5% 14%


11.3 14.7 -3.4 11.5 13.5 -2.0

10.3 13.4 -3.0 10.5 11.5 -1.1

13.1 18.2 -5.1 13.4 14.9 -1.5

8.0 9.5 -1.6 7.9 9.1 -1.1

7% 26% -19% 10% 12% -2%

46% 27% 19% 45% 34% 12%


14.0 27.3 -13.3 13.5 25.1 -11.6

12.2 22.1 -9.8 11.8 21.5 -9.7

16.8 30.5 -13.7 16.2 28.7 -12.4

9.4 17.7 -8.3 9.2 16.5 -7.3

21% 72% -51% 18% 66% -48%

31% 0% 31% 33% 1% 32%

Source: NBER, Bloomberg, Goldman Sachs Global Investment Research

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Need for speed - vol of vol suggests risk of larger and faster vol spikes S&P 500 vol spikes and have in recent years become both larger and faster. As we highlighted before, vol of vol has generally increased si nce the Great Moderation (see also Global Strategy Paper: The upside of boring, June 21, 2017) – already after the ‘flash crash’ in May 2010, parallels were drawn to ‘Black Monday’ in 1987. Since then, and again more recently, there have been several days with sharp equity declines and high intraday volatility. Exhibit 19 shows that the 10-year average volatility of S&P 500 1-month volatility has increased since the 2000s. The 5-year vol of vol has increased even more recently, indicating that this is not skewed by the GFC. With higher vol of vol, the risk of volatility overshooting relative to fundamentals has i ncreased.

The increase in vol of vol likely also reflects changes in the market microstructure: (1) changes in bank regulation such as Dodd-Frank and the Volcker rule, which have reduced liquidity across assets (see Top of Mind: A Look at Liquidity, August 2, 2015); (2) the rise of systematic investing, e.g., passive/smart beta strategies that reduce liquidit y can drive crowding; (3) CTAs, risk parity and volatility target funds, that often invest very


procyclically; (4) levered or liquidit y-constrained exchange-traded products, e.g, on high yield credit or commodities; and (5) short vol carry strategies, e.g. short VIX ETPs. As a result, we think there is an increased risk that volatility starts to disconnect again from fundamentals due to the decline in liquidity across markets (see Global Markets Daily: Post-VIX postscript: Is Liquidity the New Leverage?, March 19, 2018). Exhibit 19: Vol of vol has trended up since the GFC Volatility of S&P 500 1-month volatility (daily) 180%

1-year 5-year

170%

10-year

160% 150% 140% 130% 120% 110% 100% 90% 80% 70% 38

43

48

53

58

63

68

73

78

83

88

93

98

03

08

13

18


Low vol cluster is broken - signals from volatility are more mixed Volatility tends to cluster – if volatility is very low, it has on average stayed low in the subsequent 12 months, limiting risks for investors somewhat (Exhibit 20). The recent low vol regime has come to an end (the grey box below provides a short review of this). The end of a low vol cluster is inevitable and, similarly, very long periods of high vol are unlikely. With an increasing time horizon (>1 year), the signal from current levels

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for future volatility weakens; for example, on a 5-year horizon volatility tends to pick up from low levels and maximum drawdowns become larger.

Also, the vol clustering effect has somewhat weakened since the 1990s : the predictive power of current S&P 500 1-month volatility for next months has declined (Exhibit 21). Similarly, the predictive power of current volatility for the next 12 months has declined compared with the last 100 years (Exhibit 22). We think this reflects to some extent the rising vol of vol since the mid-1980s, which drives faster regime shifts and can also drive large changes in volatility that are less linked to slower-moving fundamentals and more driven by markets. As a result volatility forecasting models that are based on history, e.g. GARCH models, may be less l ikely to work well. Exhibit 20: Volatility tends to linger at extremes in the near term - current levels provide little signal


S&P 500 1-month volatility Percentile Level From to From to 0% 10% 2.5 7.3 10% 20% 7.3 8.7 20% 30% 8.7 10.0 30% 40% 10.0 11.2 40% 50% 11.2 12.6 50% 60% 12.6 14.2 60% 70% 14.2 16.4 70% 80% 16.4 20.0 80% 90% 20.0 27.3 90% 100% 27.3 106.7 Average since 1928:

1 month 7.9 9.7 10.5 11.4 12.5 13.7 14.8 17.4 21.3 34.6 15.4

Average S&P 500 volatility in the subsequent... 3 months 6 months 12 months 2 years 8.7 8.9 9.3 9.8 10.3 10.7 11.1 12.3 11.5 12.1 12.2 12.9 12.2 12.7 12.8 13.1 13.3 14.0 13.9 14.4 14.3 14.7 15.2 15.6 15.6 16.0 16.8 17.2 17.5 17.8 18.5 18.2 22.0 21.9 22.1 21.8 32.7 31.7 30.2 28.1 15.9 16.1 16.4 16.7

5 years 10.5 13.1 14.1 14.2 15.1 15.3 16.5 17.2 20.1 23.9 16.9


From current levels of S&P 500 1-month volatility, several high volatility episodes have followed in the subsequent 12 months. This suggests that the signal from volatility alone is increasingly limited and there is a wider range of possible outcomes. As a result, with less anchored vol, risk appetite is less well supported as the distribution of risks is shifting less favourable. High volatility episodes often persist as equity drawdowns tend to be clustered in time, as i nvestors need time to adjust their portfolios to a potential new, higher vol regime. Exhibit 21: In the short term, very low volatility tends to increase the likelihood of vol staying low

120%

R² since 1928 = 0.76 R² since 1990 = 0.54

y t i l i t a 100% l o v h t n o 80% m 1 0 0 60% 5 P & S t n 40% e u q e s b 20% u S

Exhibit 22: Shorter-dated volatility has less predictive power for the medium term and the relationship has weakened since the 1990s y t i l i t a l o v h t n o m 2 1 0 0 5 P & S t n e u q e s b u S

0%

80%

R² since 1928 = 0.42 R² since 1990 = 0.15

70% 60% 50% 40% 30% 20% 10% 0%

0%

20%

40%

60%

80%

S&P 500 1-month volatility


16 April 2018

100%

120%

0%

20%

40%

60%

80%

100%

120%



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Goldman Sachs


All good things must come to an end — a review of the recent low vol regime The recent low vol regime started in mid-2016 and lasted roughly 19 months until February 2018. As discussed in Global Strategy Paper: The upside of boring, long periods of low vol (where the S&P 500 volatility is below 10% for more than si x months) have not been uncommon; we identified 15 low vol periods since 1928, which lasted on average 22 months. This one was shorter compared with those since the 1990s and those in the 1960s, which often lasted in excess of two years. But in terms of average levels of volatility, it has been one of the least volatile – only the regime in 1963-65 was less volatile. Exhibit 23: Average volatility was particularly low, also close to levels in the 1960s Distribution of S&P 500 3-month volatility during low vol regimes (duration in brackets) 18

25th/75th Percentile

Average

16 14


12 10 8 6 4 2 43-45 (15m)

49-50 (11m)

51-53 (16m)

53-54 (15m)

58-62 (45m)

63-65 (17m)

66-69 (31m)

70-71 (9m)

71-72 (7m)

77-78 (21m)

85 (11m)

92-96 (43m)

03-07 (41m)

12-14 (25m)

16-18 (19m)


Indeed, the recent regime resulted in one of the longest periods of S&P 500 1-month volatility below its long-term average of 15%, comparable to the late 1990s. But more extreme has been the number of days spent in the bottom quartile (below 10%), which peaked at 185 days and has onl y been surpassed in the 1960s (Exhibit 24). This low vol regime was also extreme in another way: the S&P 500 had the longest period since 1929 without a correction of more than 5%, at 404 days (beating the 1992-96 low vol regime by 5 days). But it also resulted in the l ongest period without a 3% S&P 500 correction (311 days). Exhibit 24: One of the longest number of consecutive days with low, below-average volatility

Exhibit 25: During the recent low vol regime the S&P 500 had its longest period without a 5% correction

Consecutive days of S&P 500 1m vol below 25th/50th percentile

Consecutive days without a S&P 500 correction

450

450

400

400

350

350

300

300

250

250

200

200

150

150

100

100

50

50

0

0 28

33

38 43 48 53 58 63 68 73 Days below 50th percentile (13%)

78

83 88 93 98 03 08 13 Days below 25th percentile (10%)

Source: Bloomber g, Goldman Sachs Global Invest ment Resear ch

16 April 2018

18

29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93 97 01 05 09 13 17 Days since last 5% correction Days since last 3% correction


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Goldman Sachs


Benchmarking the current episode to historical ends of low vol regimes shows a larger and faster-than-normal pick-up of realised vol, illustrating higher vol of vol compared with histor y. The initial normalisation of the vol spike was similarly large and fast. However, what has been unusual is that volatility picked up again and remained elevated. When the other 14 low vol regimes since 1928 ended, S&P 500 1-month vol usually settled at 10-12% on average after 2-3 months but very seldom stayed above the long-term average of 15%, whereas current levels remain well above that (Exhibit 26). Exhibit 26: Vol spike has been larger than those during historical ends of low vol regimes S&P 500 1-month volatility during and after a historical low vol regime ends (since 1928) 28

25th/75th Percentile

26

Average Current

24 22 20 18 16


14 12 10 8 6 4 2 -9m

0

-6m

+3m

-3m

1 year before

+12m

+6m

1 year after

Low vol regime end


Moving out of a low vol period does not have to come with a large correction. Usually, volatility spikes and equities settle into a higher volatility regime first before large equit y corrections, which tend to come 6-24 months later; the average drawdown was less than 5%. The S&P 500 drawdown at the end of the recent low vol regime was slightly larger than normal, in line with the larger-than-normal vol spike due to higher vol of vol (Exhibit 27). Contagion across assets has been similar to previous ends of low vol regimes: while cross-asset volatility has picked up from its lows, it has declined to below-average levels again (Exhibit 28). Exhibit 27: End of low vol regimes does not mean a bear market is imminent

Exhibit 28: Cross asset vol tends to increa se after low vol period end but results are mixed

S&P 500 performance during and after the end of a low vol regime (since 1928)

Percentile of 1-month cross-asset volatility ex equity during and after the end of a low vol regime (since 1970)

120

70%


115


60%

110 105

50%

100 40% 95 90

30%

85 20% 80 -18m

75

1 year before

-12m

+6m

-6m

Low vol regime end

S ou rc e: Blo omb er g, G old ma n S ac hs Glo ba l In ve st me nt Res ea rc h

16 April 2018

+12m

+18m

1 year after

10%

-9m

1 year before

-6m

+3m

-3m

Low vol regime end

+6m

+12m

1 year after

S ou rc e: Blo omb er g, Da ta st re am, Go ld ma n Sa ch s Gl ob al In ve st me nt Re se ar ch

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Goldman Sachs


Probable cause — potential macro and market drivers of vol regimes Establishing probable cause looking at macro and market drivers of vol regimes As volatility tends to lead macro, is driven by sentiment and aggregates lots of drivers and risks, forecasting volatility and timing regimes is hard. In an attempt to forecast different volatility regimes, we l ook at three broad categories of potential drivers: macro (growth, inflation and monetary policy), macro uncertainty (macro volatility and policy uncertai nty) and markets (financial markets stress). Of course, it is often a combination of those that conditions a new vol regime. For example, a weaker growth/inflation mix makes markets more vulnerable to political risk.

To assess the ‘probable cause’ of a vol regime, we looked at a wide range of indicators in each category that are linked to S&P 50 0 volatility historically (see M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

Appendix for an overview and description of these). We narrow these indicators down to 26 based on their correlation with S&P 500 1- and 6-month volatility, and the likelihood of them being at their extremes in the different regimes (with data since 1990).

Causation via correlation - narrowing down macro and market drivers of volatility Of course, correlation does not mean causation but i t helps narrow down the indicators: Exhibit 29 shows the highest positive or negative correlation with S& P 500 1- and 6-month vol. For most indicators, the change is more important than the level. Exhibit 29: Growth and rising valuations tend to be negatively correlated with volatility, while credit spreads, macro uncertainty and cross-asset vol are positively linked Correlation with S&P 500 volatility (data since 1990) US HY Spread BAA-AAA spread Rates vol Cross asset vol GSCI Vol Unemp. rate 6m chg CPI dispersion GDP revision vol Inflation revision vol US HY Spread 12m chg NFP vol (1y) T-bill revision vol GDP dispersion EPU 12m chg CPI vol (1y) MBS credit spread EPU TED spread US 10y-2y 12m chg T-bills dispersion Fed funds 12m chg ISM manufacturing Shiller PE 12m chg PCE 6m % chg

6-month

NFP 3m chg

1-month

US CAI 3m avg -80%

-60%

-40%

-20%

0%

20%

40%

60%

80%

100%

Source: Bloomberg, Consensus Economics, Haver Analytics, Goldman Sachs Global Investment Research

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Goldman Sachs


Credit spreads tend to have the strongest positive correlation for S&P 500 vol, closely followed by volatility in other asset classes. Rates volatility is particularly highly correlated with equi ty vol. From a macro point of view, the 6-month change in the US unemployment rate has a strong positive correlation, while the 3-month change in non-farm payrolls and the level of the US current activity indicator (CAI) have a strong negative link. We find CPI inflation levels are less important than consensus revisions and dispersion. Also, unsurprisingly, rising Shiller P/Es tend to come with lower volatility.

Establishing probable cause - assessing the likelihood of high and low vol regimes To assess what volatility regime we are in, we can also look at the likelihood of those indicators being at extreme levels (Exhibit 30) – for details of the definition of quintiles, etc., see again the Appendix. For example, since 1990 in roughly 97% of months

spent in S&P 500 high vol regimes, US HY credit spreads were in the top quintile (above 698bp) – shifting to Q4 (between 553bp and 698bp) lowers the likelihood of being in a high vol regime sharply (to 48%). M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

Wide and widening credit spreads across markets tend to increase the probability of being in a high vol regime most, while worsening growth momentum, i.e., large 3-month declines in our US CAI and in non-farm payrolls, also increase risk of a higher vol regime. Low macro uncertainty, a Fed rate hike cycle and low cross-asset volatility tend to increase the probabilit y of low vol regimes. But, as we discuss in the grey box below, those probabilities are not always linear and also distributions can change over time. As a result, the combination of levels and changes of the indicators is

important. Also, for low vol regimes, we find being at moderate levels of those indicators often lowers the probability of a regime shift to high vol as there is less risk of a reversal. Exhibit 30: Wider credit spreads and sharp declines in equity valuations are very likely in high vol regimes, while during low vol regimes the Fed tends to hike, cross-asset vol is low and the yield curve flattens Likelihood of a being in high or low vol regime depending on the top/bottom quintile of each variable (data since 1990, dotted line = unconditional probability) Fed funds 12m chg (Q5)

US HY Spread (Q5) MBS credit spread (Q5)

GSCI Vol (Q1)

Shiller PE 12m chg (Q1) US HY Spread 12m chg (Q5) NFP 3m chg (Q1) BAA-AAA spread (Q5) US CAI 3m avg (Q1) Cross asset vol (Q5) NFP vol (1y) (Q5) TED spread (Q5) EPU 12m chg (Q5) GDP dispersion (Q5) GDP revision vol (Q5) Unemp. rate 6m chg (Q5) ISM manufacturing (Q1) CPI dispersion (Q5) GSCI Vol (Q5) US 10y-2y 12m chg (Q5) T-bill revision vol (Q5) PCE 6m % chg (Q1) Fed funds 12m chg (Q1) Rates vol (Q5) Inflation revision vol (Q5) EPU (Q5) T-bills dispersion (Q5) CPI vol (1y) (Q5)

GDP revision vol (Q1) Cross asset vol (Q1) US 10y-2y 12m chg (Q1) T-bills dispersion (Q1) T-bill revision vol (Q1) EPU 12m chg (Q1) NFP vol (1y) (Q1) ISM manufacturing (Q5) Unemp. rate 6m chg (Q1) BAA-AAA spread (Q1) US HY Spread 12m chg (Q1) US CAI 3m avg (Q5) Rates vol (Q1) US HY Spread (Q1) GDP dispersion (Q1)

High vol regime 0%

1 0%

2 0%

3 0%

4 0%

5 0%

6 0%

7 0%

8 0%

9 0% 10 0%

CPI vol (1y) (Q1) EPU (Q1) CPI dispersion (Q1) NFP 3m chg (Q5) PCE 6m % chg (Q5) Inflation revision vol (Q1) TED spread (Q1) Shiller PE 12m chg (Q5) MBS credit spread (Q1)

Q1 = bottom quintile (low) Q5 = top quintile (high) Low vol regime 0%

1 0%

2 0%

3 0%

4 0%

5 0%

6 0%

7 0%

8 0%

9 0% 1 00 %

Source: Bloomberg, Consensus Economics, Haver Analytics, Goldman Sachs Global Investment Research

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Goldman Sachs


Problems of ‘probable cause’ of vol regimes and the risk of wrongful conviction What is extreme now may not necessarily be extreme in the future, as there are regime shifts in the indicators. For example, rates volatility has declined with the ‘Great Moderation’ and swings in macro data, such as the ISM, US CAI or non-farm payrolls, have become smaller. An ISM above 57 is currently a much more positive signal of a strong macro backdrop than it was in the 1960s (Exhibit 31). To avoid regime shifts in the data, we look at only recent history, i.e., since 1990, and assume a similar distribution in the future. Also, the relationship of the probability with the indicator can shift: since the 1990s, a high or low ISM has increased the probability of a low or high vol regime respectively much more (Exhibit 32). Exhibit 31: A high and rising ISM usually increases the probability of being in a low vol regime

Exhibit 32: Since the 1990s a high ISM made a low vol regime more likely and a low ISM higher vol more likely

ISM manufacturing (green shading = low vol regime, orange shading = high vol regime)

Probability based on ISM manufacturing quintiles (data since 1948, dashed lines since 1990)

75

80%


Probability High vol regime Probability Low vol regime

70

70%

65 60% 60 50%

55 50

40%

45

30%

40 20% 35 10%

30 25

0% 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 02 05 08 11 14 17


Bottom quintile

Q2

Q3

Q4

Top quintile


Also, extreme levels for macro and valuations can also increase the probability of a reversal. Since 1990, in roughly 85% of months spent in high vol regimes, BAA credit spreads were in the top quintile (Exhibit 33). But if credit spreads are already in the bottom quintile, indicating a strong backdrop right now, this also increases the risk of a sharp repricing of credit risk. The highest probability of being in a low vol regime is when credit spreads are in Q2, i.e., not yet very tight (Exhibit 34). Exhibit 33: During low vol regimes, credit spreads tend to tighten - very tight levels often indicate risk of a regime shift

Exhibit 34: Especially since the 1990s, high credit spreads increased the probability of being in a high vol regime

BAA-AAA spread (green shading = low vol regime, orange shading = high vol regime)

Probability based on BAA-AAA spread (data since 1950, dashed lines since 1990)

350

90%

Probability High vol regime Probability Low vol regime

80%

300

70% 250 60% 200

50%

150

40% 30%

100 20% 50

10%

0

0% 51 54 57 60 63 66 69 72 75 78 81 84 87 90 93 96 99 02 05 08 11 14 17

Source: Bloomberg, Haver, Goldman Sachs Global Investment Research

16 April 2018

Bottom quintile

Q2

Q3

Q4

Top quintile


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Goldman Sachs


Narrowing down the suspects - a probability model for vol regimes We estimate the probability of being in different regimes through logit models 1, which helps to narrow down the variables to those with the most predictive power: �

For macro, we use ISM manufacturing (level), the 6-month change in the U S unemployment rate and the 12-month rolling change in the Fed funds rate.

�

For macro uncertainty, we use only the 12-month change in economic pol icy uncertainty (EPU) and 1-year volatility of GDP consensus revisions; the other variables, while correlated, did not increase model performance materially.

�

Of the market indicators, we use US 10-yr rates vol, S&P GSCI vol, 12-month changes in US HY credit and US 10y-2y yield as well as TED spreads.

The combined model helps to recognise regimes with probabilities of rising/falling into them. However, it struggles to anticipate regime shifts, especially if vol of vol is

high. This is particularly the case right now – the model still indicates a continued high (albeit falling) probability of low vol but a still low probability of high vol (Exhibit 35).


Exhibit 35: The probability of a low vol regime is still high while that of a high vol regime remains low Probability of different S&P 500 vol regimes (green shading = low vol regime, orange shading = high vol regime, dotted line = unconditional probability of high and low vol regime) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 90

92

94 96 98 00 02 Average probability S&P 500 low vol regime

04

06

08 10 12 14 16 Average probability of S&P 500 high vol regime

18

Source: Bloomberg, Datastream, Haver Analytics, Goldman Sachs Global Investment Research

Tracking the probabilities for the individual categories reveals, unsurprisingly, that the market indicators tend to lead the macro, especially at the onset of high vol regimes, and have the highest R-squared (Exhibit 36). Also, the model does a better job of forecasting low vol regimes than high vol regimes, especially with non-market variables. This suggests the former are more driven by fundamentals while the latter, especially regime shifts to high vol, are – at least initiall y – less linked to fundamentals (Exhibit 37).

1

A logit model estimates the relationship of several variables to a binary outcome (i.e., being in a high (low) vol regime or not). Using model estimates, one can then construct probabilities of the binary outcome occurring given current variable values. Using all the variables creates several problems: (1) there is a risk of overfitting, (2) the indicators are very correlated, and (3) the market indicators lead and dominate the macro. As a result, we run logit models for each category (macro, uncertainty and markets) and within those narrow the variables down to the most statistically significant which add most to the explanatory power. The overall probability is the average of the 3 models. We run separate logit models for high and low vol regimes.

16 April 2018

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Goldman Sachs


Exhibit 36: Macro indicators are starting to signal a lower probability of being in a low vol regime

Exhibit 37: The probability of a high vol regime, especially based on market indicators, remains low

Probability of S&P 500 low vol regime based on different indicators (green shading = low vol regime, dotted line = unconditional probability, 38%)

Probability of S&P 500 high vol regime (orange shading = high vol regime, dotted line = unconditional probability, 39%)

100%

100%

90%

90%

80%

80%

70%

70%

60%

60%

50%

50%

40%

40%

30%

30%

20%

20%

10%

10% 0%

0% 90


92 94 96 M ac ro ( R2 =2 6% )

98

00 02 04 M ar ke t ( R2 =4 0% )

06

08 10 12 14 16 18 M ac ro U nc er ta in ty ( R2 =4 0% )

Source: Bloomberg, Datastream, Haver, Goldman Sachs Global Investment Research

90

92

94

96

M ac ro ( R2 =1 7% )

98

00

02

04

06

Ma rk et ( R2= 44 %)

08

10

12

14

16

18

U nce rt ai nt y ( R2 =2 6% )

Source: Bloomberg, Datastream, Haver, Goldman Sachs Global Investment Research

Feeling the heat - but so far little sign of a broad trend towards higher vol Another approach to track the likelihood of hi gh and low vol regimes is a heatmap. The advantage of this approach is that it has more breadth as different drivers can lead the vol regime shifts (Exhibit 38). So far, we still see little reason for a high vol regime:

most indicators are still green , although growth has softened. The same is true for uncertainty, which is broadly green, with the exception of inflation revision volatility and economic policy uncertainty (EPU), which have picked up. Of the market variables, since the 1990s at least, US HY credit spreads and the TED spread have been among the best predictors of vol regimes – while they widened in Q1 they have stabilised since April. Exhibit 38: Our heatmap shows the market and macro backdrop during different S&P 500 volatility regimes Percentile for different indicators (data since 1990) 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2 00 8 2 00 9 2 01 0 2011 2012 2013 20 14 2 01 5 2 01 6 2 01 7 2018 S&P 500 volatility 6-month

Combined signals All Macro indicators Macro uncertainty Market indicators

Macro indicators ISM (level) US CAI (3m avg) PCE (6m % chg) US unemployment (6m chg) Non-farm payrolls (3m chg) Fed funds rate (12m chg)

Macro uncertainty NFP vol (1y) Inflation vol (1y) T-Bill forec. revision vol (1y) CPI forec. revision vol (1y) GDP forec. revision vol (1y) T-Bill dispersion (3m avg) CPI dispersion (3m avg) GDP dispersion (3m avg) EPU index (3m avg) EPU index (12m change)

Market indicators BAA-AAA spread (level) US HY credit spread (level) US HY spread (12m chg) TED spread (level) MBS credit spread (level) Shiller P/E (12m chg) Cross-asset vol US 10-year rates vol GSCI vol US yield curve (12m chg)

Source: Bloomberg, Haver Analytics, Datastream, Consensus Economics, Goldman Sachs Global Investment Research

16 April 2018

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Goldman Sachs


Higher but not high - most indicators still point to lower volatility levels Based on most of the macro, market and uncertainty indicators, it still appears somewhat unlikely that we have entered a new persistent high vol regime. That said, equity volatility has often led the macro, and regime shifts are difficult to predict; indeed, the same has been true this time. Of course, the recent increase in vol has likely been exacerbated by technicals. We still think bear market risk remains low and expect positive equity returns in 2018. Still a similarly low level of S&P 500 vol to

that in 2017 appears unlikely - the macro backdrop has worsened compared with l ast year, and macro and policy uncertainty have increased.

The ‘Goldilocks’ backdrop of accelerating global growth with anchored inflation and easy monetary policy appears less likely from here. S&P 500 volatility tends to be lowest when growth accelerates (ISM above 50 and rising) and inflation pressures are limited (Exhibit 39). It tends to pick up during slowdowns and is highest during contractions (ISM below 50 and falling). Both the ISM and global PMIs have peaked and there has been a sharp decl ine in macro surprises globally. In addition, inflation has


picked up, albeit primarily in the US. The pace of slowdown matters from here: in 2004-07, for example, it lasted nearly two years and did not drive a high vol regime. While growth is softening, it remains healthy and our economists see low recession risk near term. Also, compared with the past two recessions there is less build-up of financial imbalances that are at risk of unwinding.

But investors also have to digest higher uncertainty due to (1) volatility in the US tech sector, in part due to concerns over regulation, (2) rising risk of global ‘trade wars’, (3) rising uncertainty on the ‘central bank put’, and the ‘beginning of the end of QE’ and (4) rising geopolitical tensions in the Middle East. In addition, US political uncertainty will likely rise into mid-term elections, which tends to drive higher volatility. There have also been signs of worsening liquidit y conditions, with LIBOR/OIS spreads widening and upward pressure on shorter-dated US credit spreads. But, as our Credit team has highlighted, this is mostly driven by technicals, in contrast to previous liquidity crises, and is less of a reason for concern. And, while US HY credit spreads have started to widen and the US yield curve has flattened, levels of both are not yet consistent with high vol regimes. Still, as market indicators tend to lead regime shifts, a stabilisation of credit and rates markets is a strong signal for vol to decline. Exhibit 39: A worsening growth/inflation mix is likely to result in less anchored volatility Data since 1952 (inflation in line is below 3% and above 1%) Av er ag e S& P 5 00 1-m on th vo la ti li ty ISM manufacturing Above 50 Below 50 Up Down Down Up p w U o n L w o D n o i t a l f n I

p e U n i l - n n w I o D p h U g n i H w o D

Pr op or ti on of mo nt hs wi th vo l b el ow 10% ISM manufacturing Above 50 Below 50 Up Down Down Up

Pr op or ti on of mo nt hs wi th vo l a bo ve 18 % ISM manufacturing Above 50 Below 50 Up Down Down Up

9.9

13.5

NM

NM

68%

21%

NM

NM

8%

21%

NM

NM

9.7

NM

NM

NM

55%

NM

NM

NM

0%

NM

NM

NM

11.1

15.2

18.5

10.8

49%

32%

22%

57%

17%

20%

44%

9%

11.5

12.2

16.4

12.1

44%

50%

35%

29%

7%

16%

30%

0%

13.0

14.7

16.6

NM

57%

24%

14%

NM

11%

19%

38%

NM

11.0

14.4

16.4

13.9

40%

25%

17%

27%

1%

17%

24%

9%


16 April 2018

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Goldman Sachs


From the low to the high (vol) life — asset allocation implications The end of ‘boring’ - lower risk-adjusted returns for equities For asset allocators, the end of the low vol regime points to lower risk-adjusted returns, especially for equities. At the beginning of 2018 and towards the end of the recent low vol regime, the 12-month return / volatility ratio for the S&P 500 peaked at 4.2, one of the highest levels in the last 100 years; such high levels are often reached during low vol regimes, which makes ‘boring’ markets ‘exciting’ for asset allocators (Exhibit 40). The last time similarly high risk-adjusted returns were reached was in the mid-1990s, and in the 1960s. During higher vol regimes there is the potential for sharp recoveries after equity drawdowns but it is still very difficult to generate long periods of sustained higher risk-adjusted equity returns. Exhibit 40: High sharpe ratios in low vol regimes makes ‘boring’ markets more ‘exciting’ M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

S&P 500 12-month rolling return/ volatility ratio (green shading = low vol regime, orange shading = high vol regime) 6.0 5.0 4.0 3.0 2.0 1.0 0.0 -1.0 -2.0 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99 01 03 05 07 09 11 13 15 17


More risk in multi-asset portfolios, also with bonds less good hedges Equities are usually the main source of risk in multi-asset portfolios and a shift to a higher vol regime suggests a more defensive stance. This is particularly the case for risk parity funds and cross-asset volatility t arget funds, which increase risk based on volatility by asset class and on a portfolio level. 2017 was also one of the best years for a 60/40 portfolio since 1962: the return/volatility ratio was 3.6x. Only the recovery years of 1985 and 1995, as well as 1965, were stronger. While the 60/40 return, at 12%, was only slightly above average, the 60/40 volatility in 2017, at 3.2%, competes with the lowest volatility years since 1928 (Exhibit 41).

Portfolio risk will be higher also if bonds are less good hedges and there is less potential for diversification. Since the 1990s bonds have provided a hedge for equities in periods of higher volatility, allowing multi-asset investors to run higher risk/leverage levels – equity/bond correlations tend to turn more negative during high vol regimes due to the ‘central bank put’. But, right now, as both bonds and equities appear expensive,

16 April 2018

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Goldman Sachs


bonds may be less good hedges for equities in drawdowns (see Global Strategy Paper: The Balanced Bear Part 1: Low(er) returns and latent drawdown risk , November 28, 2017). Equity/bond correlations have already turned positive at the beginning of the year, resulting in more volatility for multi-asset portfolios (Exhibit 42). Exhibit 41: Risk-adjusted performance of multi-asset balanced portfolios is usually closely linked to equity volatility...

Exhibit 42: ...and more positive equity/bond correlations might result in higher risk in multi-asset portfolios

60/40 portfolio (60% S&P 500, 40% US 10-year bond) 12-month rolling return/ volatility ratio (green shading = low vol regime, orange shading = high vol regime)

US equity/bond correlation (green shading = low vol regime, orange shading = high vol regime)

6.0

1.0

5.0

0.8 0.6

4.0

0.4

3.0

0.2 2.0 0.0 1.0 -0.2 0.0


-0.4

-1.0

-0.6

-2.0

3-month

-0.8

-3.0

12-month

-1.0 63

66

69

72

75

78

81

84

87

90

93

96

99

02

05

08

11

14

17

Source: Bloomberg, Haver Analytics, Goldman Sachs Global Investment Research

63

66

69

72

75

78

81

84

87

90

93

96

99

02

05

08

11

14

17

Source: Bloomberg, Haver Analytics, Goldman Sachs Global Investment Research

Volatility across assets tends to follow S&P 500 vol regimes closely Also, usually if S&P 500 vol is low or high, the same is true across assets : cross-asset volatility has st arted to pick up YTD, although it remains below average (Exhibit 43). Only in the 1980s has there been a large disconnect, where equity volatility was not particularly high but volatility across assets was in the top quartile. This was driven in particular by high fixed income volatility due to the monetary tightening by the Fed in response to the high levels of inflation in the 1970s. But, on average, levels of volatility are more clearly different to normal levels in high vol regimes: the gap bet ween normal and low vol regimes is less pronounced (Exhibit 44). Finally, for FX volatility the gap of levels of volatility between S&P 500 high and low vol regimes is the smallest. Exhibit 43: Volatility across assets tends to move together

Exhibit 44: FX volatility seems least linked to equity volatility

Average cross-asset percentile of 1-month realised volatility (green shading = low vol regime, orange shading = high vol regime)

Average percentile of 1-month realised volatility for different assets

100%

80%

90%

70%

80%

Low vol

Neither

High vol

Credit

Average crossasset

60%

70%

50%

60% 40% 50% 30%

40%

20%

30% 20%

10%

10%

0% Equity

0%

Bond

FX

Commodity

70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 12 14 16 18

Source: Bloomberg, Haver Analytics, Datastream, Goldman Sachs Global Investment Research

16 April 2018

Source: Bloomberg, Haver Analytics, Datastream, Goldman Sachs Global Investment Research

24

Goldman Sachs


Low vol regimes are ‘risk on’ and carry-friendly, high vol are not Unsurprisingly, low vol periods are generally ‘risk on’ and carry-friendly, with strong returns in equities and credit and muted performance of safe havens. Equities are the most sensitive to a change in volatility regime, with much lower returns in high vol regimes, while bond returns, especially US 30Y, are getting stronger (Exhibit 45). S&P 500 usually outperforms non-US equities during high vol regimes. While US IG credit total returns tends to benefit from lower bond yields, US HY credit tends to suffer more from widening credit spreads. Gold tends to benefit from ‘flight to safety’ in higher vol regimes, as does the Yen. Exhibit 45: Low vol regimes tend to be positive for risky assets, while high vol regimes are not Average monthly return during different volatility regimes (total return, data since 1990 where available) 2.0%

Equities

Bonds

Commodities

Credit

FX Low Vol

1.5%


Neither High Vol

1.0%

0.5%

0.0%

-0.5%

-1.0% S&P 500

MSCI Europe

Topix

MSCI EM

US 10Y

US 30Y

Germany Japan 10Y DJ Corp 10Y (IG)

US HY

Gold

Oil

GSCI

EUR

JPY

GBP

Source: Datastream, Haver Analytics, Goldman Sachs Global Investment Research

Valuations tend to be negatively correlated to volatility : for both equity and credit, they tend to increase in low vol and decrease in high vol regimes (Exhibit 46). US HY credit spreads are very closely linked to levels of volatility (Exhibit 47). However, there can be strong returns and increases of valuations for risky assets when the regime is neither low nor high vol, as such periods often include transitions out of bear markets, when vol can stay elevated for longer but markets are al ready recovering strongly. Exhibit 46: Low vol regimes tend to come with rising valuations...

Exhibit 47: ...while higher vol coincides with higher risk premia

Average monthly change (data since 1990)

US HY credit spread and S&P 500 1-month realised volatility

0.9%

10

0.7%

8 6

0.5%

4

0.3%

2

0.1% -0.1% -0.3% -0.5%

Low Vol Neither

-0.7%

High vol

-0.9% NTM PE (% chg)

Shiller PE (% chg)

BAA-AAA (bps, RHS)

US HY (bps, RHS)

US ERP (bps, RHS)

US 10Y Yield (bps, RHS)

2000

US HY credit spread

1800

S&P 500 1-month vol (RHS)

1400

0

1200

-2

1000

-4

800

-6

600

-8

400

-10

200

16 April 2018

60

50

1600

40

30

20

10

0

0 85

Source: I/B/E/S, Shiller, GFD, Goldman Sachs Global Investment Research

R2 = 0.56

87

89

91

93

95

97

99

01

03

05

07

09

11

13

15

17


25

Goldman Sachs


Chasing your tail risk - more risk of larger moves in high vol regimes In low vol regimes the distribution of S&P 500 1-month returns is skewed positively and tails are limited; as we discussed in Global Strategy Paper: The upside of boring, this also lowers the risk of larger equit y drawdowns and thus allows investors to take more risk in equi ties. But in high vol regimes the S&P 500 1-month returns are more negatively skewed compared with low vol regimes, and there are more tails, both negative and positive (Exhibit 48). Larger tails create more opportunities for market timing, which requires investors to capture positive, while avoiding negative, tails. Of course, market timing is very difficult and, when chasing your tail risks, there is always the risk of just chasing your tail. Exhibit 48: In low vol regimes the distribution of S&P 500 returns has less tails and a more positive skew Distribution of S&P 500 1-month returns during different vol regimes (since 1928) 35%

High vol regime Low vol regime

30%


Neither

25%

20%

15%

10%

5%

0% below -8%

-8% to -6%

-6% to -4%

-4% to -2%

-2% to 0%

0% to 2%

2% to 4%

4% to 6%

6% to 8%

above 8%

S&P 500 1-month return


Volatility as a market timing signal for when to buy the dip Volatility can serve as a market timing signal: large equity drawdowns during vol spikes create opportunities to ‘buy the dip’. After vol spikes, the asymmetry of returns in the medium term often improves as markets often overshoot due to sharp shifts in risk appetite. The S&P 50 0 12-month return after a large vol spike tends to be more positive (Exhibit 49). This is particularly true since 1990. Since then, from S&P 500 1-month volatility levels of more than 40% the S&P 500 had mostly positive returns in the subsequent 12 months. But high volatility also i ncreases the risk of an equit y drawdown lasting longer and becoming larger, especially if the macro backdrop worsens. Exhibit 50 shows that the medium-term asymmetry of returns improves with the size of the vol spike. But, due to vol clustering at high levels, near-term returns tend to remain very poor after a large vol spike. That said, after vol spikes of more than 20%, the hit ratio of having positive S&P 500 returns over the subsequent two years is 100%. While the recent S&P 500 vol spike was large, the peak was relatively low compared with

16 April 2018

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Goldman Sachs


history; thus, the signal from volatility is not necessarily indicating very good asymmetry of equity returns yet. Exhibit 49: Since 1990, from realised vol levels above 40, subsequent 12-month returns have seldom been negative

Exhibit 50: Asymmetry of equity returns improves after a large vol spike

S&P 500 1-month vol and subsequent 12-month returns

Average subsequent S&P 500 return from different vol spikes. Vol spikes defined by: vol (1m) above 20% and 1m change in vol (data since 1990)

175%

Since 1927

n r u t e125% r

Since 1990

h t n o m 2 75% 1 0 0 5 P & 25% S t n e u q e -25% s b u S

-75% 0


20

40

60

80

100



120

Vol spike   10 12 14 16 18 20 22 24 Average

1 month -2.1% -9.4% -12.3% -17.6% -21.3% -27.5% -41.1% -50.7% 9.4%

        3 months 6 months 1 year 5.1% 6.0% 7.0% 5.4% 8.7% 9.7% 7.1% 11.1% 12.6% 5.6% 11.9% 14.9% 4.2% 12.8% 17.1% 0.2% 11.3% 17.3% -9.9% 6.5% 17.0% -19.0% 1.7% 15.7% 9.4% 9.4% 9.6%

2 years 7.7% 9.8% 12.3% 13.9% 15.0% 16.0% 16.0% 15.2% 9.5%

Vol spike   10 12 14 16 18 20 22 24 Average

1 month 58% 54% 55% 54% 51% 49% 37% 29% 63%

Hit ratio of positive S&P 500 returns in the next... 3 months 6 months 1 year 58% 56% 64% 59% 62% 72% 62% 68% 80% 60% 67% 87% 58% 64% 93% 56% 63% 94% 47% 53% 92% 39% 49% 90% 69% 74% 80%

2 years 70% 78% 87% 92% 97% 100% 100% 100% 80%


Historically option selling strategies performed better in high vol regimes While the sample size is limited (data since 1988), we can look at CBOE systematic option strategy indices2 to see which strategies perform best in different vol regimes. In low vol regimes, options are usually cheap, but for good reason, and as a result investors need to be selective. During low vol regimes the returns of just buying the S&P 500 outright are tough to beat. But based on a comparison of monthly returns (see Exhibit 51), selling ATM puts systematically (the CBOE PUT index) has

historically provided better risk-adjusted returns, and which across vol regimes provided the highest return/volatility ratios. Buying puts, despite being cheap, has historically less successful i n low vol clusters as equity drawdown risk is limited. To hedge the risk of smaller corrections, we recommended shorter-dated put spreads (98-93%) on the S&P 500. The combination of low implied volatility and high skew resulted in higher payout multiples than they usually have. Also, cash extraction via calls can be attractive in low vol regime to add risk in a capital efficient way.

2

Descriptions of CBOE S&P 500 systematic option strategy indices: Buy-Write (BXY Index) – Performance of a hypothetical 2% OTM buywrite strategy on the S&P 500 Index. The BXY is a pas sive total return index based on (1) buying a n S&P 500 stock index portfolio, and ( 2) selling a near-term S&P 500 Index c all option, generally on the third Friday of each month. Put-Write (PUT Index) – Pass ive investment strategy which consists of overlaying S&P 500 short put options over a money market a ccount invested in 1- and 3-month T-Bills. The puts are struck ATM and are sold on a monthly basis, usually on the 3rd Friday of the month. Put Protection Index (PPUT Index) – Performance of a hypothetical risk- management strategy that consists of a long position indexed to the S&P 500 I ndex and a rolling long position in monthly 5% OTM put options. Iron Butterfly Index (BFLY Index) – The index tracks the performance of a hypothetical options trading strategy that: (1) sells a rolling monthly ATM put and call option, (2) buys a rolling monthly 5% OTM put and call option to reduce the risk and (3) holds a money market a ccount invested in 1-month T-Bills.

16 April 2018

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Goldman Sachs


With rising volatility, we find that systematic option selling strategies have performed better since 1988 (Exhibit 51). In high vol regimes, systematic call overwriting (the CBOE BXY index, which sells 1-month 102% calls) has performed better and the iron butterfly overlay (the CBOE BFLY index, which sells a 1-month straddle to buy a 5% OTM strangle) has performed best. This is because this strategy benefits most from the higher carry in high vol regimes (and it buys back the tail risk).

Buying OTM puts systematically (the CBOE PPUT index, which buys 1-month 95% puts) has seldom paid – but since 1988 the best opportunity to outperform with put hedging has been in high vol regimes, although even then market timing is required. Being in neither regime drives mixed results for systematic option strategies: risk-adjusted returns tend to be higher for selling options but absolute are not. Exhibit 51: Systematic overwriting strategies tend to outperform outside of low vol regimes CBOE option strategy indices vs. S&P 500 (green shading = low vol regime, orange shading = high vol regime) 180


160 140 120 100 80 60 40 20 0 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16 17 18 BXY PUT PPUT BFLY

Regime Low Vol

Neither

High Vol

Avg 1-month return Avg 1-month vol Return/ vol. Avg 1-month return Avg 1-month vol Return/ vol. Avg 1-month return Avg 1-month vol Return/ vol.

S&P 500 (Total return) 1.3% 9.6% 1.8 1.4% 12.5% 1.4 0.2% 22.5% 0.1

Buy-write (BXY) 1.1% 7.9% 1.8 1.2% 9.9% 1.6 0.4% 17.4% 0.3

Put-write (PUT) 0.9% 4.9% 2.3 1.1% 6.8% 2.1 0.6% 13.7% 0.6

Put Protection (PPUT) 1.0% 8.8% 1.5 1.0% 11.0% 1.1 0.0% 16.8% 0.0

Butterfly (BFLY) 0.2% 8.7% 0.3 0.6% 9.7% 0.8 0.6% 11.3% 0.7


Of course, option selling strategies not onl y depend on the level of volatility at which you sell, but also on subsequent performance – with a higher vol and a more rangebound market we would look to sell calls on rallies and sell puts on corrections tactically (Exhibit 52). But the higher volatility improves the asymmetry for option selling strategies; for example, the PUT index on average has outperformed the S&P 500 with realised S&P 500 1-month vol above 20%, even in corrections of more than 4% (Exhibit 53). However, while those strategies had better average performance than the S&P 50 0 in periods of higher vol, they are likely to underperform in sharp rallies. They also have more negative skew in strong, low vol equity rallies during low vol regimes (Exhibit 54). In particular, systematic put selling tends to have more negative skew in low vol

16 April 2018

28

Goldman Sachs


regimes but also outperformed the S&P 500 materially in more instances during high vol regimes (Exhibit 55). Exhibit 52: Call overwriting looks more attractive at higher volatility levels...

Exhibit 53: ...and the same is true for put writing

Average 1-month return of S&P 500 Buy-write index (BXY, 102% 1m call) vs. S&P 500 (total return, data since 1988)

Average 1-month return of S&P 500 Put-write index (PUT, 100% 1m put) vs. S&P 500 (total return, data since 1988)

S&P 500 1-month realised volatility at entry n r u t < -4.1% e r -4% - -2% h t n o -2% - 0% m 1 0% - 2% 0 0 2% - 4% 5 P 4% - 5% & S 5% - 23%

Avg.


S&P 500 1-month realised volatility at entry

<7

7-9

9 - 11

11 - 14

14 - 19

19 - 24

24 - 89 Avg.

-0.3

1.0

1.0

1.0

1.2

2.0

2.7

1.5

0.1

0.7

0.6

1.0

1.2

1.8

1.7

1.0

0.2

0.4

0.5

0.5

0.8

1.3

1.3

0.6

0.0

0.2

0.1

0.3

0.4

0.7

1.0

0.3

-0.4

-0.3

-0.4

-0.4

-0.4

0.0

0.2 -0.3

-1.3

-1.0

-1.1

-1.3

-1.3

-1.1

0.0 -1.1

-2.5

-2.0

-2.3

-2.6

-3.0

-2.3

-1.9 -2.4

-0.2

0.0

0.0

-0.1

-0.2

0.2

0.5

n r u t < -4.1% e r -4% - -2% h t n o -2% - 0% m 1 0% - 2% 0 0 2% - 4% 5 P 4% - 5% & S 5% - 23%

Avg.

<7

7-9

9 - 11

11 - 14

14 - 19

19 - 24

0.6

2.9

2.8

2.9

2.4

4.0

24 - 89 Avg. 4.3

3.2

1.0

2.1

2.0

2.4

2.5

3.2

3.2

2.3

0.7

1.0

1.2

1.3

1.7

2.1

1.8

1.3

-0.3

0.0

0.0

0.2

0.4

0.8

0.8

0.2

-1.5

-1.4

-1.3

-1.1

-1.0

-0.6

-0.3 -1.1

-2.8

-2.4

-2.4

-2.4

-2.2

-1.9

-1.0 -2.2

-4.1

-4.3

-4.2

-4.0

-4.1

-3.7

-3.5 -3.9

-0.6

-0.1

0.1

0.0

-0.1

0.3

0.5



Exhibit 54: While during higher vol periods BXY outperforms, it has negative skew in low vol regimes

Exhibit 55: Systematic put selling tends to outperform (with positive tails) in high vol regimes but has negative skew in low vol periods

Distribution of relative 1-month returns of BXY vs. S&P 500 (total return, data since 1988)

0 1 -

70% 60%

Distribution of relative 1-month returns PUT vs. S&P 500 (total return, data since 1988)

6 High vol

50%

Low Vol

45%

Neither

40%

50%

35%

40%

30%

0 0 1 -

% 6

High vol Low Vol Neither

25% 30%

20% 15%

20%

10%

10%

5% 0% below 6

-6 to -4

-4 to -2

-2 to 0

0 to 2

2 to 4

4 to 6

Relative 1-month return vs. S&P 500


above 6

0% below 6

-6 to -4

-4 to -2

-2 to 0

0 to 2

2 to 4

4 to 6

above 6

Relative 1-month return vs. S&P 500


Cross-asset volatility overview - high US equity vol is the odd one out Currently, the somewhat elevated S&P 500 implied volatility (in line with realised) is the odd one out, both across equity markets and other assets (see also SPX Volatility Continues to Outpace Global Indices , April 16, 2018); MSCI EM vol is the only region that is also somewhat elevated. From a cross-asset perspective, US HY credit implied volatility, which is usually closely linked to S&P 500 vol, has recently diverged (in line with credit spreads disconnecting from volatility), and looks cheap (Exhibit 56). The same is the case for rates volatility, which remains very anchored, especially in Europe. Finally, considering the strong performance of Gold and Yen in high vol regimes, implied vol levels appear low.

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Exhibit 56: Cross-asset volatility overview Percentile based on last 10-year Equities S&P EURO Nikkei FTSE MSCI MSCI 500 STOXX 50 225 100 EM EAFE Implied (3-month ATM, %) 15.2 13.9 17.2 12.0 20.1 11.9 Current: Percentile: 45% 6% 14% 16% 35% 8% 2.0 2.1 2.8 4.6 2.1 3M change: 6.0 22.1 22.7 17.8 25.3 2 0.3 Average: 18.1 35.9 37.1 37.1 33.5 45.2 3 6.2 95th: 10.0 13.6 14.9 10.4 15.2 10.9 5th: Realised (%) 15.8 22.6 13.8 13.8 9.8 1-month: 23.4 Percentile: 84% 33% 63% 49% 46% 22% 16.7 21.4 22.6 16.7 17.2 16.5 Average:

Rates Credit Commodities Currencies USD USD EUR EUR iTraxx EUR/ JPY/ GBP/ CDX IG CDX HY WTI Go ld C op pe r 2-year 10-year 2-year 10-year Europe USD USD USD 3.0 37% 0.5 4.0 9.4 1.5

3.7 2% 0.2 6.0 10.7 3.9

0.9 3% -0.1 3.2 7.5 1.0

2.3 1% -0.1 4.5 7.6 2.7

46.2 29% 6.3 57.4 97.2 38.9

33.7 6% 4.1 50.8 74.5 32.3

45.9 13% 4.1 64.6 103.6 40.9

24.9 22% 5.7 34.5 59.7 17.1

11.7 8% 2.0 18.7 34.5 10.8

18.3 20% 1.2 27.4 49.7 15.5

6.4 5% -0.8 10.5 16.4 6.4

7.4 6% 0.0 10.9 15.7 7.2

7.6 25% 0.6 9.9 16.5 5.8

2.9 50% 4.1

3.6 17% 5.5

0.5 5% 2.4

1.9 3% 3.8

50.8 84% 40.3

35.7 58% 35.2

32.4 19% 46.8

27.2 43% 34.7

10.0 9% 17.6

16.3 22% 24.9

6.2 15% 9.7

7.1 24% 10.1

6.5 19% 9.5

Source: Goldman Sachs Global Investment Research

Although ‘implieds’ are elevated, the implied-realised spread for the S&P 500 is very low (Exhibit 57). EUROSTOXX 50 and MSCI EAFE implied volatility are trading at their lowest level since the G FC relative to S&P 500 (Exhibit 58). The difference in M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

realised volatility helps explain this. Indeed, the S&P 500 beta to MSCI World has increased to 1.1 (in part due to the Tech sector), while MSCI EAFE i s now at just 0.9, whereas historically it has been the other way around. We like selling S&P 500 calls outright (see Options Research: VIX Remains Above 2017 Range: SPX Calls Are Expensive, March 6, 2018) and also to buy options on non-US equity markets appear attractive.

The potential for larger moves has increased, but we would be selective on hedging (see Optimal Hedges (Part 1): Major Market Risks, April 2, 2018). After the recent correction for the S&P 500, skew (the cost of puts vs. call s) is high again, but the levels of volatility are still much higher. As volatility resets lower, we still like put spreads to protect from smaller corrections. Moreover, high vol periods are in flatter vol term structures, making longer maturities more appealing compared to 2017: the S&P 500 vol term structure has flattened materially (Exhibit 60). Exhibit 57: Credit spread volatility has trended down recently, while equity vol is still high

Exhibit 58: S&P 500 realised vol has been high compared with where implied vol is now

US HY CDS and S&P 500 3-month ATM implied vol

3-month implied ATM volatility vs 1-month realised

38

100

S&P 500 3-month implied ATM Vol

2.5x

Implied (3m) vs realised (1m) 10-year Percentile (RHS)

US CDS HY 3-month implied ATM Vol (RHS) 2.0x

33

70% 1.5x

60% 50%

70 1.0x

23

90% 80%

85

28

100%

40% 30%

55

0.5x

20%

18

10% 40

13

8

25 10

11

12

13

14


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16

17

18

0.0x

r a e y 2 R U E

M E I C S M

e p o r u E x x a r T i

r a e y 0 1 R U E

E F A E I C S M

d D l S o U / G P B G

r e p p o C

r a e y 2 D S U

D S U / Y P J

D S U / R U E

r a e y 0 1 D S U

0 Y I T G E 0 5 2 0 H W I 5 0 5 X X 1 2 i P X S E D e D S k & C C T k i S F N

0%


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Exhibit 59: Implied vol for non-US equities trades at a large discount to S&P 500

Exhibit 60: Equity volatility term structure is now the most fla t across assets

3-month ATM implied volatility ratio vs. S&P 500

Aggregate vol term structure using assets from exhibit 56 indexed to 3-month level

2.2

1.9

EUROSTOXX 50 MSCI EAFE Nikkei 225

2.0

Equity Commodity FX

1.7

Rates

1.8

Credit 1.5

1.6 1.4

1.3

1.2

1.1

1.0 0.9 0.8 0.6

0.7 10


11

12

13

14

15

16

17

18

1m

3m

6m

1y

2y

3y

4y

5y



Exhibit 61: The S&P 500 vol term structure has flattened materially

Exhibit 62: Normalised skew has often increased during low vol periods and fallen with high vol

12-month vs 3-month implied ATM volatility (ratio)

3-month skew = (25% delta put vol - 25 delta call vol)/ATM vol 1.6

0.6

12m vs 3m vol ratio 6-month average

1.5

0.5

1.4 1.3

0.4 1.2 1.1 0.3 1.0 0.9

0.2

0.8

Skew (3m) 6-month average

0.7

0.1 99

00

01

02

03

04

05

06

07

08

09


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10

11

12

13

14

15

16

17

18

99

00

01

02

03

04

05

06

07

08

09

10

11

12

13

14

15

16

17

18


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Appendix 1: Historical comparison of S&P 500 volatility regimes Exhibit 63: Historical comparison of different S&P 500 volatility regimes


Low vol regimes Start End Dec-43 Mar-45 Jul-49 Jun-50 Dec-51 Mar-53 Oct-53 Dec-54 Jun-58 Mar-62 Dec-63 May-65 Nov-66 Jun-69 Nov-70 J ul-71 Dec-71 Jul-72 Jan-77 Oct-78 Feb-85 Dec-85 Jul-92 Feb-96 Sep-03 Feb-07 Aug-12 Sep-14 Jun-16 Feb-18 Average:

Length (months) 14 11 15 14 46 16 31 8 7 20 10 43 42 25 19 22

S&P 500 1-month volatility Average Median 7 5th 25th Max 9 8 10 8 12 9 9 11 8 14 8 7 9 6 12 9 8 10 7 13 9 9 10 7 15 5 5 6 4 7 8 8 10 7 16 8 8 9 7 11 8 8 9 7 10 10 10 11 9 15 10 10 10 9 13 9 9 11 7 15 11 10 12 9 17 11 11 13 9 18 8 7 9 6 20 9 9 10 7 20

Min 5 7 5 5 5 3 4 5 6 6 7 5 6 5 3 3

S&P 500 6-month volatility Average Median 7 5th 25th Max 9 9 10 9 13 10 10 11 10 12 8 8 9 7 10 10 10 12 8 13 9 9 10 8 11 7 6 9 5 10 9 9 10 8 14 10 9 12 8 18 10 10 10 8 12 10 10 11 9 12 10 10 11 10 12 9 9 10 8 11 11 11 12 10 18 12 12 12 11 14 9 8 12 7 16 10 10 11 8 18

Min 8 8 7 7 7 5 7 7 8 9 9 7 7 9 6 5

High vol regimes Start End Dec-28 Sep-36 Apr-37 Mar-41 Feb-46 Jun-47 May-48 Dec-48 Jun-50 Dec-50 Apr-62 Nov-62 Nov-73 Oct-75 Aug-82 Feb-83 Mar-87 Jun-88 Aug-90 Mar-91 Apr-97 May-03 Jul-07 Sep-10 Aug-11 Jan-12 Aug-15 Mar-16 Average:

Length (months) 93 47 16 7 6 7 23 6 15 7 73 38 5 7 25

S&P 500 1-month volatility Average Median 7 5th 25th Max 30 24 39 19 108 24 22 31 16 54 19 16 23 13 44 18 17 26 13 31 17 14 20 13 31 18 14 21 11 39 19 18 23 16 35 23 22 27 19 30 25 19 24 15 100 19 19 21 16 26 21 19 24 16 47 27 21 29 17 90 32 30 32 28 49 20 19 23 16 32 24 21 28 16 108

Min 8 6 9 8 10 7 10 14 9 11 9 7 17 10 6

S&P 500 6-month volatility Average Median 7 5th 25th Max 32 27 46 19 59 26 25 30 21 39 19 17 24 16 25 17 17 17 16 20 16 16 17 15 18 17 19 20 17 22 20 19 23 17 26 19 20 22 16 22 29 23 44 16 46 17 18 19 16 20 21 20 24 18 32 27 21 33 18 58 26 27 30 24 30 18 17 19 17 21 25 21 27 18 59

Min 14 11 13 13 12 7 15 13 13 12 13 12 16 11 7

Neither Start End Sep-36 Apr-37 Mar-41 Dec-43 Mar-45 Feb-46 Jun-47 May-48 Dec-48 Jul-49 Jun-50 Jun-50 Dec-50 Dec-51 Mar-53 Oct-53 Dec-54 Jun-58 Mar-62 Apr-62 Nov-62 Dec-63 May-65 Nov-66 Jun-69 Nov-70 Jul-71 Dec-71 Jul-72 Nov-73 Oct-75 Jan-77 Oct-78 Aug-82 Feb-83 Feb-85 Dec-85 Mar-87 Jun-88 Aug-90 Mar-91 Jul-92 Feb-96 Apr-97 May-03 Sep-03 Feb-07 Jul-07 Sep-10 Aug-11 Jan-12 Aug-12 Sep-14 Aug-15 Mar-16 Jun-16 Average:

Length (months) 8 33 11 11 7 0 11 7 41 1 13 18 16 5 16 15 46 25 15 25 16 14 4 5 10 8 11 4 14

S&P 500 1-month volatility Average Median 7 5th 25th Max 14 14 16 13 18 13 12 14 10 29 13 13 14 11 17 12 12 14 10 17 12 11 13 11 16 11 11 11 11 11 11 11 13 9 16 12 10 12 8 25 12 11 14 9 32 7 7 7 7 7 8 7 8 6 20 9 8 13 5 21 13 12 15 11 32 12 11 15 9 18 13 12 15 9 21 11 11 13 10 18 14 14 16 11 24 13 12 14 11 19 15 15 16 13 23 13 12 14 11 27 12 13 14 10 18 12 12 15 10 19 16 16 17 15 19 12 12 14 9 19 13 13 15 11 18 13 13 15 11 21 13 12 15 10 19 11 10 12 10 18 12 12 14 10 32

Min 11 7 7 7 7 10 6 6 5 6 5 3 7 7 5 7 7 8 10 8 7 7 11 7 6 8 5 8 3

S&P 500 6-month volatility Average Median 7 5th 25th Max 15 14 15 14 18 14 14 15 12 18 12 12 13 11 14 13 12 15 12 16 15 15 16 12 17 9 9 9 9 9 12 12 14 11 18 10 9 10 9 13 13 12 15 11 17 7 7 7 7 7 10 8 12 7 21 8 8 9 7 15 13 11 18 11 19 10 10 11 10 12 12 11 14 11 15 12 12 14 10 15 14 14 16 13 17 14 13 14 12 22 14 14 16 13 17 14 13 16 12 21 14 13 15 13 18 12 12 12 11 13 20 21 21 19 22 10 10 11 10 12 15 13 17 12 22 19 18 23 14 30 12 13 13 11 14 16 16 17 16 18 13 13 15 11 30

Min 13 9 9 11 11 9 10 8 8 7 6 5 8 8 8 10 10 11 10 11 11 9 18 7 12 13 9 15 5


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Appendix 2: Overview of macro and market drivers of vol regimes Description of indicators US ISM manufacturing (PMI), US Unemployment rate (U-3), US Personal consumer spending (PCE), Non-farm payroll (NFP), US CPI inflation (headline), Fed funds rate, US yield curve (10y-2y) : Changes are based on absolute variations. US current activity indicator (CAI) : It tracks US economic activity, at monthly frequency. It is a good proxy of GDP growth.

US macro surprise index (MAP) : It tracks US economic data surprises, at daily frequency. Change based on absolute variations.

Shiller P/E ratio : Source - Shiller’s website. US equity/bond correlation: S&P 500 vs. US 10Y bond correlation (weekly returns).


Cross asset vol percentile : Average percentile since 1970 of 6-month volatility of US HY, US 10-year bond, S&P GSCI, G old. Change based on absolute variations.

Volatility of rates, S&P GSCI and Gold : 6-month volatility on daily return of US 10-year bond, S&P GSCI total return index and Gold spot price.

US HY spread (bp) : BAML US HY Corporate Master II index. BAA-AAA Moody’s spread (bp): Moody’s long-term corporate bond yield spread. MBS Spread (bp): BAML Mortgages 30-year spread.

TED Spread (bp): It is computed as the difference between USD 3-month Libor rate and 3-month generic government yield.

US Cyclicals vs Defensives: Based on monthly rebalancing and market cap weights. Cyclicals sectors: Oil & Gas, Chemicals, Basic res., Con. & mat., Industrials G&S, Auto & Parts, Retail, Media, Travel & Leis., Banks, Insurance, Real estate, Fin. Svs, Technology; Defensives sectors: Food & Bev., Personal & H/H Goods, Healthcare, Telecom, Utilities. Change based on percentage variations.

Equity flows (12-month sum, $ bn): Equity flows into US domiciled funds and ETFs. US Economic Policy Uncertainty (3m avg): Made up of three components: (1) newspaper coverage of policy-related economic uncertainty; (2) number of federal tax code provisions set to expire in future years; and (3) disagreement among economic forecasters as a proxy for uncertainty.

Consensus forecast dispersion (3m avg): Standard deviation of professional forecasters’ estimates for the next 12-months of CPI inflation, T-Bill and GDP growth.

Consensus forecast revision vol : Standard deviation of MoM revision change of next 12-month consensus estimates. Standard deviation based on a 1-year window.

ISM, Inflation, NFP and Unemployment Volatility : Standard deviation of MoM change over 12-month window. Inflation vol is based on the MoM % CPI change. 16 April 2018

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Exhibit 64: Probability of vol regimes based on different indicators (data since 1990) green shading = higher probability of low vol regime, orange shading = higher probability of high vol regime Indicator


ISM manufacturing (PMI) 3m change 6m change 12m change US current activity indicator (CAI) 3m change 6m change 12m change US macro surprise-MAP ( since 2000) 3m change 6m change 12m change US unemployment rate s r o 3m change t a 6m change c i d 12m change n i PCE spending o r 3m % change c a 6m % change M 12m % change Non-farm payrolls 3m change 6m change 12m change US CPI inflation (headline) 3m change 6m change 12m change Fed funds Rate 3m change 6m change 12m change Shiller PE 3m % change 6m % change 12m % change US equity/bond correlation 3-month window 6-month window 12-month window Cross asset vol percentile (6m) US 10-year rates vol (6m) GSCI vol (6m) Gold vol (6m) US HY spread (bp) 3m change 6m change 12m change BAA-AAA Moody's spread (bp) s r o 3m change t a 6m change c i d 12m change n i TED spread (bp) t e 3m change k r a 6m change M 12m change MBS spread (since 1997, bp) 3m change 6m change 12m change US cyclicals vs. defensives 3m % change 6m % change 12m % change Equity flows (12m sum, $ bn) 3m change 6m change 12m change US yield curve (10y-2y) 3m change 6m change 12m change Economic policy uncert. (3m avg) 3m change 6m change 12m change y Consensus forecast disp. (3m avg) t n CPI inflation i a t GDP r e T-bills forecast c n u Cons. forecast revision vol (1y) o CPI inflation r c a GDP M T-bills forecast ISM vol (1y) Inflation vol (1y) NFP vol (1y) Unemployment Vol (1y)

R2 for S&P 500 vol 1m 6m 20% 30% 8% 1% 8% 6% 6% 8% 28% 50% 8% 3% 9% 10% 10% 15% 1 6% 15% 3% 0% 5% 1% 5% 5% 1% 4% 20% 35% 23% 43% 18% 36%

Correlation with S&P 500 vol 1m 6m -4 5% -5 5% -2 8% -1 0% -2 8% -2 4% -2 5% -2 9% -5 2% -7 1% -2 8% -1 8% -2 9% -3 1% -3 1% -3 9% -3 9% -3 8% -17% 1% -2 2% -1 2% -2 1% -2 2% 7% 20% 45% 59% 48% 66% 42% 60%

Percentile of indicator 20% 49.1 -2.3 -3.7 -5.2 1.5 -0.7 -1.1 -1.6 -0.5 -0.7 -0.8 -0.7 4.6 -0.2 -0.4 -0.7

40% 51.5 -0.8 -1.0 -1.5 2.4 -0.3 -0.3 -0.5 -0.1 -0.2 -0.2 -0.1 5.3 -0.1 -0.2 -0.4

60% 53.6 0.8 1.4 1.6 3.3 0.2 0.3 0.5 0.2 0.2 0.3 0.3 5.8 0.0 -0.1 -0.2

80% 56.1 2.7 3.6 6.0 4.2 0.7 1.0 1.6 0.6 0.8 0.7 0.8 7.3 0.2 0.2 0.5

Probability of low vol regime 100% 61.4 9.8 17.7 21.6 5.7 5.0 7.9 10.0 1.6 2.2 3.3 2.9 10.0 1.5 2.6 4.0

Q2 32% 37% 43% 34% 34% 34% 29% 32% 30% 61% 58% 42% 38% 49% 56% 63%

Q3 32% 46% 33% 41% 49% 49% 57% 52% 53% 47% 58% 53% 48% 37% 48% 42%

Q4 50% 37% 48% 47% 51% 54% 46% 44% 58% 66% 50% 45% 54% 32% 28% 28%

Q5 60% 38% 37% 39% 56% 32% 37% 41% 54% 32% 37% 55% 24% 9% 0% 3%

Q1 74% 47% 63% 64% 85% 59% 66% 74% 51% 45% 45% 50% 65% 16% 18% 13%

Q2 38% 50% 37% 31% 34% 49% 47% 37% 53% 29% 32% 29% 37% 34% 26% 21%

Q3 29% 33% 34% 33% 18% 27% 18% 21% 35% 37% 29% 21% 24% 34% 30% 37%

Q4 29% 30% 25% 27% 22% 26% 34% 26% 25% 18% 26% 42% 28% 38% 43% 49%

Q5 24% 33% 35% 39% 34% 32% 28% 35% 27% 42% 39% 29% 40% 71% 76% 74%

28% 22% 26%

30% 28% 27%

50% 46% 38%

45% 57% 60%

38% 38% 40%

60% 65% 54%

43% 43% 43%

24% 24% 29%

24% 22% 21%

43% 40% 46%

21% 18% 11%

24% 35% 27%

-4 6% -4 2% -3 3%

-4 9% -5 9% -5 2%

1% 2% 4%

1% 2% 5%

1% 3% 6%

2% 3% 6%

25% 21% 14% 0% 5% 3% 1% 1% 10% 11% 15% 0% 30% 29% 25%

48% 44% 32% 5% 8% 12% 5% 2% 14% 18% 22% 0% 9% 25% 35%

-5 0% -4 5% -3 8% -7% -2 1% -1 6% -7% -7% -3 2% -3 3% -3 9% -1% -5 5% -5 4% -5 0%

-7 0% -6 7% -5 7% -23% -2 8% -3 5% -23% -16% -3 8% -4 2% -4 7% -5% -3 0% -5 0% -5 9%

15 33 -152 1.6 -0.5 -0.7 -1.2 0.2 -0.2 -0.6 -1.1 20 -3% -5% -6%

410 942 1 850 2.2 -0.1 -0.2 -0.2 1.5 0.0 0.0 -0.2 23 0% 1% 2%

601 1176 2295 2.8 0.1 0.2 0.3 4.0 0.0 0.0 0.0 26 2% 4% 8%

761 1474 2857 3.3 0.5 0.7 1.1 5.4 0.2 0.3 0.7 29 6% 9% 15%

1142 2112 3905 6.4 4.2 4.5 3.5 8.3 0.9 1.5 2.7 44 23% 41% 58%

0% 0% 4% 21% 2 4% 1 6% 1 8% 37% 7% 7% 7% 18% 13% 9% 1%

35% 37% 31% 50% 44% 51% 41% 44% 37% 34% 25% 49% 38% 43% 59%

70% 72% 69% 51% 46% 52% 63% 54% 43% 38% 39% 60% 54% 54% 52%

44% 47% 62% 47% 37% 43% 41% 34% 30% 37% 39% 51% 57% 50% 44%

41% 35% 25% 22% 40% 28% 28% 21% 75% 74% 79% 13% 28% 35% 34%

85% 82% 74% 54% 47% 43% 44% 27% 63% 63% 63% 47% 74% 88% 93%

31% 35% 37% 38% 34% 35% 34% 35% 37% 41% 49% 28% 34% 28% 24%

13% 6% 10% 30% 30% 28% 16% 39% 34% 34% 32% 18% 19% 18% 15%

26% 21% 16% 19% 40% 32% 35% 32% 38% 31% 31% 18% 24% 19% 10%

37% 49% 56% 51% 43% 54% 63% 59% 22% 25% 18% 82% 43% 40% 51%

7% 6% 5% 27% 21% 25% 19% 52% 26% 28% 32% 43% 17% 18% 24% 25% 2% 1% 2% 24% 0% 0% 3%

9% 11% 9% 49% 51% 45% 35% 71% 2% 15% 34% 6 3% 2% 12% 27% 13% 3% 2% 0% 20% 4% 2% 0%

-2 6% -2 5% -2 3% 52% 46% 50% 44% 72% 51% 53% 57% 66% 41% 43% 49% 50% 14% 12% 1 6% 49% 2% 6% 1 6%

-3 1% -3 3% -3 0% 70% 71% 67% 59% 84% 15% 38% 58% 80% 14% 34% 52% 35% -18% -14% -2% 45% -21% -15% -3%

-0.6 -0.5 -0.4 30.0 5.8 13.1 10.2 361 -76 -107 -143 68 -12 -16 -26 23 -11 -16 -19 24 -12 -16 -20

-0.3 -0.3 -0.3 43.0 6.3 17.6 13.2 456 -29 -38 -67 81 -4 -5 -8 35 -3 -3 -3 36 -4 -4 -6

0.1 0.0 0.0 54.7 7.2 21.2 15.2 552 7 8 18 92 2 2 4 48 2 4 4 49 4 5 6

0.4 0.4 0.4 67.0 8.5 24.9 18.8 697 42 92 155 114 10 14 26 67 12 15 16 69 13 17 26

0.9 0.8 0.7 98.5 15.5 54.2 38.9 1978 1150 1321 1403 343 191 204 233 315 224 182 164 156 82 80 89

24% 22% 21% 66% 53% 75% 50% 51% 19% 3 7% 57% 59% 34% 43% 63% 34% 22% 21% 16% 30% 27% 28% 21%

30% 24% 40% 35% 56% 34% 43% 87% 63% 51% 62% 61% 54% 50% 51% 56% 43% 39% 51% 40% 51% 43% 46%

49% 55% 46% 54% 39% 19% 36% 45% 51% 60% 48% 41% 43% 49% 48% 50% 55% 52% 44% 60% 37% 41% 48%

50% 49% 49% 34% 26% 44% 28% 7% 48% 41% 24% 29% 44% 41% 25% 42% 41% 49% 45% 39% 35% 49% 51%

38% 40% 35% 1% 16% 18% 34% 0% 10% 1% 0% 1% 15% 9% 4% 7% 31% 30% 35% 0% 28% 16% 10%

49% 49% 40% 7% 13% 3% 16% 22% 50% 34% 19% 32% 40% 32% 25% 44% 54% 51% 55% 51% 61% 63% 70%

57% 51% 48% 34% 26% 37% 41% 4% 15% 15% 10% 22% 26% 31% 28% 21% 38% 35% 28% 25% 38% 40% 35%

37% 39% 46% 25% 39% 48% 37% 22% 27% 16% 31% 25% 29% 24% 24% 13% 15% 24% 32% 21% 40% 39% 32%

24% 30% 38% 43% 51% 38% 43% 47% 30% 40% 44% 29% 35% 29% 41% 32% 31% 26% 22% 46% 46% 29% 24%

28% 26% 24% 84% 63% 68% 56% 97% 71% 88% 88% 85% 63% 76% 75% 82% 54% 56% 56% 96% 52% 67% 76%

10% 13% 12% 1% 15% 12% 11% 1% 4% 5% 10% 10% 11% 15% 20% 12% 19% 12% 5% 17% 15% 18% 17% 1% 12% 15% 8%

2% 9% 16% 6% 16% 21% 20% 3% 4% 6% 10% 19% 3% 14% 26% 18% 36% 26% 3% 29% 35% 35% 28% 6% 25% 29% 10%

-3 1% -3 6% -3 4% -1 0% -3 9% -3 4% -3 3% 10% 20% 22% 31% 32% 34% 38% 45% 34% 43% 35% 22% 42% 39% 42% 41% 11% 35% 39% 28%

-1 4% -3 1% -4 0% -2 4% -4 0% -4 6% -4 5% 18% 19% 25% 32% 43% 18% 38% 51% 42% 60% 51% 18% 54% 59% 59% 53% 25% 50% 54% 31%

-4% -5% -7% 78 -27 -46 -78 0.3 -0.2 -0.4 -0.6 78 -15 -18 -23 31% 0.26 0.24 0.28 32% 0.1 0.1 0.1 1.3 0.1 76 0.10

-1% -1% -2% 134 -2 -4 -8 0.9 -0.1 -0.1 -0.2 94 -3 -5 -7 4 4% 0.29 0.29 0.36 4 4% 0.1 0.1 0.1 1.5 0.2 93 0.12

2% 2% 2% 209 9 15 28 1.5 0.0 0.1 0.1 108 4 5 5 5 6% 0.33 0.34 0.42 5 6% 0.1 0.2 0.2 1.7 0.2 108 0.13

5% 6% 9% 260 26 49 72 2.1 0.2 0.4 0.8 131 14 19 22 7 0% 0.38 0.42 0.51 6 9% 0.2 0.2 0.2 2.1 0.3 124 0.15

21% 27% 41% 419 125 203 348 2.8 1.0 1.5 2.1 216 75 73 78 98% 0.91 0.71 0.78 99% 0.6 0.6 0.4 3.9 0.8 279 0.22

18% 18% 3% 19% 12% 9% 9% 31% 53% 60% 66% 47% 38% 46% 63% 60% 46% 51% 64% 60% 35% 71% 64% 46% 50% 60% 46%

43% 40% 28% 48% 37% 37% 40% 46% 58% 48% 43% 49% 50% 54% 59% 48% 54% 55% 34% 66% 60% 57% 38% 43% 34% 35% 43%

48% 42% 57% 32% 49% 41% 15% 37% 29% 43% 43% 39% 43% 39% 27% 37% 49% 36% 34% 56% 62% 51% 37% 33% 31% 48% 36%

46% 51% 54% 40% 37% 34% 66% 38% 31% 23% 25% 41% 40% 34% 32% 41% 43% 51% 24% 11% 37% 18% 35% 44% 31% 46% 37%

35% 40% 49% 51% 56% 69% 62% 38% 21% 17% 14% 15% 19% 18% 9% 6% 0% 0% 35% 6% 5% 0% 23% 25% 44% 1% 29%

58% 61% 70% 32% 74% 74% 69% 52% 35% 22% 10% 32% 37% 28% 19% 27% 42% 19% 13% 35% 50% 20% 18% 38% 34% 7% 28%

28% 36% 31% 43% 39% 37% 40% 28% 22% 29% 46% 32% 31% 24% 18% 27% 31% 19% 37% 22% 29% 37% 38% 32% 24% 40% 43%

31% 25% 22% 49% 18% 31% 44% 36% 41% 41% 29% 28% 31% 27% 36% 28% 28% 40% 42% 16% 9% 23% 23% 43% 52% 34% 36%

34% 31% 27% 43% 36% 30% 18% 41% 40% 38% 40% 41% 29% 47% 41% 37% 24% 37% 48% 52% 43% 35% 46% 38% 44% 29% 43%

43% 41% 44% 26% 28% 22% 22% 36% 54% 61% 67% 59% 65% 68% 79% 78% 69% 78% 54% 69% 61% 77% 67% 41% 40% 82% 44%

3% 5% 9%

Probability of high vol regime

Q1 15% 3 2% 30% 29% 0% 2 1% 2 2% 21% 17% 1 8% 2 1% 2 9% 26% 63% 59% 54%

Note: Cons. Forecast disp. (3m avg) and Consensus forecast vol (1y) stats are referring to the average percentile level of subcomponents


16 April 2018

34

Goldman Sachs


Exhibit 65: Probability of vol regimes based on different indicators (data since 1950, where available) green shading = higher probability of low vol regime, orange shading = higher probability of high vol regime Indicator


ISM manufacturing (PMI) 3m change 6m change 12m change US current activity indicator (CAI) 3m change 6m change 12m change US macro surprise-MAP 3m change 6m change 12m change US unemployment rate s r 3m change o t a 6m change c i d 12m change n i PCE spending o r c 3m % change a M 6m % change 12m % change Non-farm payrolls 3m change 6m change 12m change US CPI inflation (headline) 3m change 6m change 12m change Fed funds Rate 3m change 6m change 12m change Shiller PE 3m % change 6m % change 12m % change US equity/bond correlation 3-month window 6-month window 12-month window Cross asset vol percentile (6m) US 10-year rates vol (6m) GSCI vol (6m) Gold vol (6m) US HY spread (bps) 3m change 6m change 12m change BAA-AAA Moody's spread (bps) s r o 3m change t a 6m change c i d 12m change n i TED spread (bps) t e 3m change k r a 6m change M 12m change MBS spread (bps) 3m change 6m change 12m change US cyclicals vs. defensives 3m % change 6m % change 12m % change Equity flows (12m sum, $ bn) 3m change 6m change 12m change US yield curve (10y-2y) 3m change 6m change 12m change Economic policy uncert. (3m avg) 3m change 6m change 12m change Consensus forecast disp. (3m avg) y t n CPI inflation i a t GDP r e T-bills forecast c n u Cons. forecast revision vol (1y) o CPI inflation r c a GDP M T-bills forecast ISM vol (1y) Inflation vol (1y) NFP vol (1y) Unemployment Vol (1y)

Correlation with S&P 500 vol 1m 6m -23% -31% -1 4% - 10 % -1 5% - 16 % -1 2% - 17 % -38% -52% -1 4% - 10 % -1 5% - 18 % -1 9% - 24 % -39% -38% -17% 1% -2 2% - 12 % -2 1% - 22 % 15% 25% 23% 32% 23% 34% 19% 30%

Start date 1951

1973

2000

1951

P er cen ti le o f i nd ic at or 20% 47.8 -3.4 -5.2 -7.8 1.5 -0.9 -1.4 -2.2 -0.5 -0.7 -0.8 -0.7 4.4 -0.3 -0.4 -0.8

40% 5 1.8 -1.1 -2.0 -2.2 2.6 -0.3 -0.4 -0.6 - 0.1 -0.2 -0.2 -0.1 5.3 -0.1 -0.2 -0.4

60% 5 5.0 0.9 1.2 2.2 3.7 0.2 0.2 0.4 0.2 0.2 0.3 0.3 5.9 0.0 0.0 -0.1

80% 5 8.2 3.3 4.6 7.4 4.6 0.8 1.1 1.6 0.6 0.8 0.7 0.8 7.2 0.2 0.3 0.7

100% 7 2.1 20.9 28.8 31.0 8.0 7.6 9.8 12.8 1.6 2.2 3.3 2.9 10.8 2.1 2.9 4.0

U nco nd . Prob.

Probability of low vol regime

37% 37% 37% 37% 30% 29% 29% 29% 42% 45% 45% 45% 37% 37% 37% 37%

Q1 25% 26% 20% 29% 0% 14% 11% 11% 17% 18% 21% 29% 35% 48% 48% 37%

Q2 28% 29% 34% 28% 32% 31% 25% 29% 30% 61% 58% 42% 39% 43% 43% 49%

Q3 34% 45% 37% 41% 41% 37% 45% 41% 53% 47% 58% 53% 40% 41% 45% 46%

Q4 49% 38% 45% 45% 34% 39% 38% 44% 58% 66% 50% 45% 55% 34% 29% 28%

Q5 49% 45% 48% 41% 42% 27% 28% 23% 54% 32% 37% 55% 17% 19% 20% 24%

Uncond. Prob.

Probability of high vol regime

23% 23% 23% 23% 32% 32% 32% 32% 38% 34% 34% 34% 23% 23% 23% 23%

Q1 32% 19% 26% 25% 68% 35% 44% 49% 51% 45% 45% 50% 20% 11% 9% 15%

Q2 30% 32% 25% 29% 27% 44% 41% 36% 53% 29% 32% 29% 27% 22% 22% 13%

Q3 23% 23% 21% 21% 18% 24% 17% 18% 35% 37% 29% 21% 24% 19% 16% 20%

Q4 21% 20% 23% 19% 25% 29% 31% 29% 25% 18% 26% 42% 16% 22% 24% 26%

Q5 7% 19% 18% 19% 20% 30% 28% 29% 27% 42% 39% 29% 27% 39% 42% 39%

1961 -2 6% -2 5% -2 2%

- 28 % - 35 % - 30 %

1% 2% 4%

1% 3% 6%

2% 3% 7%

2% 5% 9%

5% 8% 14%

36% 36% 36%

30% 31% 36%

44% 43% 42%

39% 42% 42%

41% 30% 32%

26% 32% 27%

26% 26% 26%

41% 48% 42%

27% 22% 26%

18% 22% 24%

25% 22% 27%

19% 17% 12%

-3 7% -3 4% -2 8% 7% -8% -3% 4% 1% -1 0% -1 1% -1 5% 6% -4 0% -3 6% -3 1%

- 52 % - 50 % - 43 % 3% -14% -13% -1% -4% - 18 % - 21 % - 23 % 6% - 21 % - 35 % - 38 %

142 3 13 2 40 1.5 -0.5 -0.9 -1.4 1.5 -0.4 -0.8 -1.3 12 -4% -7% -10%

417 89 2 1 81 7 2.5 -0.1 -0.3 -0.3 3.5 0.0 0.0 -0.1 17 -1% 0% 0%

613 1 20 1 2 3 88 3.4 0.2 0.2 0.4 5.3 0.1 0.2 0.4 21 2% 4% 7%

782 1 51 9 30 05 5.1 0.5 0.8 1.4 7.6 0.5 0.9 1.4 25 6% 9% 16%

1739 3 022 4 902 14.6 5.6 7.2 10.7 19.1 8.0 10.1 10.0 44 26% 41% 58%

35% 35% 35% 37% 37% 37% 37% 36% 36% 36% 36% 37% 37% 37% 37%

6% 9% 15% 43% 31% 28% 22% 42% 18% 21% 27% 22% 17% 10% 10%

33% 32% 32% 47% 42% 44% 55% 48% 34% 38% 31% 25% 34% 35% 44%

60% 63% 58% 51% 40% 50% 53% 50% 38% 33% 36% 40% 47% 52% 52%

42% 38% 42% 27% 42% 39% 37% 29% 43% 39% 36% 60% 53% 50% 46%

33% 31% 26% 17% 29% 22% 17% 10% 47% 46% 48% 36% 34% 36% 32%

26% 26% 26% 23% 23% 23% 23% 24% 24% 24% 24% 23% 23% 23% 23%

61% 57% 54% 23% 28% 24% 23% 28% 37% 37% 37% 15% 43% 48% 51%

19% 23% 22% 27% 20% 19% 18% 20% 30% 33% 29% 23% 17% 17% 16%

10% 7% 9% 14% 19% 16% 14% 16% 25% 24% 29% 16% 13% 11% 11%

19% 18% 18% 29% 23% 22% 20% 40% 16% 21% 17% 16% 12% 11% 8%

23% 27% 30% 20% 23% 31% 38% 15% 12% 7% 9% 43% 28% 26% 26%

-2 2% -2 1% -2 0% 45% 38% 43% 22% 63% 44% 48% 49% 45% 25% 28% 32% 46% 22% 16% 25% 49% 2% 6% 16%

- 26 % - 29 % - 28 % 58% 51% 56% 26% 74% 13% 35% 51% 56% 12% 26% 36% 38% -13% -8% 10% 45% -21% -15% -3%

-0.3 -0.3 -0.3 30.6 4.2 1 1.6 1 1.5 368 - 66 -103 -132 64 - 11 - 14 -22 23 - 13 - 17 -23 24 -12 -16 -20

0.1 0.1 0.0 42.9 5.9 14 .6 14 .4 448 -24 -33 -66 77 -3 -5 -8 37 -3 -3 -4 36 -4 -4 -6

0.3 0.3 0.3 54.8 6.8 1 8. 4 1 7. 8 534 9 11 25 92 2 2 3 55 3 4 4 49 4 5 6

0.5 0.5 0.4 66.9 8.5 2 3.1 2 4.1 671 48 99 152 123 10 15 22 84 13 16 19 69 13 17 26

0.9 0.8 0.7 98.5 17.0 5 4.2 6 8.2 1978 1150 1321 1403 343 191 204 233 315 224 182 205 156 82 80 89

34% 34% 34% 30% 33% 31% 30% 35% 35% 33% 33% 37% 37% 37% 37% 33% 34% 34% 34% 34% 35% 35% 35%

26% 24% 31% 62% 41% 57% 48% 58% 24% 37% 56% 44% 30% 36% 46% 34% 13% 15% 9% 30% 27% 28% 21%

46% 50% 43% 27% 51% 34% 35% 70% 55% 43% 49% 65% 50% 51% 47% 54% 42% 37% 48% 40% 51% 43% 46%

41% 43% 42% 40% 39% 16% 33% 36% 42% 54% 44% 45% 50% 49% 42% 48% 54% 51% 46% 60% 37% 41% 48%

31% 27% 28% 22% 24% 29% 26% 11% 42% 32% 17% 22% 43% 38% 36% 28% 37% 48% 45% 39% 35% 49% 51%

24% 25% 25% 1% 12% 17% 10% 0% 11% 0% 0% 9% 11% 10% 13% 1% 24% 22% 24% 0% 28% 16% 10%

27% 27% 27% 30% 27% 31% 30% 37% 37% 38% 38% 23% 23% 23% 23% 38% 39% 39% 39% 48% 48% 48% 48%

54% 50% 42% 6% 13% 3% 18% 19% 45% 33% 19% 12% 26% 21% 14% 44% 58% 52% 52% 51% 61% 63% 70%

27% 31% 35% 19% 12% 19% 34% 13% 20% 21% 18% 12% 19% 18% 15% 19% 33% 33% 27% 25% 38% 40% 35%

15% 21% 28% 19% 28% 28% 26% 27% 29% 15% 34% 19% 11% 15% 21% 19% 17% 24% 31% 21% 40% 39% 32%

15% 11% 10% 49% 38% 38% 38% 33% 25% 38% 36% 28% 22% 21% 20% 41% 33% 24% 24% 46% 46% 29% 24%

22% 21% 18% 58% 44% 65% 35% 91% 64% 81% 81% 42% 34% 39% 42% 69% 54% 61% 62% 96% 52% 67% 76%

-2 4% -2 7% -2 4% -7% -3 5% -3 0% -28% 15% 10% 13% 18% 27% 23% 32% 37% 34% 43% 35% 22% 42% 39% 42% 41% -9% 23% 6% -7%

- 10 % - 24 % - 28 % -19% - 37 % - 42 % -40% 25% 15% 20% 24% 39% 13% 37% 46% 42% 60% 51% 18% 54% 59% 59% 53% -7% 33% 12% -7%

-4% -6% -8% 31 - 22 - 37 -60 0.0 -0.3 -0.4 -0.6 81 - 15 -19 -23 31% 0 .2 6 0 .2 4 0.28 32% 0.1 0.1 0.1 1.5 0.1 82 0.1

-1% -2% -3% 105 -1 -3 -1 0.4 -0.1 -0.1 -0.2 96 -4 -5 -8 44% 0. 29 0. 29 0.36 44% 0.1 0.1 0.1 1.9 0.2 104 0.1

1% 2% 2% 173 7 11 21 0.8 0.0 0.1 0.1 111 4 4 3 56% 0 .3 3 0 .3 4 0.42 56% 0.1 0.2 0.2 2.3 0.2 123 0.2

5% 7% 10% 251 21 38 58 1.4 0.3 0.4 0.6 129 14 18 20 70% 0 .3 8 0 .4 2 0.51 69% 0.2 0.2 0.2 3.0 0.3 165 0.2

23% 33% 41% 419 125 203 348 2.8 3.1 2.2 2.5 216 119 73 78 98% 0 .9 1 0 .7 1 0.78 99% 0.6 0.6 0.4 6.0 0.8 385 0.4

31% 31% 31% 35% 35% 35% 35% 37% 37% 37% 37% 35% 35% 34% 34% 33% 38% 38% 38% 40% 39% 39% 39% 37% 37% 37% 37%

13% 13% 8% 14% 14% 10% 9% 23% 41% 39% 46% 44% 34% 38% 55% 60% 46% 51% 64% 60% 35% 71% 64% 40% 49% 46% 43%

39% 34% 31% 31% 34% 33% 34% 48% 48% 48% 32% 47% 39% 48% 53% 48% 54% 55% 34% 66% 60% 57% 38% 33% 35% 37% 37%

40% 43% 47% 46% 35% 34% 18% 39% 37% 44% 42% 30% 42% 37% 18% 37% 49% 36% 34% 56% 62% 51% 37% 42% 43% 42% 39%

37% 38% 41% 34% 39% 37% 52% 36% 35% 30% 39% 39% 37% 30% 32% 41% 43% 51% 24% 11% 37% 18% 35% 36% 32% 29% 35%

25% 26% 28% 49% 53% 61% 63% 39% 24% 23% 26% 14% 23% 16% 9% 6% 0% 0% 35% 6% 5% 0% 23% 33% 25% 30% 30%

32% 32% 32% 37% 37% 37% 37% 23% 23% 23% 23% 37% 37% 38% 38% 39% 39% 39% 39% 39% 39% 39% 39% 23% 23% 23% 23%

41% 44% 44% 21% 69% 73% 66% 14% 17% 14% 6% 32% 38% 29% 23% 27% 42% 19% 13% 35% 50% 20% 18% 29% 23% 9% 25%

16% 26% 32% 44% 42% 34% 35% 22% 13% 15% 22% 30% 28% 25% 18% 27% 31% 19% 37% 22% 29% 37% 38% 39% 14% 33% 33%

31% 20% 27% 39% 18% 26% 41% 14% 27% 22% 17% 28% 33% 25% 32% 28% 28% 40% 42% 16% 9% 23% 23% 9% 15% 26% 27%

31% 30% 23% 49% 23% 27% 19% 27% 24% 24% 27% 39% 27% 43% 43% 37% 24% 37% 48% 52% 43% 35% 46% 20% 30% 20% 14%

38% 37% 31% 30% 33% 24% 21% 36% 31% 38% 41% 55% 59% 69% 74% 78% 69% 78% 54% 69% 61% 77% 67% 17% 30% 25% 14%

1961

1951

1955

1951

1964

1971 1963 1971 1971 1986

1951

1987

1997

1974

1985

1951

1986

1991

1992

1952 1986

1986

Note: Cons. Forecast disp. (3m avg) and Consensus forecast vol (1y) stats are referring to the average percentile level of subcomponents


16 April 2018

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Goldman Sachs


Appendix 3: Correlation matrix of macro and market drivers Exhibit 66: Correlation matrix among Macro, Markets and Macro Uncertainty indicators (data since 1990) Macro Indicators

s r o t a c i d n I


o r c a M

1.0

US CAI

0.8

1.0

PCE 6m % chg

0.5

0.8

1.0

-0.6

-0.8

-0.6

1.0

0.6

0.9

0.7

-0.9

1.0

0.5

0.6

0.4

-0.6

0.7

NFP 3m chg

Fed fund 12m chg

Cross Shiller PE Asset Vol 12m chg Perc.

Rates Vol

GSCI Vol

US HY Spread

US HY 12m chg

Macro Uncertainty Indicators BAA spread

TED Spread

US Yield Curve 12m chg

0.6

0.7

0.5

-0.5

0.6

0.4

1.0

Cross Asset Vol Perc.

-0.3

-0.6

-0.5

0.5

-0.6

-0.4

-0.5

1.0

Rates Vol

-0.3

-0.5

-0.5

0.5

-0.6

-0.4

-0.4

0.8

1.0

GSCI Vol

-0.5

-0.7

-0.6

0.7

-0.7

-0.3

-0.5

0.8

0.6

1.0

US HY Spread

-0.7

-0.8

-0.7

0.7

-0.8

-0.6

-0.7

0.7

0.7

0.7

1.0

US HY 12m chg

-0.6

-0.6

-0.4

0.4

-0.4

-0.3

-0.6

0.3

0.3

0.4

0.6

1.0

BAA spread

-0.5

-0.8

-0.8

0.7

-0.8

-0.5

-0.6

0.7

0.7

0.7

0.9

0.6

1.0

TED Spread

-0.3

-0.3

-0.2

0.3

-0.2

-0.2

-0.1

0.1

0.1

0.2

0.3

0.6

0.3

1.0

-0.4

-0.5

-0.3

0.6

-0.6

-0.8

-0.3

0.3

0.3

0.2

0.4

0.1

0.3

0.2

1.0

EPU 12m chg

CPI Forecast Disp.

GDP Forecast Disp.

Bills Forecast Disp.

CPI Revision vol (1y)

GDP Revision vol (1y)

Bills Revision vol (1y)

Inflation vol (1y)

-0.2

-0.5

-0.5

0.3

-0.4

-0.4

-0.3

0.5

0.5

0.3

0.6

0.1

0.5

-0.1

0.2

1.0

EPU 12m chg

-0.5

-0.5

-0.3

0.5

-0.4

-0.3

-0.5

0.4

0.4

0.5

0.5

0.6

0.4

0.4

0.2

0.4

1.0

CPI Forecast Disp.

-0.4

-0.6

-0.6

0.7

-0.7

-0.5

-0.3

0.5

0.6

0.7

0.7

0.2

0.7

0.3

0.3

0.5

0.4

1.0

GDP Forecast Disp.

-0.4

-0.5

-0.4

0.7

-0.7

-0.6

-0.3

0.4

0.5

0.4

0.6

0.1

0.5

0.2

0.5

0.4

0.3

0.6

1.0

Bills Forecast Disp.

-0.2

-0.2

0.0

0.4

-0.3

-0.2

-0.3

0.1

0.2

0.2

0.2

0.1

0.1

0.2

0.3

-0.3

0.2

0.3

0.4

1.0

CPI Revision vol (1y)

-0.3

-0.6

-0.7

0.7

-0.7

-0.4

-0.4

0.6

0.6

0.7

0.6

0.3

0.7

0.1

0.2

0.4

0.3

0.7

0.5

0.1

1.0

GDP Revision vol (1y)

-0.3

-0.5

-0.4

0.6

-0.7

-0.6

-0.5

0.5

0.6

0.5

0.7

0.1

0.5

-0.1

0.4

0.4

0.2

0.5

0.6

0.3

0.7

1.0

Bills Revision vol (1y)

-0.5

-0.5

-0.3

0.7

-0.6

-0.5

-0.5

0.3

0.6

0.4

0.6

0.4

0.5

0.3

0.4

0.2

0.4

0.5

0.6

0.6

0.4

0.6

1.0

Inflation vol (1y)

-0.3

-0.6

-0.6

0.6

-0.6

-0.2

-0.4

0.5

0.4

0.7

0.5

0.3

0.7

0.2

0.2

0.2

0.3

0.6

0.3

0.1

0.8

0.4

0.3

1.0

NFP vol (1y)

-0.3

-0.5

-0.4

0.5

-0.6

-0.3

-0.2

0.5

0.5

0.6

0.6

0.0

0.5

0.1

0.2

0.4

0.3

0.7

0.6

0.4

0.6

0.6

0.4

0.5

EPU 3m avg

EPU 3m avg

NFP vol (1y)

1.0

Shiller PE 12m chg

US Yield Curve 12m chg

s r o t a c i d n I y t n i a t r e c n U o r c a M

Markets Indicators NFP 3m chg

ISM

Fed fund 12m chg

s r o t a c i d n I s t e k r a M

Unemp. 6m chg

ISM

Unemp. 6m chg

US CAI

PCE 6m % chg

Indicator

1.0


16 April 2018

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Goldman Sachs


Option specific disclosures Price target methodology: Please refer to the analyst’s previously published research for methodology and risks associated with equity price targets.

Pricing Disclosure: Option prices and volatility levels in this note are indicative only, and are based on our estimates of recent mid-market levels (unless otherwise noted). All prices and levels exclude transaction costs unless otherwise stated.

General Options Risks – The risks below and any other options risks mentioned in this research report pertain both to specific derivative trade recommendations mentioned and to discussion of general opportunities and advantages of derivative strategies. Unless otherwise noted, options strategies mentioned in this report may be a combination of the strategies below and therefore carry with them the risks of those strategies. M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

Buying Options - Investors who buy call (put) options risk loss of the entire premium paid if the underlying security finishes below (above) the strike price at expiration. Investors who buy call or put spreads also risk a maximum loss of the premium paid. The maximum gain on a long call or put spread is the difference between the strike prices, less the premium paid.

Selling Options - Investors who sell calls on securities they do not own risk unlimited loss of the security price less the strike price. Investors who sell covered calls (sell calls while owning the underlying security) risk having to deliver the underlying security or pay the difference between the security price and the strike price, depending on whether the option is settled by physical delivery or cash-settled. Investors who sell puts risk loss of the strike price less the premium received for selling the put. Investors who sell put or call spreads risk a maximum loss of the difference between the strikes less the premium received, while their maximum gain is the premium received. For options settled by physical delivery, the above risks assume the options buyer or seller, buys or sells the resulting securities at the settlement price on expiry.

16 April 2018

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Goldman Sachs


Disclosure Appendix Reg AC We, Christian Mueller-Glissmann, CFA, Alessio Rizzi and Ian Wright, hereby certify that all of the views expressed in this report accurately reflect our personal views about the subject company or companies and its or their securities. We also certify that no part of our compensation was, is or will be, directly or indirectly, related to the specific recommendations or views expressed in this report. Unless otherwise stated, the individuals listed on the cover page of this report are analysts in Goldman Sachs’ Global Investment Research division.

Disclosures Distribution of ratings/investment banking relationships Goldman Sachs Investment Research global Equity coverage universe Rating Distribution

Global


Investment Banking Relationships

Buy

Hold

Sell

Buy

Hold

Sell

35%

53%

12%

63%

57%

51%

As of April 1, 2018, Goldman Sachs Global Investment Research had investment ratings on 2,896 equity securities. Goldman Sachs assigns stocks as Buys and Sells on various regional Investment Lists; stocks not so assigned are deemed Neutral. Such assignments equate to Buy, Hold and Sell for the purposes of the above disclosure required by the FINRA Rules. See ‘Ratings, Coverage groups and views and related definitions’ below. The Investment Banking Relationships chart reflects the percentage of subject companies within each rating category for whom Goldman Sachs has provided investment banking services within the previous twelve months.

Disclosures required by United States laws and regulations See company-specific regulatory disclosures above for any of the following disclosures required as to companies referred to in this report: manager or co-manager in a pending transaction; 1% or other ownership; compensation for certain services; types of client relationships; managed/co-managed public offerings in prior periods; directorships; for equity securities, market making and/or specialist role. Goldman Sachs trades or may trade as a principal in debt securities (or in related derivatives) of issuers discussed in this report. The following are additional required disclosures: Ownership and material conflicts of interest: Goldman Sachs policy prohibits its analysts, professionals reporting to analysts and members of their households from owning securities of any company in the analyst’s area of coverage. Analyst compensation: Analysts are paid in part based on the profitability of Goldman Sachs, which includes investment banking revenues. Analyst as officer or director: Goldman Sachs policy generally prohibits its analysts, persons reporting to analysts or members of their households from serving as an officer, director or advisor of any company in the analyst’s area of coverage. Non-U.S. Analysts: Non-U.S. analysts may not be associated persons of Goldman Sachs & Co. LLC and therefore may not be subject to FINRA Rule 2241 or FINRA Rule 2242 restrictions on communications with subject company, public appearances and trading securities held by the analysts.

Additional disclosures required under the laws and regulations of jurisdictions other than the United States The following disclosures are those required by the jurisdiction indicated, except to the extent already made above pursuant to United States laws and regulations. Australia: Goldman Sachs Australia Pty Ltd and its affiliates are not authorised deposit-taking institutions (as that term is defined in the Banking Act 1959 (Cth)) in Australia and do not provide banking services, nor carry on a banking business, in Australia. This research, and any access to it, is intended only for “wholesale clients” within the meaning of the Australian Corporations Act, unless otherwise agreed by Goldman Sachs. In producing research reports, members of the Global Investment Research Division of Goldman Sachs Australia may attend site visits and other meetings hosted by the companies and other entities which are the subject of its research reports. In some instances the costs of such site visits or meetings may be met in part or in whole by the issuers concerned if Goldman Sachs Australia considers it is appropriate and reasonable in the specific circumstances relating to the site visit or meeting. To the extent that the contents of this document contains any financial product advice, it is general advice only and has been prepared by Goldman Sachs without taking into account a client’s objectives, financial situation or needs. A client should, before acting on any such advice, consider the appropriateness of the advice having regard to the client’s own objectives, financial situation and needs. Brazil: Disclosure information in relation to CVM Instruction 483 is available at http://www.gs.com/worldwide/brazil/area/gir/index.html. Where applicable, the Brazil-registered analyst primarily responsible for the content of this research report, as defined in Article 16 of CVM Instruction 483, is the first author named at the beginning of this report, unless indicated otherwise at the end of the text. Canada: Goldman Sachs Canada Inc. is an affiliate of The Goldman Sachs Group Inc. and therefore is included in the company specific disclosures relating to Goldman Sachs (as defined above). Goldman Sachs Canada Inc. has approved of, and agreed to take responsibility for, this research report in Canada if and to the extent that Goldman Sachs Canada Inc. disseminates this research report to its clients. Hong Kong: Further information on the securities of covered companies referred to in this research may be obtained on request from Goldman Sachs (Asia) L.L.C. India: Further information on the subject company or companies referred to in this research may be obtained from Goldman Sachs (India) Securities Private Limited, Research Analyst - SEBI Registration Number INH000001493, 951-A, Rational House, Appasaheb Marathe Marg, Prabhadevi, Mumbai 400 025, India, Corporate Identity Number U74140MH2006FTC160634, Phone +91 22 6616 9000, Fax +91 22 6616 9001. Goldman Sachs may beneficially own 1% or more of the securities (as such term is defined in clause 2 (h) the Indian Securities Contracts (Regulation) Act, 1956) of the subject company or companies referred to in this research report. Japan: See below. Korea: Further information on the subject company or companies referred to in this research may be obtained from Goldman Sachs (Asia) L.L.C., Seoul Branch. New Zealand: Goldman Sachs New Zealand Limited and its affiliates are neither “registered banks” nor “deposit takers” (as defined in the Reserve Bank of New Zealand Act 1989) in New Zealand. This research, and any access to it, is intended for “wholesale clients” (as defined in the Financial Advisers Act 2008) unless otherwise agreed by Goldman Sachs. Russia: Research reports distributed in the Russian Federation are not advertising as defined in the Russian legislation, but are information and analysis not having product promotion as their main purpose and do not provide appraisal within the meaning of the Russian legislation on appraisal activity. Singapore: Further information on the covered companies referred to in this research may be obtained from Goldman Sachs (Singapore) Pte. (Company Number: 198602165W). Taiwan: This material is for reference only and must not be reprinted without permission. Investors should carefully consider their own investment risk. Investment results are the responsibility of the individual investor. United Kingdom: Persons who would be categorized as retail clients in the United Kingdom, as such term is defined in the rules of the Financial Conduct Authority, should read this research in conjunction with prior Goldman Sachs research on the covered companies referred to herein and should refer to the risk warnings that have been sent to them by Goldman Sachs International. A copy of these risks warnings, and a glossary of certain financial terms used in this report, are available from Goldman Sachs International on request.

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European Union: Disclosure information in relation to Article 4 (1) (d) and Article 6 (2) of the European Commission Directive 2003/125/EC is available at http://www.gs.com/disclosures/europeanpolicy.html which states the European Policy for Managing Conflicts of Interest in Connection with Investment Research. Japan: Goldman Sachs Japan Co., Ltd. is a Financial Instrument Dealer registered with the Kanto Financial Bureau under registration number Kinsho 69, and a member of Japan Securities Dealers Association, Financial Futures Association of Japan and Type II Financial Instruments Firms Association. Sales and purchase of equities are subject to commission pre-determined with clients plus consumption tax. See company-specific disclosures as to any applicable disclosures required by Japanese stock exchanges, the Japanese Securities Dealers Association or the Japanese Securities Finance Company.

Ratings, coverage groups and views and related definitions Buy (B), Neutral (N), Sell (S) - Analysts recommend stocks as Buys or Sells for inclusion on various regional Investment Lists. Being assigned a Buy or Sell on an Investment List is determined by a stock’s total return potential relative to its coverage. Any stock not assigned as a Buy or a Sell on an Investment List with an active rating (i.e., a stock that is not Rating Suspended, Not Rated, Coverage Suspended or Not Covered), is deemed Neutral. Each regional Investment Review Committee manages various regional Investment Lists to a global guideline of 25%-35% of stocks as Buy and 10%-15% of stocks as Sell; however, the distribution of Buys and Sells in any particular analyst’s coverage group may vary as determined by the regional Investment Review Committee. Additionally, each Investment Review Committee manages Regional Conviction lists, which represent investment recommendations focused on the size of the total return potential and/or the likelihood of the realization of the return across their respective areas of covera ge. The addition or removal of stocks from such Conviction lists do not represent a change in the analysts’ investment rating for such stocks. Total return potential represents the upside or downside differential between the current share price and the price target, including all paid or anticipated dividends, expected during the time horizon associated with the price target. Price targets are required for all covered stocks. The total return potential, price target and associated time horizon are stated in each report adding or reiterating an Investment List membership.


Coverage groups and views: A list of all stocks in each coverage group is available by primary analyst, stock and coverage group at http://www.gs.com/research/hedge.html. The analyst assigns one of the following coverage views which represents the analyst’s investment outlook on the coverage group relative to the group’s historical fundamentals and/or valuation. Attractive (A). The investment outlook over the following 12 months is favorable relative to the coverage group’s historical fundamentals and/or valuation. Neutral (N). The investment outlook over the following 12 months is neutral relative to the coverage group’s historical fundamentals and/or valuation. Cautious (C). The investment outlook over the following 12 months is unfavorable relative to the coverage group’s historical fundamentals and/or valuation. Not Rated (NR). The investment rating and target price have been removed pursuant to Goldman Sachs policy when Goldman Sachs is acting in an advisory capacity in a merger or strategic transaction involving this company and in certain other circumstances. Rating Suspended (RS). Goldman Sachs Research has suspended the investment rating and price target for this stock, because there is not a sufficient fundamental basis for determining, or there are legal, regulatory or policy constraints around publishing, an investment rating or target. The previous investment rating and price target, if any, are no longer in effect for this stock and should not be relied upon. Coverage Suspended (CS). Goldman Sachs has suspended coverage of this company. Not Covered (NC). Goldman Sachs does not cover this company. Not Available or Not Applicable (NA). The information is not available for display or is not applicable. Not Meaningful (NM). The information is not meaningful and is therefore excluded.

Global product; distributing entities The Global Investment Research Division of Goldman Sachs produces and distributes research products for clients of Goldman Sachs on a global basis. Analysts based in Goldman Sachs offices around the world produce equity research on industries and companies, and research on macroeconomics, currencies, commodities and portfolio strategy. This research is disseminated in Australia by Goldman Sachs Australia Pty Ltd (ABN 21 006 797 897); in Brazil by Goldman Sachs do Brasil Corretora de Títulos e Valores Mobiliários S.A.; Ombudsman Goldman Sachs Brazil: 0800 727 5764 and / or [email protected]. Available Weekdays (except holidays), from 9am to 6pm. Ouvidoria Goldman Sachs Brasil: 0800 727 5764 e/ou [email protected]. Horário de funcionamento: segunda-feira à sexta-feira (exceto feriados), das 9h às 18h; in Canada by either Goldman Sachs Canada Inc. or Goldman Sachs & Co. LLC; in Hong Kong by Goldman Sachs (Asia) L.L.C.; in India by Goldman Sachs (India) Securities Private Ltd.; in Japan by Goldman Sachs Japan Co., Ltd.; in the Republic of Korea by Goldman Sachs (Asia) L.L.C., Seoul Branch; in New Zealand by Goldman Sachs New Zealand Limited; in Russia by OOO Goldman Sachs; in Singapore by Goldman Sachs (Singapore) Pte. (Company Number: 198602165W); and in the United States of America by Goldman Sachs & Co. LLC. Goldman Sachs International has approved this research in connection with its distribution in the United Kingdom and European Union.

European Union: Goldman Sachs International authorised by the Prudential Regulation Authority and regulated by the Financial Conduct Authority and the Prudential Regulation Authority, has approved this research in connection with its distribution in the European Union and United Kingdom; Goldman Sachs AG and Goldman Sachs International Zweigniederlassung Frankfurt, regulated by the Bundesanstalt für Finanzdienstleistungsaufsicht, may also distribute research in Germany.

General disclosures This research is for our clients only. Other than disclosures relating to Goldman Sachs, this research is based on current public information that we consider reliable, but we do not represent it is accurate or complete, and it should not be relied on as such. The information, opinions, estimates and forecasts contained herein are as of the date hereof and are subject to change without prior notification. We seek to update our research as appropriate, but various regulations may prevent us from doing so. Other than certain industry reports published on a periodic basis, the large majority of reports are published at irregular intervals as appropriate in the analyst’s judgment. Goldman Sachs conducts a global full-service, integrated investment banking, investment management, and brokerage business. We have investment banking and other business relationships with a substantial percentage of the companies covered by our Global Investment Research Division. Goldman Sachs & Co. LLC, the United States broker dealer, is a member of SIPC (http://www.sipc.org). Our salespeople, traders, and other professionals may provide oral or written market commentary or trading strategies to our clients and principal trading desks that reflect opinions that are contrary to the opinions expressed in this research. Our asset management area, principal trading desks and investing businesses may make investment decisions that are inconsistent with the recommendations or views expressed in this research. The analysts named in this report may have from time to time discussed with our clients, including Goldman Sachs salespersons and traders, or may discuss in this report, trading strategies that reference catalysts or events that may have a near-term impact on the market price of the equity securities discussed in this report, which impact may be directionally counter to the analyst’s published price target expectations for such stocks. Any such trading strategies are distinct from and do not affect the analyst’s fundamental equity rating for such stocks, which rating reflects a stock’s return potential relative to its coverage group as described herein. We and our affiliates, officers, directors, and employees, excluding equity and credit analysts, will from time to time have long or short positions in, act as principal in, and buy or sell, the securities or derivatives, if any, referred to in this research.

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The views attributed to third party presenters at Goldman Sachs arranged conferences, including individuals from other parts of Goldman Sachs, do not necessarily reflect those of Global Investment Research and are not an official view of Goldman Sachs. Any third party referenced herein, including any salespeople, traders and other professionals or members of their household, may have positions in the products mentioned that are inconsistent with the views expressed by analysts named in this report. This research is not an offer to sell or the solicitation of an offer to buy any security in any jurisdiction where such an offer or solicitation would be illegal. It does not constitute a personal recommendation or take into account the particular investment objectives, financial situations, or needs of individual clients. Clients should consider whether any advice or recommendation in this research is suitable for their particular circumstances and, if appropriate, seek professional advice, including tax advice. The price and value of investments referred to in this research and the income from them may fluctuate. Past performance is not a guide to future performance, future returns are not guaranteed, and a loss of original capital may occur. Fluctuations in exchange rates could have adverse effects on the value or price of, or income derived from, certain investments. Certain transactions, including those involving futures, options, and other derivatives, give rise to substantial risk and are not suitable for all investors. Investors should review current options disclosure documents which are available from Goldman Sachs sales representatives or at http://www.theocc.com/about/publications/character-risks.jsp. Transaction costs may be significant in option strategies calling for multiple purchase and sales of options such as spreads. Supporting documentation will be supplied upon request.

Differing Levels of Service provided by Global Investment Research: The level and types of services provided to you by the Global Investment Research division of GS may vary as compared to that provided to internal and other external clients of GS, depending on various factors including your individual preferences as to the frequency and manner of receiving communication, your risk profile and investment focus and perspective (e.g., marketwide, sector specific, long term, short term), the size and scope of your overall client relationship with GS, and legal and regulatory constraints. As an example, certain clients may request to receive notifications when research on specific securities is published, and certain clients may request that specific data underlying analysts’ fundamental analysis available on our internal client websites be delivered to them electronically through data feeds or otherwise. No change to an analyst’s fundamental research views (e.g., ratings, price targets, or material changes to earnings estimates for equity securities), will be communicated to any client prior to inclusion of such information in a research report broadly disseminated through electronic publication to our internal client websites or through other means, as necessary, to all clients who are entitled to receive such reports. M O C . V N I N O G Y L O P @ A V O Z A K S S A R E f o e s u e v i s u l c x e e h t r o F

All research reports are disseminated and available to all clients simultaneously through electronic publication to our internal client websites. Not all research content is redistributed to our clients or available to third-party aggregators, nor is Goldman Sachs responsible for the redistribution of our research by third party aggregators. For research, models or other data related to one or more securities, markets or asset classes (including related services) that may be available to you, please contact your GS representative or go to http://360.gs.com. Disclosure information is also available at http://www.gs.com/research/hedge.html or from Research Compliance, 200 West Street, New York, NY 10282.

© 2018 Goldman Sachs. No part of this material may be (i) copied, photocopied or duplicated in any form by any means or (ii) redistributed without the prior written consent of The Goldman Sachs Group, Inc.

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