FinQuiz
Formula Sheet
Reading 5: The Behavioral Finance Perspective 1.
Expected utility (U) = ! (U values of outcomes " Respective Prob)
2.
Subjective expected U of an individual =! [u (xi) " Prob (xi)]
3.
Bayes’ formula = P (A|B) = [P (B|A) / P (B)]" P (A)
4.
Risk premium = Certainty equivalent – Expected value
5.
Perceived value of each outcome = = U = w (p1) v (x1) + w (p 2) v (x2) + … + w (pn) v (xn)
6.
1.
After-tax (AT) Real required return (RR) % =
!"#$%&' ( *$+,#*$- $./$%-#&,*$( #% 0$1* %
2$& 3%4$(&15"$ 6(($&( 7*89$:&$- %$$-( #% 0$1* %
=
2.
3.
AT Nominal RR % =
4.
Pre-tax income needed = AT income needed / (1-tax rate)
5.
Pre-tax Nominal RR = (Pre-tax income needed / Total investable assets) + Inf%
If Portfolio returns are tax-deferred: 6. Pre-tax projected expenditure $ = AT projected expenditure $ / (1 – tax rate) 7.
Pre-tax real RR % = Pre-tax projected expenditures $ / Total investable assets
8.
Pre-tax nominal RR = (1 + Pre-tax real RR %) " (1 + Inflation rate%) – 1
If Portfolio returns are NOT tax-deferred: 9. AT real RR% = AT projected expenditures $ / Total Investable assets
7*89$:&$- %$$-( #% 0$1* % 2$& 3%4$(&15"$ 6(($&(
+ Current Annual (Ann) Inflation (Inf) % = Or AT real RR% + Current Ann Inf%
exempt Invst " wt of Tax-exempt Invst) – Inf rate Or
Total Investable assets = Current Portfolio -Current year cash outflows + Current year cash inflows
10. AT nominal RR% = (1 + AT real RR%) " (1 + Inf%) – 1
2$& 3%4$(&15"$ 6(($&(
" wt of Tax-exempt Invst)] " (1 – tax rate) + (Expected total R of Tax-
AT Nominal RR% = ; < => ?@AB ??C " (1 + Current Ann Inf %) – 1
Abnormal return (R) = Actual R – Expected R
Reading 8: Managing Individual Investor Portfolios
CFA Level III 2018
11. Procedure of converting nominal, pre-tax figures into real, after-tax return: Real AT R = [Expected total R – (Expected total R of Tax-exempt Invst •
•
Real AT R =[(Taxable R of asset class 1 " wt of asset class 1) + (Taxable R of asset class 2 " wt of asset class 2) + …+ (Taxable return of asset class n " wt of asset class n)] " (1 – tax rate) + (Expected total R of Tax-exempt Invst " wt of Tax-exempt Invst) – Infrate
Reading 9: Taxes and Private Wealth Management in a Global Context 1.
Average tax rate = Total tax liability / Total taxable income
2.
AT Return = r " (1 – ti)
3.
AT Future Accumulations after n years = FVIFi= Initial Invst " [1 + r (1 – t i)]n
4.
Tax drag ($) on capital accumulation = Acc capital without tax – Acc capital with tax
5.
Tax drag (%) on capital accumulation = (Acc capital without tax – Acccapital with tax) / (Acc capital without tax – Initial investment)
FinQuiz
6.
Returns-Based Taxes: Deferred Capital Gains: •
•
7.
Cost Basis •
•
8.
AT Future Accumulations after n years = FVIFcg= InitialInvst. " [(1 + r) n (1 – tcg) + tcg] Value of a capital gain tax deferral = AT future accumulations in deferred taxes – AT future accumulations in accrued annually taxes
Capital gain/loss = Selling price – Cost basis AT Future Accumulation = FVIF cgb= Initial Invst " [(1 + r) n (1 – tcg) + tcg – n (1 – B) tcg] =Initial Invst " [(1 + r) (1 – tcg) + (tcg " B)] Where, B = Cost basis tcg " B = Return of basis at the end of the Invst.horizon. When cost basis = initial Invst !B=1, n FVIFcg=Initial investment " [(1 + r) (1 – tcg) + tcg]
Wealth-Based Taxes AT Future Acc = FVIF w = Initial Invst [(1 + r) (1 – t w)] n Where, tw = Ann wealth tax rate •
9.
Blended Taxing Environments a) Proportion of total return from Dividends (pd), taxed at a rate of t d. pd = Dividends ($) / Total dollar return
Formula Sheet
b) % of total return from Interest income (pi), taxed at a rate of t i. pi = Interest ($) / Total dollar return c) % of total return from Realized capital gain (pcg), taxed at a rate of t cg. pcg = Realized Capital gain ($) / Total dollar return d) Unrealized capital gain return: Total Dollar Return = Dividends + Interest income + Realized Capital gain + Unrealized capital gain Total realized tax rate = [(p i" ti) + (pd" td)+ (pcg" tcg)] 10. Effective Ann AT R = r* = r (1 – p iti – pdtd – pcgtcg) = r (1 – total realized tax rate) Where, r = Pre-tax overall return on the portfolio and r*= Effective ann AT R 11. Effective Capital Gains Tax = T* = t cg (1 – pi – pd – pcg) / (1 – piti – pdtd – pcgtcg) 12. Future AT acc. = FVIF Taxable = Initial Invst [(1 + r*)n (1 – T*) + T* – (1 – B) t cg] 13. Initial Invst (1 + Accrual Equivalent R)n = Future AT Acc 14. Accrual Equivalent R = (Future AT Acc / Initial Invst) 1/n – 1 15. Accrual Equivalent Tax Rates = r (1 – T AE) = R AE 1D AE = TAE = 1D
EFG E
CFA Level III 2018
16. In Tax Deferred accounts (TDAs) Future AT Acc = FVIF TDA = Initial Invst[(1 + r) n (1 – Tn)] 17. In Tax-exempt accounts FVIF taxEx = Initial Invst (1 + r) n FVIF TDA = FVIF taxEx (1 – Tn) •
18. AT asset wt of an asset class (%) = AT MV of asset class ($) / Total AT value of Portfolio ($) 19. AT Initial invst in tax-exempt accounts = (1 – T0) 20. FV of a pretax $ invested in a tax-exempt account = (1 – T0) (1 + r) n 21. FV of a pretax $ invested in a TDA = (1 + r) n (1 – Tn) 22. Investors AT risk = S.D of pre-tax R (1 – Tax rate) = #(1 – T) 23. Tax alpha from tax-loss harvesting (or Tax savings) =Capital gain tax with unrealized losses – Capital gain tax with realized Or losses Tax alpha from tax-loss harvesting = Capital loss " Tax rate 24. Pretax R taxed as a short-term gain needed to generate the AT R equal to long-term AT R = Long-term gain after-tax return / (1 –short-term gains tax rate)
FinQuiz
Formula Sheet
Reading 10: Estate Planning in a Global Context 1.
2.
3.
Estate =Financial assets + Tangible personal assets + Immoveab le property + Intellectual property Discretionary wealth or Excess capital = Assets – Core capital
#
5.
6.
Value of a taxable gift (if gift & asset (bequeathed) have equal AT R ) = (1 – Tg) / (1 – Te) 10. The relative after-tax value of 1. gift the when the donor pays gift tax and when the recipient’s estate will not be taxable (assuming r g = r e and tig = tie): HIJKLK\]OPQRS T
p(Survival j ) ! Spending j
j "1
4.
9.
Core Capital (CC) Spending Needs = N
CC needed to maintain given spending pattern = Annual Spending needs / Sustainable Spending rate
8.
Taxable Gifts = HIJKLK\]OPQRS T Z UXJW Z UVN[ UXS Y[ UXJ[
UVNW UXS YW
extended model hi model hij T $"
kl m SnU UVN l m opql r klstpUVdlr SnU pUVN Vvrl u
Income yield (payout) = SwSK] wfdwQfd KffaK] QfxwyO QfQSQK] oaNxzKbO oNQxO
Mortality wghtd. NPV = mNPV 0 = T m opbl r \l SnU pUVNrl
; D gd < gd gO f
; D gO Reading 13: Managing Institutional Investor Portfolio
12. Relative value of generation skipping = 1 / (1 – T1) 13. Charitable Gratuitous Transfers =
2.
Min RR for a fully-funded PP = Discount rate used to calculate the PV of plan liabilities
3.
Desired R for a fully-funded PP = Discount rate used to calculate the PV of plan liabilities + Excess Target return
RV CharitableGift
Z
Relative value of the tax-free gift = 1 / (1 – Te)
Human Capital hij T
Defined-Benefit Plans: 1. Funded Status of Pension Plan (PP) = MV of PP assets – PV of PP liabilities
UVN[ UXS Y[ Z UXJ[
7.
f
11. Size of the partial gift credit = Size of the gift " TgTe
Tax-Free Gifts = HIJKLMNOOPQRS T UVNW UXS YW
!"
^I_O`aObS
; < cO ; D eQO
(1+ r )
Reading 12: Risk Management for Individuals
3.
^IPQRS
; < cd ; D eQd
T
j
Expected Real spending = Real annual spending " Combined probability
CFA Level III 2018
=
(1 + rg )
n
=
FV CharitableGift FV Bequest n
+
T oi [1 + re (1! t ie )] (1 ! T e ) n
[1 + r (1 ! t )] (1 ! T ) e
ie
e
14. Credit method = TC = Max [TR , TS] 15. Exemption method = TE = TS 16. Deduction method = TD = TR + TS – TR TS
4. Net cash outflow = Benefit payme nts – Pension contributions Foundations 5. Min R requirement (req) = Min Ann spending rate + InvstMgmtExp+ Expected Inf rate
FinQuiz
Or Min Rreq = [(1 + Min Ann spending rate) " (1 + Invst Mgmt. Exp) " (1 + Expected Inf rate)] -1 6.
Foundation’s liquidity req = Anticipated cash needs (captured in a foundation’s distributions prescribed by minimum spending rate*) + Unanticipated cash needs (not captured in a foundation’s distributions prescribed) – Contributions made to the foundation. * It includes Minimum annual spending rate (including “overhead” expenses e.g. salaries) + Investment management expenses
7.
Endowments Ann Spending ($) = % of an endowment’s Or current MV AnnSpending ($) = % of an endowment’s avg trailing MV
8.
Simple spending rule = Spending t = Spending rate " Endowment’s End MVt-1
9.
Rolling 3-yr Avg spending rule =Spendingt = Spending rate " Endowment’s Avg MV of the last 3 fiscal yr-ends i.e. ! Spending t = Spending rate " (1/3) [Endowment’s End MVt-1+ Endowment’s End MVt-2 + Endowment’s End MVt-3]
Formula Sheet
10. Geometric smoothing rule = Spendingt = WghtAvg of the prior yr’s spending adjusted for Inf + Spending rate " Beg MV of the prior fiscal yr i.e. ! Spending t = Smoothing rate " [Spendingt-1 " (1 + Inf t-1 t-1)] + (1 – Smoothing rate) " (Spending rate " Beg MVt-1 of the endowment) 11. Min ReqRoR = Spending rate + Cost of generating Invst R + Expected Infrate Or Min ReqRoR = [(1 + Spending rate) " (1 + Cost of generating Invst R) " (1 + Expected Inf rate)] -1 12. Liquidity needs = Ann spending needs + Capital commitments + Portfolio rebalancing expenses – Contributions by donor 13. Neutrality Spending Rate = Real ex pected R = Expected total R – Inf Life Insurance Companies 14. Cash value = Initial premium paid + Any accrued interest on that premium 15. Policy reserve = PV of future benefits - PV of future net premiums 16. Surplus = Total assets of an insurance company - Total liabilities of an insurance company
CFA Level III 2018
Non-Life Insurance Compan ies 17. Combined Ratio = (Total amount of claims paid out + Insurer's opera ting costs) / Premium income Banks 18. Net interest margin = p{fSONObS {fxwyOX{fSONObS |LoOfbOr }~d |KNfQfd }bbOSb mOS {fSONObS {fxwyO
=
}~d |KNfQfd }bbOSb
19. Interest spread = Avg yield on earning assets – Average percent cost of interest bearing liabilities 20. Leverage-adjusted duration gap (LADG) = DA – (k "DL) Where, k= MV of liabilities / MV of assets = L/A 21. Change in MV of net worth of a bank (resulting from interest rate shock) $ - LADG " Size of bank " Size of interest rate shock
FinQuiz
Formula Sheet
Reading 14: Capital Market Expectations 1.
11. Earnings g rate = Nominal GDP g rate + Excess Corp g (for the index companies)
Multiple-regression analysis: A = %0 + %1 B + %2 C + &
3.
Time series analysis: A = %0 + %1 Lagged values of A + %2 Lagged values of B + %2 Lagged values of C + &
4.
Shrinkage Estimator = (Wt of historical estimate " Historical parameter estimate) + (Wt of Target parameter estimate " Target parameter estimate)
5.
Shrinkage estimator of Cov matrix = (Wt of historical Cov " Historical Cov) + (Wt of Target Cov " Target Cov)
6.
Vol in Period t = #2t = %#2t-1 + (1 – %) &2t
7.
Multifactor Model: R on Asset i = R i = ai + bi1F1 + bi2F2 + … + biK FK + &i
8.
Value of asset at time t 0 =
9.
10. Nominal GDP = Real g rate in GDP + Expected long-run Inf rate
Precision of the estimate of the population mean ! 1 / •€ € €‚ƒ„
2.
CFA Level III 2018
…M KS SQyO S ‡ SnU UV†QbxwafS NKSO l
Expected RoR on Equity = ˆ#4 /$* (‰1*$ 1& &#Š$ ‹ pUVŒ Ž *1&$r !,**$%& (‰1*$ /*#:$
+ LT g rate
= Div Yield + Capital Gains Yield
†
12. Expected RoR on Equity $ - 'S + i + g
20. Inf P = Yield of conventional Govt. bonds (at a given maturity) – Yield on Infindexed bonds of the same maturity 21. Default RP = Expected default loss in yield terms + P for the non-diversifiable risk of default
+ 'PE -'S = Positive repurchase yield +'S = Negative repurchase yield 'PE = Expected Repricing Return 13. Labor supply g = Pop g rate + Labor force participation g rate 14. Expected income R = D/P - 'S 15. Expected nominal earnings g R = i + g 16. Expected Capital gains R = Expected nominal earnings grate + Expected repricing R 17. Asset’s expected return E (R i) = Rf + (RP) 1 + (RP) 2 + …+ (RP) K 18. Expected bond R [E (R b)] = Real Rf + Inf premium + Default RP + Illiquidity P + Maturity P+ Tax P 19. Inf P = AvgInf rate expected over the maturity of the debt + P (or discount) for the prob attached to higher Inf than expected (or greater disinflation)
22. Maturity P = Interest rate on longermaturity, liquid Treasury debt - Interest rate on short-term Treasury debt 23. Equity RP = Expected ROE (e.g. expected return on the S&P 500) – YTM on a longterm Govt. bond (e.g. 10-year U.S. Treasury bond R) 24. Expected ROE using Bond-yield-plus-RP method = YTM on a LT Govt bond + Equity RP 25. Expected ROA E (R i) = Domestic Rf R + (%i) " [Expected R on the world market portfolio – Domestic Rf rate of R] Where,%i = The asset’s sensitivity to R on the world mktportf = Cov (R i, R M) / Var (R M) 26. Asset class RP i= Sharpe ratio of the world market portfolio " Asset’s own volatility (#i) " Asset class’s correlation with the world mktportf ((i,M) RPi = (RPM / #M) " #i " (i,M Where, Sharpe Ratio of the world market portfolio = Expected excess R / S.D of the
FinQuiz
Formula Sheet
world mktportf " represents systematic or nondiversifiable risk = RP M / #M
35. Neutral Level of Interest Rate = Target In f Rate + Eco g
27. RP for a completely segmented market (RPi) = Asset’s own volatility ( #i) " Sharpe ratio of the world mktportf
36. Taylor rule equation: R optimal optimal =R neutral neutral + [0.5 " (GDPgforecast – GDPg trend)] + [0.5 " (Iforecast – Itarget)]
28. RP of the asset class, assuming partial segmentation = (Degree of integration " RP under perfectly integrated markets) + ({1 - Degree of integration} " RP under completely segmented markets)
37. Trend g in GDP = g from labor inputs + g from ! in labor productivity
CFA Level III 2018
Reading 15: Equity Market Valuation 1.
29. Illiquidity P = Required RoR on an illiquid asset at which its Sharpe ratio = mkt’s Sharpe ratio – ICAPM required RoR
38. g from labor inputs = g in potential labor force size + g in actual labor force participation
Where,Y = Total real economic output A = Total factor productivity (TFP) K = capital stock ) = Output elasticity of K L = Labor input % = Output elasticity of L 2.
39. g from ! in labor productivity = g from capital inputs + TFP g* TFP g = g associated with increased efficiency in using capital inputs.
31. Beta of asset 1 =
& ( 1 ' ) (1, m) # $$ !! ( % "
32. Beta of asset 2 =
& ( 2 ' ) (2, m) # $$ !! ( % " m
33. GDP (using expenditure approach) = Consumption + Invst + ! in Inventories + Govt spending + (Expo- Impo)
0
6 6
<’
“ “
< ;D ’
Œ Œ
Solow Residual = % 'TFP = % 'Y – ) (%'K) – (1 – )) %'L
4.
H-Model: Value per share at time 0 =
41. Consumer spending g = ) + %1Lagged consumer income g + %2Interest rate
ˆ‹ ˆ#(:8,%& *1&$XŒ (,(&1#%5"$ ˆ#4 Ž *1&$
" ;<
”> „„–A—•A‚B@ „„–A—•A‚B@ ˜—ƒ ˜—ƒ ™ šA–@ < ›,/$* %8*Š1" Ž /$*#8-
42. Investment g = ) + %1Lagged GDP g+ %2Interest rate
œ
ž> Ÿ—™Ÿ@š ˜—ƒ ™ šA–@ D ”> „„–A—•A‚B@ ˜—ƒ ™ šA–@
43. Consumer Income g = Consumer spending growth lagged one period 5.
34. Output Gap = Potential value of GDP – Actual value of GDP
‘
3. 40. GDP g = ) + %1Consumer spending g + %2Investment g
m
Cobb-Douglas Production Function Y (assuming constant R to Scale) = ln (Y) = ln (A) + )ln (K) + (1 – )) ln (L) Or 0
•
30. Cov b/w any two assets = Asset 1 beta " Asset 2 beta " Var of the mkt
Cobb-Douglas Production Function Y = A" K )" L%
Gordon g Div discount model: Value per share at time 0 =
ˆ UVŽ *X Ž
FinQuiz
6.
Formula Sheet
CFA Level III 2018
Forward justified P/E = 3%&*#%(#: 41",$
12. 10-year Moving Average Price/Earnings [P / 10-year MA (E)] =
0* 1‰$1- $./$:&$- ¡1*%#%Ž(
1.
After-tax Portfolio Return = r at at = r pt(1-t)
2.
Expected Equity Return (dividend income + Price Appreciation) = r at at = pd r pt (1-td) + pa r pt (1-tcg) where, pd & pa are proportion attributed to dividend income & price appreciation respectively.
3.
¸ÁÂÃÄeÃÅ ÆÇeÃc eÆÁ ÈeÆÉÅÆcÅÊËÆeÊ¾É T ½}J = ½J (1-t)
¤$1" 8* 3%¥X1-9,(&$-¦ ›§ ¨‹‹ NQxO {f©OL
7.
Fed Model:
ª84#%Ž 64Ž 8¥ /*$:$-#%Ž U‹ «*( 8¥ ¤$1" 8* 3%¥ 1-9 ¡1*%#%Ž(
¢£- j/$*1&#%Ž j/$*1&#%Ž ¡1*%#%Ž( ¡U
TLong-term US
3%-$. Œ$4$" 7‹
*The stock index and reported earnings are adjusted for Inflation using the CPI
Treasury securities
8.
Yardeni Model: =
E 1 =
P
y B ! d " LTEG
0
Where,E1/P0=Justified (forward) earnings yield on equities yB=Moody’s A-rated corporate bond yield LTEG= Consensus 5-yr earnings g forecast for the S&P 500 d=Discount or Weighting factor that represents the weight assigned by the market to the earnings projections
13. Real Stock Price Index t = (Nominal SPI t " CPI base yr ) / CPI t 14. Real Earnings t = (Nominal Earnings t " CPI base year ) / CPI t+1 15. Tobin’s q =
Reading 19: Currency Management: An Introduction 1.
ª¬8¥ -$5&Vª¬ 8¥ $+,#&« ¤$/"1:$Š$%& :8(& 8¥ 1(($&( ¡+,#&« ª“& !1/
Equity q =
2$& 8*&‰ 7*#:$ /$* (‰1*$ 28 8¥ ›‰1*$( j®›
Bid Fwd rate = Bid Spot exchange (X) rate +
=
2.
¤$/"1:Š$%& :8(& 8¥ 1(($&(Xª¬ 8¥ "#15#"#&#$(
Ì#- ¢£- /8#%&( U‹À‹‹‹
Offer Fwd rate = Offer Spot X rate + j¥¥$* ¢£-- /8#%&( U‹À‹‹‹
9.
Yardeni estimated fair value of P/E ratio =
P0
Reading 16: Introduction to Asset Allocation
1 =
E
1
y B ! d " LTEG
1.
10. Fair value of equity mkt under Yardeni Model (P0) = P0
d
=
E 1 P0
LTEG
?—„¯° =„„@– =„„@– =BB€±A–—€• =BB€±A–—€• T ² T
4.
To convert spot rate into a forward quote when points are represented as %, Spot X rate " (1 + % prem) Spot X rate " (1 - % disct)
U ´XNu ³
y B ! d " LTEG
œ ·y T ¸ Hy D ¹º¹¹»¼½y
2.
²Q i¾¿ cQ À c T
U f
(/8& Í *1&$
–1
µ¶
Reading 17: Principles of Asset Allocation 1.
ÎÏÐ ÑÒÓÔ r tÀ
FwdPrem/Disc % =
E 1 =
11. Discount/weighting factor (d) =
y B !
¦
(/8& Í *1&$Xp
3.
½œ
Reading 18: Asset Allocation with Real-world Constraints
5.
Mark-to-MV on dealer’s position = ›$&&"$Š$%& -1« !¢ UVˆ#(:& *1&$¦
Ó Õ
FinQuiz
6.
Formula Sheet
CF at settlement = Original contract size " (All-in-fwd rate for new, offsetting fwd position – Original fwd rate)
15. Long Straddle = Long atm put opt (with delta of -0.5) + Long atm call opt (with delta of +0.5)
CFA Level III 2018
23. Min or Optimal hedge ratio = " (R DC DC; R FX FX) "
! S.D ( R ) $ # & " S.D ( R ) % DC FX
7.
Hedge Ratio = 28Š#%1" ¬1",$ 8¥ -$*#41$( :8%&*1:& ª¬ 8¥ &‰$ ‰$-Ž$- 1(($&
8.
R DC DC =(1 + R FC FC)(1 + R FX FX)–1
9.
R DC DC (for multiple foreign assets) = n
! (1 !
i
+ R
FC , i
) (1
+ R
FX , i
) "1
i=1
16. Short Straddle = Short ATM put opt (with delta of -0.5) + Short ATM call opt (with delta of +0.5) ATM = at the money opt = option
Reading 20: Market Indexes and Benchmarks 1.
Periodic R (Factor model based) = Rp = a p + b1F1 + b2F2+…+ bK FK + & p
2.
For one factor model Rp = a p + % pR I + & p Where,R I = periodic R on mktindex a p = “zero factor” % p = beta = sensitivity & p = residual return
18. Long Risk reversal = Long Call opt + Short Put opt
3.
MV of stock = No of Shares Outstanding " Current Stock Mkt Price
19. Short Risk reversal = Long Put opt + Short Call opt
4.
Stock wgt(float-weighted index) = Mktcap wght " Free-float adjustment factor
5.
Price-weighted index (PWI) = (P1+P2+…+Pn) /n
17. Long Strangle: Long OTM put option + Long OTM call opt OTM = out of the money
10. Total risk of DC returns = T ½ œ H†… ‘
½ œ HM… < ½ œ HMÖ < ×½ HM… ½ HMÖ Ø HM… À HMÖ
11. % ! in spot X rate (% 'SH/L) = Interest rate on high-yield currency (iH) – Interest rate on low-yield currency (iL) 12. Forward Rate Bias =
¢Ù®ÚX›Ù®Ú ›Ù®Ú
T
Ó ÛÜ Ó UV#Ú ÛÜ
20. Short seagull position = Long protective (ATM) put + Short deep OTM Call opt + Short deep OTM Put opt
#Ù X#Ú
13. Net delta of the combined p osition = Option delta + Delta hedge
21. Long seagull position = Short ATM call + Long deep-OTM Call opt + Long deepOTM Put opt
1. 22. Hedge ratio =
14. Size of Delta hedge (that would set net delta of the overall position to 0) = Option’s delta " Nominal size of the contract
Reading 21: Introduction to Fixed-Income Portfolio Management
7*#%:#/1" ¥1:$ 41",$ 8¥ &‰$ -$*#41$( :8%&*1:& ,($- 1( 1 ‰$-Ž$ 7*#%:#/1" ¥1:$ 8¥ &‰$ ‰$-Ž$- 1(($&
E(R)$Yield income + Rolldown Return + ¸Áº Ý D ¸Áº ¸Áº icÃÅÊe Þ¾ÈÈÃÈ Þ¾ÈÈÃÈ < dKQfb
¸Áº ißccÃÉÄà
]wbbOb
FinQuiz
2.
Formula Sheet
Roll Down return =
3.
_wf© NQxOGZáºX_wf© NQxOâ[Wº
7.
_wf© NQxOâ[Wº
3.
CFA Level III 2018
rp =
Asset BPV + ïÝ
qèKo _ã U‹‹
8.
T c{ <
ãâ
c{ D c_
ãG
LeverageFuture =
5.
Dollar Interset = Principal ?@å€ ?A–@ p˜A°„®æç¹r
4.
Passive investment using Equity Index futures = Long cash + Long futures on the underlying index
5.
Passive investment using Equity total return swaps = Long cash + Long swap on the index
6.
R on Portf = b0 + (b1 " R on Index style 1) + (b2 " R on Index style 2) +…. (b n " R on Index style n) + &
7.
RoR of Equitized Mkt neutral strategy = (G/L on long & short securities positions + G/L on long futures position + Interest earned on cash from short sale) / Portfolio Equity Active wgt = Stock’s wgt in actively managed portf – Stock’s wgt in B
Asset BPV óÈÈÃe àÊÃñÅÈ < hÃÅôà òÝI hÃÅôà àÊÃñÅÈ ‘ ÞÊÆðÊñÊeà òÝI ÞÊÆðÊñÊeà àÊÃñÅÈ
mwSQwfK] ãK]aOXäKNdQf
4.
Reading 23: Yield Curve Strategies
äKNdQf
1.
Effective Portfolio Duration ‘ mwSQwfK] owNSRw]Qw ~K]aO wNSRw]Qw O`aQSv
Reading 22: Liability-driven and Index-based Strategies 1.
*1:ø#%Ž ¤#(ø 8* 6:$ ¤#(ø
ÞÊÆðÊñÊeà òÝI
T
ãG
6:$ ¤
T
wNSRw]Qw EOSaNf
wNSRw]Qw O`aQSv N{ ã GVãâ X ãâN_
2.
Convexity = äKxº†aNKSQwf¶ VäKxº†aNKSQwfV†QboONbQwf
îßcÆeʾÉ
Total return ‘ D; ÃÉź ÃÇÇÃÄeÊ¿Ã ÅßcÆeÊ¾É ÅßcÆeÊ¾É ÃÉź ÃÉź õgö D ðÃôº ðÃôº õgö < ðÃôº ðÃôº õgö
UV…Kbz R]wè vQO]© ¶
2.
Reading 24: Fixed Income Active Management: Credit Strategies
Future Contracts=Nf = éQK\Q]QSv wNSRw]Qw _ãX}bbOS owNSRw]Qw _ã MaSaNOb _ã
3.
4.
5.
Future BPV ‘ yPè
ABO =
PBO =
UVN ë
…Mêëì
U
U
N
N UVN í
D
yPè UVè ë UVN ë
¸ÇÇÃÄeÊ¿Ã îßcÆeÊ¾É îßcÆeÊ¾É T ãX X ãV
U
D
N UVN í
œ…aN~O ã
1.
Excess Return = XR = (È ( È e) e )D È÷î
2.
Expected XR = EXR = (È ( È e) e )D È ÷î D eÂÞ eÂÞ where ÂÞ T ÃÁº Âc¾ðÆðÊñÊeà Âc¾ðÆðÊñÊeà ¾Ç ñ¾ÈÈ ÃÁº ñ¾ÈÈ
8.
_ãêëì
U
6.
Information Ratio =
Reading 25: Equity Portfolio Management
9.
Info Ratio $ Info Coefficient " ù•€ úš@Aû–Ÿ
10. Risk-adjusted Expected Active R= 2 U A = r A – " A #$ A
N
1. 2.
Active R = Portf’s R – B’s return B = benchmark Tracking Risk (active risk) = ann S.D of active R
11. Portfolio Active R = % #nU ü™– A„„—™•@û –€ —–Ÿ ý•™š pŸ=—r =±–—ƒ@ ? € –Ÿ@ —–Ÿ ý•™š pš=—r
FinQuiz
Formula Sheet
CFA Level III 2018
12. Portfolio Active Risk = A„„—™•@û –€ —–Ÿ ý•™@š œ =±–—ƒ@ ? € —–Ÿ ýA•A™@š œ
% ü™– #nU
2.
Marketable minority interest ($) = Marketable controlling interest value ($) – minority interest discount ($)
3.
Marketability discount ($) = Marketable minority interest ($) " marketability discount (%)
12. Rolling R = RR R t –(n-1) / n
n,t =
(R t + R t-1 t-1 + R t-2 t-2 + … +
13. Downside Deviation = T 13. Mngr’s “true” active R = Mngr’s R Mngr’s Normal B 14. Mnger’s “misfit” active R = Mnger’s normal B R - Investor’s B 15. Total Active Risk = œ
gcßà óÄeÊ¿Ã HÊÈþ < öÊÈÇÊe óÄeÊ¿Ã HÊÈþ œ Where, True active risk = S.D of true active R Misfit risk = S.D of misfit active R 16. True Information Ratio = ª%Ž*ÿ( *,$ 6:$ ¤ ª%Ž*ÿ( *,$ 6:$ *#(ø
Z ¦ ¶ Y!t yQf Nl XN À‹
fXU
where, r* = threshold
4. Non-Marketable minority intere st ($) = Marketable minority interest ($) marketability discount ($) 5. Total R on Commodity Index = Collateral R + Roll R + Spot R
14. Semi-deviation = T
6.
16. Sortino Ratio = (Annualized RoR – Annualized Rf*) / Downside Deviation
Monthly Roll R = ' in futures contract price over the month - ' in spot price over the month 7. Compensation structure of Hedge Funds (comprises of ) Management fee (or AUM fee) + Incentive fee
Z ¶ Y!t yQf Nl XK~dº ywfSz]v NOSaNfÀ‹
fXU
15. Sharpe ratio = (Annualized RoR – Annualized Rf rate) / Annualized S.D.
17. Gain-to-loss Ratio = 28 8¥ Š8%&‰( £#&‰V4$ ¤ 28 8¥ Š8%&‰( £#&‰X4$ ¤ 64Ž ,/ Š8%&‰ ¤
64Ž -8£% Š8%&‰ ¤
17. Investors’ net of fees alpha = Gross of fees alpha (or mngr’s alpha) – Investment mgmt fees
8.
9. Reading 26: Alternative Investments Portfolio Management 1.
Minority interest discount ($) = marketable controlling interest value ($) " minority interest(%) discount = (investor’s interest in equity " total equity value) " minority interest discount(%)
Management fee= % of NAV (net asset value generally ranges from 1-2%) Incentive fee = % of profits (specified by the investment terms)
10. Incentive fee (when High Water mark Provision) = (positive difference between ending NAV and HWM NAV) " incentive fee %. 11. Hedge Fund R = [(End value) – (Beg value)] / (Beg value)
18. Calmar ratio = Compound Annualized ROR / ABS* (Maximum Drawdown) 19. Sterling ratio= Compound Annualized ROR / ABS* (Average Drawdown - 10%) where, *ABS = Absolute Value
FinQuiz
Formula Sheet
Reading 27: Risk Management 9. 1.
Delta Normal Method: VAR = E(R) – zvalue (S.D) Daily E(R) = Annual E(R) / 250 Daily S.D = Annual S.D. / ×»¹ Monthly E(R) = Annual E(R) / 12 Monthly S.D = Annual S.D. /
Sortino Ratio =
ª$1% /8*&¥ ¤Xª#% 1::$/&15"$ ¤
××
Annual VAR = Daily VAR " ×»¹ 2.
3.
4.
Diversification effect = Sum of individual VARs – Total VAR Incremental VAR=Portf’s VAR inclu a specified asset – Portf’s VAR exclu that asset.
=0 Effective % = Combined position R in % / Market R in % Synthetic Cash: Long Stock + Short Futures = Long risk-free bond
8.
Synthetic Stock: Long Stock = Long Rf bond + Long Futures
Š1. -*1£-8£%
Reading 28: Risk Management Applications of Forward and Futures Strategies 1.
% = CovSI / # •
•
2.
9.
2 I
•
CovSI= covariance b/w stock portf& index 2
# I= var of index.
$% of stock portf = % of stock portf " MV of stock portf = %s S
3.
Future $ % = %f " f where, %f = Futures contract beta
5.
Value Long = Spot t – [Forward / (1 + r) n]
4.
6.
Swap ValueLong = PV inflows – PV outflows
Target level of beta exposure: %T S = %s S + Nf %f f ú D ú › ž )¥ T ú¥ "
•
•
•
7.
"#û "#û ±€•–šA±– ƒAB@Œ8%Žn Mè© EKSO UVEMì
8.
l ë%l&' lY &' lY( ([
UVEM$
ïÝ
Sharpe Ratio =
ª$1% /8*&¥ ¤X¤¥ ›ºˆ 8¥ /8*&¥ ¤
l ë %l&' lY &' lY( ([
D
and %T
7.
¡./$:&$- 64$*1Ž$ ¤ 8% 1% #%4(& #% 1 Ž#4$% «*
Tail Value at Risk (TVAR) or Conditional Tail Expectation = VAR + expected loss in excess of VAR
qowS EKSOì®$ ì® $
¥
6.
¡./$:&$- ¤ 8% 1% #%4(&
;×
›
ÌÎ
Reducing % to zero: )¥ T
:1/#&1" 1& *#(ø Š$1(,*$
11. R over Max Drawdown =
XÌ*
5.
ˆ8£%(#-$ -$4#1%
10. Risk Adjusted R on Capital =
Daily E(R) = Monthly E(R) / 22 Daily S.D = Monthly S.D. /
CFA Level III 2018
Nf =
ˆ$(#*$- Ì$&1 !‰1%Ž$
¢,&,*$( Ì$&1 78*&¥8"#8 ¬1",$
"
¢,&,*$( :8%&*1:& 7*#:$
*Actual futures price = Quoted futures price " Multiplier
Creating a Synthetic Index Fund: No of futures contract = N f * = {V "(1 + r) T}/ (q"f) where, N f * = No of futures contracts q = multiplier V = Portfolio value Amount needed to invest in bonds = V* = (Nf *" q" f) / (1 + r) T Equity purchased = (Nf * "q) / (1 + *) T where, % = dividend yield Pay-off of Nf * futures contracts = Nf *" q "(ST –f) where,S T Index value at time T T =
Reading 29: Risk Management Applications of Options Strategies 1.
Covered Call = Long stock position + Short call position a) Value at expiration = V T = ST – max (0, ST – X)
FinQuiz
b) c) d) e) 2.
3.
Profit = VT – S0 + c0 Maximum Profit = X – S 0 + c0 Max loss (when ST = 0) = S 0 – c0 Breakeven =ST* = S0 – c0
Protective Put = Long stock position + Long Put position a) Value at expiration: VT = ST + max (0, X - ST) b) Profit = VT – S0 - p0 c) Maximum Profit = + d) Maximum Loss = S0 + p0 – X e) Breakeven =ST* = S0 + p0 Bull Call Spread = Long Call (lower exercise price) + Short Call (higher exercise price) a) Initial value = V0 = c1 – c2 b) Value at expiration: VT = value of long call – Value of short call = max (0, ST – X1) - max (0, S T – X2) c) Profit = V T – c1 + c2 d) Maximum Profit = X2 – X1 – c1 + c2 e) Maximum Loss = c1 – c2 f) Breakeven =ST* = X1 + c1 – c2
4.
Bull Put spread = Long Put (lower XP) + Short Put (higher XP). Identical to the sale of Bear Put Spread XP = exercise price
Formula Sheet
5.
Bear Put Spread = Long Put (higher XP) + Short Put (lower XP) a) Initial value = V 0 = p2 – p1 b) Value at expiration: VT = value of long put – value of short put = max (0, X2 - ST) - max (0, X1 - ST) c) Profit = VT – p2 + p1 d) Max Profit = X 2 – X1 – p2 + p1 e) MaxLoss = p2 – p1 f) Breakeven =ST* = X2 – p2 + p1
CFA Level III 2018
e)
8.
Two breakeven points i. Breakeven =ST* = X1 + net premium = X1 + c1 – 2c2 + c3 ii. Breakeven = ST* = 2X2 – X1 – Net premium = 2X 2 – X1 – (c1 – 2c2 + c3 ) = 2X2 – X1 – c1 + 2c2 - c3
Short Butterfly Spread (Using Call) = Selling calls with XP of X 1 and X3 and buying two calls with XP of X 2. Max Profit = c 1 + c3 – 2c2 •
6.
7.
Bear Call Spread = Short Call (lower XP) + Long Call (higher XP). Identical to the sale of Bull Call Spread. Long Butterfly Spread (Using Call) = Long Butterfly Spread = Long Bull call spread + Short Bull call spread (or Long Bear call spread) Long Butterfly Spread = (Buy the call with XP of X1 and sell the call with XP of X 2) + (Buy the call with XP of X 3 and sell the call with XP of X 2). where, X1< X2 < X3 and Cost of X 1 (c1) > Cost of X2 (c2) > Cost of X 3 (c3)
a)
Value at expiration: VT = max (0, ST – X1) – 2 max (0, S T – X2) + max (0, S T – X3) b) Profit = VT – c1 + 2c2 - c3 c) Max Profit = X 2 – X1 – c1 + 2c2 – c3 d) Maximum Loss = c1 – 2c2 + c3
9.
Long Butterfly Spread (Using Puts) = (Buy put with XP of X 3 and sell put with XP of X2) + (Buy the put with XP of X 1 and sell the put with XP of X 2) where,X1< X2 < X3 and Cost of X1 (p1) < Cost of X2 (p2)
10. Short Butterfly Spread (Using Puts) = Short butterfly spread = Selling puts with XPs of X1 and X3 and buying two puts with XP of X2. Max Profit = p 3 + p1 – 2p2 •
11. For zero-cost collar a) Initial value of position = V0 = S0 b) Value at expiration: VT = ST + max (0, X1 - ST) – max (0, ST – X2) c) Profit = V T – V0 = VT –S0 d) Max Profit = X 2 – S0 e) Max Loss = S0 – X1 f) Breakeven =ST* = S0
FinQuiz
12. Straddle = Buying a put and a call with same strike price on the same underlying with the same expiration; both options are at-the-money.
Formula Sheet
17. Long Box-spread= (buy call with XPof X1 and sell call with XP of X 2) + (buy put with XP of X 2 and sell put with XP of X 1).
b) c) d) e)
Value at expiration: VT = max (0, ST X) + max (0, X– S T) Profit = VT –p0 - c0 Max Profit = + Max Loss = p0 + c0 Breakeven = ST* = X ± (p0 + c0)
13. Short Straddle: Selling a put and a call with same strike price on the same underlying with the same expiration; both options are at-the-money. •
•
Adding call option to a straddle “Strap”. Adding put option to a straddle “Strip”.
14. Long Strangle = buying the put and call on the same underlying with the same expiration but with different exercise prices. 15. Short Strangle = selling the put and call on the same underlying with the same expiration but with different exercise prices . 16. Box-spread = Bull spread + Bear spread
22. Floorlet Pay-Off = NP " (0, X rate LIBOR on previous reset date) " ˆ1«( #% ($&&"$Š$%& /$*#8-
a) a)
CFA Level III 2018
b) c) d) e) f)
Initial value of the box spread = Net premium = c 1 – c2 + p2 – p1. Value at expiration: VT = X2 –X1 Profit = X 2 –X1 - (c1 – c2 + p2 – p1) Max Profit = same as profit Max Loss = no loss is possible given fair option prices Breakeven =ST* = no break-even; the transaction always earns Rf rate, given fair option prices.
18. Pay-off of an interest rate Call Option= (NP) " max (0, Underlying rate at expiration – X-rate) " ˆ1«( #% ,%-$*"«#%Ž *1&$ +,‹
19. Pay-off of an interest rate Put Option= (NP) " max (0, X-rate - Underlying rate at expiration) "
ˆ1«( #% ,%-$*"«#%Ž *1&$ +,‹
20. Loan Interest payment = NP " (LIBOR on previous reset date + Spread ) " ˆ1«( #% ($&&"$Š$%& /$*#8+,‹
21. Cap Pay-Off = NP " (0, LIBOR on previous reset date – X rate) " ˆ1«( #% ($&&"$Š$%& /$*#8+,‹
+,‹
23. Effective Interest = Interest received on the loan + Floorlet pay-off 24. Delta =
!‰1%Ž$ #% j/% 7*#:$
=
!‰1%Ž$ #% -%-$*"«#%Ž 7*#:$
! ›
25. Size of the Long position = Nc / Ns = - 1 / ('C / 'S) = -1 / Delta where, Nc = No of call options Ns = No of stocks 26. Hedging using non-identical option: a) b) c)
One option has a delta of '1. Other option has a delta of '2. Value of the position = V = N 1 c1 + N2c2 where, N =option quantity & c =option price d.) To delta hedge: Desired Quantity of option 1 relative to option 2 =
ˆ$"&1 8¥ 8/% œ ˆ$"&1 8¥ 8/% U
N1 / N2 = - 'c2 / 'c1 27. Gamma =
!‰1%Ž$ #% -$"&1 !‰1%Ž$ #% ,%-$*"«#%Ž /*#:$
28. Gamma hedge = Position in underlying + Positions in two options
FinQuiz
29. Vega =
!‰1%Ž$ #% j/% /*#:$ !‰1%Ž$ #% ¬8"1&#"#&« 8¥ &‰$ ,%-$*"«#%Ž
Formula Sheet
3.
Reading 30: Risk Management Applications of Swap Strategies
4.
1. NP of a swap (to manage D of portf.) =
5.
). T ). T / /7
3.
When LIBOR > b, inverse floater issuer should buy an interest rate cap with the following features:
•
•
4.
exercise rate of b NP = NP of inverse floater Each caplet expires on the interest rate reset date of the swap/loan Whenever Libor > b, Caplet payoff = (L – b) " NP
Synthetic Dual-currency Bond = Ordinary bond issued in one currency Currency swap (with no principal payments)
Reading 31: Execution of Portfolio Decisions 1.
28 8¥ (‰1*$( %8& &*1-$-
Avg Effective Spread (ES) =
Share Volume Wgtd (VW) ES = [(V of shares traded for order 1 " ES of order 1) + (V of shares traded for order 2 " ES of order 2) + + (V of shares traded for order n " ES of order n)/n
8&1" %8 8¥ (‰1*$( #% 1% 8*-$* !1%:$""1% /*#:$ 6j*#Ž#%1" Ì /*#:$
Effective Spread = 2 " (Actual Execution Price – MidQuote)
%
6.
12. Missed Trade Opp Cost =
œ
ªˆÔÏ0Ñ
Inverse Floater Coupon rate = b – LIBOR
•
ªø& Ì#- 7*#:$Vªø& 6(ø 7*#:$
¡› 8¥ 8*-$* UV ¡› 8¥ 8*-$* œ V 4V ¡› 8¥ 8*-$* %
ªˆÓ0123Ó XªˆÚ
2.
•
Mid-Quote =
CFA Level III 2018
j*#Ž#%1" Ì /*#:$
where B = benchmark 13. IC = Commissions & Fees as % + Realized profit or loss + Delay costs + M issed trade opp costs 14. Estimated Implicit Costs for “Buy” = Trade Size " (Trade Price – B Price)
!
7.
VW Avg price = Avg P (security traded during the day) Where, weight is the fraction of the day’s volume associated with the trade
15. Estimated Implicit Costs for “Sale” = Trade Size " (B Price - Trade Price) Reading 32: Monitoring and Rebalancing 1. •
8.
9.
Mkt-adj Implementation Shortfall (IS) = I cost – Predicted R estimated using Mkt model Trade Size relative to Available Liquidity =
•
•
j*-$* (#5$ 64Ž -1#"« 48",Š$
10. Realized profit/loss = Execution price – Relevant decision price
Buy and Hold Strategy: Portfolio value = Investment in stocks + Floor value Portfolio R = % in stock " R on stocks Cushion = Investment in stocks = Portfolio value – Floor value
2.
Target Investment in Stocks under Constant Mix Strategy = Target proportion in stocks " Portfolio Value
3.
Target Investment in Stocks under Constant Proportion Strategy = Target proportion in stocks " (Portfolio Value – Floor value)
Bid-ask Spread = Ask price – Bid price 28 8¥ (‰1*$( 1:&,1""« &*1-$-
11. Delay costs = 8&1" 28 8¥ (‰1*$( #% 1% 8*-$* 2.
Inside/Mkt bid-ask spread = Inside/Mkt Ask Price – Inside/Mkt Bid Price
6:&,1" &*1-#%Ž /*#:$ 8% ˆ1« & X !7 8% -1« &XU Ì$%:‰Š1*ø :"8(#%Ž /*#:$ 8% -1« -1« &
where CP = closing price
FinQuiz
Formula Sheet
Reading 33: Evaluating Portfolio Performance 1. •
Account’s rate of return during evaluation period ‘t’ when there are no external cash flows =
5.
ª¬ p$%- 8¥ /$*#8-rXª¬ p5$Ž 8¥ /$*#8-r ª¬ p5$Ž 8¥ /$*#8•
when a contribution received (start of the period) = ª¬ p$%- 8¥ /$*#8-rX ª¬ p5$Ž 8¥ /$*#8-rV:8%&*#5,%
CFA Level III 2018
L(i) = No of time units by which the i th CF is separated from beg of evaluation period
15. Fundamental rule of Active Mgmt: Impact = (active) wght " R
Compound g rate or geometric mean R = 1/n (1 + r t,1 - 1 t,1) " (1 + r t,2 t,2) " …" (1+ r t,n t,n) Where, n = No of yrs in measurement period
16. ! in value of fund = Total amount of net contributions
6.
Style = Manager’s B portf - Mrkt index
7.
Active Mgmt = Manager’s portf – B
8.
Portf R = MrkeIndex + Style + Active Mgmt
9.
Periodic R on an a/c (factor-based model) = ) p + (b1 " F1) + (b2 " F2) + …+ (bk " Fk ) + & p
17. Ending value of a fund under the Net Contributions investment strategy = Beginning value + Net contributions
ª¬ p5$Ž 8¥ /$*#8-rV !8%&*#5,% •
when a withdrawal is made (start of the period) = ª¬ p$%- 8¥ /$*#8-rX ª¬ 5$Ž 8¥ /$*#8- X:8%&*#5,% ª¬ 5$Ž 8¥ /$*#8- X !8%&*#5,%
•
when a contribution is received at the end of the evaluation period = ª¬ p$%- 8¥ /$*#8-r X :8%&*#5,% Xª¬ 5$Ž 8¥ /$*#8ª¬ 5$Ž 8¥ /$*#8-
•
when a withdrawal is made at the end of the evaluation period = ª¬ $%- 8¥ /$*#8- V :8%&*#5,% :8%&*#5,% Xª¬ 5$Ž 8¥ 8¥ /$*#8-
10. Benchmark coverage = ª¬ 8¥ ($:,*#&#$( &‰1& 1*$ /*$($%& #% 58&‰ Ì § owNSR
ª¬ 5$Ž 8¥ /$*#8-
2.
TWR (when no external CFs) = ªø& 41",$ 1& $%- 8¥ /$*#8-Xªø& 41",$ 1& 5$Ž#%%#%Ž 8¥ /$*#8ªø& 41",$ 1& 5$Ž#%%#%Ž 8¥ /$*#8-
3.
TWR (entire evaluation period) = (1 + r t,1 t,1) " (1 + r t,2 t,2) " …" (1 + r t,n t,n) – 1
18. ! in Fund’s value = End value of a fund under the Rf asset Invst strategy – Begvalue (i.e. ending value of the fund under the Net Contributions investment strategy) 19. R-metric perspective: Incremental R contribution of the Asset Category 6 investment strategy = #nU üQ p? …Q D ?R r
8&1" ª¬ 8¥ /8*&¥
11. Active position = Wght of a security in an account - Wght of the same security in B 12. Value-added R on a long-short portf = Portf R – B
20. Value-metric perspective: Incremental contribution of the Asset Category investment strategy = Sum [(Each asset category’s policy proportion of the Fund’s beg value and all net ex ternal cash inflows) " (Asset category’s B RoR - Rf rate)]
13. RoR for a long-short portf = 4.
MWR = MV1= MV0(1+R)m+CF1(1+R)mL(1) m–L(n) +…+CFn(1+R) where, m = No of time units in evaluation period
7®Œ *$(,"&#%Ž ¥*8Š ‰$-Ž$ ¥,%- (&*1&$Ž« 6Š8,%& 8¥ 1(($&( 1& *#(ø
14.
=
7®Œ *$(,"&#%Ž ¥*8Š ‰$-Ž$ ¥,%- (&*1&$Ž« 65(8",&$ 41",$ 8¥ 1"" p "8%Ž /8(#%( V (‰8*& /8(#%(r
21. Aggregate manager B R under B level invstmnt strategy = Wghtd* Avg of IndMngr’s B R
FinQuiz
Formula Sheet
22. Return-metric perspective: Incremental return contribution of the B strategy = 6 #nU
ª 9nU üQ üQ7
c_Q7 6 š…Q
30. Value-added return under Holdings-based q or “buy-and-hold” attribution= 9nU üo7 šo7 D
23. Value-metric perspective: Incremental contribution of the B strategy = Sum [each manager’s policy proportion of the total fund’s beg value and net external cash inflows " (manager’s B R – R of manager’s asset category)] 24. Misfit R or Style bias = R generated by the aggregate of the managers’ B - R generated by the aggregate of the asset category B
CFA Level III 2018
39. Trading activity = Total Portf R – (Interest rate mgmt effect + sector/quality effect + security selection effect)
› 9nU ü_7 š_7
40. Alpha = # = r P ! [r f 31. Value-added Return = Pure sector allocation + Allocation/selection interaction + Within sector selection 32. Pure sector Allocation =
f QXU
üo7 D
› 9nU 8_7
c7 D
26. Return-metric perspective: Contribution of the Investment Managers strategy = š{ä T 6 #nU
ª 9nU üQ ü#9
š}Q7 D š _Q7
27. Allocation Effects incremental contribution = Fund’s ending value - Value calculated at the Investment Managers level
f QXU
ü7 D ü_7 pšQ D š _7 r
35. Interest rate Mgmt contribution = Agg R(re-priced securities) - R of entire Treasury universe 36. Sector/quality return = Gross R - External interest rate effect - Interest rate Mgmt effect 37. Security selection effect for each security = Total R of a security - all the other components.
28. Value-added/active return = Portf R – B R 29. Security-by-security analysis: šQ T % #nU
üoQ D ü_Q pšQ D š _ r
38. Portf security selection effect = Mkt value WghtdAvg of all individual security selection effects
9F
43. M2 = cR <
µF
EFXNu µF
½ä
c_7 34. Allocation/selection Interaction =
E F XNu
EF XNu
42. Sharpe ratio =
44. Information ratio = :H} T 25. Return to the Investment managers level = Sum (active managers’ returns – their benchmark returns)
" P (r M ! r f )]
41. Treynor’s measure = g} T
ü_7 pš_7 D š _ r 33. Within sector Selection =
+
EFXEâ µFsâ
