Chapter 6 Risk and Return, and the Capital Asset Pricing Model Defne the ollowing terms, using graphs or equations to illustrate your answers wherever easible: a. Stand-alone risk; risk; probability distribution b. !pe"ted rate o return, r# ". $ontinuous probability distribution d. Stand S tandard ard dev deviat iation ion,, % ; varia va rian"e, n"e, %&; "oe'"ient o variation, $( e. )isk aversion; reali*ed rate o return, k# . )isk premium or Sto"k i, )+ i; market risk premium, )+ g. $apital sset +ri"ing odel $+/ h. !pe"ted return on a portolio, k# p; market portolio i. $orrelation "oe'"ient, r; "orrelation 0. arket risk; diversifable diversifable risk; relevant risk k. 1eta "oe'"ient, b; average sto"k2s beta, b l. Se"urity arket 3ine S3/; S3 equation m. Slope o S3 as a measure o risk aversion 4-&/ 5he probability distribution o a less risky e!pe"ted return is more peaked than that o a riskier return. 6hat shape would the probability distribution have or a/ "ompletely "ertain returns and b/ "ompletely un"ertain returns7 4-8/ Se"urity has an e!pe"ted return o 9 per"ent, a standard deviation o e!pe"ted returns o 8 per"ent, a "orrelation "oe'"ient with the market o .8, and a beta "oe'"ient o .. Se"urity 1 has an e!pe"ted return o <& per"ent, a standard deviation o returns o <
per"ent, a "orrelation with the market o .9, and a beta "oe'"ient o <.. 6hi"h se"urity is riskier7 6hy7 4-=/ Suppose you owned a portolio "onsisting o >&, worth o long-term ?.S. government bonds. a. 6ould your portolio be riskless7 b. @ow suppose you hold a portolio "onsisting o >&, worth o 8-day 5reasury 5reasury bills. very 8 days your bills mature, and you reinvest the prin"ipal >&,/ in a new bat"h o bills. ssume that you live on the investment in"ome rom your port-olio and that you want to maintain a "onstant standard o living. As your portolio truly riskless7 ". $an you think o any asset that would be "ompletely riskless7 $ould someone develop su"h an asset7 !plain. / lie insuran"e poli"y is a fnan"ial asset. 5he premiums paid represent the investment2s "ost. a. Bow would you "al"ulate the e!pe"ted return on a lie insuran"e poli"y7 b. Suppose the owner o a lie insuran"e poli"y has no other fnan"ial assets C the per-son2s only other asset is human "apital,E or lietime earnings "apa"ity " apa"ity.. 6hat is the "orrelation "oe'"ient between returns on the insuran"e poli"y and returns on the poli"yholder2s human "apital7 ". 3ie insuran"e "ompanies have to pay administrative "osts and sales representatives2 "ommissions; hen"e, the e!pe"ted rate o return on insuran"e premiums is generally
low, or even negative. ?se the portolio "on"ept to e!plain why low, people buy lie in-suran"e in spite o negative e!pe"ted returns. 4-/ A investors2 aversion to risk in"reased, would the risk premium on a high-beta sto"k in-"rease more or less than that on a low-beta sto"k7 !plain. 4-4/ A a "ompany2s beta were to double, would its e!pe"ted return double7 4-9/ As it possible to "onstru"t a portolio o sto"ks that has an e!pe"ted return equal to the risk-ree rate7 S3F-5S5 +)G13S S5-
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a. $al"ulate the average rate o return or ea"h sto"k during the year period. ssume that someone held a portolio "onsisting o per"ent o Sto"k and per"ent o Sto"k 1. 6hat would have been the reali*ed rate o return on the portolio in ea"h year7 6hat would have been the average re-turn on the portolio during this period7 b. @ow "al"ulate the standard deviation o returns or ea"h sto"k and or the portolio. ?se quation 4-.
". 3ooking at the annual returns data on the two sto"ks, would you guess that the "orrelation "oe'"ient between returns on the two sto"ks is "loser to .J or to .J7 d. A you added more sto"ks at random to the portolio, whi"h o the ollowing is the most a""urate statement o what would happen to %p7
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a. 6hat is the holding "ompany2s beta7 b. ssume that the risk-ree rate is 4 per"ent and the market risk premium is per"ent. 6hat is the holding "ompany2s required rate o return7 ". $)A is "onsidering a "hange in its strategi" o"us; it will redu"e its relian"e on the ele"tri" utility subsidiary, so the per"entage o its business rom this subsidiary will be per"ent. t the same time, $)A will in"rease its relian"e on the internationalNspe"ial pro0e"ts division, so the per"entage o its business rom that subsidiary will rise to < per"ent. 6hat will be the shareholders2 required rate o return i $)A adopts these "hanges7 +)G13S 4-8, invested in a sto"k that has a beta o .J and >=, invested in a sto"k with a beta o <.=. A these
are the only two investments in her portolio, what is her portolio2s beta7 4-&/ ssume that the risk-ree rate is per"ent and the market risk premium is 4 per"ent. 6hat is the e!pe"ted return or the overall sto"k market7 6hat is the required rate o return on a sto"k that has a beta o <.&7 4-8/ ssume that the risk-ree rate is 4 per"ent and the e!pe"ted return on the market is <8 per"ent. 6hat is the required rate o return on a sto"k that has a beta o .97 4-=/ sto"k2s e!pe"ted return has the ollowing distribution: )5 ) 5 GF )5?)@
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$al"ulate the sto"k2s e!pe"ted return, standard deviation, and "oe'"ient o variation.
4-/5he market and Sto"k O have the ollowing probability distributions: +)G11A3A5H I I .8 <K &K .= M .8 9, investment in ea"h o & diQerent "ommon sto"ks. 5he portolio beta is equal to <.<&. @ow, @ow, suppose you have de"ided de"id ed to sell one o the sto"ks in your portolio with a beta equal to <. or >9, and to use these pro"eeds to buy another sto"k or your portolio. ssume the new sto"k2s beta is equal to <.9. $al"ulate your portolio2s new beta.
4-M/ Suppose you are the money manager o a >= million investment und. 5he und "onsists o = sto"ks with the ollowing investments and betas: S5G$I
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A the market2s required rate o return is <= per"ent and the riskree rate is 4 per"ent, what is the und2s required rate o return7 4-</ Hou Hou have a >& million mill ion portolio "onsisting o a ><, investment in ea"h o & diQerent sto"ks. 5he portolio has a beta equal to <.<. Hou Hou are "onsidering selling selli ng ><, worth o one sto"k that has a beta equal to .M and using the pro"eeds to pur"hase an-other sto"k that has a beta equal to <.=. 6hat will be the new beta o your portolio ollowing this transa"tion7 4-<
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ssume that the risk-ree rate is 4 per"ent and the market risk premium is per"ent. a. 6hat are the betas o Sto"ks R and H7 b. 6hat are the required rates o return or Sto"ks R and H7 ". 6hat is the required rate o return or a portolio "onsisting o J per"ent o Sto"k R and & per"ent o Sto"k H7 d. A Sto"k R2s e!pe"ted return is && per"ent, is Sto"k R under- or overvalued7
S+)DSB5 +)G13 1artman Andustries2 sto"k pri"es and dividends, along with the 6ilshire Ande!, are shown below or the period
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a. ?se the data given to "al"ulate annual returns or 1artman, )eynolds, and the 6ilshire Ande!, and then "al"ulate average returns over the -year period. b. $al"ulate the standard deviations o the returns or 1artman, )eynolds, and the 6ilshire . Bint: ?se the sample standard deviation ormula given in Footnote to this "hapter, "hapter, whi"h "orresponds to the S5D( un"tion in !"el./ ". @ow "al"ulate the "oe'"ients o variation or 1artman, )eynolds, and the 6ilshire . d. $onstru"t a s"atter diagram graph that shows 1artman2s and )eynolds2 returns on the verti"al a!is and the market inde!2s returns on the hori*ontal a!is.
e. stimate 1artman2s and )eynolds2 betas by running regressions o their returns against the 6ilshire 2s returns. re these betas "onsistent with your graph7 . 5he risk-ree rate on long-term 5reasury 5reasury bonds is 4.= per"ent. ssume that the av-erage annual return on the 6ilshire is nota good estimate o the market2s market2s re-quired re-quired return it is too high, so use << per"ent as the e!pe"ted return on the mar-ket. @ow use the S3 equation to "al"ulate the two "ompanies2 required returns. g. A you ormed a portolio that "onsisted o per"ent o 1artman sto"k and per-"ent o )eynolds sto"k, what would be the beta and the required return or the port-olio7 h. Suppose an investor wants to in"lude 1artman Andustries2 sto"k in his or her portolio. Sto"ks , 1, and $ are "urrently in the portolio, and their betas are .94M, .MJ, and <.=&8, respe"tively. respe"tively. $al"ulate the new portolio2s required return i it "onsists o & per"ent o 1artman, < per"ent o Sto"k , = per"ent o Sto"k 1, and & per"ent o Sto"k $.
