Chapter 6 Risk, Return, and the Capital Asset Pricing Model

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1 Whch s better? (1) 6% return wth no rsk, or (2) 20% return wth rsk. Chapter 6 Rsk, Return, and the Captal Asset Prcng Model Cannot say - need to know how much rsk comes wth the 20% return. What do we know so far? We know why returns (rates) vary between dfferent securtes! * r nom = r + IP + DRP + LP + MRP r nom * r = = nomnal rate real rate (pure compensaton) IRP = nflaton-rsk premum (change n cost of goods) DRP = default-rsk premum (ablty to pay P & I) LP = lqudty premum (ablty to convert to cash) MP = maturty rsk premum (äp/ä) * where r + IP = r RF But ths does not quantfy rsk We want to quantfy rsk. Today s concepts (1) quantfy rsk (2) tells us how much return we need for a gven level of rsk. I. Rsk and Return for ndvdual assets Rsk = P( Actual returns < Expected returns ) ex. 2 year Treasury bond - hold untl maturty, pays 6%/yr expected return = 6% [ r = 6%] If hold untl maturty Actual return = 6% [ r = 6% ] Therefore r = r or P [r < r ]=0% no rsk!

2 Buy a 20 year STN bond to hold for 2 years expected return = 20% [ r = 20% ] Probablt y 50% 25% 25% Actual Return 0% 20% 60% r 20% r = p * r =.50(.00) +.25(.20) +.25(.60) =.20 How to measure rsk and return: for ndvdual asset calculate: r = expected rate of return 6 = standard devaton whch measures the dsperson around the mean (measure of rsk) 2 1/2 6 = [ (r - r ) p ] Instrument r 6 T-Bond STN Bond 6% 20% 0% 24.5% Stock A has the followng probablty dstrbuton of expected returns: Probablty Rate of Return % What s Stock A's expected rate of return and standard devaton?

3 II. Rsk and Return for portfolos Expected Portfolo Return r p= x * r x = proporton of portfolo nvested n asset. Portfolo standard devaton /2 6 p = [x A6 A + x B6 B + 2xAx B pab6a6 B] where, x + x = 100% A B p (rho) = correlaton coeffcent = measures comovement between 2 securtes ex. Indvdual expected return and standard devaton prob MGM STN % 9% 15% -3% 12% 27% r 9% 12% % 10.6% What does standard devaton tell us?

4 Portfolo expected return and standard devaton x Stock r 6 40% 60% MGM STN 9% 12% 4.24% 10.6% r p 10.8% 6 p, f p =+1 6 p, f p=0 6, f p=-1 p 8.0% 6.6% 4.7% Portfolo Expected Return: r p = (.40)(.09) + (.60)(.12) = 10.8% Portfolo Standard Devaton: say p=1, perfect postve correlaton 6 p = [(.4) (4.24) + (.6) (10.6) + 2(.4)(.6)(1)(4.24)(10.6)] 1/2 = [64.9] = 8% /2 p=0, no correlaton, 6 p = 6.6% p=-1, perfect negatve correlaton, 6 p =4.7% Remember: less correlaton equates to lower rsk!! III. Effcent Portfolos - The portfolo that provdes the hghest return for a gven level of rsk - or lowest rsk for a partcular expected return. Therefore combne assets n a portfolo to get hghest expected return for gven rsk (6 p) For each asset some rsk can be elmnated when combned wth other assets n a portfolo (unless p=+1) Combne assets n such a manner to get Effcent Portfolo.

5 Look at an ndvdual stock Total Rsk = 6 Some rsk can be elmnated by ncludng the stock n a portfolo -call ths that can be elmnated dversfable or company-specfc rsk. Some rsk can not be elmnated - call ths nondversfable or market rsk. Rsk that s mportant to nvestors s nondversfable or market rsk. rsk averson (def) - dslke rsk IV. Beta - CAPM Beta = Measure of Market Rsk - the rsk that s relevant to nvestors. BETA (ß) measures of a partcular stock's varaton n return relatve to the market. 2 2 ß = cov(r,r m)/6 m = pm66 m/6 m = p m * ( 6 / 6 m ) ß = 1.0 ß > 1.0 ß < 1.0 ß = 0.0 moves exactly wth market moves more than market (> rsk) moves less than market (< rsk) no rsk (Rsk-Free) CAPM = Captal Asset Prcng Model r = r RF + ß ( r m - r RF ) ( r - r ) = market rsk premum m RF ex. T-Bll = r = 5%, r = 12% RF m For T-Bll ß=0, no rsk r T-Bll = 5% + ( 0 )( 12% - 5% ) = 5% For IBM ß=0.7 r IBM = 5% + ( 0.7 )( 12% - 5% ) = 9.9%

6 What does the CAPM tell us? What s our expected return at a gven level of rsk (the rsk that s mportant to an nvestor holdng a well-dversfed portfolo. SML = Securty Market Lne

7 How many stocks (assets) do we need to hold to approxmate a well-dversfed portfolo? Hold everythng - market portfolo - elmnates all dversfable rsk - Impossble! Hold 8-10 assets - closely approxmates market (elmnates most dversfable rsk) Holdng a Portfolo - Market Rsk (nondversfable rsk) Effcent Markets Hypothess (def) securtes are farly prced - market prce reflects all publcly avalable nformaton. What does ths mean for nvestors? P 0 = far prce accordng to publc nformaton r = depends on rsk relatve to market rsk (ß) Just buy securtes and form your portfolo accordng to rsk preference.

8 Recap: Rsk vs. Return Goal: to quantfy rsk and return so we can compare and choose nvestment opportuntes. We saw how to calculate expected return r = p and rsk r * 2 1/2 6 = [ (r - r ) p ] But f we form a portfolo we can elmnate some rsk - f we form portfolo n such a manner to elmnate all extra (dversfable) rsk we have effcent portfolo (def). Assumes that everyone (nvestors) are brght enough to hold a well-dversfed effcent portfolo. Only rsk that matters s nondversfable rsk (market rsk) - measured by ß Use CAPM and ß to calculate expected return for relevant rsk. Rsk and Return are quantfed!!!! Therefore nvestors want to own effcent portfolos. Whch ones? The one that correspond to the level of rsk they want to assume. ( trade-off: Rsk - Return )