Lecture 14: Implementing CAPM

Transcription

1 Lecture 14: Implementng CAPM Queston: So, how do I apply the CAPM? Current readng: Brealey and Myers, Chapter 9 Reader, Chapter 15 M. Spegel and R. Stanton,

2 Key Results So Far All nvestors should splt ther money between the market portfolo and the rsk-free asset. In practce, buy an ndex fund, or an exchange traded fund. The Captal Asset Prcng Model: r β = = r f + β Cov Var [ ( E rm ) rf ] ( r, rm ) ( r ). m, Expected return s related to the stock s beta Depends on covarance wth the market: Market Rsk Does not depend on ts varance: Frm Specfc Rsk Remember our dversfcaton example M. Spegel and R. Stanton,

3 Expected Return and Beta 1 What s the expected return on a stock wth β = 0? Answer s r f : Same return as rsk-free asset! Why? Thnk about nsurng lots of houses aganst fre. Each ndvdually s rsky, but When you dversfy by nsurng lots of houses, overall portfolo becomes rskless. M. Spegel and R. Stanton,

4 Expected Return and Beta 2 What s the expected return on a stock wth β < 0? If β < 0, then r < r f! You d accept a return lower than the rsk-free rate? Why? It pays off most when you most need the money.» All your other nvestments have gone down n value Ths stock provdes you wth nsurance It s more valuable than a rsk-free payoff. M. Spegel and R. Stanton,

5 Interpretng/Estmatng β Cov( r, ) rm β s defned by β ( ). = Var rm Does ths look famlar? r on It s the slope we get when we regress rm. ( r r ) on ( r r ). In practce, regress excess returns, r r f f m f β = slope of regresson lne r m r f M. Spegel and R. Stanton,

6 Estmatng Beta So to estmate the beta of a partcular stock, Regress (excess) returns on the stock aganst (excess) returns on the market portfolo (e.g. S&P 500 ndex). The slope of the regresson lne s your estmate of beta. Do the same for other frms n same ndustry to reduce uncertanty Now plug the estmate nto the formula: r = r f + β (r m -r f ). M. Spegel and R. Stanton,

7 Where to get data? Where to get the data to estmate the β of, say, IBM? One easy to use (and free) source s Yahoo! Fnance: IBM (IBM): S&P 500 (^SPX): 3m T-Bll (^IRX): You can also download data from Datastream, avalable n the lbrary. M. Spegel and R. Stanton,

8 Importng data nto Excel Yahoo s Web ste allows you to download data as a spreadsheet manually. Excel (at least 97 on) allows you to download data from Web stes automatcally usng Get External Data (under the Tools menu). M. Spegel and R. Stanton,

9 What rsk free rate to use? In the regresson, f usng (say) monthly returns, you need a monthly rsk-free rate. The 3m T-Bll rate s a good number to start wth. Shorter maturty T-Blls are rather volatle. Important: You need to convert the quoted number to a monthly rate correctly: Yahoo quotes the rate as a dscount Datastream quotes the rate lke the ask yeld n the WSJ M. Spegel and R. Stanton,

10 Example - Estmatng IBM beta (data from Yahoo) Yahoo quotes dscount Convert to monthly r f Prce Monthly Return Excess Return Date IBM S&P 3m T-Bll IBM S&P 3m T-Bll IBM S&P 9/1/ % % % % % 8/1/ % % % % % 7/1/ % % % % % 6/1/ % % % % % 5/1/ % % % % % 4/1/ % % % % % 3/1/ % % % % % 2/1/ % % % % % 1/1/ % % % % % 12/1/ % % % % % 11/1/ % % % % % 10/1/ % % % % % Now regress IBM excess return aganst S&P excess return. M. Spegel and R. Stanton,

11 Convertng quoted rates to true r f : Yahoo Slght smplfcaton: Assume ¼ year to maturty. Yahoo quotes a dscount of 6.11% on 8/1/00 Prce = 100 x (1 6.11% x 90/360) = $ month rate = (100/ ) 1 = 1.551% One month r f = /3 1 = 0.514% Note: ths s r f for the month endng 9/1/00 M. Spegel and R. Stanton,

12 Convertng quoted rates to true r f : Datastream Datastream quotes a yeld of 6.25% on 8/1/00. 3 month rate = 6.25% / 4 = % One month r f = /3 1 = 0.518% Note: ths s r f for the month endng 9/1/00. Ths s not dentcal to the result we calculated from Yahoo, but t s close. Numbers only quoted to 2 sgnfcant fgures. May use dfferent data sources. M. Spegel and R. Stanton,

13 Runnng the Regresson To perform regresson, use Excel s regresson tool Tools -> Data Analyss -> Regresson Need to nstall Analyss Toolpack addn frst. Do not fx ntercept to be zero. Can also use bult n SLOPE() command. From 2 yrs monthly data, IBM vs S&P, we get: Coeffcents Standard Error Intercept S&P Estmate of β M. Spegel and R. Stanton,

14 Interpretng R 2 The regresson also reports an R 2 value 0.32 n our example. What does t tell us? The regresson can be wrtten as r ( ) rf = β rm rf + ε. So var( 2 r r ) = β var( r r ) + var( ε). f m f Total rsk = Market rsk + Frm-specfc rsk R 2 s defned as: 2 ( 2 β var rm rf ) R = var( = r r ) f Market rsk Total rsk Market rsk = Market rsk + Frm - specfc rsk. M. Spegel and R. Stanton,