Capital Asset Pricing Model (CAPM)

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1 Captal Asset Prcng odel (CAP) Expected Return A undaental queston n nance: How do we deterne the expected return o an asset? Based on rsk? How do we easure the rsk? What s the approprate expected return or a gven level o rsk? These questons are addressed by asset prcng odels. What should be ABC s share prce? ABC s share prce ABC Inc. s expected to pay a lqudatng (.e., ternal) dvdend o $11 per share one year ro today. The requred rsk preu or the stock s 7%. The rsk ree rate o return s 5% Prce =? The Expected Return Sgncance o the expected return: The requred return helps deterne asset values. Captal Budgetng Deternng the expected (or requred) rate o return s necessary or evaluatng projects orecast cash lows dscount cash lows at the requred rate o return calculate the NPV o the project 1

2 Total Rsk The total rsk o an ndvdual stock has two coponents Systeatc Rsk For nstance, There could be a war There could be an econoc recesson There could be a oregn econoc crss These are all exaples o rsk aced by the entre arket, and are part o our econoc syste. Ths s called systeatc rsk. It cannot be elnated. Unsysteatc Rsk For nstance, A r ght go bankrupt A r ght get sued A r n a partcular ndustry ght be the target o new regulatons These are all exaples o r-specc rsk, also called unsysteatc rsk. Holdng a well-dversed portolo elnates r-specc rsk. Systeatc and Unsysteatc Rsk Unsysteatc rsk o ndvdual assets can be elnated by holdng a dversed portolo, such as the arket portolo. Ths rsk does not add to the total rsk o the portolo, and thereore should not be copensated The systeatc rsk o ndvdual assets cannot be elnated, and thereore should be approprate rsk easure. Whch s the Approprate easure o Rsk? Standard devaton o an asset's rate o return s a useul easure o ts stand-alone rsk It s not an approprate easure o the asset's rsk when t s part o a portolo. Because nvestors care about the return and rsk o ther entre portolos, and not the return and rsk o ndvdual asset per se. CAP Rsk preu on the arket depends on the average rsk averson o all arket partcpants Rsk preu on an ndvdual securty s a uncton o ts covarance wth the arket portolo

3 Rsk Preu o the arket Portolo ( E( r ) r ) y = Aσ Our easure o systeatc rsk s called beta, and s dened as the covarance between the y = 1 E( r ) r = Aσ return o a stock and the return on the arket portolo, dvded by the varance o the return on the arket portolo: The rsk preu o the arket portolo s proportonal to the average rsk averson across all nvestors and the rsk o the arket portolo, whch s easured by the varance o the arket returns. easurng Systeatc Rsk ( R R ) ( R ) Cov, β = Var The Captal Asset Prcng odel In equlbru, the arket prce o the rsk should be equal between ndvdual rsky asset and the arket portolo. E( r ) r Cov E E( r ) r = ( r, r ) Var( r ) Cov( r ) ( ) ( ), r ( r ) r = E( r ) r Var r The Captal Asset Prcng odel The expected return on any asset can be wrtten as: E(R ) R where = β excess return or rsk Cov β = σ ( E(R ) R ) ( R, R ) preu Intuton Intuton argnal utlty n good states and bad states Hgh beta hgh rsk hgh expected return low prce An Exaple The expected arket return s 1%. The rsk ree rate s 6%. What s the expected return o a stock wth a beta o 0.8? E(R)= What s the expected return o a stock wth a beta o 1? What s the expected return o a stock wth a beta o 0? (no calculaton needed) 3

4 CAP All nvestors wll hold the sae portolo or rsky assets arket portolo. arket portolo contans all securtes and the proporton o each securty s ts arket value as a percentage o total arket value. How to Estate Beta We estate beta usng Ordnary Least Squares regresson o the CAP equaton, where returns are expressed n excess return or: R = R + β R R + e ( ) ( R R ) = β ( R R ) + e Y = βx + e where e s an error ter whch relects rspecc rsk not beng captured by beta. How to Estate Beta Data Analyss Copute the excess returns o the stock Copute the excess returns o the arket porolo (proxed by S&P 500 Index) Regress excess returns o the stock on the excess returns o the S&P 500 ndex The regresson coecent on the S&P 500 ndex excess returns s the beta o the stock Regresson Regresson 4

5 Regresson Regresson Lnear Regresson Securty Characterstc lne Stock Returns Excess Return on Asset Dstance ro the lne to the ponts are the error terṣ Characterstc Lne Beta or the r s the slope o ths lne. arket Returns Jensen Alpha or the r s the ntercept o ths lne. Excess Return on arket The Securty arket Lne Iplcatons or Actve Portolo Strategy Expected Return Underprced Securtes E(arket Return) A Rsk-ree Return + alpha Securty arket Lne - alpha B Overprced Securtes Alpha s the derence between the average stock return and the CAP expected return Invest n stocks that are underprced, or have postve alpha, whch s deterned ro the asset prcng odel, such as the CAP. Beta o the arket = 1.00 Beta 5

6 ult-actor Asset Prcng odels The Captal asset prcng odel (CAP) stpulates that there s only one rsk actor, that s, the return on the arket portolo. So the cross-sectonal varatons n expected returns should be explaned by assets beta. Hgh beta hgh expected return Low beta low expected return ult-actor Asset Prcng odels In practce, CAP does not peror well One-actor odel s too restrctve Poor proxy or arket portolo An alternatve approach s to use a ultactor odel (analogy, E.g., predctng a person s weght) What are the actors that aect expected returns? ult-actor Asset Prcng odels acroeconoc-based rsk actor odels Based on undaental rsks such as nlaton, nterest rates and ndustral producton Characterstc-based rsk actor odels The prese s that returns on stocks wth certan characterstcs are proxes or undaental rsks acroeconoc odels Chen, Roll, and Ross (1986) arket return onthly growth rate n ndustral producton Change n nlaton Derence between expected and actual nlaton Unantcpated change n credt spread Unantcpated change n ter spread acroeconoc odels Burester, Roll, and Ross (1994) Condence rsk Te horzon rsk Inlaton rsk Busness cycle rsk arket tng rsk Characterstc-based odels Faa and French (1993) three-actor odel arket return SB, the return to a portolo o sall cap stocks less the return to a portolo o large cap stocks HL, the return to a portolo o stocks wth hgh book-to-arket ratos less the return to a portolo o low book-to-arket stocks 6

7 Faa-French Three-actor odel CAP : R R R R Faa French = α + b = α + b ( R R ) + e ( R R ) + s SB + h HL + e BARRA BARRA characterstc-based rsk actors (13) volatlty, oentu, sze, sze nonlnearty, tradng actvty, growth, earnngs yeld, value, earnngs varablty, leverage, currency senstvty, dvdend yeld, nonestaton ndcator 7

Outline. CAPM: Introduction. The Capital Asset Pricing Model (CAPM) Professor Lasse H. Pedersen. Key questions: Answer: CAPM

Outline. CAPM: Introduction. The Capital Asset Pricing Model (CAPM) Professor Lasse H. Pedersen. Key questions: Answer: CAPM The Catal Asset Prcng odel (CAP) Proessor Lasse H. Pedersen Pro. Lasse H. Pedersen 1 Key questons: Outlne What s the equlbrum requred return, E(R), o a stock? What s the equlbrum rce o a stock? Whch ortolos