Return and Risk: The Capital Asset Pricing Models: CAPM and APT Text: Chapter 10 and 11
Portfolio Theory Ex1, Two portfolio Portfolio 1: a single investment A: with expected return : 1 and variance 25 Portfolio 2: equally weighted combination of two uncorrelated investments: with expected return of 1, and variances 25 Both have the same expected return : 1, but the variance of portfolio 2 is .52*25 + .52*25 = 12.5 Portfolio 2 is preferred than portfolio 1. It is because the zero covariance diversifies some of the return volatility.
A portfolio of two risky assets Ex2: Asset 1 has expected return of .22 and SD of .32 Asset 2 has expected return of .13 and SD of .23 Covariance is .01104 X1 X2 E(rp~) (rp~) 0 1 .13 .23 .2 .8 .148 .2037 .4 .6 .166 .2018 .6 .4 .184 .2250 .8 .2 .202 .2668 1 0 .22 .32
Efficient Portfolio Frontier s
Efficient Sets and Diversification = -1 -1 < r < 1 r = 1 s
What about portfolio of n assets? Expected return of portfolio Standard deviation of portfolio’s return.
Markowitz Portfolio Theory Combining stocks into portfolios can reduce standard deviation below the level obtained from a simple weighted average calculation. Less than perfect correlation coefficients make this possible. The various weighted combinations of stocks that create this standard deviations constitute the set of efficient portfolios.
Combination of risk-free and risky asset p2 = x1212, Thus, : p = x11, x1 = p / 1 E(rp~) = x1r1 + x2 rf = p*(r1/1) + x2 rf Expected return of portfolio . Asset 1 rf Standard deviation of portfolio’s return.
Which risky asset to choose? Capital market line . Y S . X Risk-free rate (Rf ) Standard deviation of portfolio’s return.
Which Risky Asset To Choose? Expected return of portfolio . Capital market line Borrowing . 5 Y . S Lending 4 . Risk-free rate (Rf ) X Standard deviation of portfolio’s return.
The Chosen Portfolio, M Will different individual have different choice of different risky portfolio asset? What if different individual holds the same expectation (homogeneous expectation), that is, .market reflects all the information? What does portfolio S look like? All investors will invest in portfolio S, regardless of their risk aversion. But they may NOT have the same portion of their wealth in the two assets.
. . . Security Market Line T Rm M S Rf 0.8 1 Expected return on security (%) . Security market line (SML) T . Rm M . S Rf Beta of security 0.8 1
Security Market Line For a well diversified portfolio, the risk measure of individual stock is not the SD of return, it is beta. Investors are not rewarded with any return for bearing any unsystematic risk. Why should equilibrium prices of securities fall on SML? If point A lies above the Security market line, then investors will bid up the price until the return goes back on line If point B lies below the security market line, then investors will sell the security, push down the price until it goes back on line.
Capital Asset Pricing Model If investors hold market portfolio, how do they measure the risk of individual securities? The covariance with the markets, that is Beta. CAPM, for any security i, E (ri~) = rf + i [E(rm~ - rf)], where, E(rm~ - rf) : expected market risk premium i = COV(ri~, rm~)/m2
Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-2002 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0
Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1931-65 SML 30 20 10 Investors Market Portfolio Portfolio Beta 1.0
Beta vs. Average Risk Premium Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 1966-2002 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0
Company Size vs. Average Return Testing the CAPM Company Size vs. Average Return Average Return (%) Smallest Largest Company size
Book-Market vs. Average Return Testing the CAPM Book-Market vs. Average Return Average Return (%) Lowest Book-Market Ratio Highest
About CAPM Why does CAPM not hold ? Is CAPM dead? Expected return vs. real return Short term or long term effect? The contribution of CAPM How the financial markets may price risky assets How to measure a risky asset’s risk How to calculate expected rate of return.
The Measurement Of Beta Choice of market proxy The time period Measurement error: the problem of overestimate for high beta and underestimate for low beta stocks Instability over time
Arbitrage Pricing Theory Alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + … Return = a + bfactor1(rfactor1) + bf2(rf2) + …
Arbitrage Pricing Theory Estimated risk premiums for taking on risk factors (1978-1990)