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Return and Risk: The Capital Asset Pricing Models: CAPM and APT

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Presentation on theme: "Return and Risk: The Capital Asset Pricing Models: CAPM and APT"— Presentation transcript:

1 Return and Risk: The Capital Asset Pricing Models: CAPM and APT
Text: Chapter 10 and 11

2 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 = 12.5 Portfolio 2 is preferred than portfolio 1. It is because the zero covariance diversifies some of the return volatility.

3 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 X X E(rp~) (rp~)

4 Efficient Portfolio Frontier
s

5 Efficient Sets and Diversification
= -1 -1 < r < 1 r = 1 s

6 What about portfolio of n assets?
Expected return of portfolio Standard deviation of portfolio’s return.

7 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.

8 Combination of risk-free and risky asset
p2 = x1212, Thus, : p = x11, 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.

9 Which risky asset to choose?
Capital market line . Y S . X Risk-free rate (Rf ) Standard deviation of portfolio’s return.

10 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.

11 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.

12 . . . 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

13 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.

14 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

15 Beta vs. Average Risk Premium
Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0

16 Beta vs. Average Risk Premium
Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium SML 30 20 10 Investors Market Portfolio Portfolio Beta 1.0

17 Beta vs. Average Risk Premium
Testing the CAPM Beta vs. Average Risk Premium Avg Risk Premium 30 20 10 SML Investors Market Portfolio Portfolio Beta 1.0

18 Company Size vs. Average Return
Testing the CAPM Company Size vs. Average Return Average Return (%) Smallest Largest Company size

19 Book-Market vs. Average Return
Testing the CAPM Book-Market vs. Average Return Average Return (%) Lowest Book-Market Ratio Highest

20 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.

21 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

22 Arbitrage Pricing Theory
Alternative to CAPM Expected Risk Premium = r - rf = Bfactor1(rfactor1 - rf) + Bf2(rf2 - rf) + … Return = a + bfactor1(rfactor1) + bf2(rf2) + …

23 Arbitrage Pricing Theory
Estimated risk premiums for taking on risk factors ( )


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