BKM Chapter 13 - Empirical Evidence on Security Returns

Question 1

Test Procedure to test CAPM - Two-stage Regression

Answer 1

1. Setting Up the Sample Data - gather historical return data for the past 60 months. Use a broad market index like the S&P 500 to represent the market and gather historical monthly returns for 100 different stocks.
2. Estimating the Security Characteristic Line - Then do the first pass regression using a single index model with the S&P return as the index. The point of this step is to get estimates of beta for each stock, so 100 different regressions will be performed with 60 data points in each regression.
3. *Estimating the Security Market Line *- Now, do a second pass regression using the average excess returns, betas and residual variances for the 100 stocks. In this regresion, you will have one data point for each stock reflecting the average excess return during the 60 month time period for that stock (r_i-r_fBar), and estimate of the beta, and estimate of the residual variance (reflecting all of the non-systematic risk) and an estimate of the excess market return for the 60 month period.

Question 2

What should the regression coefficients from the 2nd pass coefficient be if CAPM is valid? Explain.

Answer 2

γ₀=0, γ₁= avg (r_m-r_f), γ₂=0.

Regression: r_i - r_f (bar) = γ₀ + γ₁β(hat)_i + γ₂σ(hat)²_ei + ε

CAPM: E(R_i) = β_i * E(R_M)

According to CAPM, the expected excess return on securities should only be determined by systematic risk, and that γ₀ and γ₂ must be significantly close to zero, which is consistent with the assumption that non systematic should not be priced. γ₁ should be average excess return on market index.

If γ₀ is statistically different from zero and positive, it would be consistent with the zero beta version of the model.

Question 3

Early tests completed by researchers seemed to reject the CAPM. Identify and explain the concerns about the validity of the tests.

Answer 3

1. The market index used is not the true market portfolio - CAMP can not be tested because the proxies used for the market portfolio do not come close to the portfolio of all risky assets called for by the model
2. Investors can not borrow or lend at the risk free rate, which is assumed in the simple version of CAPM
3. Asset volatility cause large measurement errors in the betas in the first pass regression - Stock returns are extremely volatile which lessens the precision of any tests of average return

Question 4

Despite the findings of the empirical research that raises questions about certain aspects of the CAPM, what two major conclusions of CAPM are largely supported?

Answer 4

Expected returns increase linearly with systematic risk;

Expected returns are not affected by non-systematic risk.

Question 5

Explanations of the empirical results of Fama-French 3-Factor Model vs. CAPM

Answer 5

1. Risk Based Interpretations

Size and value factors must be priced factors for risks not captured in CAPM. For instance, they may capture risks associated with the business cycle or the risks associated with time varying betas and market risk premiums. Portfolios with a high degree of sensitivity (correlation) to these factors earn higher returns.

2. Behavioral Interpretations

that investors irrationally prefer firms with good performance, high prices and lower book-to-market ratios, perhaps because they incorrectly extrapolate good recent performance too far into the future.

Question 6

Describe the Equity Premium Puzzel

Answer 6

Mehra and Prescott found that over the period 1889 - 1978, investors have been excessively rewarded for bearing risk. The excess market return observed in the US seemed too large to be consistent with economic theory and reasonable levels of risk aversion.

Question 7

Explanations for the Equity Premium Puzzel

Answer 7

1. Investors just got lucky - they weren’t expecting high market risk premiums, but they were fortunate to earn them.
2. the puzzle is based only on the returns in the US stock market rather than on all global markets including those that have since shut down. The inclusion of only the most successful market creates a survivorship bias.
3. It’s using CAPM as benchmark, which does not include certain risks. E.g. when the restriction on risk free lending and borrowing is included, we can get a risk premium higher than what CAPM suggests. Another example is liquidity premium.
4. loss aversion and narrow framing can cause investors to have higher effective levels of risk aversion that leads to higher market risk premiums.

Question 8

All10 manual pg 212, 2001Q11

Answer 8

check standard answer from CAS