Chapter 8

The correlation between the Charlottesville International Fund and the EAFE Market Index is 1.0. The expected return on the EAFE Index is 11%, the expected return on Charlottesville International Fund is 9%, and the risk-free return on EAFE countries is 3%. Based on this analysis, what is the implied beta of Charlottesville International?

9 = 3 + β (11 − 3) ==> β = 0.75

Assume the correlation coefficient between Baker Fund and the S&P 500 stock index is .70. What percentage of Baker Fund's total risk is specific (i.e., nonsystematic)?

The R^2 of the regression is .70^2 = .49 Therefore, 51% of total variance is unexplained by the market; this is nonsystematic risk.

What are the advanatages of the index model compared to the Markowitz procedure for obtaining an efficiently diversified portfolio? What are its disadvantages?

The advantage of the index model, compared to the Markowitz procedure, is the vastly reduced number of estimates required. In addition, the large number of estimates required for the Markowitz procedure can result in large aggregate estimation errors when implementing the procedure. The disadvantage of the index model arises from the model's assumption that return residuals are uncorrelated. This assumption will be incorrect if the index used omits a significant risk factor.

How does the magnitude of firm-specific risk affect the extent to which an active investor will be willing to depart from an indexed portfolio?

The answer to this question can be seen from the formulas for w 0 (equation 8.20) and w* (equation 8.21). Other things held equal, w 0 is smaller the greater the residual variance of a candidate asset for inclusion in the portfolio. Further, we see that regardless of beta, when w 0 decreases, so does w*. Therefore, other things equal, the greater the residual variance of an asset, the smaller its position in the optimal risky portfolio. That is, increased firm-specific risk reduces the extent to which an active investor will be willing to depart from an indexed portfolio.

What is the basic trade-off when departing from pure indexing in favor of an actively managed portfolio?

The trade-off entailed in departing from pure indexing in favor of an actively managed portfolio is between the probability (or the possibility) of superior performance against the certainty of additional management fees.

Beta and standard deviation differ as risk measures in that beta measures: a) Only unsystematic risk, while standard deviation measures total risk. b) Only systematic risk, while standard deviation measures total risk. c) Both systematic and unsystematic risk, while standard deviation measures only unsystematic risk. d) Both systematic and unsystematic risk, while standard deviation measures only systematic risk.

b) Only systematic risk, while standard deviation measures total risk.

The concept of beta is most closely associated with: a) Correlation coefficients b) Mean-variance analysis c) Nonsystematic risk d) Systematic risk

d) Systematic risk