投資學第10版習題答案-在線瀏覽
2024-09-05 04:09本頁面
【正文】 e ponents:(l) The variance due to the mon market factor: (2) The variance due to firm specific unanticipated events: In this model: The number of parameter estimates is:n = 60 estimates of the mean E(ri )n = 60 estimates of the sensitivity coefficient β i n = 60 estimates of the firmspecific variance σ2(ei )1 estimate of the market mean E(rM )1 estimate of the market varianceTherefore, in total, 182 estimates.The single index model reduces the total number of required estimates from 1,890 to 182. In general, the number of parameter estimates is reduced from:6. a. The standard deviation of each individual stock is given by: Since βA = , βB = , σ(eA ) = 30%, σ(eB ) = 40%, and σM = 22%, we get:σA = ( 222 + 302 )1/2 = %σB = ( 222 + 402 )1/2 = % b. The expected rate of return on a portfolio is the weighted average of the expected returns of the individual securities:E(rP ) = wA E(rA ) + wB E(rB ) + wf rf E(rP ) = ( 13%) + ( 18%) + ( 8%) = 14%The beta of a portfolio is similarly a weighted average of the betas of the individual securities:βP = wA βA + wB βB + wf β f βP = ( ) + ( ) + ( ) = The variance of this portfolio is:whereis the systematic ponent andis the nonsystematic ponent. Since the residuals (ei ) are uncorrelated, the nonsystematic variance is:= ( 302 ) + ( 402 ) + ( 0) = 405where σ2(eA ) and σ2(eB ) are the firmspecific (nonsystematic) variances of Stocks A and B, and σ2(e f ), the nonsystematic variance of Tbills, is zero. The residual standard deviation of the portfolio is thus:σ(eP ) = (405)1/2 = %The total variance of the portfolio is then:The total standard deviation is %.7. a. The two figures depict the stocks’ security characteristic lines (SCL). Stock A has higher firmspecific risk because the deviations of the observations from the SCL are larger for Stock A than for Stock B. Deviations are measured by the vertical distance of each observation from the SCL.b. Beta is the slope of the SCL, which is the measure of systematic risk. The SCL for Stock B is steeper。 hence Stock B’s systematic risk is greater. c. The R2 (or squared correlation coefficient) of the SCL is the ratio of the explained variance of the stock’s return to total variance, and the total variance is the sum of the explained variance plus the unexplained variance (the stock’s residual variance):Since the explained variance for Stock B is greater than for Stock A (the explained variance is, which is greater since its beta is higher), and its residual variance is smaller, its R2 is higher than Stock A’s. d. Alpha is the intercept of the SCL with the expected return axis. Stock A has a small positive alpha whereas Stock B has a negative alpha。 A difference of: The only moderate improvement in performance results from only a small position taken in the active portfolio A because of its large residual variance.d. To calculate the makeup of the plete portfolio, first pute the beta, the mean excess return, and the variance of the optimal risky portfolio:βP = wM + (wA βA ) = + [(–) 180。 (–%)] + ( 8%) = %Since A = , the optimal position in this portfolio is:In contrast, with a passive strategy:224。 =A 180。 (–) =B
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