c. Discuss the advantages of the single-index model over the Markowitz model in terms of numbers...

 

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c. Discuss the advantages of the single-index model over the Markowitz model in terms of numbers of variable estimates required and in terms of understanding risk relationships. For a 50 security portfolio, the Markowitz model requires the following parameter estimates: n = 50 estimates of expected returns; n = 50 estimates of variances: (n²-n)/2 = 1,225 estimates of covariances; or 1,325 estimates. For a 50 security portfolio, the single-index model requires the following parameter estimates: n = 50 estimates of expected excess returns, E(R); n = 50 estimates of sensitivity coefficients, ß; n = 50 estimates of the firm-specific variances, o²(e) 1 estimate for the variance of the common macroeconomic factor, o²m; or (3n+ 1 =151) estimates. In addition, the single-index model provides further insight by recognizing that different firms have different sensitivities to macroeconomic events. The model also summarizes the distinction between macroeconomic and firm-specific risk factors. Feedback: This question is designed to ascertain that the student understands the significant simplifications and improvements offered by the single-index model over the Markowitz model. d. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 132 stocks in order to construct a meanvariance efficient portfolio constrained by 132 investments. Calculate the number of covariance they will need to calculate? (n²-n)/2 = (17,424 - 132)/2 = 8,646 covariances must be calculated. Question 02 a. The optimal proportion of the risky asset in the complete portfolio is given by the equation y* = [E(re)-rl(.01A times the variance of P). For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. The optimal proportion in y is the one that maximizes the investor's utility. Utility is positively related to the risk premium [E(re)-r]. This makes sense because the more expected return an investor gets, the happier he is. The variable "A" represents the degree of risk aversion. As risk aversion increases, "A" increases. This causes y* to decrease because we are dividing by a higher number. It makes sense that a more risk-averse investor would hold a smaller proportion of his complete portfolio in the risky asset and a higher proportion in the risk-free asset. Finally, the standard deviation of the risky portfolio is inversely related to y*. As P's risk increases, we are again dividing by a larger number, making y* smaller. This corresponds with the risk averse investor's dislike of risk as measured by standard deviation. Feedback: This allows the students to explore the nature of the equation that was derived by maximizing the investor's expected utility. The student can illustrate an understanding of the variables that supersedes the application of the equation in calculating the optimal proportion in P. c. Discuss the advantages of the single-index model over the Markowitz model in terms of numbers of variable estimates required and in terms of understanding risk relationships. For a 50 security portfolio, the Markowitz model requires the following parameter estimates: n = 50 estimates of expected returns; n = 50 estimates of variances: (n²-n)/2 = 1,225 estimates of covariances; or 1,325 estimates. For a 50 security portfolio, the single-index model requires the following parameter estimates: n = 50 estimates of expected excess returns, E(R); n = 50 estimates of sensitivity coefficients, ß; n = 50 estimates of the firm-specific variances, o²(e) 1 estimate for the variance of the common macroeconomic factor, o²m; or (3n+ 1 =151) estimates. In addition, the single-index model provides further insight by recognizing that different firms have different sensitivities to macroeconomic events. The model also summarizes the distinction between macroeconomic and firm-specific risk factors. Feedback: This question is designed to ascertain that the student understands the significant simplifications and improvements offered by the single-index model over the Markowitz model. d. Assume that stock market returns do not resemble a single-index structure. An investment fund analyzes 132 stocks in order to construct a meanvariance efficient portfolio constrained by 132 investments. Calculate the number of covariance they will need to calculate? (n²-n)/2 = (17,424 - 132)/2 = 8,646 covariances must be calculated. Question 02 a. The optimal proportion of the risky asset in the complete portfolio is given by the equation y* = [E(re)-rl(.01A times the variance of P). For each of the variables on the right side of the equation, discuss the impact of the variable's effect on y* and why the nature of the relationship makes sense intuitively. Assume the investor is risk averse. The optimal proportion in y is the one that maximizes the investor's utility. Utility is positively related to the risk premium [E(re)-r]. This makes sense because the more expected return an investor gets, the happier he is. The variable "A" represents the degree of risk aversion. As risk aversion increases, "A" increases. This causes y* to decrease because we are dividing by a higher number. It makes sense that a more risk-averse investor would hold a smaller proportion of his complete portfolio in the risky asset and a higher proportion in the risk-free asset. Finally, the standard deviation of the risky portfolio is inversely related to y*. As P's risk increases, we are again dividing by a larger number, making y* smaller. This corresponds with the risk averse investor's dislike of risk as measured by standard deviation. Feedback: This allows the students to explore the nature of the equation that was derived by maximizing the investor's expected utility. The student can illustrate an understanding of the variables that supersedes the application of the equation in calculating the optimal proportion in P.

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c The singleindex model offers several advantages over the Markowitz model in terms of the number of ... View the full answer