Question 22: Parameter Uncertainty and James Stein Model (14 marks) Table 3 below provides the sample mean of the rate of return to National Bank of Australia (NBA), the variance of NAB sample mean, the average return of all banks in Australia and its variance. Table 3. Estimates of expected return and estimate uncertainty Parameter Value 15% Sample mean of NAB return (; ) Variance of NAB sample mean (O? /T) 4% Average return of all banks (r*) 10% Variance of average return of all banks of 2% all banks (7; -r*)?/(N 3) ) N i=1 a) Calculate the estimate of NAB expected return when the equal weight method is used to combine NAB sample mean and the average return of all banks. (2 marks) b) Calculate the variance of this estimate and comment on whether the method helps to reduce uncertainty. (3 marks) c) Calculate the estimate of NAB expected return using James Stein method. What is the rationale of James Stein method? (4 marks) d) What is the practical approach to obtain accurate estimates of the standard deviation (that represents risk) of stock returns? (2 marks) e) Explain how the single index model helps to alleviate the problem of estimating the correlation matrix when constructing the optimal portfolio from a large number of stocks. (3 marks) Question 22: Parameter Uncertainty and James Stein Model (14 marks) Table 3 below provides the sample mean of the rate of return to National Bank of Australia (NBA), the variance of NAB sample mean, the average return of all banks in Australia and its variance. Table 3. Estimates of expected return and estimate uncertainty Parameter Value 15% Sample mean of NAB return (; ) Variance of NAB sample mean (O? /T) 4% Average return of all banks (r*) 10% Variance of average return of all banks of 2% all banks (7; -r*)?/(N 3) ) N i=1 a) Calculate the estimate of NAB expected return when the equal weight method is used to combine NAB sample mean and the average return of all banks. (2 marks) b) Calculate the variance of this estimate and comment on whether the method helps to reduce uncertainty. (3 marks) c) Calculate the estimate of NAB expected return using James Stein method. What is the rationale of James Stein method? (4 marks) d) What is the practical approach to obtain accurate estimates of the standard deviation (that represents risk) of stock returns? (2 marks) e) Explain how the single index model helps to alleviate the problem of estimating the correlation matrix when constructing the optimal portfolio from a large number of stocks