Reference no: EM132459575
1. The table below shows the capital market forecasts for portfolios H, J, and K, respectively. Use the information to answer questions (a) through (f). Show the calculation steps that support your answers.
State of economy. Probability. Return on Port H. Return on Port J Return on Port K
Good 0.2 20% 16%. 2%
Mild 0.6 10% 8% 12%
Bad 0.2 5% 4% 17%
(a) What are the expected returns of portfolios H, J, and K, respectively?
(b) What are the deviations from their own expected returns of portfolios H, J, and K in three scenarios, respectively? [Hint: you need to find nine different numbers for this question.]
(c) What are the variances of the returns of portfolios H, J, and K, respectively? (Round to six decimal places, i.e., four decimal places in percentage.)
(d) What are the standard deviations of the returns of portfolios H, J, and K, respectively?
(e) What are (1) the covariance between the returns of portfolios H and J, (2) the covariance between the returns of portfolios H and K, and (3) the covariance between the returns of portfolios J and K, respectively? (Round to six decimal places, i.e., four decimal places in percentage.)
(f) What are (1) the correlation coefficient between the returns of portfolios H and J, (2) the correlation coefficient between the returns of portfolios H and K, and (3) the correlation coefficient between the returns of portfolios J and K, respectively?
2. Show that the Sharpe ratio is the same for any portfolios on the same Capital Allocation Line (CAL).
3. Suppose you can invest in fund R&R (named after Risk and Return), which manages a portfolio with an expected return of 15% and a standard deviation of 20%. At the same time, the T-bill rate is 8%.
Answer questions (a) and (b) and show the calculations that support your answers.
(a) For an investor whose complete portfolio consists of 70% R&R and 30% T-bills, what is the implied risk aversion of this investor?
(b) For an investor with a risk aversion of 5 and allocates her investment budget between R&R and T-bills, what is the proportion ( ) that she would allocate to R&R that generates the highest expected return while satisfying her risk tolerance?