2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A...
The universe of available securities includes two risky stocks A and B, and a risk-free asset. The data for the universe are as follows: Assets Expected Return Standard Deviation Stock A 6% 25% Stock B 12% 42% Risk free 5% 0 The correlation coefficient between A and B is -0.2. The investor maximizes a utility function U=E(r)−σ2 (i.e. she has a coefficient of risk aversion equal to 2). Assume that to maximize his utility when there is no available risk-free...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure rate of return rj, the risky asset has a random rate of return r. Suppose the utility function of an investor is U(x) =--. The initial wealth is wo, the dollar amount invested in the risky asset is θ. r is normally distributed with mean μ and variance σ2. Based on the maximum utility framework, find the optimal investment strategy 6. (25...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure rate of return rj, the risky asset has a random rate of return r. Suppose the utility function of an investor is U(x) =--. The initial wealth is wo, the dollar amount invested in the risky asset is θ. r is normally distributed with mean μ and variance σ2. Based on the maximum utility framework, find the optimal investment strategy 6. (25...
An investor's risk aversion determines her a. optimal mix of assets in her risky portfolio b. risk-free rate on borrowing c. Sharpe ratio d. capital allocation line e. optimal risky portfolio f. risk-free rate on lending
Tom has $10,000. He can invest the money in (1) a corporate bond, (2) a stock, and (3) the risk-free T-bill. The table below provides these assets’ expected returns and standard deviations: Bond (D) Stock (E) T-Bill (F) Expected Return 5% 10% 2% Standard Deviation 10% 20% 0 The coefficient of correlation between the corporate bond and the stock (ρDE) is 30%. Tom has a risk aversion coefficient of A=5. To construct the optimal portfolio with two risky assets and...
Exercise 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ~ N(u,02). Show that the CARA utility u(r) = -e-Ar gives the same optimal allocation of wealth to the risky asset as the mean-variance utility function we used in class. That is, show that E[r] – rf OCARA = AO2 Hint: Use the fact that if a random variable x is distributed normally with mean Mx and variance...
(2*5) Consider a market with many risky assets and a risk-free security. Asset’s returns are not perfectly correlated. All the CAPM assumptions hold and the market is in equilibrium. The risk-free rate is 5%, the expected return on the market is 15%. Mr. T and Mrs. R are two investors with mean-variance utility functions and different risk-aversion coefficients. They both invest into efficient portfolios composed of the market portfolio and the risk-free security. Mr. T’s portfolio has an expected return...
Suppose that you have found the optimal risky combination using all risky assets available in the economy, and that this optimal risky portfolio has an expected return of 0.1 and standard deviation of 0.2. The T-bill rate is 0.05. If your risk-return preferences are best described by the utility function in this class, with a risk-aversion coefficient of 5.2. What is the expected return on your optimal complete portfolio? Round your answer to 4 decimal places. For example if your...
Intro Assume that there are only two stocks in the economy, stock A and stock B. The risk-free asset has a return of 3%. The optimal risky portfolio, i.e., the portfolio with the highest Sharpe ratio, is given below: A BC Stock A Stock B Risk-free asset 2 Expected return 0.062 0.075 0.03 3 Variance 0.1521 0.0484 4 Standard deviation 0.39 0.22 5 Covariance 0.02574 D Optimal risky portfolio 8 Weights 9 Expected return 10 Variance 11 Standard deviation 12...
A. Capital Allocation Lines The optimal CAL is found as the ray from the risk free rate that is tangent to the _____________ and is called the ________________. efficient frontier; CML minimum variance portfolio; high range CAL indifference curve; SML lower half of the investment opportunity set; CAPM B. Capital Allocation Portfolio 1 has a standard deviation of 35% and a Sharpe ratio of 0.48. Portfolio 2 has a standard deviation of 29% and a Sharpe ratio of 0.44. Portfolio...