Suppose investors are risk averse. Which asset has the highest required return: a risk free asset...
Suppose investors are risk averse. Which asset has the highest required return: a risk free asset or a risky asset? Assume that the expected future payoff for the two assets is the same. Explain.
Homework Answers
When the investors are risk averse, then a risk free asset has the highest required return because an investor who is risk averse will more likely invest his/her money in a risk free asset than a risky asset and since the utility function of the investor is increasing at a decreasing rate with increase in the money, the person will always prefer a risk free asset as compared to a risky asset. If a person chooses a risky asset than the investor has to be compensated with risk premium for the risk taken to purchase the risky asset. Thus, it can be stated that if the investor is risk averse, then a risk free asset provides highest required return to the investor as compared to the risky asset.
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Suppose investors are risk averse. Which asset has the highest
required return: a risk free asset...
Exercise 2. Suppose that there is one risk free asset with return rf and one risky...
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...
Suppose there are two assets, one is risk-free and one is risky. The risk-free asset has a sure r...
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...
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 that risk-averse investors expect the return on a stock to be µ per annum and...
Suppose that risk-averse investors expect the return on a stock to be µ per annum and the risk-free rate is r per annum. In a binomial tree, if µ < r, the real probability of an increase in the stock price is lower than the risk-neutral probability of the increase. (a) True (b) False
A) Calculate the required return for an asset that has a beta of 1.5, given a risk-free rate of 3...
a) Calculate the required return for an asset that has a beta of 1.5, given a risk-free rate of 3% and a market return of 10% b) If investor have become more risk averse due to recent political risk events and the market return rises to 12%, what the required rate of return for the same asset? c) Use your findings in part a to graph the initial security market lines (SML), and then use your findings in part b...
2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A...
2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A and B, have mean-variance utility functions (with different risk aversion coef- ficients). Let P denote investor A's optimal portfolio of risky and risk-free assets and let Q denote investor B's optimal portfolio of risky and risk-free assets. P and Q have expected returns and standard deviations given by P Q E[R] St. Dev. 0.2 0.45 0.1 0.25 (a) What is the risk-free interest rate...
Suppose a risk-free asset has a 5 percent return and a second asset has an expected...
Suppose a risk-free asset has a 5 percent return and a second asset has an expected return of 13 percent with a standard deviation of 23 percent. A portfolio consisting 10 percent of the risk-free asset and 90 percent of the second asset. What is the Sharpe ratio of this portfolio?
Suppose there are three assets: A, B, and C. Asset A’s expected return and standard deviation are 1 percent and 1 percent. Asset B has the same expected return and standard deviation as Asset A. However, the correlation coefficient of Assets A and B is −0
Suppose there are three assets: A, B, and C. Asset A’s expected return and
standard deviation are 1 percent and 1 percent. Asset B has the same expected
return and standard deviation as Asset A. However, the correlation coefficient of
Assets A and B is −0.25. Asset C’s return is independent of the other two assets.
The expected return and standard deviation of Asset C are 0.5 percent and 1
percent.
(a) Find a portfolio of the three assets that...
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%...
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...
Suppose the risk-free interest rate is 3 %, and the stock market will return either plus...
Suppose the risk-free interest rate is 3 %, and the stock market will return either plus 34 % or negative 19 % each year, with each outcome equally likely. Compare the following two investment strategies: (1) invest for one year in the risk-free investment, and one year in the market, or (2) invest for both years in the market. a. Which strategy has the highest expected final payoff? b. Which strategy has the highest standard deviation for the final payoff?...
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...
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...
2. Consider an economy with 2 risky assets and one risk free asset. Two investors, A and B, have mean-variance utility functions (with different risk aversion coef- ficients). Let P denote investor A's optimal portfolio of risky and risk-free assets and let Q denote investor B's optimal portfolio of risky and risk-free assets. P and Q have expected returns and standard deviations given by P Q E[R] St. Dev. 0.2 0.45 0.1 0.25 (a) What is the risk-free interest rate...
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...
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