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Problem 1 . ( 1 5 points ) Suppose an investor wants to invest V 0 = 1 0 0 0 in 5 stocks and
Problem points Suppose an investor wants to invest in stocks and riskfree asset over an investment horizon of day. The return on the riskfree asset is exp and the oneday returns for the stocks have expected values and standard deviations given by a Determine the optimal amounts to be invested today in the stocks and the bond in order to maximize the expected portfolio value tomorrow when the standard deviation of the portfolio value tomorrow is not allowed to exceed The investor supposes that all returns are uncorrelated with each other. Shortselling is allowed. b Suppose instead that you want to maximize the expected value of but now allowing for a portfolio standard deviation up to Explain how you can compute the new optimal investment amounts from the ones in a by multiplication with a constant. c Under the same conditions as in a suppose all random returns are normally distributed. What is the distribution of the optimal portfolio value? Plot the density function of the optimal portfolio value. Use Matlab when necessary
Problem points Suppose an investor wants to invest in stocks and riskfree asset over an investment horizon of day.
The return on the riskfree asset is exp and the oneday returns for the stocks have expected values and standard deviations given by
a Determine the optimal amounts to be invested today in the stocks and the bond in order to maximize the expected portfolio value tomorrow when the standard deviation of the portfolio value tomorrow is not allowed to exceed The investor supposes that all returns are uncorrelated with each other. Shortselling is allowed.
b Suppose instead that you want to maximize the expected value of but now allowing for a portfolio standard deviation up to Explain how you can compute the new optimal investment amounts from the ones in a by multiplication with a constant.
c Under the same conditions as in a suppose all random returns are normally distributed. What is the distribution of the optimal portfolio value? Plot the density function of the optimal portfolio value.
Use Matlab when necessary
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