Please do the following two questions:

1. Suppose you can invest your money in two assets: A and B. Asset A is risky and its rates of return depend on the state of the economy as follows:

2. Recall that wA denotes the portfolio weight of asset A (proportion of funds invested in A) and wB

1. denotes the portfolio weight of asset B, with wA ? wB ? 1 . The coefficient ? , ?1 ? ? ? 1 measures the correlation between the returns of the assets A and B.

Econ 331 Financial Economics Spring 2017 Assignment 1 Due date: Monday, September 4. Please submit your assignment by 5:00 pm in 40.214. Question 1 Suppose you can invest your money in two assets: A and B. Asset A is risky and its rates of return depend on the state of the economy as follows: State Boom Moderate Growth Recession Probability 0.3 0.4 0.3 Rate of return on A (%) 64 20 -23 Asset B is risk free with the rate of return of 5%. (a) Compute the expected return on asset A and its standard deviation. (b) Compute the expected rate of return and standard deviation of your portfolio if you invest a proportion wA of your money the asset A and 1 wA in asset B. (c) In a graph, represent the different combinations of the portfolio expected return and standard deviation, ( rP , P ) , you can obtain by varying wA . Label on the graph the points corresponding to the following values of wA : 0, 0.25, 0.5, 1. (d) Suppose you decide to adhere to the following rule when constructing your portfolio: never accept portfolios which have standard deviation that is larger than the expected value of the portfolio return. What is the maximum proportion wAMax that you can invest in A without violating this rule? Illustrate your answer on a graph. (e) Does the rule described in (d) guarantee that you will never lose money on your investment? Explain your answer. Question 2 Consider the formula for the variance of the portfolio of two assets discussed in class: 2 P wA2 2 A wB2 2 B 2wAwB A B Recall that wA denotes the portfolio weight of asset A (proportion of funds invested in A) and wB denotes the portfolio weight of asset B, with wA wB 1 . The coefficient , 1 1 measures the correlation between the returns of the assets A and B. (a) Rewrite the above formula as a function of wA only (recall that wA wB 1) (b) Find the portfolio weight w*A which minimizes portfolio variance. (Differentiate the variance expression with respect to wA and solve the FOC for w*A ) 1 . What is the value of w*A in this case? What is the standard deviation of the (c) Suppose that portfolio with wA (d) Suppose that w*A ? A 12 and B 20 . Find the variance minimizing portfolio weight of asset A for each of the following values of the correlation coefficient: 1, 0, 0.3 and 1