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 Probability Rate of return on A (%)

Boom 0.3 64

Moderate Growth 0.4 20

Recession 0.3 -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 ,s 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 that have a standard deviation that is larger than the expected value of the portfolio return. What is the maximum proportion wMaxthat you can invest in A without violating this rule? Illustrateyour answer on a graph.

(e)Does the rule described in (d) guarantee that you will never lose money on your investment? Explain your answer.