7, Note that this is an extension of Question 6 from Problem Set #2. Suppose there are three possible states of the market,-1 (good),j -2 (average) and j -3 (bad). Each state occurs with probability p and for each, the returns for three assets (AB and C) denoted R. R,B and R c are given in the following table: State (0) 1/3 1/3 1/3 0.34 0.10 -0.10 0.20 0.10 0.00 0.10 0.10 0.10 From the table, we see that asset C is a riskless asset with a sure return of 10%. Also, let the utility function for the investor be U(R-In(1+ R) where In represents the natural logarithm and R is the realized net return of an asset or portfolio. (Note that if you plug in values for R and plot the results, you will get a graph that looks something like what I had on the board in class on Monday. a. Calculate the expected return and standard deviation associated with each asset. b. Ra nk the three portfolios from least to most risky using an appropriate measure. Specify the measure you are using. c. Show that for assets A and B, an investor with the given utility function always prefers a sure payment equal to the expected return of that asset rather than holding the asset itself. For asset C show that the investor would be indifferent. Recall that as discussed in lecture, the expected utility associated with holding a particular asset k A, B, C is given by n your calculations in part c, rank the desirability of each asset according to the preferences of the investor Suppose that a fourth asset, Asset D, is available and is a portfolio consisting of equal shares of Assets A, B, and C. Calculate the expected return and standard deviation of Asset D. Is it preferred to Assets A, B and C? Explain and justify your answer. e