Assume that the return for the risk-free asset is rf=0.0004 and the rate of return on the risky asset is ra. Using a long span of data we estimate that the mean of ra is p=0.007. The standard deviation of rp is p=0.04.

Part 1

What is the Sharpe ratio of the risky asset?

Part 2

What is the intercept of the Capital Allocation Line ?

(By intercept we mean the coordinate on the vertical axis of the point where the line intersects the vertical axis)

Part 3

What is the slope of the Capital Allocation Line?

Part 4

Consider a portfolio with a share w invested in the risky asset and (1-w) in the risk free asset. What is the Sharpe ratio of this portfolio?

Part 5

If a share w=0.8 of your portfolio is invested in the risky asset (and 1-w in the risk free asset), what is the expected return (_c) of your portfolio?

Part 6

If a share w=0.8 of your portfolio is invested in the risky asset (and 1-w in the risk free asset), what is the standard deviation of returns (_c) from your portfolio?

Part 7

Instead of taking w as given, now we will find the optimal w for an investor with risk preferences described by the following utility function: U=_c-10_c² . What is the optimal value of w that maximizes the investor's utility given the available capital allocations? (To solve this part, first substitute expression for _c and _c in the utility functions, then take the first order derivative with respect to w, set it equal to zero and solve for w.)

Part 8

Consider a different investor, whose preferences are described by the following utility function: U=_c-A_c² ,where A is the investor's degree of risk aversion. What is the investor's degree of risk aversion if the investor's optimal choice is to hold only shares of the risky asset?

Problem3 Intro Assume that the return for the risk-free asset is r 0.0004 and the rate of return on the risky asset is ra. Using a long span of data we estimate that the mean of ra is ,-0.007. The standard deviation of rp is ,-0.04