Suppose an investor has the utility function U(R,s) = R - 0.3s^2 (Here, R denotes the expected rate of return (R) of their investment portfolio and s denotes the risk associated with that portfolio, but this information is not necessary to solve this problem.)
a. Find a formula for the marginal rate of substitution in consumption (MRSC) of s for R. [Hint: This is the absolute value of the slope of the indifference curve, when R is on the vertical axis and s is on the horizontal axis.]
According to the Capital Asset Pricing Model, if there is a risk-free asset with a return of 4 percent, and if the market return is 10 percent with a standard deviation of 20 percent, then the investor faces a constraint of R = 4 + (10-4)/20s or R = 4 + 0.4s
b. Compute the slope of the constraint, dR/ds .
c. Compute the values of R and s that this investor will choose. [Hint: Set your answer to (a) equal to your answer to (b) and solve for s. Then insert this into the constraint to find R.]