Investor Tastes over Risk and Return: Suppose you are considering where to Invest money for the future.

Question:

A: Like most investors, you care about the expected return on your investment as well as the risk associated with the investment. But different investors are willing to make different kinds of tradeoffs relative to risk and return.

(a) On a graph, put risk on the horizontal axis and expected return on the vertical. (For purposes of this exercise, don't worry about the precise units in which these are expressed.) Where in your graph would you locate "safe" investments like inflation indexed government bonds €” investments for which you can predict the rate of return with certainty?

(b) Pick one of these "safe" investment bundles of risk and return and label it A. Then pick a riskier investment bundle B that an investor could plausibly find equally attractive (given that risk is bad in the eyes of investors while expected returns are good).

(c) If your tastes are convex and you only have investments A and B to choose from, would you prefer diversifying your investment portfolio by putting half of your investment in A and half in B?

(d) If your tastes are non-convex, would you find such diversification attractive?

B: Suppose an investor has utility function u(x₁,x₂) = (R ˆ’x₁)x₂ where x₁ represents the risk associated with an investment, x₂ is the expected return and R is a constant.

(a)What is the MRS of risk for return for this investor.

(b) Suppose A is a risk free investment, with xf = 0, and suppose that B is risky but our investor is indifferent between A and B. What must the return Investor Tastes over Risk and Return: Suppose you are considering the risk-free investment be in terms of

(c) Do this investor's tastes satisfy convexity? Illustrate by considering whether this investor would be willing to switch from A or B in part (b) to putting half his investment in A and half in B.

(d) Suppose R = 10 for our investor. Imagine he is offered the following 3 investment portfolios:

(1) a no-risk portfolio of government bonds with expected return of 2 and 0 risk; (2) a high risk portfolio of volatile stocks with expected return of 10 and risk of 8; or a portfolio that consists half of government bonds and half of volatile stocks, with expected return of 6 and risk of 4.

Which would he choose?

(e) Suppose a second investor is offered the same three choices. This investor is identical to the first in every way, except that R in his utility function is equal to 20 instead of 10. Which

portfolio will he choose?

(f) True or False: The first investor's tastes are convex while the second one's are not.

(g) What value of R would make the investor choose the no-risk portfolio?

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