Question

Consider an investor with preferences given by the utility function U = E(r) - 0.5A0- and there are two portfolios with the following characteristics: Portfolio A Portfolio B E(r) = 0.148 O=0.16 E(T) = 0.082 o= 0.068 (a) Suppose that the investor has a level of risk aversion of A = 4. Which portfolio should the investor choose? [3 Points] (6) Suppose that the investor has a level of risk aversion of A = 6. Which portfolio should the investor choose? [3 Points] (C) Suppose the investor has a level of risk aversion of A = 4 What must the return be on a risk-free asset in order for the investor to be indifferent between investing in the risk-free asset and Portfolio B? [3 Points] (d) Suppose the investor has a level of risk aversion of A = 4. Calculate the risk-premium associated with Portfolio B. Assume that the risk-free rate is the same as your answer in Part(c). [3 Points]

Answer 1

a.  

U = E(r) - 0.5 A. s^2

A = 4

Portfolio A:

E(r) = 0.148

s =0.16

Portfolio B

E(r) = 0.082

s =0.068

putting these values in the equation

portfolio A, U = 0.148 - 0.5*4* (0.16^2) =0.0968

portfolio B, U = 0.082 - 0.5*4*(0.068^2) = 0.0727

As we see, the investor gets higher utility from portfolio A, so it should be selected.

b. Again using the above equations, with A = 6

we get portfolio A = 0.0712

B =0.0681

As we see, the investor gets higher utility from portfolio A, so it should be selected.

Although the investor is more risk averse in this scenario compared to first one, but still the utility from portfolio A is slightly better that that of B.

c.

Fir a risk free asset, the standard deviation = 0

and with A =4, we'll equate the risk free asset utility with that of portfolio B

E(r) - 0.5*0 = 0.082 - 0.5*4*(0.068^2)

So expected return from risk free asset E(r) =0.0727 = 7.27%

d.

Return from the portfolio B at A=4 => =0.0727 = 7.27%

also the expected return from the risk free asset is also the same as that of portfolio B.

So risk premium of B should be same as that risk free asset i.e. = 0

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