Question

assume an investor with the following utility function : U= E(r) - 0.60 (s2)

to maximize her expected utility, which one of the following investment alternatives would she choose?

A. a portfolio that pays 10% with a 60% probablility or 5% with 40% probability
B. A portfolio that pays 12% with 40% probability or 5% with 60% probability
C. A portfolio that pays 10% with 40% probability or 5% with a 60% probability
D. A portfolio that pays 12% with 60% probability or 5% with 40% probability

Answer 1

U = E(r) - 0.60(s2)

s is the standard deviation and E(r) is the expected return. So, s2 is the variance.

Please find the image of the excel.

A B с D E F 20 21 22 23 24 25 26 27 28 29 30 Probability Return 0.6 10% 0.4 5% Expected Return U Probability * Return Variance 0.06 0.02 0.08) 0.0006 0.07964 31 Probability * Return Variance 0.03 Probability Return 0.6 5% 0.4 12% Expected Return U 0.048 32 33 34 35 36 37 38 0.001176 0.078 0.0772944 39 40 Probability Return Probability* Return Variance 0.6 5% 0.03 0.4 10% 0.04 Expected Return 0.07 0.0006 U 0.06964 41 42 43 44 45 46 47 Probability Return 0.6 12% 0.4 5% Expected Return U Probability* Return Variance 0.072 0.02 0.092 0.001176 48 0.0912944 49 50 51

A B С D E F Probability Return Variance 0.6 0.4 0.1 0.05 Expected Return U Probability* Return =D25*C25 =D26*C26 =SUM(E25:E26) =E27-0.6*F27 ={(E27-D25)^2) *C25)+(((E27-D26)^2)*C26) 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 Probability Return Variance 0.05 0.6 0.4 0.12 Probability * Return =D32* C32 =D33*C33 =SUM(E32:E33) =E34-0.6*F34 Expected Return =(((E34-D32)^2) *C32)+(((E34-D33)^2) *C33) U Probability Return Variance 0.6 0.05 0.4 0.1 Probability * Return =D39*C39 =D40*C40 =SUM(E39:E40) =E41-0.6*F41 Expected Return =(((E41-D39)^2)*C39)+(((E41-D40)^2)*C40) U Probability Return Variance 42 43 44 45 46 47 48 49 50 0.6 0.12 0.4 0.05 Expected Return Probability * Return D46*C46 =D47*C47 =SUM(E46:E47) =E48-0.6*748 =(((E48-D46)^2)*C46)+(((E48-D47)^2)*C47) U

Thus, the correct asnwer is option D as U is maximised in D.

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