Question

Suppose two investments have the same three payoffs but the probability associated with each payoff differs, as illustrated in the table below:

Payoff Probability (Investment A) Probability (Investment B)

$300 0.10 0.30

$250 0.80 0.40

$200 0.10 0.30

Find the expected return and standard deviation of each investment. Jill has the utility function U=5I, where I denotes the payoff.

Answer 1

For Investment A, the expected return is $250, and the standard deviation is $35.36. For Investment B, the expected return is $250, and the standard deviation is $28.87.

Step-by-step explanation:

To calculate the expected return, we multiply each payoff by its respective probability and sum the results.

For Investment A: (0.10 * $300) + (0.80 * $250) + (0.10 * $200) = $250.

For Investment B: (0.30 * $300) + (0.40 * $250) + (0.30 * $200) = $250.

To calculate the standard deviation, we use the formula:

Standard deviation = sqrt[Σ(Probability * (Payoff - Expected Return)^2]. The standard deviation for Investment A is $35.36, and for Investment B, it is $28.87.

Both investments have the same expected return of $250, but Investment B has a lower standard deviation, making it less risky. Considering Jill's utility function U=5I, she may prefer Investment B as it provides the same expected return with lower risk, aligning with the concept of risk-averse behavior in utility theory.