Investment Portfolio Comparison

C

To determine which investor has invested in the optimal portfolio, we need to compare the portfolios of Bill Smythe and Katherine Banning based on their expected return and standard deviation.

1. Expected Return: Bill Smythe's portfolio has an expected return of 14%, while Katherine Banning's portfolio has an expected return of 19%. Higher expected return indicates a potentially better investment in terms of returns.

2. Standard Deviation: Bill Smythe's portfolio has a standard deviation of 10%, while Katherine Banning's portfolio has a standard deviation of 12%. Standard deviation measures the volatility or risk of an investment. A lower standard deviation indicates lower risk.

Now let's evaluate the answer choices one by one:

A. Smythe, since his portfolio has minimized total risk. This answer choice states that Bill Smythe's portfolio has minimized total risk. However, based on the given information, Bill Smythe's portfolio has a higher standard deviation than Katherine Banning's portfolio, indicating higher risk. Therefore, this answer is incorrect.

B. Banning, since the expected return per unit of risk is higher for her investment. This answer choice suggests that Katherine Banning has a higher expected return per unit of risk. To calculate the expected return per unit of risk, we divide the expected return by the standard deviation. Let's calculate this for both portfolios:

For Bill Smythe: Expected return per unit of risk = 14% / 10% = 1.4

For Katherine Banning: Expected return per unit of risk = 19% / 12% ≈ 1.58

As we can see, Katherine Banning's expected return per unit of risk is indeed higher than Bill Smythe's. Therefore, this answer choice is correct.

C. Both, since the optimal portfolio depends on an investor's individual utility function. This answer choice states that both investors have invested in the optimal portfolio based on their individual utility function. While individual preferences and utility functions can vary, the question does not provide any information about their utility functions. Therefore, we cannot conclude that both investors have invested in the optimal portfolio. This answer choice is incorrect.

In conclusion, the correct answer is B. Banning, since the expected return per unit of risk is higher for her investment. Based on the given information, Katherine Banning's portfolio offers a higher expected return per unit of risk compared to Bill Smythe's portfolio.