Question

You are considering the risk-return profile of two mutual funds for investment. the relatively risky fund promises an expected return of 7.5% with a standard deviation of 11.2%. the relatively less risky fund promises an expected return and standard deviation of 4.8% and 6.7%, respectively. assume that the returns are approximately normally distributed. a-1. calculate the probability of earning a negative return for each fund. note: do not round intermediate calculations. round your final answers to 4 decimal places.

Answer 1

The probability of earning a negative return for the risky fund is approximately 0.2514, and for the less risky fund, it is approximately 0.2368, after looking up the calculated Z-scores in a Z-table and rounding to four decimal places.

Step-by-step explanation:

To calculate the probability of earning a negative return for each mutual fund, we'll model the returns using a normal distribution with the respective expected returns and standard deviations. We use the Z-score formula to find the number of standard deviations our point of interest (a return of 0%) is from the mean (expected return).

For the relatively risky fund with an expected return of 7.5% and standard deviation of 11.2%, the Z-score is calculated as:

Z = (0 - 7.5%) / 11.2%

Z ≈ -0.6696

For the relatively less risky fund with an expected return of 4.8% and a standard deviation of 6.7%, the Z-score is:

Z = (0 - 4.8%) / 6.7%

Z ≈ -0.7164

Next, we look up these Z-scores on a standard normal distribution table to find the probabilities of a negative return.

Using a Z-table and rounding to four decimal places:

Probability of a negative return (risky fund) ≈ 0.2514

Probability of a negative return (less risky fund) ≈ 0.2368

Thus, the fund with a higher expected return also has a higher probability of a negative return, reflecting its higher risk.