Final answer:
To calculate the probability of a negative return for two mutual funds, one with high risk and one with less risk, we use the Z-score formula and standard normal distribution. The Z-score measures how many standard deviations a zero return is from the mean, and this value is then used to find the corresponding probability of a negative return.
Step-by-step explanation:
The student asks about calculating the probability of earning a negative return for two mutual funds with different risk-return profiles. To find the probability of a negative return, we'll assume a normal distribution of returns for both funds due to the provided expected return and standard deviation. For the riskier fund with an expected return of 12.5% and a standard deviation of 19.2%, and the less risky fund with an expected return of 4.1% and a standard deviation of 5.9%, we can use the Z-score formula to find the probability.
Z-score is calculated as (X - μ) / σ, where X is the value for which you want to find the probability, μ is the mean or expected return, and σ is the standard deviation. Here, the value of X is 0 (since we're looking for the probability of a negative return), so the Z-score would indicate how many standard deviations away from the mean a zero return is.
For the risky fund, the Z-score is (0 - 12.5) / 19.2, and for the less risky fund, (0 - 4.1) / 5.9. After calculating the Z-scores, we'd consult the standard normal distribution table or use a statistical software to find the corresponding probabilities.
Understanding the risk-return tradeoff and the expected rate of return is essential for making informed investment decisions. Investments with higher risk typically offer higher potential returns to compensate investors for the increased uncertainty. The probability of a negative return is just one aspect of the overall risk.