Which of the following values represents a safe estimate for a portfolio's downside risk at the 95% confidence level?

To determine a safe estimate for a portfolio's downside risk at the 95% confidence level, it's important to understand how downside risk is quantified in the context of statistical measures. Downside risk typically refers to the risk of experiencing losses, which can be effectively measured using standard deviation, particularly in a normally distributed return scenario.

At the 95% confidence level, we are looking to estimate the potential loss that could occur in the worst 5% of scenarios. For a normally distributed return, the value corresponding to the 95% confidence interval can be derived from the properties of the normal distribution. Specifically, the z-score that captures the left tail of the normal distribution at the 95% confidence level is approximately 1.65. This means that around 95% of the returns can be expected to fall within 1.65 standard deviations of the mean.

By multiplying the standard deviation of returns by 1.65, you can estimate the downside risk—that is, the expected loss that would occur in the most adverse 5% of scenarios. This provides a reasonably safe estimate because it effectively incorporates the volatility of the portfolio while recognizing the statistical distribution of return outcomes.

Thus, using 1.65 times the standard deviation offers a practical and