Interpretation of Portfolio VaR

Very Hard Risk Management Applications Value At Risk

Consider an investment manager who is evaluating the potential risks associated with a new portfolio consisting of various asset classes, including equities, fixed income, and derivatives. The manager wishes to estimate the Value at Risk (VaR) for this portfolio over a one-day holding period at a 95% confidence level.

To calculate the VaR, the manager uses historical simulation, examining the returns from the past 250 trading days. Of the 250 observed returns, the manager finds that 12 of these returns have been losses that exceeded the estimated threshold for the 5% worst-case scenarios.

Given these findings, which of the following interpretations about the portfolio's VaR is most accurate?

The estimated one-day VaR is $X if the portfolio's value is $1 million, indicating that there is a 5% chance the portfolio will lose more than $X on any given day.

The estimated one-day VaR is $X which reflects that the portfolio is expected to lose exactly $X on 5% of trading days.

The estimated one-day VaR is $X meaning there is a margin of safety of $X beyond which losses are expected to occur on only 5% of trading days.

Hint

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