Understanding Value at Risk in Portfolio Management

Hard Risk Management Applications Value At Risk

XYZ Asset Management has constructed a diversified portfolio consisting of equities and corporate bonds. The firm wishes to assess the risk of potential losses in this portfolio using Value at Risk (VaR). The portfolio's current market value is $10 million, and the expected annual return is 8%, with a volatility of 15%. After employing a historical simulation method, the firm observed that, under normal market conditions, the maximum loss over a one-month horizon was $1.2 million in 95% of the cases.

XYZ wants to understand its risks better and considers adjustments to their risk profile. Specifically, they are contemplating how much capital they should reserve based on their VaR calculation to handle potential adverse movements confidently. Which of the following scenarios best represents the implications of holding a 95% VaR of $1.2 million?

There is a 5% chance that the portfolio could lose more than $1.2 million in one month.

Holding a VaR of $1.2 million implies they will not lose more than $1.2 million in 95% of the months.

To be fully insulated against market downturns, they should hold capital equal to the expected losses of $1.2 million plus their expected return.

Hint

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