Understanding Value at Risk Implications

Very Hard Risk Management Applications Value At Risk

Consider a financial institution that utilizes a historical simulation approach to calculate its Value at Risk (VaR). The institution has a portfolio of assets that exhibits considerable volatility, and it is crucial for management to understand the potential losses over a specific period. The portfolio return distribution is defined based on the historical returns of the asset classes within the portfolio over the past year.

During the calculation, the institution determines that at a 95% confidence level, the 1-day VaR of the portfolio amounts to $1 million. However, due to some recent changes in the market, the institution faces questions about this estimation.

Assuming that the returns of the portfolio are normally distributed, which of the following statements correctly describes the implications of the calculated VaR?

There is a 5% chance that the portfolio will incur losses greater than $1 million on any given day.

The calculated VaR of $1 million implies that the maximum expected loss on any given day is exactly $1 million.

The institution can expect that the actual loss will not exceed $1 million 95% of the time, barring any extreme market movements.

Hint

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