
Financial Risk Manager Part 1
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A pension fund's market risk manager is tasked with calculating the annual Value at Risk (VaR) for a diversified portfolio of investment securities. The portfolio currently holds a market value of USD 7,444,000. The manager has observed that the daily variance of the portfolio’s returns is 0.0002. It is assumed there are 250 trading days in a year, with the daily returns being independent, identically distributed, and following a normal distribution with a mean of zero. Based on this information, what is the projected 1-year VaR at the 95% confidence level?
A pension fund's market risk manager is tasked with calculating the annual Value at Risk (VaR) for a diversified portfolio of investment securities. The portfolio currently holds a market value of USD 7,444,000. The manager has observed that the daily variance of the portfolio’s returns is 0.0002. It is assumed there are 250 trading days in a year, with the daily returns being independent, identically distributed, and following a normal distribution with a mean of zero. Based on this information, what is the projected 1-year VaR at the 95% confidence level?
Explanation:
The correct answer to the question is C, which is USD 2,737,737. This is calculated using the "square root rule" for scaling up the daily standard deviation to an annual figure. The daily standard deviation is derived from the daily variance by taking the square root of 0.0002, resulting in 0.01414. To estimate the annual Value at Risk (VaR) at a 95% confidence level, the following steps are taken:
- Calculate the daily standard deviation: .
- Use the square root rule to scale the daily standard deviation to an annual figure: .
- Multiply the annualized standard deviation by the portfolio's market value and the z-score corresponding to the 95% confidence level (which is approximately 1.645 for a normal distribution).
- The calculation is as follows: .
Option A is incorrect because it uses the variance instead of the standard deviation in the VaR formula. Option B is incorrect as it represents the 1-day VaR at the 95% confidence level, not the annual VaR. Option D is incorrect because it calculates the 1-year VaR at a 99% confidence level, not the 95% level required by the question.