medium · FRM Part 1 Valuation and Risk Models
A fund manager calculates the 10-day 99% Value at Risk (VaR) for a $100 million portfolio as $8 million assuming daily returns are independent and identically distributed.
If the manager later discovers that daily returns exhibit a first-order autocorrelation of ρ = 0.20, how will the 'true' 10-day VaR compare to the initial $8 million estimate?
- The 10-day VaR remains unchanged because VaR is a point-in-time measure and the square-root-of-time rule is robust.
- The true VaR will be higher only if the daily distribution is skewed, as autocorrelation affects shape but not scale.
- The true VaR will be lower because autocorrelation implies the returns are more predictable and less volatile.
- The true VaR will be higher because positive autocorrelation increases the variance of cumulative multi-day returns.
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