Risk Horizon and Holding Period

A risk number is meaningless without a time horizon attached to it: "1-day 95% VaR of $2 million" and "10-day 95% VaR of $2 million" describe very different risk profiles, even though the dollar figure is identical. The holding period is how long you assume a position stays on before it could be liquidated or re-hedged, and the risk horizon is the length of time the risk measure is meant to cover — for a regulatory capital calculation they're usually made to match, but a desk's actual holding period and the horizon its risk system reports can easily diverge.

The common shortcut for stretching a short-horizon estimate to a longer one is the square-root-of-time rule: multiply a 1-day risk figure by $\sqrt{10}$ to approximate a 10-day figure, which is exact only if returns are independent and identically distributed with constant volatility. Real markets violate both assumptions — volatility clusters, and a position can't always be liquidated smoothly over 10 days without moving the market — so the rule tends to understate the true multi-day risk, especially for illiquid positions where the assumed holding period doesn't match how quickly you could actually exit.

A 1-day VaR of $1 million scaled naively by $\sqrt{10} \approx 3.16$ gives a 10-day estimate near $3.16 million; if the position is actually illiquid enough to need 20 days to unwind without excess market impact, the true 20-day risk is materially understated by using the wrong horizon.