What are the most common problems when scaling VaR across time?

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AcadiFi · Accepted Answer

Three structural issues plague time scaling. First, volatility is time-varying; a ten-day horizon almost certainly spans regime shifts that a daily vol does not reflect, so naive scaling understates risk in quiet periods and overstates it after a shock. GARCH or EWMA models mitigate this but introduce their own parameter risk. Second, correlations are time-varying; portfolio VaR depends on a correlation matrix that tends to rise during stress — a phenomenon called correlation breakdown — so scaled VaR built from calm-period correlations misses crisis concentration. Third, liquidity horizons differ by asset class; a sovereign bond may close out in one day while a structured credit bond needs thirty. Scaling all positions to a common horizon forces inaccurate haircuts. FRTB addresses this with liquidity horizons ranging from 10 to 120 days per risk factor. ```mermaid flowchart TD V[Daily VaR] --> T{Scale by sqrt T} T --> V1[Volatility shifts
break IID] T --> C1[Correlation
breakdown] T --> L1[Liquidity
mismatch] ``` Additional issues include fat tails where tail quantiles scale faster than sqrt(n), path-dependent payoffs like barriers where the distribution at horizon depends on the full path, and funding risk where a multi-day loss may trigger margin calls absent from single-day simulations. Best practice is to simulate at the target horizon when possible and reserve scaling for short extrapolations only.

What are the most common problems when scaling VaR across time?

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