Why are overlapping returns tricky when estimating multi-day VaR?

Question

AcadiFi · Accepted Answer

Overlapping returns create more multi-day observations from the same history, but those observations are not independent. For example, ten-day return windows that roll forward one day share nine days of data. That increases the apparent sample size without creating fully new information. The result can be a smoother empirical distribution but misleading inference if dependence is ignored.

Suppose Northstar Risk Control has 1,000 daily returns and wants a ten-day VaR. Nonoverlapping ten-day blocks produce about 100 observations, which may feel too few. Overlapping windows produce nearly 991 observations, but adjacent windows are highly related. The analyst gains more percentile detail but not 991 independent observations.

```mermaid
flowchart LR
  A[Daily returns] --> B[Nonoverlapping 10-day blocks]
  A --> C[Overlapping 10-day windows]
  C --> D[More observations but dependent]
```

For FRM purposes, overlapping data is a practical tool, not a free lunch. It can help estimate an empirical multi-day distribution, but backtesting, confidence intervals, and model validation must account for dependence. If a question treats overlapping windows as independent without qualification, that is a red flag. On the exam, also state the horizon, confidence level, data source, modeling assumption, and validation step, because those choices usually explain why two reasonable VaR answers differ materially. Practice more in our FRM question bank.

Why are overlapping returns tricky when estimating multi-day VaR?

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