Choosing an EWMA Half-Life for Multi-Day VaR

Summary

The document asks how to choose the decay half-life when estimating an x-day value at risk (VaR) from an exponentially weighted moving average of return vectors. It gives the relationship between the half-life and the EWMA decay factor, then asks whether the half-life should match the VaR horizon, using a ten-day horizon as an example.

No answer or supporting analysis is included, so the document does not establish a recommended half-life or explain how the choice depends on the return process, forecast horizon, or VaR methodology. Its useful contribution is framing a practical modeling question: the VaR horizon and the rate at which observations lose weight are distinct choices that need justification. Readers should treat it as an open question rather than as guidance or evidence for a particular parameter.

Key ideas

• The EWMA decay factor can be expressed in terms of a chosen half-life.
• The document asks whether the EWMA half-life should equal the VaR horizon.
• It provides no answer or evidence supporting a particular half-life choice.

Tags

# What should the half-life be in EWMA when calculating VaR from EWMA?


# What should the half-life be in EWMA when calculating VaR from EWMA?












If we want to calculate an $x$-day VaR ($x$ is some time period in days) from an Exponentially Weighted Moving Average (EWMA) of vector of returns, what should the half-life in the decay factor in EWMA be?

When calculating the decay factor $\lambda$ from the half life $t_{1/2}$, we have

$$\lambda = \exp\left(\frac{\log(0.5)}{t_{1/2}}\right)$$

What should $t_{1/2}$ be given the VaR period? For example, if we set the VaR period to 10 days, should $t_{1/2}$ also be 10 days? If not, why not?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.