Annualizing Volatility for Overlapping Five-Day P&L Returns

Summary

The discussion explains that volatility annualization depends on the time span represented by each observation. For a sequence of overlapping five-day holding-period P&L returns, the stated convention is to treat each observation as five-day volatility and scale it to a year using the square root of the number of five-day periods in a trading year.

A second case is less precisely defined: the question refers to overlapping five-day moving-average P&L returns. The answer distinguishes this from five-day holding-period returns, interpreting it as an average P&L per day; under that interpretation, the series represents daily volatility and uses the usual daily-to-annual scaling. The distinction is conditional on what the averaged series actually measures. Annualization makes volatility figures comparable across horizons, while the chosen horizon remains a separate modeling and reporting choice.

Key ideas

• Annualization should match the time horizon represented by each return observation.
• Five-day holding-period returns are scaled as five-day volatility observations.
• An average of five days of P&L may instead represent daily volatility, depending on its construction.
• The meaning of the moving-average series must be clarified before choosing a scaling factor.

Tags

# Annualisation of volatility


# Annualisation of volatility












we all know the standard way of annualisation of volatility for a series of returns is to multiply by SQRT (252).

What if I have a sequence of overlapping 5 day PL returns used as a series of returns and in addition another sequence of overlapping 5 day Moving Average PL returns as a series of returns. How do I then annualise the volatility in each of these cases? Is is multiply by SQRT (252/5) in the first case and multiply by SQRT (252 *5) in the second case? Doesnt necessarily move the needle in either case, could I be thinking about it wrong?

## Answer by KaiSqDist (score 2, accepted)

https://quant.stackexchange.com/a/80782

The term "a sequence of overlapping 5 day PL returns" refers to overlapping 5-day holding period returns produces weekly volatility and should be annualized with SQRT(252/5).

The term "another sequence of overlapping 5 day Moving Average PL returns as a series of returns" isn't exactly clear. Do you mean the P&L of the 5-days is averaged to give an average P&L per day? In that case, the process returns produces daily volatility and it should be annualized with SQRT(252).

The whole point of annualization is just to provide an apples-to-apples comparison, the period that is used to signify that time's volatility is another thing.

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