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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?

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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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  • $\begingroup$ Risk is wrong. You have a daily P&L, therefore you should annualize using SQRT(252). It makes no sense to annualize a daily P&L derived volatility with SQRT(5)*SQRT(252), that just makes the Sharpe "more stellar" (if you annualize the volatility, you have annualize the expected return using the same multiple). If anything, I would suspect there is something strange with using a moving average P&L. I have never seen this before. $\endgroup$
    – KaiSqDist
    Commented Oct 4 at 13:04
  • $\begingroup$ Hi thanks so much for your response, it really helps. What I was saying is that I have a series of 5 day moving average pls. So my pl or pl return today is the moving average of the last 5 days including today. Tomorrow it will be the moving average of the last 5 days too but will overlap with some of the numbers from today. We initially thought you'd use SQRT 252 to annualise but this produces what we see as Stellar sharpe numbers! Risk is telling us we need to annualise using SQRT 5 * SQRT 252. SO I am very confused; this latter approach doesn't move the needle on sharpe vs bog standard calc $\endgroup$
    – V S
    Commented Oct 4 at 13:06
  • $\begingroup$ thanks - to be clear if my returns in Column S is a rolling average 5 day daily return - then to calculate my Sharpe using this 5 Day Daily MA - I take the Average of all of these returns x 252 (to annaulise returns) and to annualise the vol I take the STDEV.S (Col S) * SQRT (252) - Is that what you are saying and NOT multiply by an additional term of SQRT (5) for the denominator? Seems like we have a mixed view on this $\endgroup$
    – V S
    Commented Oct 4 at 13:15
  • $\begingroup$ Yes, that is what I am saying. That is the normal way to calculate Sharpe. $\endgroup$
    – KaiSqDist
    Commented Oct 4 at 13:20
  • $\begingroup$ Thanks so much that was v useful to follow $\endgroup$
    – V S
    Commented Oct 4 at 14:16

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