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Annualizing Daily Alpha, Returns, and Volatility

Article Quant Q&A · Author: Circus_beta
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Summary

The answer addresses how to convert daily performance statistics to annual figures using a trading-year convention. It recommends 252 trading days for daily alpha and average daily returns, and says daily volatility is annualized by multiplying by the square root of that trading-day count. For a fund return measured across multiple days, the question also raises the distinction between simple scaling and compounding, but the answer does not directly work through that example.

The guidance is concise and assumes a daily series aligned to trading days. It does not discuss alternative day-count conventions, the distinction between arithmetic and geometric return estimates, or how to handle irregular observations and holidays. It notes that log daily returns are another possible basis for annualization, without detailing the conversion.

Key ideas

  • The answer uses 252 trading days as the annualization convention for daily returns and alpha.
  • It annualizes daily volatility by scaling with the square root of the trading-day count.
  • Log returns are presented as an alternative input for annualization.
  • The response does not explain the multi-day fund compounding calculation raised in the question.

Tags

StatisticsRisk managementBacktesting
Full text
# Alpha and returns annualized


# Alpha and returns annualized












Basic question , but if I do a daily regression and get an alpha of 0.00004. Should the yearly alpha be : 0.00004 *100 *252 = 1.008% OR 0.00004 * 100 *365 = 1.46%. What is considered the yearly alpha if one wants to know the outperformance of a manager annually? Should one use 252 trading days or 365 days in a year?

Also in the case of fund that has a total performance of 25% in 500 days, should the formula to annualize be : 1.25^(252/500)-1 OR 1.25^(365/500)-1 ?

## Answer by Quantoisseur (score 2)

https://quant.stackexchange.com/a/57302

You should use 252 trading days.

To annualize returns, multiply the average daily return by 252.

To annualize volatility, multiply the daily volatility by sqrt(252).

You can also use log daily returns if you prefer.

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