Annualizing Cumulative Log Returns Over Weekly Observations

Summary

The document asks how to annualize a ten-year strategy result expressed as the sum of weekly log returns. It proposes scaling the cumulative log return by the ratio of weeks in a year to weeks observed, and asks whether that gives an annual return. The answer says this scaling is reasonable when returns do not compound, and points out that log returns are additive across time. To express a cumulative log return as an ordinary holding-period return, exponentiate it and subtract one; averaging log returns and converting in this way gives a per-period growth interpretation.

The exchange offers a short conceptual clarification rather than a complete treatment of annualized performance. It does not specify whether the reported figure is a log return or an ordinary percentage return, and the answer leaves the role of compounding and the asset class unresolved. Applying simple proportional scaling directly to an ordinary cumulative return can be misleading when returns compound. Annualization should therefore preserve the distinction between arithmetic returns and log returns, and should state the convention used.

Key ideas

• Log returns add across consecutive periods.
• Scaling a cumulative log return by periods per year gives an average annualized log-return rate.
• Convert a cumulative log return to an ordinary return by exponentiating it and subtracting one.
• Annualization conventions depend on whether compounding is included.

Tags

# Annualized Log Returns


# Annualized Log Returns












I backtested an investment strategy over ten years (521 weeks to be specific) and calculated the weekly return using log returns. The sum of all weekly returns added up to 145%. How do I annualize this return? Is my assumption correct to simply calculate: (145/521)*52 to get the annual return?

Thanks for your help

## Answer by Jan Sila (score 0, accepted)

https://quant.stackexchange.com/a/28362

Is it bonds or stocks? If there is no compounding, then I think it should be correct your way. Also if its log returns, you need to sum them and take expectation of them. That will give you the usual 1+R return. As in if you went from 100 to 105, you get 1.05.

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