Annualizing Returns Without Compounding Short-Period Gains

Summary

The document examines why annualized return can appear extreme when a monthly return exceeds 100%. It contrasts the user's compound-growth calculation, which raises the growth factor to an annualization exponent, with a proposed arithmetic annualization: scale the period return by the number of trading days in a year relative to the period length. The question also gives a separate volatility formula that scales daily volatility by the square root of the annual trading-day count.

The reply frames the issue as confusing compounding with annualizing an expected return. Its suggestion is a simple linear scaling, not a universal replacement for compound annual growth calculations. The excerpt provides no derivation, assumptions about return distributions, or clarification about whether the input is a total realized return or an average periodic return. The appropriate measure therefore depends on the purpose and return convention; the brief answer alone does not settle that choice.

Key ideas

• Compounding a large period return can produce a very large annualized growth figure.
• The reply suggests scaling a period return linearly by the annualization factor when annualizing expected returns.
• The stated volatility convention scales daily volatility by the square root of the annual trading-day count.
• Choosing between compounded growth and linear annualization depends on the return measure and analysis purpose.

Tags

# exploded annualized returns and volatilities when period return larger than 100%?


# exploded annualized returns and volatilities when period return larger than 100%?












When my monthly returns is larger than 100%, I get very weird output for annualized return and volatility as follows:

```
Return [%]          Annual Return [%]   Volatility (Ann.) [%]
198.149674908792    49341369.7397401    703.361571453399
```

the formula I used:

```
annual_return = (1 + total_return / 100) ^ (252/duration.days) -1 
annual_volatility = daily_volatility * sqrt(252)
```

total_return is the monthly returns in %.

duration.days: # days in the calculation period, usually a month

Which part did i get wrong? or there are special formula to calculate periodic returns that is larger than 100%? Thanks.

## Answer by KaiSqDist (score 1, accepted)

https://quant.stackexchange.com/a/80685

I see the problem, you are compounding, not annualizing. Annualizing the returns is just multiplying the expected returns. For example, you should divide by duration.days and multiply by 252 instead of using an exponent.

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