Annualizing Returns and Volatility from Monthly Data

Summary

The discussion addresses how to turn a series of monthly returns into annualized return and volatility estimates. An answer proposes multiplying the mean monthly return by twelve for an arithmetic annual return estimate, and multiplying the monthly return standard deviation by the square root of twelve for annualized volatility. It also notes that returns may be expressed as log returns instead.

These are common scaling conventions, but the exchange does not explain the distinction between arithmetic annualization and a compounded annual growth rate. Nor does it show calculations or assess assumptions such as stable return distributions or dependence across months. The question’s attempted product-based calculation is not corrected in detail, so readers should distinguish a geometric annualized growth measure from the simple mean-based estimate offered here.

Key ideas

• Annualized arithmetic return can be estimated as the mean monthly return multiplied by twelve.
• Annualized volatility is estimated by scaling monthly standard deviation by the square root of twelve.
• Log returns are an alternative return representation.
• The answer does not distinguish arithmetic annualization from compounded growth.

Tags

# Calculate annualized returns and annualized volatility from monthly returns?


# Calculate annualized returns and annualized volatility from monthly returns?












I have a dataset with monthly returns (In decimals)

Jan-2008, Feb-2008 .... Dec-2008, Jan-2009 .... Dec-2017

This is what I have done,

```
# Formula (((1+r1/100) * (1+r2/100) .. ) ^ 1/n ) - 1

df["Rate of Return"] = df["Rate of Return"].apply(lambda x: 1+(x/100))
ann_return = pow(df["Rate of Return"].product(), df.shape[0]) - 1
```

This doesn't yield a correct answer though. I'm just confused on how to produce a single number for Annualized Return. I have the same question for calculation on annualized volatility. Can anyone point out the correct method when you have monthly data over multiple years?

P.S. I'm new here, please point out if there is anything wrong with the way this was asked.

## Answer by Quantoisseur (score 2, accepted)

https://quant.stackexchange.com/a/57260

```
ann_return = df["Rate of Return"].mean()*12
ann_vol = df["Rate of Return"].std()*np.sqrt(12)
```

You could also use log returns if desired.

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