Annualising Data

Question

I have a 3 year performance track record of monthly returns. I am trying to calculate the Sortino Ratio, Information Ratio, Treynor index etc.

In calculating the Sharpe Ratio I have multiplied the formula by (sqrt12) to annualise. Does this apply to the other performance measures, ie. multiply by (sqrt12) to annualise it?

Thanks.

Answer 1

It depends on the ratio you are looking at. Most of them are scaled by $\sqrt{12}$, but the Treynor index is a bit different and is scaled by $12$.

Sharpe and Information ratios are both ratios of average returns to standard deviations. They are annualized by assuming that the monthly returns are IID. Hence, average monthly return is scaled up by 12 and standard deviation is scaled up by $\sqrt{12}$. Hence, the final scale factor is $\sqrt{12}$. A full description is available at How to annualize Sharpe Ratio?

The Sortino ratio is the ratio of average excess return to downside standard deviation. So, annualizing the Sortino ratio involves annualizing the downside standard deviation, but this is very similar to annualizing the standard deviation. The annual downside standard deviation is $\sqrt{12} \times$ the monthly value, and this again leaves us to scale up the monthly Sortino ratio by $\sqrt{12}$.

The Treynor ratio is the ratio of the average excess return to the market beta. The market beta does not change when considering annual returns. Hence, the Treynor ratio is scaled up by 12 because the average return is the only element that needs to be annualized.