# Multi year performance evaluations [closed]

first question here on StackExchange;

I would value your help, I am on excel working with a 3 year / 36 month investment performance. I am calculating the Sharpe Ratio as follows;

Cell KV32 = Average return (of 36 months)

Cell KX32 = risk free rate

Cell KV34 = St. Dev. of 36 months.

Formula = ((KV32 - KX32)/KV34)*Sqrt(36)

Is this the correct formula to calculate the annualized Sharpe Ratio? Also, I am calculating the M^2, Treynor, Jensons Alpha metrics etc. Do these require to be multiplied by Sqrt(36)?

Thank you in advance!!

## closed as off-topic by amdopt, Helin, Attack68♦, LocalVolatility, Bob Jansen♦Jul 31 '18 at 10:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – amdopt, Helin, Attack68, LocalVolatility, Bob Jansen
If this question can be reworded to fit the rules in the help center, please edit the question.

## 1 Answer

No, if you want to calculate the annualized sharpe ratio you should

1) make sure that your risk free rate is in monthly terms (so if it's 3% annual you need to put .03/12 in cell KX32)

2) only multiply the result by the square root of 12 (not 36).

To calculate the annualized sharpe ratio, you multiply the monthly ratio by the square root of the periodicity, in this case 12 months in a year. But, you might want to look at this thread here where it discusses some of the limitations of scaling the sharpe ratio this way, in other words, it is not necessarily completely mathematically sound.

I think where you're getting caught up is looking at it from the three year perspective, what you are actually doing is calculating your average monthly return, subtracting the monthly risk free rate, and then dividing by the average monthly standard deviation. It doesn't really matter how many years you have, you could have 20 years, the reason that you multiply by the square root of 12 is because you are using average monthly figures and you want to scale it to be yearly, if you were using daily returns, you could have any number of days, and you would still multiply by the sqrt of 252 (trading days in a year).

• I see! So its more a case of converting monthly data into annual data, not a "1 year Sharpe" into a "3 year Sharpe." So its the same formula, except [...] *sqrt(12). Also, with regards to the M^2, Jensens, Treynor ratios etc. would multiplying by Sqrt(12) be necessary in those calculations also? Thanks so much for your helpful answer! – redarT Jul 27 '18 at 21:23