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# STD and Sharpe Calculations

Discussion in 'Risk Management' started by dragonman, Jan 22, 2013.

1. ### dragonman

Hi, I have questions regarding calculating standard deviation and Sharpe ratio with respect to a stock portfolio:

1. Is a standard deviation of a stock portfolio generally expressed as % (i.e., by measuring the deviation of the stock portfolio's return from its average return)? For instance, if my portfolio returns were 2%, 3%, 4% and -5% at the recent 4 months, will the standard deviation be 4.08% or just 4.08?

2. Is a Sharpe ratio of a stock portfolio generally expressed as % as well? For instance, if the total return of the portfolio in the recent year was 10%, the risk free rate was 0.25%, and the portfolio's standard deviation was 4%, will the Sharpe ratio be 2.43% or just 2.43?

2. ### harric

1. 4.08%
2. 2.43

Be aware that typically you would use annualized standard deviation if you are using annualized returns in the calculation. Your standard deviation in this case is monthly.

3. ### dragonman

Thanks. If I want to annualize the 4.08% STD would I multiply it by 12 and make a square root to the result (so it would be 14.13%)?

Also, I want to make sure that the Sharpe ratio is usually calculated based on the annualized STD figure (and not the monthly STD figure). Please correct me if I'm wrong, thanks.

4. ### harric

You need to multiply monthly STD by SQRT(12) = 3.46

So your annualized Sharpe in this case would be 0.70

5. ### dragonman

I multiplied the monthly STD (4.08) by SQRT(12) and the result was 14.14%. Could you please elaborate how did you reach 3.46? Thanks.

6. ### harric

SQRT(12) = 3.46

7. ### dragonman

Ok, so we basically said the same thing. I referred to the final result (after multiplying 4.08 by 3.46) and you referred to the 3.46 itself. Thanks for the clarification.

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