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# Calculating Standard Deviation and Sharpe Ratio

Discussion in 'Stocks' started by dragonman, Jan 22, 2013.

1. ### dragonman

Hello,

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%?

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 is 0.25%, and the portfolio's standard deviation is 4%, will the Sharpe ratio be 2.43% or just 2.43?

Thanks in advance for any help.

2. ### dragonman

I would appreciate any response to my questions, thanks.

3. ### jbusse

Standard deviation is often expressed as a percentage.

Sharpe ratio is not a percentage.

4. ### acrary

1. In the example given, the average return would be 3.5% and the std dev would be approx. 1.29%. You're just measuring the amount of dispersement from the average (or mean). The lower the std dev, the lower the perceived risk. A common approach would be to take the average of 3.5% and divide it by the std dev. of 1.29 to get 2.71 confidence intervals before a expected losing month. 2.71 is between 95% and 99%. So if you had a reasonable sample size you could feel 95% - 99% confident of future months being profitable.

2. I prefer the Sorrentino ratio and use 0 for the target to compare multiple systems. The Sorrentino ratio doesn't penalize you for outsized returns as the Sharpe ratio does. If you have a trendfollowing system with multiple entries (as it trends in your favor), you'll have large wins and small losses. The Sharpe ratio would penalize the large wins in favor of same size trades (which is a poor way to trade a trendfollowing system).

Alan

5. ### Algo_Design_Kid

The standard deviation of a multi asset portfolio is more complex than this because it is not calculated solely on the weighted average of all the stock's standard deviation.

You will also need to know the correlation coefficent to solve the equation. I have no idea how to key in the correct keys to create the equation, but just search multi-asset portfolio standard deviation.

It is basically the sq root of..... the Weight of each in your portfolio^2 * individual st deviations^2+ 2 * the weights of each again * the correlation coefficient * the individual st deviations of each again..

2. I have never used a % with the sharpe ratio, but I could be wrong

EDIT: OOps, may have read your original question wrong. I don't think you are exactly looking for the information I gave you - sorry

6. ### harric

Alan, could you clarify where you get your numbers from? Looks like you may have plugged in +5% instead of -5%..

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