Sharpe ratio

[btowntrader54]

Hi,

I'm trying to determine the process to calculate the Sharpe ratio properly. I've included a graphic.

Is it as follows:

(Avg Fund ROI per period - Avg Benchmark ROI per period) / (Avg Fund SDev per period - Avg Benchmark SDev per period)?

Thanks

 

[MTE]

Several points.

1. You divide by the stdev of the fund not the difference between the stdev of the fund and the benchmark.

2. You take the actual return for the period not the average return, and the same goes for standard deviation.

3. It's the risk free rate not the benchmark index return that should be used. As Sharpe ratio is defined as the excess return per unit of risk.

 

[fluttrader]

The standard period used is yearly ?

 

[btowntrader54]

I figured it is on an annual basis but if there's not enough data going that far and one wanted to do it on a daily basis, is that doable or will it just be a garbage figure?

 

[vita]

Sharpe ratio calculation can be really tricky. This is one general way I'd do it.

Depending on your preferred time frame, record your daily, weekly, or monthly returns. Let's assume you are a day trader and have logged your daily returns for many months/years:

1) plot a histogram of you daily returns

2) See if the daily histogram of your returns looks like a Normal Distribution. At the very least, it should have only one mode and not many fat tail returns. If this was not the case, Stop! You cannot calculate Sharpe ratio based on daily returns. One way to solve this to plot a histogram of weekly returns and check if that looks like a Normal distribution.

3) If your daily histogram has one mode and looks Normal, you can estimate the Sharpe Ratio as follows

Annualized Sharpe=(mean(R)*252-Rbm)/(std(R)*sqrt(252))

where R is the series of your DAILY returns, and Rbm is the ANNUAL Return of a benchmark, e.g. risk free USTreasury return. The number 252 is the number of trading days per year.

If you are a longterm trader and only consider weekly returns use the same procedure and formula but replace 252 by 50 where R becomes your weekly returns.

I hope this helps.

 

[fluttrader]

Vita,



So , no way of knowing if the Sharp was calculated under the right (normal distribution) conditions ...

What is the most used period for R ? monthly , yearly ?

 

[MTE]

Generally, you would use a year of daily data points to calculate it. And as the other poster noted, for it to be a meaningful measure the returns should be approx. normal. A highly skewed distribution can result in a very high Sharpe ratio, which is misleading.

 

[vita]

Quote from fluttrader:

So , no way of knowing if the Sharp was calculated under the right (normal distribution) conditions ...

What is the most used period for R ? monthly , yearly ? [/B]

The answer to your 1st question is NO. Although the histograms are NEVER perfectly Normal, they must have only mode and not many fat tail. The value of Sharpe ratio is completely subjective. You should always ask how it is calculated and whether you can see the histogram of the returns before you can consider the reported value as fair.

The most common time frame to use is daily, but if you hold positions overnight, you should move to weekly or even monthly. But remember that Sharpe Ratio remains an annual performance metric.

 

[fluttrader]

Quote from vita:

The answer to your 1st question is NO. Although the histograms are NEVER perfectly Normal, they must have only mode and not many fat tail. The value of Sharpe ratio is completely subjective. You should always ask how it is calculated and whether you can see the histogram of the returns before you can consider the reported value as fair.

The most common time frame to use is daily, but if you hold positions overnight, you should move to weekly or even monthly. But remember that Sharpe Ratio remains an annual performance metric.

OK, thanks !

 

[raymond008375]

Quote from vita:

Sharpe ratio calculation can be really tricky. This is one general way I'd do it.

Depending on your preferred time frame, record your daily, weekly, or monthly returns. Let's assume you are a day trader and have logged your daily returns for many months/years:

1) plot a histogram of you daily returns

2) See if the daily histogram of your returns looks like a Normal Distribution. At the very least, it should have only one mode and not many fat tail returns. If this was not the case, Stop! You cannot calculate Sharpe ratio based on daily returns. One way to solve this to plot a histogram of weekly returns and check if that looks like a Normal distribution.

3) If your daily histogram has one mode and looks Normal, you can estimate the Sharpe Ratio as follows

Annualized Sharpe=(mean(R)*252-Rbm)/(std(R)*sqrt(252))

where R is the series of your DAILY returns, and Rbm is the ANNUAL Return of a benchmark, e.g. risk free USTreasury return. The number 252 is the number of trading days per year.

If you are a longterm trader and only consider weekly returns use the same procedure and formula but replace 252 by 50 where R becomes your weekly returns.

I hope this helps.

Is it really necessary to let the histrgram resemble Normality? What if it isn't Normal? I didn't see any assumption about Normality in Port. Theory by Harry Markowitz......