Tuesday, January 18, 2011

Understanding the Sharpe Ratio

This is a repost of the article I wrote on my hedge fund blog a couple years ago. Please feel free to comment here. Enjoy.

Explaining the Sharpe Ratio (again)

Having the Hedge Fund Calculator built into every product we develop is great. As we develop the platform, we get suggestions from our clients which help us enhance the number of statistics we calculate as well as the speed at which they are generated.

One of the issues that we have with statistics is that regardless of how close we stick to any given standard we find someone who interprets something  differently and gets different results. Often others “tweak” the algorithm simply out of a misunderstanding of the algorithm, other times as we will discuss later, choosing an alternate calculation intentionally creates better results.

The Sharpe ratio is one of the simplest ratios, it is also one of the ratios which is most often miscalculated. I will explain what the Sharpe ratio is, the correct way to calculate the ratio as well as a couple of the most common errors made when performing this calculation.

What is it?

The Sharpe ratio was created to answer the question “Given the same amount of risk, which investment provides me with the highest reward.” To do this the Sharpe ratio balances the returns in excess of a risk free benchmark with the standard deviation of the return set. This provides a uniform risk platform which funds with different risk levels can benchmark against.

We’re going to start our example with our return sets:

Investment Monthly Returns

 Jan Feb Mar Apr May June Jul Aug Sep Oct Nov Dec 1.64 5.85 9.22 3.51 -0.88 1.07 13.03 9.4 10.49 -5.08 n/a n/a

Risk Free Rate

The annual risk free rate which we will use for our example will be 5%. Generally the RFR will be the average yield of a risk free investment (such as a TBill) over the same time span as the investment. Since we are calculating the returns for thousands of hedge funds, many of which are not correlated to any specific index, at HedgeCo we have chosen to use the same RFR for all our funds.

Sharpe Ratio

The Sharpe ratio is defined as: Average Return – RFR / Standard Deviation. We are using monthly returns as our base so the formula looks like:

We want to get the annualized returns, so we multiply the Sharpe by the square root of 12 to get our final result of 2.567.

Where it can go wrong

As seen above, the Sharpe ratio is very simple, however many times it is overcomplicated and miscalculated. I will quickly go over a couple of the different common issues which cause discrepancies between our calculations and the individual calculations of independent hedge fund managers.

1. Different Risk Free Rate

The most common reason why our calculations may not match is because we are using a different risk free rate. This is not an error in calculation.

2. Geometric Averages & CAGR

Using a geometric average or the Compounded Annual Growth Rate as your average for the sake of the Sharpe ratio will overstate your average monthly returns and give you a better Sharpe ratio. Some will argue that compounding returns is more accurate – for the sake of this ratio I disagree.

3. Reporting Frequency

Weekly reports will probably provide a higher Standard Deviation than Monthly reports. Similarly Quarterly reports will likely smooth out the risks and provide lower standard deviation than monthly reports. Even though the year-end return may be the same, the Sharpe ratio of a fund that reports weekly may be different than the same fund when calculated using monthly reports.

4. STDEV vs. STDEVP

One other gotcha that you may see if you are using Excel is the difference between STDEV and STDEVP. The difference between these two functions are described here. If you want to use excel to calculate you Sharpe, use STDEV.

1 comment:

1. Nice article. Will you write about the Sortino Ratio as well?