Fri 5 Jan 2007
Who:This post is for people who want a way to quantify reward vs. risk in their investments or for people who know what a Sharpe Ratio is and want to learn more about it.
What: This post will discuss the meaning, calculation, and the usefulness of the Sharpe Ratio. The Sharpe Ratio is a measure of the reward to risk of a given investment.
What is this ratio of which you speak?
The Sharpe Ratio is a measure of how well an investment compensates an investor for the risk he/she takes on. First, I will show you the formula for the Sharpe Ratio and then I will go through a simple example. After that, I will discuss the conceptual meaning behind the ratio.
R is the expected return on the asset that we are evaluating. Rf is the risk-free rate which can be characterized in many ways. basically Rf refers to the rate of return one can achieve without taking on any significant (i.e. extremely low) risk. The big letter that we call E represents an expected value. In other words, the numerator of this ratio is the expected return that an asset is expected to give you above and beyond the risk free rate Rf. Finally, the denominator is the standard deviation of R. More specifically, the standard deviation of R is the square root of the variance of R, a measure of the volatility of the returns of the asset we are evaluating. I know that was a mouthful, but an example should illustrate how easy this calculation actually is. Don’t understand? It’s ok, check out the Sharpe Ratio Calculator.
A Financial Revolution Loves Examples
Assume we have a mutual fund that we expect to return 15% over the course of the next year. The mutual fund’s volatility is 10%, and the risk free rate that I can get at Emigrant Direct is 5.05%. Note: For you picky folks, yes, we’re purposely ignoring tax consequences here, for simplicity.
The Sharpe Ratio = (15.00% - 5.05%) / 10.00%
The Sharpe Ratio = 9.95% / 10.00%
The Sharpe Ratio = 0.995
Voila, a piece of cake. What does 0.995 mean? By itself, not much. The Sharpe Ratio is meant as a method for comparing different risk/reward options. So, let’s try it out. If I offered you the investment that we highlighted in our example or another investment option which has a 20% volatility (double the volatility) and a 27% return (less than double the return). Which investment would you pick? Let’s find out.
The Sharpe Ratio = (27.00% - 5.05%) / 20.00%
The Sharpe Ratio = 21.95% / 20.00%
The Sharpe Ratio = 1.098
As you can see, the second investment has a higher sharpe ratio. What this is saying is that the second investment, while riskier, provides a better risk-to-reward ratio than the first invesment does. In general, the higher the sharpe ratio, the better an investment compensates it’s investors for risk taken.
Is it Magic? Do I Wield Unstoppable Power?
Unfortunately, no. The Sharpe Ratio, like most things in life, is far from perfect. While I am a big fan of the Sharpe Ratio, I would be remiss if I did not mention the drawbacks to using the ratio and the caveats that one must keep in mind when using it as a part of an investment decision.
- The Sharpe Ratio should not be used as a blanket approach to picking investments. In our example, even though the 2nd investment has a higher Sharpe ratio, a risk-averse investor may still want to invest in the first choice. Sharpe Ratios should be used to compare investments that fit WITHIN your risk and return profiles.
- The effectiveness of the Sharpe Ratio is based on the (hotly debated) effectiveness of standard deviations as a measure of volatility. The mathematics behind it is rather complicated, but many argue that the standard deviation of an investment’s returns are not necessarily a good measure of it’s volatility. This is not to say that there aren’t many, many, individuals who have strong arguments as to why the standard deviation *is* a good measure for volatility
- An exact calculation of the Sharpe Ratio is not forward looking, and forward looking calculations of the Sharpe Ratio are estimates and projections. To calculate a Sharpe Ratio for the past performance of a fund, one must use the return and standard deviation over the previous time period in order to calculate the exact Sharpe Ratio. The values of these two quantities are unknown for the future, so any forward-looking Sharpe Ratio will be based on projections of the returns and standard deviations, which are subject to large variance.
Basically, this post was useless?
Not at all! Even though the Sharpe Ratio has some shortcomings, it does have many uses and advantages over other metrics.
- The Sharpe Ratio is an excellent tool to compare multiple investments that are all within your risk tolerance. Comparing the Sharpe Ratios of such investments will give you an excellent idea of how much each investment is compensating you for your risk as compared to the other investments.
- The Sharpe Ratio allows comparisons of investments over multiple sets of assumptions. There may be instances in which some part of an investment have a given risk-free rate and another part has a different risk-free rate. The inclusion of a risk-free rate parameter allows one to use the Sharpe Ratio to compare these options in different “universes” or circumstances.
- The Sharpe Ratio is arguably more versatile than other metrics such as Alpha and Beta (these will be discussed in a future post). While Beta needs to be based off a specific index and the precision of Alpha is based on a high R^2 (also to be discussed in a future post) value, the Sharpe Ratio has no such restrictions. A Sharpe Ratio can be used to compare different types of investments (stock funds and bond funds) using the same assumptions.
So there you have it! Does anyone have other financial metrics that they would like covered on A Financial Revolution? Any thoughts on the Sharpe Ratio or anything I may have missed or omitted? Sound off and let me hear about it.
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