Last Updated on 23 September, 2020 by Samuelsson
Created in 1966 by William Sharpe, a Nobel Prize winner in economics, the Sharpe Ratio is one of the most popular parameters used in finance for comparing the return of an investment to its risk. The ratio is simple and easy to use, but do you know what it is and what it measures?
Sharpe Ratio is the average return earned in excess of the risk-free rate, per unit of volatility or total risk. It measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. As a measure of risk-adjusted return of a financial portfolio, Sharpe Ratio can be used to compare the performance of different funds with reference to the risk taken.
In this post, you will learn the following:
- What Sharpe Ratio means and measures
- How it is calculated
- The significance of the ratio
- The uses
- How to use it to select a mutual fund
- The limitations
What does Sharpe Ratio mean?
Sharpe Ratio was developed by Nobel laureate William F. Sharpe to help investors understand the return of an investment compared to its risk. The ratio is the average return an investment earns in excess of the risk-free rate, per unit of volatility or total risk the investment takes. Volatility, as you know, is the measure of fluctuations in the price of a security or portfolio and is considered a measure of total risk involved in the investment.
Since William Sharpe’s creation of the Sharpe Ratio in 1966, it has been one of the most referenced risk/return measures used in finance. By definition, Sharpe Ratio is the measure of risk-adjusted return of a financial portfolio. A portfolio with a higher Sharpe Ratio is considered superior relative to its peers. The measure was named after William F Sharpe, a Nobel laureate and emeritus professor of finance at Stanford. The historic Sharpe Ratio is closely related to the t-statistic for measuring the statistical significance of the mean differential return.
In finance, the Sharpe Ratio measures the performance of an investment compared to a risk-free asset, after adjusting for its risk. It is defined as the difference between a portfolio’s return and the risk-free rate of return, divided by the standard deviation of the portfolio’s returns. The Sharpe Ratio, developed by William F. Sharpe, is an effective way of benchmarking the investment return compared to the amount of risk involved. It is a measurement of the risk-adjusted returns of an investment or an investment manager over time. The Sharpe Ratio indicates how well an investment performs in comparison to the rate of return on a risk-free investment.
A risk-free asset is an asset that is assumed to have zero risks. An example is the short-term U.S. Treasury bills. The return on such an asset is seen as a risk-free rate of return since investors get the return without exposing themselves to any risk. After all, the US is the richest and strongest country in the world, so their government is highly unlikely to default in its obligations. Hence, the yield for the U.S. Treasury bill is often used as the risk-free rate of return.
What Sharpe Ratio does is to measure the returns earned in excess of the risk-free rate of return and compare it with the risk taken upon investing in the security or portfolio. By viewing the excessive return in the light of the risk inherent in the investment, the investor can assess whether the return is worth the risk.
The assumption here is that the standard deviation of the return from an investment is a measure of the risks involved in the investment. So, when the risk is not commensurate with the returns, the Sharpe Ratio will be low, making the investment unattractive. But if the return far outweighs the risk, the Sharpe Ratio will be high, making the investment attractive, as there is enough return to justify the extra risk. Thus, the higher the Sharpe Ratio, the better the risk-adjusted return from the investment — which means that the ratio can be used to compare funds.
How to calculate Sharpe Ratio
Calculating the Sharpe Ratio is easy. It only requires you to compute the expected return on the asset or portfolio under review and then subtract the risk-free rate of return — here, you can use the yield of the short-term U.S. Treasury bills. Then, you divide the difference, which is called the excess return, by the standard deviation of the expected return of the investment or portfolio. Alternatively, you can calculate the Sharpe Ratio after the returns have been realized, in which case you use the actual returns instead of the expected.
The formula for calculating the Sharpe Ratio is given as follows:
Sharpe Ratio = (Re — Rf)/σe
Re = the expected return
Rf = the risk-free rate of return
σe = the standard deviation of returns which is a measure of the volatility (total risk) in the portfolio
Here are the steps to follow:
- Compute the expected returns or the actual returns on the portfolio
- Subtract the risk-free rate of return (one-year or two-year U.S. Treasury yield) from the return of the portfolio to get the excess return.
- Divide the excess return by the standard deviation of the portfolio’s expected or actual return — the standard deviation is a measure of volatility in the portfolio’s returns, which is a direct reflection of the risk involved in the portfolio.
Grading the Sharpe Ratio
So, how is the Sharpe Ratio graded? What makes a good Sharpe Ratio in which the expected or actual returns justify the risk in the investment? Here is the general guideline you can use:
- Any Sharpe Ratio less than 1.0 is not acceptable. It means that the risk is greater than the excess return, so the return does not justify the risk you are taking.
- A greater than 1.0 is considered acceptable, and the higher the better.
- A ratio greater than 2.0 is considered very good.
- A ratio of 3.0 or above is considered excellent.
What does a negative Sharpe Ratio mean?
When the Sharpe Ratio is negative, it means that the portfolio’s return is less than the risk-free rate, or that it has a negative value. In this case, the ratio offers very little information, but whichever way, you are better off investing in the risk-free asset.
The implication of Sharpe Ratio
Sharpe ratio has so much significance in the world of finance. Both retail investors and fund managers use it to evaluate potentially risky investments to know whether the returns are worth the risk. The ratio shows the extra return you are getting per unit extra risk you’re taking. So, you can use it to determine whether the higher risk associated with some investments, such as stocks and currency trading, is justified. A portfolio with higher returns may not be justified if the risk outweighs the excess return.
If you have to endure extra volatility, the extra returns have to be much higher than the risk. You don’t just choose an investment because it offers more returns than its peers if you have not considered the associated risks. Taking a lot of risk for a little extra return is not a good use of your capital because you are at a higher chance of losing big or enduring a big drawdown. The reward for enduring higher volatility has to be big enough.
Admittedly, investors have different risk preferences. While some prefer low-risk investments, others can endure higher volatility for a higher return. What is important is for the return to be worth the risk. This is where the Sharpe Ratio comes in. You can also look at it from a different angle: when an investor chooses a low-yield but more stable investment, the risk level has to be low enough to justify the lower returns, as should be the case with diversifying into more stable assets.
At the end of the day, every investor aims to maximize returns and minimize risk. But there is a limit to that because the more the returns, the more the risk, or the less the risk, the less the returns. You just have to arrive at the right balance where the risk is justified by a correspondingly huge return. And, you can use the Sharpe Ratio to make that judgment. In fact, there is an inverse but exponential relationship between the volatility of returns and the Sharpe Ratio, as you can see in the graph below.
The uses of Sharpe Ratio
There are many ways you can make use of the Sharpe ratio. Here are some of them:
Evaluating the effect of a potential high-yield investment on your portfolio
You can use the Sharpe Ratio to evaluate a potential high-yield asset you want to add to your portfolio to know whether the returns are worth the risk. For example, say you have a portfolio that returns about 12% on average each year with 6% volatility, and the current risk-free rate is 3%. Your portfolio’s Sharpe Ratio would be (12-3)/6 = 1.5
Now, let’s say you are considering adding Bitcoin to your portfolio, which could take your returns to 17% but at the same time take the volatility of your returns to 15%. Assuming the risk-free rate remains at 3%, your portfolio’s Sharpe Ratio would be (17-3)/15 = 0.93.
Since this asset reduces your portfolio’s Sharpe Ratio, despite boosting the returns, it may not be a smart addition to your portfolio because it significantly raises the volatility of your returns.
Assessing the benefit of diversifying to more stable but less rewarding asset
This is the inverse of the first example. Diversification aims to reduce risk without significantly reducing your returns. So here, you are checking whether the new asset does that effectively. For instance, let’s say your portfolio returns 15% with a volatility of 10%, while the risk-free rate is 5%. Your portfolio’s Sharpe Ratio is (15-5)/10 = 1
After diversifying to a more stable asset, your portfolio’s return was reduced to 13%, while the volatility of the returns reduced to 6%. If the rate-free rate remains at 5%, your portfolio’s Sharpe Ratio would become (13-5)/6 = 1.3.
Although the returns reduced, the Sharpe Ratio increased because the risk reduced significantly. So, the new asset brought the desired benefit of lowering your risk.
Comparing against a benchmark
You can also use the Sharpe Ratio to compare your portfolio’s returns to the returns of a popular benchmark. For example, let’s say you have a portfolio that returns a modest 9% per annum with a volatility of 5%, while the rate-free rate is 3%. At the same time, an S&P 500 index fund returns 10.6% with a volatility of 18.1%.
Your Portfolio’s Sharpe Ratio is (9-3)/5 = 1.2
S&P 500 Index Fund’s Sharpe Ratio is (10.6-3)/18.1 = 0.42
Hence, on a risk-adjustment basis, your portfolio offers a better return per unit risk. Please note that this is a very simplistic analogy.
Comparing funds (index funds, mutual funds, or ETFs)
Sharpe Ratio can be quite useful in comparing funds that are in the same category. You can use it to evaluate the performance of two funds that are facing a similar level of risk or analyze the risk levels of funds that have similar performance. More on that in the next section.
How Sharpe Ratio can help you in choosing Mutual Funds
Selecting mutual funds or choosing between two fund managers is a common use of the Sharpe ratio, but as stated above, the ratio only uses the total risk in a portfolio and doesn’t indicate where the risk is coming from. So, you don’t just use the Sharpe Ratio alone; you have to combine with other forms of analysis, such as finding out sector and the kinds of securities the funds are invested in.
Nevertheless, when selecting a mutual fund, the Sharpe Ratio can help you to do the following:
- Evaluating the fund’s strategy: You can use the Sharpe Ratio to evaluate the excess returns the funds are expected to make relative to the size of risk they are taking. This way, you can know the one that has a better risk-adjusted return, which obviously must have a better strategy.
- Gauging the right risk-return balance: Having a better return does not justify a fund’s approach to risk. On the other hand, having a lower risk (with of course lower returns) does not mean that the return/risk balance is optimal. The Sharpe Ratio can show a fund with a better risk-return balance. All things being equal, a fund with a higher Sharpe is better.
- Checking your portfolio diversification: The Sharpe Ratio can help you to determine whether the new fund you want to invest in would be of benefit to your existing portfolio. If the fund increases your portfolio’s Sharpe Ratio, it is a good addition. But if it reduces the ratio, it’s either that it’s not reducing your overall risk or not boosting your returns, so it adds no value to your investment portfolio.
The limitations of Using Sharpe Ratio
By using a standard deviation as a measure of volatility (risk), the ratio assumes that the returns are normally distributed, but this is not the case in the financial markets, as violent price spikes occur in the market from time to time. Also, it assumes that the maximum price movement is the same in either direction — up or down. But we know that the stocks are limited on the downside to zero while the upside is potentially limitless.
Again, the Sharpe Ratio does not show where the risk is coming or the makeup of a portfolio. A portfolio that is concentrated in one sector can have a high Sharpe ratio, implying an optimal risk-return balance, while it has a high portfolio risk or industry risk.