Any investment you make is going to come with some sort of risk, and calculating risk-adjusted returns can be quite helpful in determining if the potential reward is worth the risk. By evaluating different options in this manner, you can get a better sense of how much any one potential investment will benefit you based on your goals.
For example, a stock might provide higher returns than putting the same amount into a certificate of deposit (CD). But suppose the stock is only likely to return, say, 6% per year, while a CD pays 5%. Meanwhile, the stock has a decent likelihood of losing value, while the CD is essentially secure at 5%. So, you have to ask yourself if the extra 1% in possible returns is worth the risk.
This is where the Sharpe ratio comes in handy. Measuring investment returns in relation to risk, the Sharpe ratio calculation is widely used among professional investment managers. While it may be a more advanced metric, individual investors can also use it to get a better sense of whether an investment is worthwhile.
What is the Sharpe ratio?
Definition of Sharpe ratio
The Sharpe ratio is a financial metric that helps you determine whether the risk you've taken on has generated high enough returns compared to the returns you might have seen without taking on risk.
It can be used to evaluate either an individual asset or a portfolio of assets. An investor can calculate the Sharpe ratio using either historical or expected returns, and it also takes into account volatility to gauge the risk of the asset losing value vs. potential gains.
William F. Sharpe developed the Sharpe ratio in 1966 as an investment performance analysis tool. In 1990, Sharpe won the Nobel Prize in Economic Sciences.
To calculate the Sharpe ratio, you first need your portfolio's (or the asset's) rate of return — either historical or forecast returns, depending on your preference.
Next, you need the rate of what's considered a risk-free investment, such as the 10-year Treasury bond. Subtract this risk-free rate from your portfolio's rate of return to find the excess return, or what your investment gives you above the Treasury bond (or whatever you're using as the risk-free rate).
Finally, you divide the difference between those two components by the standard deviation of the portfolio's return, meaning the range above or below the average return that the portfolio has delivered in the past or is expected to deliver.
Sharpe ratio formula
The Sharpe ratio formula is fairly simple. Here's what it looks like:
Sharpe ratio variables
The three variables needed to calculate the Sharpe ratio include:
Return of portfolio: This is what your portfolio has earned, or what you expect to earn, over a given amount of time as a percentage of what you have invested. For example, if a fund has averaged 10% annual returns over its lifetime, you would input 10% here.
Risk-free rate: This figure acts as your benchmark, or what you would've earned without virtually any risk. The Sharpe ratio often uses Treasury securities here because of their unlikeliness to default. For example, you might use a 5-year Treasury Note rate to calculate the Sharpe ratio for your portfolio over the past five years.
Standard deviation: This measurement of volatility indicates how much a return fluctuates over a period of time. Expressed as a positive number, the standard deviation accounts for both downside and upside changes. The higher the number, the more risk, which is reflected in the Sharpe ratio.
"The impetus behind the ratio is taking standard deviation and volatility to find a simple numerical value," says Randy Frederick, managing director of trading and derivatives for the Schwab Center for Financial Research.
Volatility is often understood as a bad thing, Frederick points out. But really, volatility means you're seeing price upsides along with downsides over time, and if the upside is high enough, you might be willing to stomach those drops. The Sharpe ratio takes these factors and spits out a number that can tell you how your investments are doing relative to the risk.
Sharpe ratio example
Let's say you have an exchange-traded fund (ETF) with a 5-year, 30% return (Rp = 30).
Meanwhile, the 5-year Treasury has a rate of 4% (Rf = 4).
In this example, let's assume the standard deviation is 20% (σp = 20).
Now we can fill out the Sharpe ratio calculation.
Sharpe ratio = (30 — 4) ÷ 20
Sharpe ratio = 26 ÷ 20
Sharpe ratio = 1.3
Typically, anything at a 1 or above is considered good, so this 1.3 ratio indicates that the volatility may be worth it, given the high potential for returns that greatly exceed the risk-free rate.
How the Sharpe ratio works
Calculating and interpreting the Sharpe ratio
Generally, the higher the Sharpe ratio, the better. A high Sharpe ratio means the risk is paying off in the form of above-average returns. A low Sharpe ratio — or even a negative Sharpe ratio — probably means that you're better off taking the risk-free rate of return or switching to an investment with a better Sharpe ratio.
What is a good Sharpe ratio?
While a good Sharpe ratio is somewhat subjective, the generally accepted ranges include:
- Under 1.0 is considered bad
- 1.0 is considered acceptable or good
- 2.0 or higher is rated as very good
- 3.0 or higher is considered excellent
That said, some investors might not want to engage in an investment with a very high Sharpe ratio, because even if the potential gains are very high on a risk-adjusted basis, they might not be willing to take that level of risk.
For example, a penny stock might have returned 200% over the past five years, but the standard deviation was 50%, and the risk-free rate was 4%. This would equal a Sharpe ratio of 3.92, which seems great, but maybe you're not willing to take the chance of investing your life savings into an asset that might fall by 50%, when instead you could take the relative surety of 4% returns from a Treasury bond.
One way to increase your Sharpe ratio while managing overall risk is to have a diversified portfolio. A main concept of Modern Portfolio Theory, diversification — particularly across multiple asset classes — can help drive slow, steady growth over time and help your portfolio weather the ups and downs of the markets.
How to use the Sharpe ratio
The Sharpe ratio is a measurement that gives investors insights into investments' returns relative to risk. It is largely used by institutional investors such as hedge funds and other types of fund managers, but that doesn't mean everyday investors can't benefit from this metric.
Quick tip: You may not have to know how to calculate the Sharpe ratio yourself. Your brokerage may provide it for you in your account documents, or you can ask your investment manager about it.
The Sharpe ratio in portfolio management
The Sharpe ratio can be used to evaluate overall portfolios. For example, an investor could use it to assess the risk-adjusted returns of two potential portfolios, such as looking at what their ratios would be if their portfolio was 100% in stocks vs. 60% stocks/40% bonds. Or, an investor might look at a fund manager's overall portfolio by using the Sharpe ratio to see if the returns seem to justify the risk.
The Sharpe ratio for individual investment decisions
Investors can also use the Sharpe ratio to evaluate the risk-adjusted returns of an individual asset, and they can leverage this knowledge to determine whether they think it's a suitable investment. For example, you might look at the Sharpe ratio of two different stocks to get a sense of whether the high volatility of one is worth the potential returns, or if you're more comfortable going with the more stable stock.
Limitations of the Sharpe ratio
Dependency on normal distribution of returns
Investors should keep in mind that there are several Sharpe ratio limitations and considerations. One criticism of this ratio is that it assumes a normal distribution of returns. A normal distribution has results that are symmetric in relation to the mean. In other words, there are an equal number of results to the left and right of that mean.
Further, in a normal distribution, data points are more likely to show up near the mean, or middle result, than further from the mean.
An example of something that follows a normal distribution would be height. There are generally an equal number of people who are taller and shorter than the average height, and results closer to the mean happen more frequently than results further away from that mean.
In practice, the returns associated with an investment strategy do not always follow a normal distribution. Many financial institutions, for example, hedge funds, harness investment strategies that can create distributions of returns that are not perfectly symmetrical.
Time horizon
The Sharpe ratio can also have limitations related to an investor's time horizon.
For example, let's say you use the Sharpe ratio using numbers around a three-year investment. If you only end up holding your investment for a year, that ratio won't really apply to your investment anymore, as you might be more exposed to short-term volatility than you realized. Conversely, a Sharpe ratio that covers a short period might give a long-term investor false confidence.
Moreover, if you're not calculating the Sharpe ratio yourself but just looking at what someone publishes, you don't necessarily know the time horizon that it refers to. Maybe it was one year, maybe it was five, and if you don't know the specifics, the investment might not align with your risk tolerance as much as you thought.
Quick tip: You might not want to use the Sharpe ratio if you plan to trade investments within a year. The calculation often measures long-term volatility, and it may mislead your short-term investment strategy.
Doesn't specify leverage
An investment strategy might involve using leverage, with borrowed money used to buy more assets. That might amplify returns, but it can also increase losses during a downturn. So, a portfolio might have a high Sharpe ratio because leverage was used to boost returns, but unless you analyze the details, you might not realize that the potential volatility is more than you're comfortable with.
Measures total volatility
Another limitation of the Sharpe ratio is that it measures total volatility. So, an asset that frequently swings up before coming back to its baseline might have a similar standard deviation to one that frequently dips into the red.
Sensitivity to the risk-free rate
The Sharpe ratio depends heavily on the benchmark used to determine the risk-free rate, which then sets the level of comparison for the asset or portfolio being evaluated.
When selecting appropriate benchmarks, investors frequently select lower-risk assets, for example, Treasury bonds, with durations similar to the intended investment horizon. Yet that risk-free rate can change over time, such as if inflation drives yields up. That then changes the Sharpe ratio, but you might not be recalculating it, thus causing you to potentially be in a riskier investment than you realized, relative to the risk-free rate.
Improving your investment strategy with the Sharpe ratio
Identifying higher Sharpe ratio opportunities
The Sharpe ratio can be used to compare different portfolios and determine which ones have higher risk-adjusted returns. It can also be used to single out individual assets with higher risk-adjusted returns.
By incorporating assets with a higher Sharpe ratio into a portfolio, an investor can potentially earn more without risking higher losses, or at least taking a level of risk commensurate with the potential returns.
Adjusting risk management
The Sharpe ratio might also change your approach to risk management. You might find, for example, that some of your investments barely earn more than the risk-free rate, yet their chances for losses are much higher. In that case, you might prefer to reduce risk by choosing the risk-free asset.
Sharpe ratio vs. Sortino ratio
The Sortino ratio, created by Frank A. Sortino, is a relative of the Sharpe ratio that accounts more for downside risk.
The main difference is that the Sortino ratio only looks at the downside portion of the standard deviation, not the general standard deviation. This tends to help if viewing investments from a more risk-averse and short-term perspective.
That said, a Sharpe ratio that accounts for upside volatility might do a better job of capturing the full picture of risk, such as how sometimes big gains are followed by contractions.
Also, the Sortino ratio only uses historical averages, not projected returns, as some Sharpe ratio calculations do.
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FAQs about the Sharpe ratio
How do you calculate the Sharpe ratio?
Learning how to calculate Sharpe ratio is relatively easy. Start by subtracting a particular portfolio's or asset's return rate from the risk-free rate of return (such as a Treasury bond) and then divide that result by the standard deviation of the portfolio's average return.
Is the Sharpe ratio applicable to all types of investments?
The Sharpe ratio can be used to evaluate all types of investments, but its usefulness can vary significantly depending on the investment in question. For example, an illiquid asset might not have as much volatility if it is not priced often, but it might still be risky.
How should investors interpret the Sharpe ratio when comparing investments?
A higher Sharpe ratio indicates that a particular investment will have better risk-adjusted returns. However, investors must keep in mind that this particular ratio has its limitations, and they should consider other aspects of risk and reward, such as looking at liquidity and leverage, if applicable.
What Sharpe ratio is good?
Typically, a Sharpe ratio of 1.0 or above is considered good. It's not always easy to attain a high Sharpe ratio, but if it falls below 1, that indicates the potential return might not be worth the risk.
What does a Sharpe ratio of 1.0 mean?
A Sharpe ratio of 1.0 generally means that an investment provides a good level of return relative to its volatility. This indicates that the investment not only provides a higher level of return than the risk-free rate, but also that the excess return is proportional to the volatility.
