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Investing Basics Investor Professor Risk

Online Exclusive: Understanding Risk-Adjusted Returns via the Sharpe Ratio

When comparing the performance of two securities, funds or portfolios, investors must consider risk-adjusted returns to see if they are being adequately compensated for the risk they are assuming.

by Matthew Bajkowski | February 2022

A basic premise of sound investing is that investors are naturally risk-averse. Investors seek the lowest level of risk for a given level of return and, alternatively, will not take on additional risk unless there is a higher chance of greater return.

The relationship between risk and return is an essential concept in finance, which argues that riskier investments should compensate investors with higher returns and safer investments should not experience exorbitant price fluctuations.

Though this is common knowledge, many individual investors neglect to take the time to actually look at an investment’s risk, or volatility, before purchasing.

When comparing the performance of two securities, funds or portfolios, investors should consider risk-adjusted returns to see if they are being adequately compensated for the risk they are assuming. The goal is to achieve the largest return per unit of risk.

Two common risk-adjusted measures used in investing include the Treynor ratio, which relies on beta to adjust for market-related risk, and the Sharpe ratio, which considers overall volatility. Here, we focus on the Sharpe ratio.

Sharpe Ratio Formula

William Sharpe devised the Sharpe ratio in 1966 to measure the risk/return relationship. When analyzing the Sharpe ratio, the higher the value, the more excess return investors might expect to receive for the volatility they are exposed to by holding an asset. Similarly, a risk-free asset or a portfolio would have a Sharpe ratio of zero.

William Sharpe

The Sharpe ratio subtracts the risk-free rate of return from the average rate of return of the investment you are evaluating. Then, that difference is divided by the standard deviation of your chosen investment’s rate of return.

The Sharpe ratio was originally developed as a forecasting tool, but it can also be used to calculate a historical risk-adjusted return. Expected average returns are used to calculate the forward-looking ratio, whereas actual returns are used in the historical ratio.

The expected return is also known as the required rate of return because it represents the minimum return investors require to compensate them for the added risk, which includes both the riskiness of the investment and the time value of money.

The risk-free rate is the return investors require to compensate for the time value of money alone. Typically, investors use the return on U.S. Treasury bills for the risk-free rate because it is reasonable to assume the U.S. government will not default on its debt obligations, and thus investors need only be compensated for the time their capital is tied up in the security.

The Sharpe ratio requires that the risk-free rate of return represents its average return over the time period under evaluation. An investor calculating the ratio for a three-year period must use the average rate of return on T-bills over the same three-year period.

Traditionally, the shortest-dated bill is used since it is the least volatile. However, some argue the risk-free security should match the duration of the investment. Since equities theoretically have an infinite duration, one could argue that the longest-dated bill should be used.

The standard deviation of a security measures how far its returns deviate on average from its mean (or average) return. Standard deviation is a common indicator used to measure the volatility, and thus the riskiness, of an investment. For instance, an investment that deviates only 3% from its mean on average is judged as less risky than an investment with a 20% average deviation.

Calculating the Sharpe Ratio

The Sharpe ratio measures the return of an investment that exceeds the risk-free rate, per unit of standard deviation. Here, it is calculated by taking the average rate of return of the investment, subtracting the risk-free rate and then dividing this result by the investment’s standard deviation.

Sharpe Ratio = (Rx – Rf) ÷ StdDev(Rx)

Where:

Rx = average rate of return from investment X

Rf = risk-free rate

StdDev(Rx) = standard deviation of Rx

 

Weaknesses of the Sharpe Ratio

The Sharpe ratio provides valuable information only when compared with another investment. To illustrate, if Company A has a Sharpe ratio of 1.0, does that make it a good investment? What if its competitor, Company B, has a Sharpe ratio of 3.0? All else equal, Company B is more attractive because, although Company A appears to have a high ratio, Company B’s ratio is better.

Moreover, negative Sharpe ratios—which are quite common during bear markets—do not provide useful information because the risk-free asset is then outperforming the investment on a risk-adjusted basis. In that case, investors often flood the bond market in search of the highest risk-adjusted returns available.

Since standard deviation measures total risk, the Sharpe ratio does not determine which investment is best for a diversified portfolio, rather it shows which investment is better of the two being compared. The total risk of an investment comprises both firm-specific and systemic risk, whereas a well-diversified portfolio should contain virtually no firm-specific risk because it is offset by the other securities. Therefore, it may be appropriate to choose an investment with a lower Sharpe ratio in the interest of maintaining a well-diversified portfolio.

Standard deviation requires that an investment’s returns are normally distributed. That is, they must take the shape of a bell curve. The Sharpe ratio is not a suitable measurement for investments with asymmetric expected returns.

Even if returns are normally distributed, bell curves have real limitations. For instance, they do not take big market moves into account, which can impact long-term returns and affect leveraged investments.

Furthermore, the time period used in the calculation will affect results. Going too far back may not provide an accurate representation of the current situation.

Standard deviation includes movement in every direction, which many consider a weakness because it does not differentiate between upside and downside volatility.

However, because standard deviation and volatility measure the predictability of an investment, which is then translated into risk, high volatility means returns are inconsistent. The strong upside performance of a highly volatile stock can turn severely negative in an instant; thus, it is still a risky investment.

Conclusion

Risk-adjusted returns may sound complicated but are conceptually broad and simple. Potential representations of risk-adjusted returns—such as alpha, beta, R-squared, standard deviation, the Treynor ratio and the Sharpe ratio—can serve as a gauge for the risk (volatility) of an investment.

When comparing investment returns, it may be neglectful to only look at the performance figures. As an investor, you expect compensation for a riskier investment. With awareness of an equity, fund or portfolio’s risk-adjusted performance, you can adequately assess whether the risk is justified by its return.

Online Exclusive: Understanding Risk-Adjusted Returns via the Sharpe Ratio Video

We think you’d like this related webinar! Individual Investor Show: Improve Your Allocation by Gauging Risk and Ranking Asset Returns


Discussion

JOHN L from NJ posted over 4 years ago:

Sharp ratio and risk adjusted returns are meaningless. For the long term investor; risk is not equal to volatility. Only compound growth matters.


ROBERT A from NC posted over 4 years ago:

I'm with John from NJ! The Sharpe Ratio and "risk adjusted" rate of return are simply meaningless catchphrases of conventional wisdom that tends to hobble one's portfolio.


TIM R from OH posted over 4 years ago:

Good explanation of the Sharpe. Some thoughts: The use of the Sharpe for comparison is helpful as one tool in the box. I believe the real risk measure of an investment is permanent loss of capital or opportunity for better return over a defined holding period. Considerations in this would be portfolio diversification as alluded to in the article and sources of risk, i.e. credit, interest rate, default, currency, sector etc.


RONALDO J from IL posted over 4 years ago:

Risk is universally defined as the frequency of an event (i.e., probability) times the outcome of an event (i.e., consequences). The Sharpe Ratio was orginally designed to compare various investment asset classes (e.g., bonds versus equities) where the risk-free rate is assumed to be the long term Treasury Bond Rate as a means to normalized these returns against the no selection option (i.e., guarantee return from the U.S. Government). Sharpe Ratio comparisons can be useful along with using other benchmarks (e.g., Beta) for volatility assessments. I feel that volatility is very important for traders since for short to medium time periods the average returns will change (i.e., bull or bear regimes). For investors, fundamental economic factors like sales growth, market share and free cash flow are more important than volatility. If you have identifed an outstanding company or investment and the prices come down you should buy more of it to increase overall portfolio returns.


D K from CA posted over 4 years ago:

There's a graphic interpretation of the Sharpe ratio not widely appreciated,namely that the risk level of a portfolio can be managed separately from the asset allocation. You can leverage up to a higher risk level by buying more of the asset allocation on margin or leverage down to a lower risk level by investing part of the portfolio risk free (i.e., in cash). In a plot of rate of return (y-axis) against risk level (x-axis), the risk free rate is a point on the y-axis and the Sharpe Ratio is the slope of the line from that point through the point plotted for the portfolio. Assuming margin cost and return on the cash investment are at the risk free rate, any leveraged portfolio would be a point on this line of leverage. The Modiglianis used this the belie the claim that "you can't eat risk adjusted return". Say allocation A has a higher Sharpe Ratio (steeper line!) than allocation B, but the latter has a higher return at a higher risk level: just leverage allocation A up to allocation B's risk level and the higher "risk adjusted" return is very real.


JOHN L from NJ posted over 4 years ago:

The Sharpe ratio is old finance technology based on theories we now know are not valid. The entire theoretical construct of CAPM is not supported by real world results. We have known for decades that Beta (risk measure based on volatility) is not positively related to returns. Low Beta (volatility) stocks as a group have returns that are equivalent to high Beta stocks as a group. Volatility does not explain differences in return. Therefore, risk adjusting returns based on a volatility measure is not meaningful.


D K from CA posted over 4 years ago:

I'm not sure which real world John L invests in. For forty years I have invested in a very simple one, diversify across asset classes and use rebalancing to produce gains. That is: sell high, buy low, sell higher, and so on. The greater the volatility, the more effective this approach! This is not "timing the market", there may be multiple rebalancing transactions as the market continues to move in the same direction. But I have always fully recovered to my prior high long before the S&P 500. Does slow me down on the long steady climbs, but hey, I still making money.


JOHN L from NJ posted over 4 years ago:

D K - Are you comparing your stock market performance to the S&P 500 total return index (includes reinvested dividends)? If so, I am impressed at your 40 years of out performance! This is the first I have heard of a stock market asset class re-balancing approach that beat the returns of buy and hold.


D K from CA posted over 4 years ago:

To be clear, the index is not an investment. I generally compare investment results to Vanguard index funds with distributions reinvested. For the distinction, consider the "great recession". Both the index and the fund topped out October 9, 2007. My portfolio retraced to its May 16, 2008 high by January 8, 2010. The vfinx fund with distributions reinvested recovered by August16, 2012; but the index did not retrace to its high until March 28. 2013. Recovery of both the fund and my portfolio determined by compounding daily rates of total return, ignoring cash flows. Your "40 years of out perfomance!" ignores my last remark. I've now been through two long marches of underperformance to any pure equity investment. All instances of outperforming them were in moderating and rocketing out of crashes (I sleep well even with very large losses since my approach has always made more on the rebound!). I recently played with a cash flow based benchmark, and my results (just 24 years with good cash flow records) were very comparable to the good old 60/40 vfinx / vbmfx mix - all distributions reinvested and rebalanced annually. For my full 44 years, the annualized return is 7.8%, but as Einstein once said: compounding is the killer app!


JOHN L from NJ posted over 4 years ago:

D K - Thank you for expanding on your investment approach. Everyone has their own style. I am always 100% invested in equity. No need for re-balancing. The ride is rough but the long term compounding is rewarding.


D K from CA posted over 4 years ago:

I am prepared to concede that return does not correlate with volatility. I thought why not check the data. I screen scraped Yahoo!'s quarterly performance data for eighteen Vanguard funds (not all index funds) with at least 24 years of data. I calculated Annualized Compound Rate (ACR) for performance and Annualized Standard Deviation (ASD) for volatility. The correlation was about 84%: the return was not due to the "risk level" but there was definitely a correlation. In some other analysis about the so-called lost decade (actually 12 years because the S&P 500 was 1229 at the end of 1998 and 1258 at the end of 2010), I calculated ACR and ASD for 26 rolling periods of 10 years each. The correlation was -92% !!! That's right: during the lost decade with two major bear markets, volatility was high with low returns while the two long stretches preceding and following were fairly steady rises: lower volatility with smashing returns.


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