What is the Sharpe ratio?
The Sharpe ratio (also referred to as the Sharpe Index or Modified Sharpe ratio) is a financial metric commonly used to calculate the performance of a financial portfolio or investment. It is a measure that enables investors to understand the risk-adjusted return of a portfolio or investment.
Put differently, the Sharpe ratio is a metric that calculates the performance of a financial portfolio by considering its risk.
The inventor of the Sharpe ratio
The Sharpe ratio is named after its inventor, an American economist, William Forsyth Sharpe (born in 1934).
Sharpe developed the capital asset pricing model (CAPM) in the 1960s. The CAPM has become a fundamental concept in the management of portfolios and in financial economics. It describes the relationship between systematic risks and investment returns.
The Sharpe ratio is based on the capital asset pricing model.
Together with Harry Markowitz and Merton Miller, Sharpe received the Nobel Prize in Economic Sciences in 1990. In a press release on October 16, 1990, the Royal Swedish Academy of Sciences referred to the three recipients as ‘pioneers in the theory of financial economics and corporate finance.’
The Academy awarded the Nobel Prize to Sharpe ‘for his contributions to the theory of price formation for financial assets, the so-called, Capital Asset Pricing Model (CAPM).’
Calculating the Sharpe ratio
The formula used to calculate the Sharpe ratio is as follows:
Sharpe ratio = (Rx – Rf)/StdDev Rx
Where:
- Rx = Expected return of portfolio
- Rf = Risk-free rate of return
- StdDev Rx = Standard deviation of portfolio’s excess return.
The Sharpe ratio can be applied to calculate the past performance of a financial portfolio or its expected future performance.
Understanding and interpreting the Sharpe ratio
The Sharpe ratio is a well-known and reputable metric to measure risk-adjusted relative returns on an investment or investment portfolio.
The risk-free rate of return (Rf) was originally used in the formula to indicate an investor’s hypothetical minimal borrowing costs.
The ratio is all about reducing volatility and maximising risks. Simply put, the Sharpe ratio indicates how much excess return an investor is receiving in return for the extra volatility tolerated as the ‘cost’ for holding a riskier investment.
Investment portfolios that have a higher return, but are also accompanied by considerably higher risk, are not the best portfolio for an investor. Traders, as well as investors, should regard volatility as the price (cost) involved for holding investments (assets) with potentially large returns.
As in most things in life, the theorem – There ain’t no such thing as a free lunch (TANSTAAFL) – also applies to investments.
Ultimately, the personal preference and risk profile of an investor determine whether he/she is willing to carry the potential risk for a higher return.
The numerator (Rx – Rf) of the formula to calculate the Sharpe ratio refers to the so-called excess return, indicating the difference between the return on the investment portfolio and the return on risk-free assets. The difference must have a positive value because a negative value would indicate that an investor could have generated a better return than the one obtained by a fund manager, had he or she invested in risk-free financial instruments.
The denominator (StdDev Rx) indicates the volatility – standard deviation – of the investment portfolio return
The Sharpe ratio is mostly used as a tool for selecting funds.
Examples of the Sharpe ratio
- Example #1
Let us assume that investor A wants to add a fund to her portfolio that has a return of 10% over the past year with a current risk-free rate of 4%. The volatility of the returns was 9%.
Sharpe ratio = (10% – 4%)/9%
= 6%/9%
= 66.67% or 0.67
By adding a new fund, investor A expects that the return of her portfolio will fall to 8%, but that the volatility will also drop to 5%. If the risk-free rate stays 4%, then the calculation is as follows:
Sharpe ratio = (8% – 4%)/5%
= 4%/5%
= 80% or 0.80
While the returns have decreased, the Sharpe ratio has increased. Hence, on a risk-adjusted basis the returns have also improved.
- Example #2
Let us say we have two investments (X and Y) with the following information:
Investment X
Portfolio return: 35%
Risk-free rate: 20%
Standard deviation: 10%
Investment Y
Portfolio return: 55%
Risk-free rate: 20%
Standard deviation: 70%
Initially, it seems that investment Y outperformed investment X. Let us now evaluate this assumption by applying the Sharpe ratio.
- Investment X
Sharpe ratio = (35% – 20%)/10%
= 15%/10%
= 150% or 1.5
- Investment Y
Sharpe ratio = (55% – 20%)/70%
= 35%/70%
= 50% or 0.5
The Sharpe ratio shows that investment X performed better in relation to the relative risk involved in the investment. Put differently, the numbers indicate that investment Y is taking on substantially more risk than investment X, with a higher possibility of eventually suffering losses.
Advantages of the Sharpe ratio
The Sharpe ratio can be used to assess the performance of an individual stock or the total performance of an investment portfolio, consisting of a collection of investments.
It provides a clear picture to investors, enabling them to ascertain whether the risk they take is offering good returns or not.
The ratio is an excellent indicator to observe the volatility of the stocks of a company.
Limitations of the Sharpe ratio
Although a well-known and well-reputed measure of risk-adjusted return on an investment, the Sharpe ratio also has limitations. Such as:
- The lack of volatility data.
- Illiquid assets can push an overall investment portfolio’s standard deviation down, which can affect the Sharpe ratio.
- The Sharpe ratio is a lagging indicator that ‘accounts for the historical distribution of returns and volatility. Therefore, the ratio provides no indication of forecast of future risks and returns,’ according to Trading Sim.
A negative Sharpe ratio
The Sharpe ratio is negative when excess return is negative, meaning the return on an investment portfolio or an investment is lower than the risk-free rate.
However, a negative Sharpe ratio provides not much useful information.
The Sharpe ratio versus the Treynor ratio
The Treynor ratio, also referred to as the reward-to-volatility ratio, was developed by Jack Treynor (1930 – 2016), an American economist who was one of the inventors of the Capital Asset Pricing Model (CAPM).
While the Sharpe ratio looks at an investment portfolio return against the rate of return for a risk-free investment, the Treynor ratio divides excess return over a risk-free rate or benchmark (such as the S&P 500 index) by the beta coefficient of an investment portfolio, or security, as a metric of its systematic risk exposure.
The systematic risk refers to the sensitivity of an investment portfolio, security, or fund to market movements and fluctuations.
Put differently, the beta coefficient determines the degree to which the volatility of an investment or security correlates to the volatility of a financial market.
The Teynor ratio enables investors to determine whether they are being compensated for additional risk above the risk created by the market.
For instance, an investment portfolio with a return of 15%, versus an overall market return of 11%, will only be assessed on the excess of 4% (15% – 11%).
What is a good Sharpe ratio?
Sharpe ratio margins:
- Less than 1 = bad or sub-optimal.
- 1 – 1.99 = acceptable to good.
- 2 – 2.99 = particularly good
- Greater than 3 = excellent
Hence, the higher the Sharpe ratio of a portfolio or fund, the better its returns have been in relation to the amount of investment risk taken.
Frequently asked questions
What is the Sharpe ratio, and why is it important?
The Sharpe ratio is a financial metric used to evaluate the risk-adjusted return of an investment or portfolio. It helps investors understand whether the returns justify the risk taken. A higher Sharpe ratio indicates better risk-adjusted returns.
What is considered a good Sharpe ratio?
A Sharpe ratio is evaluated as follows:
Less than 1: Sub-optimal
1 – 1.99: Acceptable to good
2 – 2.99: Particularly good
Greater than 3: Excellent
The higher the Sharpe ratio, the better the investment’s risk-adjusted performance.
How is the Sharpe ratio used in investment decision-making?
The Sharpe ratio helps investors evaluate the risk-adjusted performance of a portfolio or investment. A higher Sharpe ratio indicates better returns relative to the risk taken, making it a useful tool for comparing different investment options.
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