The Sharpe Ratio facilitates the comparison of investment returns with their corresponding risks. It highlights the insight that excess returns over periods might signify greater volatility and risk rather than investing finesse.
Economist William F. Sharpe proposed this ratio in 1966, originating from his work on the Capital Asset Pricing Model (CAPM), which earned him the Nobel Prize in 1990.
Key Takeaways
- The Sharpe ratio divides a portfolio’s excess returns by its volatility to assess risk-adjusted performance.
- Excess returns exceed an industry benchmark or the risk-free rate of return.
- The formula can utilize historical returns or forecasts.
- Higher Sharpe ratios favorably compare similar portfolios.
- The Sharpe ratio has certain limitations and may be overstated for specific strategies.
Formula and Calculation of the Sharpe Ratio
In its most straightforward form:
$$ \text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}.$$
where:
- $R_p$ = return of portfolio
- $R_f$ = risk-free rate
- $σ_p$ = standard deviation of the portfolio’s excess return
Standard deviation is derived from the variability of returns over time.
For example, the numerator of a 10-year Sharpe ratio might average 120 monthly return differentials against an industry benchmark. Its denominator is the standard deviation of these monthly returns:
- Calculate return variance each period, square it, and sum the squares.
- Divide the sum by the number of periods.
- Take the square root of the quotient.
What the Sharpe Ratio Can Tell You
One vital use of the Sharpe ratio is comparing risk-adjusted relative returns to investment benchmarks or specific strategies:
- It defines risk-free rate assumptions and potential return variances.
- Evaluates whether returns follow historic or expected volatility patterns.
- Highlights investment skills versus risk after adjusting for standard deviation formulas.
- Aids in distinguishing luck from smart investment decisions.
For instance, during the Dot-Com Bubble or recent meme stock frenzies, low-quality, speculative stocks might outperform blue chips. However, the Sharpe ratio can vett relative manager skill amid market volatilities.
Sharpe Ratio Pitfalls
In practice, the Sharpe ratio:
- Can be manipulated via selective return intervals.
- Depends on correct[inappropriate usage](normal statistical distributions), overstating tail risks.
- Faces issues from market phenomena like herding or serial correlations, distorting actual volatility.
Sharpe Alternatives: The Sortino and the Treynor
Recognizing inherent flaws, the Sortino and Treynor Ratios serve as key alternatives:
- Sortino Ratio: Adjusts for only downside risk by ignoring above-average returns.
- Treynor Ratio: Considers excess returns above a benchmark/risk-free rate balanced against beta or systematic market-related risk exposure.
Example of How to Use Sharpe Ratio
Suppose an investor evaluates a hedge fund addition to a portfolio reaching 18% annual return with 12% annualized volatility. If this allocation lowers expected returns to 15% but reduces volatility to 8%, the new projected Sharpe ratio potentially appears favorable:
- Original Performance: (18 - 3) / 12 = 1.25 (based on historic return/volatility).
- Adjusted Performance: (15 - 3) / 8 = 1.5
Should the new Sharpe matrix outperform, it testifies to infer good risk-adjusted benefits.
What Is a Good Sharpe Ratio?
Generally, reviews describe ratios beyond 1 as “good.” Yet, the actual merit relies on peer or market-specific context, often urging performance assessments within its comparable basket.
How Is the Sharpe Ratio Calculated?
To calculate:
- Subtract the risk-free rate from portfolio returns (using suitable yield proxies like Treasury bonds).
- Divide by the portfolio standard deviation of the remaining return.
What Is the Sharpe Ratio of S&P 500?
As of June 30, 2023, the S&P 500 displayed a Sharpe Ratio of 0.88.
The Bottom Line
The Sharpe ratio, formulated by William F. Sharpe, assists investors in juxtaposing returns against risks. It emphasizes similar fund/unit trust performance, ensuring investments’ risk tendencies align accordingly.
Related Terms: Sortino Ratio, Treynor Ratio, Capital Asset Pricing Model, risk-free rate, standard deviation, beta, volatility
References
- Stanford University. “The Sharpe Ratio”.
- The Nobel Prize. “William F. Sharpe”.
- PortfoliosLab. “S&P 500 Portfolio”.
