sharpe ratio¶
The Sharpe ratio is a measure of risk-adjusted return used to evaluate the performance of an investment, portfolio, or strategy. It shows whether an investment's returns are due to smart investment decisions or just excessive risk.
Calculation and Formula¶
The Sharpe ratio is calculated by taking the excess return of the investment over a risk-free rate and dividing it by the standard deviation of those returns.
$$\text{Sharpe Ratio} = \frac{R_p - R_f}{\sigma_p}$$
| Variable | Description |
|---|---|
| $\mathbf{R_p}$ | The average return of the investment or portfolio. |
| $\mathbf{R_f}$ | The risk-free rate of return (e.g., the yield of a short-term U.S. Treasury Bill). |
| $\mathbf{R_p - R_f}$ | The excess return of the investment (the premium for taking risk). |
| $\mathbf{\sigma_p}$ | The standard deviation of the portfolio's excess return (a measure of its volatility/risk). |
Interpretation¶
In general, a higher Sharpe ratio is better. It indicates that the investment is generating more return for each unit of risk (volatility) taken.
Sharpe Ratio > 1.0: Considered acceptable or good.
Sharpe Ratio > 2.0: Considered very good (often described as excellent).
Sharpe Ratio > 3.0: Considered exceptional.
Key takeaway:
The ratio is a powerful tool because it penalizes performance that is achieved simply by taking on more risk. If two portfolios have the same return, the one with the lower volatility (and thus higher Sharpe ratio) is the better investment.
History¶
The Sharpe ratio was developed by Nobel laureate William F. Sharpe in 1966, originally published as the "reward-to-variability ratio." It is one of the most fundamental metrics in modern portfolio theory (MPT).
How to use sharpe ratio¶
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5520741
This paper reviews the pitfalls of naive Sharpe ratio analysis and provides a comprehensive framework for its proper use.