ARTIFICIAL INTELLIGENCE

The Sharpe Ratio is a key finance metric measuring an investment’s excess return (above the risk-free rate) per unit of its total risk (volatility/standard deviation), with a higher ratio indicating better risk-adjusted performance. – Sharpe Ratio –

The Sharpe Ratio is a fundamental metric in finance that quantifies an investment’s or portfolio’s risk-adjusted performance by measuring the excess return over the risk-free rate per unit of total risk, typically represented by the standard deviation of returns. A higher ratio indicates superior returns relative to the volatility borne, enabling investors to compare assets or portfolios on an apples-to-apples basis despite differing risk profiles.^1,2,3

Formula and Calculation

The Sharpe Ratio is calculated using the formula:

\text{Sharpe Ratio} = \frac{R_a - R_f}{\sigma_a}

Where:

• ( R_a ): Average return of the asset or portfolio (often annualised).^3,4
• ( R_f ): Risk-free rate (e.g., yield on government bonds or Treasury bills).^1,3
• ( \sigma_a ): Standard deviation of the asset’s returns, measuring volatility or total risk.^1,2,5

To compute it:

1. Determine the asset’s historical or expected average return.
2. Subtract the risk-free rate to find excess return.
3. Divide by the standard deviation, derived from return variance.^3,4

For example, if an investment yields 40% return with a 20% risk-free rate and 5% standard deviation, the Sharpe Ratio is (40% – 20%) / 5% = 4. In contrast, a 60% return with 80% standard deviation yields (60% – 20%) / 80% = 0.5, showing the lower-volatility option performs better on a risk-adjusted basis.⁴

Interpretation

• >2: Excellent; strong excess returns for the risk.³
• 1-2: Good; adequate compensation for volatility.^2,3
• =1: Decent; return proportional to risk.^2,3
• <1: Suboptimal; insufficient returns for the risk.³
• ?0: Poor; underperforms risk-free assets.^3,5

This metric excels for comparing investments with varying risk levels, such as mutual funds, but assumes normal return distributions and total risk (not distinguishing systematic from idiosyncratic risk).^1,2,5

Limitations

The Sharpe Ratio treats upside and downside volatility equally, may underperform in non-normal distributions, and relies on historical data that may not predict future performance. Variants like the Sortino Ratio address some flaws by focusing on downside risk.^1,2,5

Key Theorist: William F. Sharpe

The best related strategy theorist is William F. Sharpe (born 16 June 1934), the metric’s creator and originator of the Capital Asset Pricing Model (CAPM), which underpins modern portfolio theory.

Biography

Sharpe earned a BA in economics from UCLA (1955), an MA (1956), and PhD (1961) from Stanford University. He joined Stanford’s Graduate School of Business faculty in 1970, becoming STANCO 25 Professor Emeritus of Finance. His seminal 1964 paper, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” introduced CAPM, positing that expected return correlates linearly with systematic risk (beta). In 1990, Sharpe shared the Nobel Memorial Prize in Economic Sciences with Harry Markowitz and Merton Miller for pioneering financial economics, particularly portfolio selection and asset pricing.^1,5,7,9

Relationship to the Sharpe Ratio

Sharpe developed the ratio in his 1966 paper “Mutual Fund Performance,” published in the Journal of Business, to evaluate active managers’ skill beyond raw returns. It extends CAPM by normalising excess returns (alpha-like) by total volatility, rewarding efficient risk-taking. By 1994, he refined it in “The Sharpe Ratio” on his Stanford site, linking it to t-statistics for statistical significance. The metric remains the “golden industry standard” for risk-adjusted performance, integral to strategies like passive indexing and factor investing that Sharpe championed.^1,5,7,9

References

1. https://en.wikipedia.org/wiki/Sharpe_ratio

2. https://www.businessinsider.com/personal-finance/investing/sharpe-ratio

3. https://www.kotakmf.com/Information/blogs/sharpe-ratio_

4. https://www.cmcmarkets.com/en-gb/fundamental-analysis/what-is-the-sharpe-ratio

5. https://corporatefinanceinstitute.com/resources/career-map/sell-side/risk-management/sharpe-ratio-definition-formula/

6. https://www.personalfinancelab.com/glossary/sharpe-ratio/

7. https://www.risk.net/definition/sharpe-ratio

8. https://www.youtube.com/watch?v=96Aenz0hNKI

9. https://web.stanford.edu/~wfsharpe/art/sr/sr.htm