Sharpe Ratio How to Calculate

Sharpe Ratio Calculator

Enter values and click 'Calculate' to see the Sharpe Ratio.

function calculateSharpeRatio() { var portfolioReturnInput = document.getElementById('portfolioReturn').value; var riskFreeRateInput = document.getElementById('riskFreeRate').value; var portfolioStdDevInput = document.getElementById('portfolioStdDev').value; var rp = parseFloat(portfolioReturnInput); var rf = parseFloat(riskFreeRateInput); var stdDev = parseFloat(portfolioStdDevInput); var resultDiv = document.getElementById('sharpeResult'); if (isNaN(rp) || isNaN(rf) || isNaN(stdDev)) { resultDiv.innerHTML = 'Please enter valid numbers for all fields.'; return; } if (stdDev <= 0) { resultDiv.innerHTML = 'Standard Deviation of Portfolio Returns must be greater than zero.'; return; } // Convert percentages to decimals for calculation var rpDecimal = rp / 100; var rfDecimal = rf / 100; var stdDevDecimal = stdDev / 100; var sharpeRatio = (rpDecimal – rfDecimal) / stdDevDecimal; resultDiv.innerHTML = 'Sharpe Ratio: ' + sharpeRatio.toFixed(4) + ''; }

Understanding the Sharpe Ratio

The Sharpe Ratio is a measure of a portfolio's risk-adjusted return. Developed by Nobel laureate William F. Sharpe, it is one of the most widely used metrics for evaluating the performance of an investment portfolio or strategy. Essentially, it tells you how much return you are getting for the amount of risk you are taking.

What Does it Measure?

The Sharpe Ratio quantifies the excess return (or risk premium) an investment generates per unit of total risk. It helps investors understand if the higher returns of a portfolio are due to smart investment decisions or simply a result of taking on excessive risk.

The Formula

The Sharpe Ratio is calculated using the following formula:

Sharpe Ratio = (R_p – R_f) / σ_p

• R_p (Portfolio Return): This is the average rate of return of the investment portfolio over a specified period.
• R_f (Risk-Free Rate): This is the return of a risk-free asset, such as a U.S. Treasury bond or a short-term government security. It represents the return an investor could expect without taking on any investment risk.
• σ_p (Standard Deviation of Portfolio Returns): This measures the volatility or total risk of the portfolio. A higher standard deviation indicates greater price fluctuations and thus higher risk.

Interpreting the Sharpe Ratio

A higher Sharpe Ratio is generally better, as it indicates that the portfolio is generating more return per unit of risk. Here's a general guideline for interpretation:

• Sharpe Ratio < 1: Poor (or sub-optimal)
• Sharpe Ratio 1.00 – 1.99: Good
• Sharpe Ratio 2.00 – 2.99: Very Good
• Sharpe Ratio ≥ 3.00: Excellent

It's important to compare Sharpe Ratios of portfolios with similar investment objectives and over the same time period. A high Sharpe Ratio suggests that the portfolio's returns are not just due to taking on more risk, but rather from superior investment management.

Example Calculation

Let's say you have a portfolio with the following characteristics:

• Portfolio Return (R_p): 12%
• Risk-Free Rate (R_f): 3%
• Standard Deviation of Portfolio Returns (σ_p): 8%

Using the formula:

Sharpe Ratio = (0.12 – 0.03) / 0.08 = 0.09 / 0.08 = 1.125

In this example, the Sharpe Ratio of 1.125 indicates a good risk-adjusted return for the portfolio.

Limitations

While powerful, the Sharpe Ratio has limitations:

• Assumes Normal Distribution: It assumes that portfolio returns are normally distributed, which is often not the case in real markets, especially during extreme events.
• Uses Standard Deviation as Risk: Standard deviation treats both upside and downside volatility as "risk." Some investors might only be concerned with downside risk.
• Backward-Looking: It's based on historical data, which may not be indicative of future performance.
• Manipulation: It can be manipulated by changing the frequency of return calculations or by smoothing returns.

Despite these limitations, the Sharpe Ratio remains a fundamental tool for investors to assess the efficiency of their portfolios in generating returns relative to the risk taken.