How to Calculate Sharpe Ratio From Daily Returns

The Sharpe Ratio is a widely recognized metric for evaluating an investment’s risk-adjusted return. It helps investors understand the return received for the risk undertaken. This ratio allows for standardized comparison of investment opportunities, showing which generates a higher return relative to its volatility. Understanding this ratio can guide decisions by illustrating performance beyond raw returns.

Understanding the Core Components

Calculating the Sharpe Ratio requires three inputs: the portfolio’s return, the risk-free rate, and the portfolio’s standard deviation. These elements provide a comprehensive view of an investment’s efficiency in generating returns for a given level of risk.

The portfolio return, when using daily data, represents the percentage change in an investment’s value from one trading day to the next. For example, if a portfolio’s value increases from $100 to $101, its daily return is 1%.

The risk-free rate is the theoretical return on an investment with no financial risk. In the United States, this rate is often approximated by the yield on short-term U.S. Treasury bills, such as the 3-month Treasury bill. These rates are considered virtually free of default risk, backed by the full faith and credit of the U.S. government. Current Treasury rates are typically found on the U.S. Department of the Treasury’s website or through the Federal Reserve.

Standard deviation measures the historical volatility or dispersion of an investment’s returns around its average return. A higher standard deviation indicates that the investment’s returns have fluctuated more widely, quantifying the level of risk associated with the investment.

Preparing Daily Data for Annualization

To calculate the Sharpe Ratio from daily returns, the daily figures must first be converted into annualized values. This process ensures all components of the ratio are expressed over a consistent annual period, allowing for proper comparison. The first step involves calculating the average of the daily returns observed over a specific period, typically a year.

To annualize the average daily return, multiply it by the number of trading days in a year. Financial markets typically operate for approximately 252 trading days annually. For instance, if the average daily return is 0.05%, multiplying 0.0005 by 252 yields an annualized return of 12.6%.

The next step involves calculating the standard deviation of the series of daily returns. This daily standard deviation quantifies the daily volatility of the investment. For example, if the daily returns are 0.05%, 0.10%, and -0.02%, the standard deviation calculation would capture the dispersion of these values.

To annualize this daily standard deviation, multiply it by the square root of the number of trading days in a year. Using the common figure of 252 trading days, the daily standard deviation is multiplied by the square root of 252, which is approximately 15.87. If the daily standard deviation is 0.8%, for instance, the annualized standard deviation would be 0.008 multiplied by 15.87, resulting in approximately 12.7%.

Completing the Sharpe Ratio Formula

With the annualized portfolio return, annualized risk-free rate, and annualized portfolio standard deviation determined, the final step involves applying these values to the Sharpe Ratio formula. This formula quantifies the excess return generated per unit of risk taken by the investment.

The Sharpe Ratio formula is expressed as: (Annualized Portfolio Return – Annualized Risk-Free Rate) / Annualized Portfolio Standard Deviation. This structure highlights the investment’s return above the risk-free benchmark, normalized by its volatility.

Consider an example where the annualized portfolio return is 12.6%, the annualized risk-free rate is 3.0%, and the annualized portfolio standard deviation is 12.7%. First, subtract the risk-free rate from the portfolio return: 0.126 minus 0.030 equals 0.096. This difference represents the excess return earned above the risk-free benchmark.

Next, divide this excess return by the annualized portfolio standard deviation. Using the example values, 0.096 divided by 0.127 yields a Sharpe Ratio of approximately 0.76.

Interpreting and Applying the Ratio

The calculated Sharpe Ratio provides a quantifiable measure of an investment’s risk-adjusted performance. A higher Sharpe Ratio indicates that an investment is generating more return for each unit of risk assumed. This means the investment is more efficiently compensating the investor for the volatility endured.

The Sharpe Ratio is useful for comparative analysis between different investment opportunities. When evaluating multiple portfolios or strategies, comparing their respective Sharpe Ratios allows investors to identify which option offers superior risk-adjusted returns. For example, an investment with a Sharpe Ratio of 1.0 is generally considered to have performed better on a risk-adjusted basis than one with a ratio of 0.5.

It is important to consider the context when interpreting the Sharpe Ratio. The specific time period over which the returns are measured can influence the ratio’s value. Consistent returns over time typically lead to a more stable and reliable Sharpe Ratio.