How to Calculate Risk-Adjusted Return

Evaluating investment performance involves more than just looking at the returns an asset generates. While high returns are desirable, they do not tell the complete story without considering the level of risk undertaken to achieve them. Risk-adjusted return provides a comprehensive framework, offering insights into how much return is earned for each unit of risk assumed. This approach helps investors make informed decisions by balancing potential gains with volatility. Understanding risk-adjusted returns allows for a more meaningful comparison of different investment opportunities, moving beyond simple percentages to a deeper evaluation of efficiency.

Understanding Foundational Concepts

Before calculating risk-adjusted returns, it is important to grasp the fundamental concepts that form the basis of these measurements. Investment “return” refers to the gain or loss generated on an investment over a period, expressed as a percentage of the initial investment. This can include capital gains from asset price appreciation, dividends from stocks, or interest payments from bonds. A basic absolute return is calculated by dividing the profit or loss by the initial investment amount.

“Risk” in investing signifies the possibility that an investment’s actual return will differ from its expected return, encompassing the potential for loss. Total risk, often measured by standard deviation, reflects the overall volatility of an investment’s returns around its average. A higher standard deviation indicates greater price fluctuations and thus higher total risk. Systematic risk, measured by Beta, represents the sensitivity of an investment’s returns to movements in the overall market. A Beta of 1.0 means the investment moves in line with the market, while a Beta greater than 1.0 suggests higher sensitivity and a Beta less than 1.0 indicates lower sensitivity.

The “risk-free rate” serves as a baseline for investment analysis, representing the theoretical return on an investment with no associated financial risk. In practice, the yield on short-term U.S. Treasury bills is commonly used as a proxy for the risk-free rate, as the U.S. government is considered to have a very low probability of default. These Treasury securities provide a return that investors can expect without taking on market or credit risk, making them a suitable benchmark for evaluating riskier investments.

Calculating Key Risk-Adjusted Return Metrics

Several metrics exist to quantify risk-adjusted returns, each offering a unique perspective on an investment’s performance relative to its risk. These calculations apply foundational concepts to provide a more nuanced evaluation.

The Sharpe Ratio measures the excess return an investment generates per unit of total risk, using standard deviation as the risk measure. A higher Sharpe Ratio indicates better risk-adjusted performance.
(Investment Return – Risk-Free Rate) / Standard Deviation of Investment.
If an investment returned 12%, the risk-free rate was 4%, and its standard deviation was 15%, the calculation would be (0.12 – 0.04) / 0.15 = 0.08 / 0.15 = 0.53. This means the investment yielded 0.53 units of excess return for each unit of total risk taken.

The Treynor Ratio evaluates an investment’s excess return per unit of systematic risk, using Beta as the risk measure. This ratio is particularly useful for diversified portfolios, as systematic risk cannot be eliminated through diversification.
(Investment Return – Risk-Free Rate) / Investment Beta.
If the same investment returned 12%, the risk-free rate was 4%, and its Beta was 1.2, the calculation would be (0.12 – 0.04) / 1.2 = 0.08 / 1.2 = 0.067. This indicates the investment generated 0.067 units of excess return for each unit of systematic risk.

Jensen’s Alpha determines the excess return of an investment compared to what would be predicted by the Capital Asset Pricing Model (CAPM), given its systematic risk. A positive Alpha suggests the investment outperformed its expected return, while a negative Alpha indicates underperformance.
Investment Return – [Risk-Free Rate + Beta (Market Return – Risk-Free Rate)].
If the investment returned 12%, the risk-free rate was 4%, its Beta was 1.2, and the market returned 10%, the calculation would be 0.12 – [0.04 + 1.2 (0.10 – 0.04)] = 0.12 – [0.04 + 1.2 0.06] = 0.12 – [0.04 + 0.072] = 0.12 – 0.112 = 0.008. The Alpha of 0.008, or 0.8%, signifies the investment outperformed its expected return by 0.8%.

The Sortino Ratio is similar to the Sharpe Ratio but focuses specifically on downside risk, measuring excess return per unit of downside deviation. Downside deviation only considers the volatility of returns below a specified target, often the risk-free rate or zero, rather than all volatility.
(Investment Return – Risk-Free Rate) / Downside Deviation of Investment.
If the investment returned 12%, the risk-free rate was 4%, and its downside deviation was 8%, the calculation would be (0.12 – 0.04) / 0.08 = 0.08 / 0.08 = 1.0. This means the investment generated 1.0 unit of excess return for each unit of negative volatility.

The Information Ratio assesses the consistency of an active manager’s outperformance relative to a benchmark, considering the volatility of those excess returns. It is often used to evaluate mutual funds or hedge funds.
(Portfolio Return – Benchmark Return) / Standard Deviation of (Portfolio Return – Benchmark Return).
If a portfolio returned 15% while its benchmark returned 10%, and the standard deviation of their return differences was 5%, the calculation would be (0.15 – 0.10) / 0.05 = 0.05 / 0.05 = 1.0. An Information Ratio of 1.0 suggests the portfolio generated 1 unit of excess return for each unit of tracking error.

Interpreting Calculated Values

Interpreting the calculated values of risk-adjusted return metrics is important for making sound investment decisions. Generally, a higher value for any of these metrics indicates better performance relative to the risk assumed. These numbers provide a standardized way to compare investments that may have vastly different absolute returns or risk profiles.

For the Sharpe Ratio, values above 1.0 are often considered good, meaning the investment is providing more return than risk. A Sharpe Ratio of 0.53, as in our example, suggests a moderate level of risk-adjusted performance. Comparing this to another investment with a Sharpe Ratio of, for instance, 0.80 would indicate the latter offers superior risk-adjusted returns.

A positive Treynor Ratio or Jensen’s Alpha suggests that the investment has generated returns exceeding what would be expected given its systematic risk. Our example’s Treynor Ratio of 0.067 and Jensen’s Alpha of 0.008 both indicate positive performance relative to systematic risk and the market. Conversely, a negative Alpha implies the investment underperformed its expected return, possibly indicating a need for reevaluation.

The Sortino Ratio, with its focus on downside risk, provides a more conservative view of risk-adjusted performance, which can be particularly useful for risk-averse investors. An investment with a Sortino Ratio of 1.0, as in our example, means its excess return is equal to its downside volatility. Comparing this to another investment, a higher Sortino Ratio would signify more favorable returns for the downside risk taken.

The Information Ratio, when applied to a managed portfolio, helps evaluate the skill of an investment manager. An Information Ratio of 1.0 suggests a manager has consistently generated excess returns relative to the benchmark, indicating strong active management. These metrics are most valuable when used for comparative analysis, allowing investors to weigh different opportunities against each other or against relevant industry benchmarks. Each metric captures a specific aspect of risk—Sharpe for total risk, Treynor for systematic risk, and Sortino for downside risk—guiding investors to select the most appropriate evaluation tool for their specific needs.