What is Risk-Adjusted Return?
The Risk-Adjusted Return is a measure of an investment’s return that takes into account the degree of risk involved in producing that return.
The objective of performing a risk-adjusted analysis is to determine the excess return that a particular investment is expected to generate relative to the risk undertaken.
- The risk-adjusted return measures an investment’s return relative to the risk undertaken to achieve the expected return.
- The standard use-case of risk-adjusted return metrics is to facilitate an “apples-to-apples” comparison of different investment opportunities with different risk profiles
- The three most common risk-adjusted return metrics used in practice are the Sharpe ratio, Sortino ratio, and Treynor ratio.
- The Sharpe Ratio calculates excess return per unit of total risk, using standard deviation as the risk measure.
- The Sortino Ratio measures excess return per unit of downside risk, utilizing downside deviation as the risk measure.
- The Treynor Ratio measures the excess return per unit of systematic (or market risk), employing beta as the risk measure.
How to Calculate Risk-Adjusted Return
The risk-adjusted return measures the implied performance of a portfolio relative to the risk assumed by the investment fund.
In practice, risk-adjusted returns provide investors with a tool to evaluate and compare investments in a more meaningful way than looking at absolute returns alone.
Therefore, the risk-adjusted return estimates the implied return on an investment relative to the risk attributable to that particular investment.
By considering both risk and return, investors can construct portfolios more in line with their risk tolerance and potentially achieve better long-term, risk-adjusted performance.
However, one critical point that must be understood is that measures of risk-adjusted return are each based on historical data (“backward-looking”) and thereby provide no guarantee of future performance (“forward-looking”).
The risk-adjusted return is, therefore, a tool for equity analysts and investors to perform a comparative analysis of investment opportunities—each with different risk profiles on an equal footing (“apples to apples”)—which is used in part to guide an investment strategy and portfolio construction.
- Risk-Return Trade-Off ➝ Comparing the risk-adjusted return on an investment matters because the insights derived provide a more comprehensive evaluation of an investment’s performance. Based on the implied risk-return trade-off, the incremental risk undertaken by an investor must be compensated with a higher return.
- Opportunity Cost of Capital ➝ The opportunity cost of capital is one of the most important concepts to understand in investing. In other words, the decision to allocate capital toward a specific investment is based on analyzing the risk-return profile of the investment opportunity and comparative analysis. The latter is performed to determine which opportunity has the most favorable risk-return profile (i.e., each investment decision is made on a relative basis).
Suppose there are two investment opportunities with comparable risk, but one has an implied risk-adjusted return of 10% while the other investment has a risk-adjusted return of 8%.
Considering the risk of capital loss is equivalent, the rational capital allocation decision should be to invest in the opportunity that yields a 10% risk-adjusted return.
Risk-Adjusted Return Formula
There are a multitude of methods for calculating the risk-adjusted returns on an investment or portfolio of securities.
The commonality among each measure of risk-adjusted return is that the expected return is relative to how much risk is attributable to the portfolio.
The three most common risk-adjusted return metrics used in practice are described in the following table:
| Risk-Adjusted Return Metric | Description |
|---|---|
| Sharpe Ratio |
|
| Sortino Ratio |
|
| Treynor Ratio |
|
Sharpe Ratio Formula
The Sharpe Ratio is the risk-adjusted return of an investment (or portfolio) measured by dividing the excess return by the standard deviation.
In short, the Sharpe ratio measures the excess return earned above the risk-free rate per unit of volatility.
The formula to calculate the Sharpe ratio subtracts the risk-free rate from the investment return and then divides the resulting figure by the investment’s standard deviation.
A higher Sharpe ratio implies a compelling risk-adjusted return, whereas a lower Sharpe ratio indicates a less attractive risk-adjusted return.
The risk-free rate is the yield earned on a security with no risk. In practice, the standard proxy for the risk-free rate is the 10-year Treasury note for companies based in the U.S.
Sortino Ratio Formula
The Sortino ratio is derived from the Sharpe ratio, with the differentiating factor being the measure of risk.
The main source of criticism for the Sharpe ratio is the denominator—the standard deviation of the investment—which is an oversimplification, according to critics.
Unlike the Sharpe ratio, the Sortino ratio only considers the standard deviation of negative returns (or “downside deviation”).
The adjustment is intended to address a shortcoming of the Sharpe ratio, which penalizes upside and downside volatility.
The intuition for using the Sortino ratio is that only the downside risk should reduce the risk-adjusted return.
Simply put, the upward price movement in the price of the security—even if volatile—should cause the expected return to increase, not decrease.
Hence, the risk adjusted return determined by the Sortino ratio reflects only the return relative to the downside risk.
Treynor Ratio Formula
The Treynor ratio measures an investment’s excess return above the risk-free rate per unit of systematic risk.
Systematic risk is measured by beta, which receives widespread criticism as a flawed measure of risk.
The concept of systematic risk—or “market risk”—refers to risk inherent to the entire market rather than impacting only one specific company or industry.
Considering the far-reaching scope of market risk, which impacts the entire economy, portfolio diversification cannot mitigate this risk.
The Treynor ratio measures the return earned from the incremental market risk.
The formula for calculating the Treynor ratio is equal to the investment return subtracted by the risk-free rate divided by the investment’s beta.
Note: The methods for measuring the risk-adjusted return are each imperfect and have their own set of flaws. Therefore, the best course of action is to view the metrics as tools to support the formation of an investment thesis.
Risk-Adjusted Return Calculation Example
Suppose we’re tasked with calculating the risk-adjusted return on a portfolio given the following set of assumptions.
Portfolio Assumptions
- Average Return of Portfolio (Rp): 10.0%
- Risk-Free Rate (rf): 4.0%
- Portfolio Beta (βp): 1.2
- Standard Deviation of Excess Return of Portfolio (σp): 12.5%
- Downside Deviation of Portfolio (σD): 10%
Starting off, we’ll calculate the Sharpe Ratio, which measures the performance of an investment compared to a risk-free security, after adjusting for its risk.
The Sharpe Ratio measures the excess return per unit of total risk, which we’ll calculate by subtracting the risk-free rate from the portfolio return and then dividing by the portfolio’s standard deviation.
Since the portfolio return assumptions were provided, we’ll plug them into the formula to arrive at a Sharpe ratio of 4.8%.
- Sharpe Ratio = (10% – 4%) ÷ 12.5% = 0.48, or 4.8%
Since our calculation of the Sharpe ratio is complete, we’ll now calculate the Sortino Ratio, which uses downside deviation instead of standard deviation to focus only on negative volatility.
Upon inputting our assumptions into the formula, we arrive at a Sortino ratio of 6.0%, which is 1.2% higher compared to the Sharpe ratio.
- Sortino Ratio = (10.0% – 4.0%) ÷ 10.0% = 0.60, or 6.0%
In the final step, we’ll calculate the Treynor ratio, which measures the returns earned in excess of a risk-free investment per unit of market risk.
The Treynor ratio is 5.0%, which we determined by subtracting the risk-free return from the portfolio return and then dividing it by the portfolio beta.
- Treynor Ratio = (10% – 4%) ÷ 1.2 = 5.0%
Portfolio Risk-Adjusted Return Summary
- Sharpe Ratio: 4.8%
- Sortino Ratio: 6.0%
- Treynor Ratio = 5.0%
Based on the insights derived from computing each risk-adjusted portfolio metric, an equity analyst at an investment fund can grasp a better understanding of the implied return with regard to portfolio risk.
Each of the risk-adjusted returns—determined using the Sharpe ratio, Sortino ratio, and Treynor ratio—provides a distinct perspective from a unique angle, so collectively, the output of the model should offer a complete analysis of the risk associated with a given portfolio.
In closing, the expected return metrics provide a comprehensive overview of the portfolio’s risk-adjusted return, accounting for total risk, downside risk, and market risk, respectively.
