The Best 5 Risk-Adjusted Return Formulas Traders Must Know
Risk-adjusted return is a concept that measures how much return an investment generates relative to the amount of risk it involves. It helps investors compare different investments based on their risk-reward profiles and choose the ones that suit their risk tolerance and objectives.
In this article, we will explain what risk-adjusted return is, why it is important in trading, and how to calculate it using various formulas. We will also provide some tools for calculating risk-adjusted returns online.
What is Risk-Adjusted Return?
Risk-adjusted return is a metric that determines how risky a trading strategy or investment is. A strategy with a high Sharpe ratio will have low drawdowns and high returns. On the other hand, a low Sharpe ratio asset incurs a lot of volatility for little return.
There are several metrics you can use to calculate risk-adjusted returns, which we will cover later in this article. You can use risk-adjusted returns to analyze individual stocks, trading strategies, investment funds, and entire portfolios.
Why Risk-Adjusted Returns are Important in Trading
Risk-adjusted returns are important in trading because they help traders evaluate their performance and optimize their strategies. By aiming for good risk-adjusted returns, traders can stay in the game longer since they minimize drawdowns, which are the declines in the value of a trading account from its peak to its trough.
Drawdowns can have a significant impact on the long-term profitability of a trader, as they require higher returns to recover from. For example, if a trader loses 50% of their account, they need to make 100% return to break even. However, if they lose only 10%, they need to make only 11% to break even.
Therefore, by reducing drawdowns, traders can preserve their capital and compound their returns more effectively. This can make a big difference in the long run, as shown in the chart below.
Risk-Adjusted Return Formulas
There are several methods of risk-adjusting performance, such as the Sharpe ratio, Treynor ratio, R-squared, Sortino ratio, and risk-adjusted return on capital. Each method has its own advantages and limitations and may yield slightly different results.
1- Sharpe Ratio
The Sharpe ratio is one of the most common ways to calculate risk-adjusted return. It was developed by Nobel laureate William Sharpe, and it measures the excess return per unit of standard deviation (or volatility).
The formula for the Sharpe ratio is:
Sharpe Ratio = Return - Risk Free Rate / Volatility
The return is the annualized return of the investment over a given period of time
The risk-free rate is the yield on a no-risk investment, such as a Treasury bill, for the relevant period of time
The volatility is the standard deviation of the investment’s returns over the same period of time
The Sharpe ratio shows how much excess return (or return above the risk-free rate) an investment generates for each unit of volatility (or risk). A higher Sharpe ratio means better risk-adjusted performance. A lower Sharpe ratio means worse risk-adjusted performance.
For example, say Mutual Fund A returned 12% over the past year and had a standard deviation of 10%, Mutual Fund B returned 10% and had a standard deviation of 7%, and the risk-free rate over the time period was 3%. The Sharpe ratios would be calculated as follows:
Mutual Fund A: (12% - 3%) / 10% = 0.9
Mutual Fund B: (10% - 3%) / 7% = 1
In this case, Mutual Fund B has a higher Sharpe ratio than Mutual Fund A, which means it has a better risk-adjusted return. Even though Mutual Fund A has a higher return, it also has a higher volatility, which reduces its risk-adjusted performance.
2- Treynor Ratio
The Treynor ratio is another way to calculate risk-adjusted return. It was developed by Jack Treynor, and it measures the excess return per unit of systematic risk (or beta).
The formula for the Treynor ratio is:
Treynor Ratio = Return − Risk Free Rate / Beta
The return, the risk-free rate, and the beta are all annualized values over a given period of time.
The Treynor ratio shows how much excess return (or return above the risk-free rate) an investment generates for each unit of systematic risk (or market risk). A higher Treynor ratio means better risk-adjusted performance. A lower Treynor ratio means worse risk-adjusted performance.
For example, say Mutual Fund C returned 15% over the past year and had a beta of 1.2, Mutual Fund D returned 13% and had a beta of 0.8, and the risk-free rate over the time period was 3%. The Treynor ratios would be calculated as follows:
Mutual Fund C: (15% - 3%) / 1.2 = 10
Mutual Fund D: (13% - 3%) / 0.8 = 12.5
In this case, Mutual Fund D has a higher Treynor ratio than Mutual Fund C, which means it has a better risk-adjusted return. Even though Mutual Fund C has a higher return, it also has a higher beta, which reduces its risk-adjusted performance.
3- R-Squared
R-squared is not a measure of risk-adjusted return per se, but it is often used in conjunction with other measures, such as the Sharpe ratio or the Treynor ratio. R-squared is a measure of how well an investment’s returns are explained by the market’s returns.
The formula for R-squared is:
R2 = Variance of Investment and Market / Variance of Investment × Variance of Market
The variance is a measure of how much the returns deviate from their average value.
The variance of investment and market is the covariance, which is a measure of how much the returns move together.
R-squared ranges from 0 to 1, where 0 means no correlation and 1 means perfect correlation. A high R-squared means that most of the investment’s returns are explained by the market’s returns, which implies that the investment has a high systematic risk (or market risk). A low R-squared means that most of the investment’s returns are not explained by the market’s returns, which implies that the investment has a low systematic risk (or market risk).
R-squared can be used to evaluate how appropriate a measure such as the Sharpe ratio or the Treynor ratio is for an investment. If R-squared is high, then using the Sharpe ratio or the Treynor ratio makes sense, as they both account for systematic risk. If R-squared is low, then using the Sharpe ratio or the Treynor ratio may not be accurate, as they may not capture the unsystematic risk (or specific risk) that affects the investment.
For example, say Mutual Fund E returned 14% over the past year and had a standard deviation of 12%, a beta of 0.9, and an R-squared of 0.8. The Sharpe ratio and the Treynor ratio would be calculated as follows:
Sharpe Ratio: (14% - 3%) / 12% = 0.92
Treynor Ratio: (14% - 3%) / 0.9 = 12.22
In this case, both measures indicate a good risk-adjusted performance, and they are consistent with each other because R-squared is high, which means that most of the fund’s returns are explained by the market’s returns.
4- Sortino Ratio
The Sortino ratio is a variation of the Sharpe ratio that only considers the downside deviation (or downside risk) instead of the standard deviation (or total risk). The downside deviation is a measure of how much the returns fall below a minimum acceptable return (or target return).
The formula for the Sortino ratio is:
Sortino Ratio = Return − Target Return / Downside Deviation
The return and the target return are annualized values over a given period of time. The target return can be any value that the investor considers acceptable, such as the risk-free rate, the inflation rate, or a personal goal. The downside deviation is calculated by taking the standard deviation of the negative returns that are below the target return.
The Sortino ratio shows how much excess return (or return above the target return) an investment generates for each unit of downside deviation (or downside risk). A higher Sortino ratio means better risk-adjusted performance. A lower Sortino ratio means worse risk-adjusted performance.
For example, say Mutual Fund G returned 18% over the past year and had a downside deviation of 8%, Mutual Fund H returned 17% and had a downside deviation of 6%, and the target return over the time period was 5%. The Sortino ratios would be calculated as follows:
Mutual Fund G: (18% - 5%) / 8% = 1.63
Mutual Fund H: (17% - 5%) / 6% = 2
In this case, Mutual Fund H has a higher Sortino ratio than Mutual Fund G, which means it has a better risk-adjusted return. Even though Mutual Fund G has a higher return, it also has a higher downside deviation, which reduces its risk-adjusted performance.
5- How to Calculate Risk-Adjusted Return on Capital
Risk-adjusted return on capital (RAROC) is a method of calculating risk-adjusted return for banks and other financial institutions. It measures the return on capital after accounting for credit risk, market risk, and operational risk.
The formula for RAROC is:
RAROC = Expected Revenue − Expected Loss − Expected Expense / Economic Capital
The expected revenue is the income generated by the assets or activities of the institution
The expected loss is the amount of money that the institution expects to lose due to credit defaults, market fluctuations, or operational failures
The expected expense is the cost of running the institution, such as salaries, taxes, and overheads
The economic capital is the amount of money that the institution needs to hold as a buffer against unexpected losses
The RAROC shows how much profit (or net income) an institution generates for each unit of economic capital (or risk capital). A higher RAROC means better risk-adjusted performance. A lower RAROC means worse risk-adjusted performance.
For example, say Bank A has an expected revenue of $10 million, an expected loss of $2 million, an expected expense of $3 million, and an economic capital of $20 million. The RAROC would be calculated as follows:
RAROC: ($10 million - $2 million - $3 million) / $20 million = 0.25
This means that Bank A generates $0.25 of profit for every $1 of economic capital.
Risk-Adjusted Return Calculators
Calculating risk-adjusted returns can be tedious and complex, especially if you have to deal with multiple investments and time periods. Fortunately, there are some online tools that can help you calculate risk-adjusted returns easily and quickly.
Here are some examples of risk-adjusted return calculators that you can use:
How You Can Use Risk-Adjusted Returns - Bottom Line
Risk-adjusted return is a vital concept for traders and investors who want to evaluate their performance and optimize their strategies. By using various methods of risk-adjusting performance, such as the Sharpe ratio, Treynor ratio, R-squared, Sortino ratio, and RAROC, traders and investors can compare different investments based on their risk-reward profiles and choose the ones that suit their risk tolerance and objectives.
Risk-adjusted returns can also help traders and investors avoid excessive drawdowns, preserve their capital, and compound their returns more effectively. By using online tools such as risk-adjusted return calculators, traders, and investors can simplify the calculation process and save time and effort.
FAQ
How do you calculate risk-adjusted return?
There are different methods of calculating risk-adjusted return, such as the Sharpe ratio, Treynor ratio, R-squared, Sortino ratio, and RAROC. Each method has its own formula and assumptions and may yield slightly different results. The general idea is to compare the return of an investment to a risk-free or a target return and divide it by a measure of risk, such as volatility, beta, or downside deviation.
Is IRR a risk-adjusted return?
IRR is not a risk-adjusted return because it does not take into account the riskiness of the cash flows or the opportunity cost of capital. To adjust IRR for risk, one can use methods such as modified IRR (MIRR), which uses different discount rates for positive and negative cash flows, or risk-adjusted IRR (RAIRR), which uses a risk premium to adjust the discount rate.
Is risk-adjusted return the Sharpe ratio?
The Sharpe ratio is one of the most common ways to calculate risk-adjusted return, but it is not the only one. There are other methods, such as the Treynor ratio, R-squared, Sortino ratio, and RAROC, that may be more suitable for different types of investments or investors.
What is risk-adjusted return in simple words?
Risk-adjusted return is a concept that measures how much return an investment generates relative to the amount of risk it involves. An asset with a high Sharpe ratio will have more of a straight line up, while an asset with a low Sharpe ratio may look like a rollercoaster of returns.
How do you calculate risk-adjusted return on a mutual fund?
One way to calculate risk-adjusted return on a mutual fund is to use the Sharpe ratio. You can use sites like Morningstar to automatically view risk-adjusted returns for mutual funds, ETFs, and stocks. Here is an example of Morningstar’s risk tab for the mutual fund FXAIX.
