What Is Risk-Adjusted Return? (Examples And Formulas) – Quantified Strategies For Traders (2022)

Last Updated on October 19, 2022 by Oddmund Groette

Risk is an inherent part of any investment, which is why investors consider risk-adjusted returns when analyzing various investment options. But what is a risk-adjusted return?

A risk-adjusted return is a measure of return that compares the potential profit from an investment to the degree of risk that must be accepted in order to achieve it. The reference point is usually a risk-free investment, such as U.S. Treasuries. Risk-adjustment returns enable the investor to compare high-risk and low-risk investments.

In this post, we take a look at risk-adjusted returns: examples and explanations.

Table of contents:

What is meant by risk-adjusted return?

There isn’t a clear-cut definition of risk-adjusted return. One of the reasons is that many disagree as to what is risk. However, risk is mostly about avoiding swings in the returns – volatility. But please keep in mind that for example Warren Buffett and Charlie Munger argue that volatility is a very poor form of measuring risk. Their logic is that even a sound business is not immune to volatility and might suffer temporarily.

That said, in the rest of the article we mostly use volatility as a measure of risk.

A risk-adjusted return is a measure of return that compares the potential profit from an investment to the degree of risk that must be accepted in order to achieve it. The reference point is usually a risk-free investment, such as U.S. Treasuries. Risk-adjustment returns enable the investor to compare between high-risk and low-risk investments.

The metric can be applied to individual stocks, investment funds, or an entire portfolio. There are different methods of getting a risk-adjusted return, and depending on the method used, the risk calculation can be expressed as a number or a rating.

Risk and behavioral biases

If you have an investment or trading strategy that is liable to swings in return, it might lead to two things:

  • You might increase the risk of ruin, especially if you are leveraged (please read here for what is the risk of ruin in trading?).
  • Swings in volatility normally leads to behavioral mistakes (behavioral mistakes and risk).

We have been trading and investing for over 20 years, and we confirm that having losses might make us do irrational things. Even when you have the best trading strategies there are, you might abandon them in the midst of a drawdown. Please read more about drawdowns and trading biases, but at the end of the day, only experience can teach you how to deal with them.

  • Why is max drawdown important in trading?
  • The most common trading biases

How do you calculate a risk-adjusted return? Formula

There are different ways to calculate a risk-adjusted return. Some of the popular methods are Sharpe Ratio, Treynor Ratio, and Jensen’s Alpha.

Sharpe Ratio

This measures the profit of an investment that exceeds the risk-free rate, per unit of standard deviation — a measure of the total risk in an investment. You calculate Sharpe Ratio by taking the return of the investment, subtracting the risk-free rate, and dividing the result by the investment’s total risk (standard deviation).

Sharpe Ratio = (Rp — Rf)/δp

Where:

  • Rp = Expected Portfolio Return
  • Rf = Risk-free Rate
  • Sigma(p) = Portfolio Beta

Generally, a higher Sharpe ratio is better, all other things being equal, but a high ratio might indicate you have a curve fitted trading strategy.

  • What is a good Sharpe Ratio?

Treynor Ratio

The Treynor ratio is calculated the same way as the Sharpe ratio, but it uses the investment’s beta in the denominator. Beta is a measurement of the volatility (systematic risk) of a security or portfolio compared to the market as a whole (usually the S&P 500).

Treynor Ratio = (Rp — Rf)/βp

Where:

  • Rp = Expected Portfolio Return
  • Rf = Risk-free Rate
  • Beta(p) = Portfolio Beta

Just like Sharpe Ratio, a higher Treynor ratio is better.

  • Treynor Ratio – what is it?

Jensen’s Alpha

Jensen’s Alpha shows the active return on investment by measuring the performance of an investment against a market index benchmark. The alpha shows the performance of the investment after its risk is considered.

αJensens = Rp — Rf — β(Rm — Rf)

Where:

  • Rp = Expected Portfolio Return
  • Rf = Risk-free Rate
  • Beta(p) = Portfolio Beta
  • Rm = Market Return

Here’s how to interpret Jensen’s Alpha:

  • Alpha < 0 means the investment was too risky for the expected return.
  • Alpha = 0 means the return earned is sufficient for the risk taken.
  • Alpha > 0 means the return earned is greater than the assumed risk.
  • Jensen Ratio – what is it?

Amibroker’s risk-adjusted return – formula and example

We mainly use the trading software called Amibroker to backtest and make trading strategies (please read our Amibroker review). The software happens to have a sensible, yet simple, calculation of risk-adjusted returns:

Annual return % divided by Exposure %

Exposure is the time spent in the market.

For example, you might have a strategy that spends 57% of the time in the market, but still has managed a return of 8.4%. Thus, the risk-adjusted return is calculated to be 14.7% (8.4 divided by 0.57).

The principles are pretty simple, but at the same time it makes intuitive sense: your capital is always at risk in the markets, and the less time spent in the market the lower the risk. If you can accomplish the same return with significantly less time spent in the market, the better!

Trading strategies with good risk-adjusted returns (examples)

We provide our readers with plenty of robust trading strategies and ideas that we believe offer excellent risk-adjusted returns. You find them here:

  • Code And Logic For All Free Strategies/Articles
  • Single Strategies Or Discounted Bundles
  • Newsletter

Should you look for high risk-adjusted returns?

Yes!

A higher risk-adjusted return means that the return is worth the risk taken. It might make more sense to have lower returns with less drawdown than to have a high return with a huge drawdown. Seeking a higher return at the expense of much greater volatility could blow your account when there is a losing streak.

But unfortunately, in trading, history is no guarantee about the future: the biggest drawdown is yet to come. Backtesting is at best just a test of the past, and the future will always play out differently.

What is the purpose of the risk-adjusted return on capital?

The purpose of the risk-adjusted return is to know whether a return is worth the risks taken to achieve the return. By calculating the risk-adjusted return of an investment, you can judge whether you would get the best possible returns on investment with minimal risk.

Risk-adjusted return example

Let’s say you want to compare the returns of two ETFs: Fund X and Fund Y. Suppose Fund Y’s return over the past year is 12% with a standard deviation of 10%, while Fund X’s return is 10% with a standard deviation of 7%. Given a risk-free rate of 3% over that period, the risk-adjusted returns of the two funds, using the Sharpe Ratio, would be:

Fund Y: (12% – 3%) / 10% = 0.9

Fund X: (10% – 3%) / 7% = 1

As you can see, although Fund Y had a higher return, Fund X had a higher risk-adjusted return — the return per unit risk taken.

What is a good risk-adjusted return?

Generally, any Sharpe Ratio above 0.75 is considered good, but you can aim for 2, which is great for most investments (however, be careful about a curve fitted strategy).

The higher the value, the better the returns per risk taken up to a certain point. Investments with a higher Sharpe Ratio may not yield the highest returns, but they may be considered the better investment because they are worth the risk.

The aim of a trader is to have smooth returns. To show you an example we can have a look at the performance of the Swedish fund manager Brummer & Partners. The chart below shows the performance of one of their funds (red line) compared the stock market (grey line):

Clearly, the red line has a smoother development compared to the stock market’s. We are confident in saying most traders would prefer the red line compared to the grey line when it comes to real and live trading. Some might argue the grey line is best because it has higher returns, but that is a conclusion based on hindsight.

Being down more than 50% during the financial crisis in 2008/09 is devastating. Brummer’s return was positive during the financial crisis and could thus start compounding at a higher level when the dust settled. Many abandons a strategy in a drawdown – hence you want a smooth and good risk-adjusted return.

At the end of the day, only yourself can evaluate what is your optimal risk-adjusted return. Each investor and trader have their own preference or tolerance for risk, thus it doesn’t make sense to look at what others do or think.

Why is the risk-adjusted return important

There is volatility in the returns of every investment, which can from come trading mistakes or trading biases. The key thing is how the volatility is managed and whether the returns are worth the level of volatility.

Traders and investors stop trading after a drawdown, not knowing that drawdowns are inevitable. By calculating their risk-adjusted returns, they can know whether their strategies are making commensurate returns.

Risk-adjusted return: trading system and performance metrics

This article has mentioned a few ways to measure risk-adjusted return. There are plenty of ways to measure risk-adjusted return, and we have only touched upon a few. We recommend that you read our slightly longer article that covers trading system and strategy performance.

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