When assessing the performance of a mutual fund or another type of investment, most attention is paid to total returns. It’s an obvious metric for many reasons, but it is certainly not the only measure by which to judge investments.

Another way of analyzing performance is to calculate risk-adjusted returns. There is an amount of risk inherent in every type of investment, and every investor has their own risk appetite, which ultimately determines portfolio allocation. Generally, when an investor takes on risk, they do so with the expectation that it will lead to excess returns that beat the market.

But is a high-risk investment that generates slightly more than a lower-risk investment really worth increased exposure to volatility?

Calculating risk-adjusted returns can give investors and financial analysts a better understanding of how two investments compare relative to the levels of risk they assume, which can help them make more informed portfolio allocation decisions that can potentially increase returns while reducing risk.

## What is risk-adjusted return?

A risk-adjusted return is the profit that an investment generates over a specific time period in context of the risk it assumes.

What is risk? While it’s a commonly used term, risk has an exact financial definition. According to Investopedia, risk is the chance that an investment’s actual performance will differ from expected outcomes. Risk can be quantified in many ways, often by looking at historical data or using standard deviation to measure price volatility.

All things being equal, a more risky investment has a greater chance of performance variation than a less risky asset. That means while there is an increased chance of above-average profits, the downside risks of losing money are also greater. This explains why investors expect excess returns when taking on risk.

However, it is important to note that investing in securities is inherently risky. There is no magic pill that can totally eliminate the risk of losing an entire investment.

That said, each asset type has a different level of risk, whether mutual funds, equities, bonds or alternative investments like derivatives and credit swaps. Investment returns beyond the market are ideal, but piling on risk to achieve excess returns is not something every investor is comfortable with.

Measuring the risk-adjusted return of portfolio investments or a group of assets can provide investors with valuable perspective. In general, if two investments perform similarly over a period of time, the one with lower risk has a better risk-adjusted return. This is determined by comparing the investment returns to a benchmark index or risk-free rate.

## Why is measuring risk-adjusted return helpful?

Investment decisions aren’t made in a vacuum. Forces like volatility and general investor behavior continually shift markets. In the riptide of financial activity, both opportunities and risks are created. Investors need an objective way of measuring returns relative to risk level in order to make the best investment decisions.

For example, even if a high-risk investment outperforms a lower-risk alternative, its risk-adjusted return may indicate those excess returns might not be worth it.

This was potentially the case in 2017 when Bitcoin growth launched into the stratosphere, approaching $20,000 per unit near the end of the year. However, the extreme volatility of Bitcoin price swings reduced the value of its excess returns, according to its risk-adjusted returns. One analysis by a Japanese investment firm at the time found that Bitcoin’s risk-adjusted return was a fraction of the risk-adjusted returns that the S&P 500 produced over the same stretch, according to Business Insider.

We know that if two investments perform the same over a given time period, the lower-risk option will have the better risk-adjusted return. But another way of looking at this is from the angle that the greater the risk, the less valuable the returns are worth. That is, additional risk can have a diminishing effect of making the possibility of excess returns less attractive in context of the downsides.

If an investment has a higher amount of risk, the excess returns it generates are reduced; whereas a low-risk investment that performs even slightly beyond expected returns may be considered more valuable.

In the end, each investor or asset manager will look to construct a portfolio that aligns with their strategy and total risk tolerance. Using risk-adjusted returns can allow them to directly compare investments with different risk levels to help judge which is the best choice according to their desires for excess returns, which are hedged by risk appetite.

## How are risk-adjusted returns calculated?

There are many ways to calculate risk-adjusted return. Some of the most commonly used methodologies include:

### Sharpe ratio

This is one of the prevailing ways to calculate risk-adjusted returns. The calculation was developed by and named after the American economist and Nobel Laureate William Sharpe.

Essentially, the Sharpe ratio isolates the average profits generated by an asset independent of risk. A higher Sharpe ratio is indicative of a more worthwhile investment and is useful when comparing opportunities or making allocation decisions.

Functionally, the Sharpe ratio calculates excess returns of an investment beyond the risk-free rate per unit of volatility using standard deviation, a statistical measure of variance. A mutual fund that returns 11% on average over four years with a standard deviation of 5 would reasonably be expected to return between 6% and 16% during any given year of that time period.

The calculation works like this:

- Subtract the risk-free rate from an asset’s return. Commonly, U.S. Treasury bills are used as the benchmark, being a known asset with near-zero risk.
- Divide that number by the standard deviation of the asset’s return. Standard deviation plots the distribution of return data. Highly concentrated data indicates less volatility, whereas a wider spread of data could signal higher volatility.

A Sharpe ratio of 0 would indicate no returns beyond the risk-free rate. For an example, let’s say:

- Mutual fund A returned 9%. Subtracting the risk-free rate of 2.5% and dividing by the standard deviation of 5 we get a Sharpe ratio of
**1.3**. - Mutual fund B returned 13%, but has a standard deviation of 11.75, which leads to a Sharpe ratio of
**0.9.**

Any ratio above 1 is generally considered good, with 2 to 3 being excellent and anything beyond that a great bet. In this way, investors can see the excess returns they can expect in exchange per unit of risk, as Mutual fund A may be considered the better investment even though it returned less on average.

### Sortino ratio

Not losing money is just as important as making money. When making investment decisions, many asset managers may be more concerned with potential downside, which is where the Sortino ratio comes into play.

The two are set up similarly and in both cases a higher ratio is considered better. However, rather than using the entire standard deviation of an asset, as the Sharpe ratio does, the Sortino ratio uses only the downward distribution of returns below average.

Using the previous example,

- Mutual fund A has a downside standard deviation of 15, leading to a Sortino ratio of
**0.44**. - Mutual fund B has a downside standard deviation of 6, leading to a Sortino ratio of
**1.75**.

Although mutual fund A has a lower standard deviation than mutual fund B, it’s more likely to underperform expected returns on average. Thus, its Sortino ratio is lower, making mutual fund B the more attractive option in certain analyses.

### Jensen’s alpha

Alpha is a familiar term for many investors. It’s a performance measure of active returns that beat the market. Jensen’s alpha adds a risk-adjusted element that measures asset performance against a benchmark index to determine active, or abnormal, returns. This is done by utilizing the asset’s beta coefficient, which is a measure of volatility.

The equation looks like: *Portfolio Return − [Risk Free Rate + Portfolio Beta x (Market Return − Risk Free Rate)]*

Continuing with our example (which assumes a 2.5% risk-free rate), let’s add in a benchmark index variable of 10.5%:

- Mutual fund A has a beta coefficient of 0.65, leading to Jensen’s alpha equaling
**1.3**. - Mutual fund B has a beta coefficient of 1.2, leading to Jensen’s alpha equaling
**0.9**.

Positive alpha indicates an investment or asset manager is beating the market. However, in this example, mutual fund B is not overperforming as much relative to the amount of risk it is taking on, in comparison to mutual fund A.

Now, when you talk about alpha, you also have to talk about beta. The two are like yin and yang of investing metrics. Whereas alpha measures performance relative to a benchmark, beta measures relative volatility. For example, beta may indicate a mutual fund is exposed to more risk than its underlying assets, like an index. Beta can be useful in constructing investing strategies that reduce risk while also capitalizing on opportunities for returns.

### R-squared

R-squared measures the relationship between a fund and its benchmark index, often expressed as a percentage from 1 to 100. While not explicitly a performance metric, R-squared can be helpful in determining whether you’re getting the best bang for your investing buck in terms of risk-adjusted returns.

R-square calculates the correlation of movements in the fund and its benchmark. An R-squared value of 100 would mean every trend in the fund’s pricing would be explained by the same movements occurring in the benchmark index. That’s not so bad if it’s a passive fund, but for an actively managed fund, that means investors would be paying management fees without anything to show for beyond index-driven movement.

In order to justify the risk taken on by active strategies, investors may need a lower R-squared value. According to Morningstar, general ranges for R-squared are:

**High correlation**: 70-100%**Average correlation**: 40-70%**Low correlation**: 1-40%

### Treynor ratio

This calculation is structured similar to the Sharpe ratio but incorporates the beta coefficient à la Jensen’s alpha. As is the case with both the Sharpe and Sortino ratios, a higher value indicates a more attractive investment opportunity. Like R-squared, it can be used as a measure of reward for a unit of risk taken on by a portfolio or fund.

- Mutual fund A’s Treynor ratio would be
**1.0** - Mutual fund B’s Treynor ratio would be
**0.88**

## Learn more about how Magma approaches risk

Calculating the risk-adjusted return is a helpful way to compare investments and assets. With this information, you can make the best decisions for your portfolio. You can even contact us to ask about the Sharpe and Treynor ratios of the Magma Total Return Fund.

Risk is a core consideration in any investment decision we make for the Magma Total Return Fund. We monitor a number of volatility signals to guide our dynamic allocation of the fund toward the most opportune asset classes in any given economic conditions.

Want to learn more about the Magma Total Return Fund and how you can invest? Reach out today for more information.