There are two types of funds: actively and passively managed. Passive funds follow an index, while active funds try to beat an index.

But what does it mean to “beat” an index? While many think it simply means providing a superior total return over a fixed period, this isn’t actually correct, especially when it comes to hedge funds. These funds are predominately in the business of providing superior risk-adjusted returns.

That “risk-adjusted” modifier is important, but what does it mean? To answer that, we must turn to the Sharpe ratio.

Developed by William F. Sharpe, the ratio shows the average return of an investment above the risk-free rate relative to total risk or volatility over the period of the investment. Sound complicated? It is.

Fortunately, with math we can make it a bit more understandable. To understand this concept, let’s first assume r = the investment’s return over a period of time, f = the risk-free rate, and d = the investment’s standard deviation of the portfolio return (i.e., the volatility of the investment’s return over the time period).

With just these three variables, we can express the Sharpe ratio formulaically thus:

**(r – f)/d**

Very simple, right? Of course, one of the tough parts is calculating an investment’s standard deviation—the math here is complex if done by hand, but fortunately no one is really expected to do that anymore; Excel formulas, Bloomberg terminals, or proprietary buy-side software will give this for you automatically.

So let’s assume we know these three things for an index, such as the S&P 500, which provides about an 8% return over the longer term. Let’s compare this to the risk-free rate of a 10-year Treasury (2.97% about now) and also assume the portfolio’s standard deviation is 13%. Now our formula looks like this:

**(8-2.97)/13 = 0.39.**

Simple, right?

Now we have calculated the Sharpe ratio of our benchmark, so let’s say that we’re comparing it to an actively managed index fund with a 5% return over the same period and a standard deviation of just 4%. Now our formula looks like this:

**(5-2.97)/4 = 0.51.**

Although our actively managed hedge fund got us smaller total returns, because of its lower volatility it has a higher Sharpe ratio (remember: higher is better for this metric). That means that, while the actively managed fund underperformed on an absolute return basis, it overperformed by a large margin on a risk-adjusted return basis.

For many retail investors, this doesn’t really matter. After all, you’re investing for decades for retirement, and the longer an investment, the less important volatility is. But for many other kinds of financial purposes—corporate finance, retirement funds, insurance funds, retail banking, etc.—liquidity demands mean risk-adjusted returns are much more important than absolute returns in many cases. Which is why many of these investors tolerate lower returns if there’s lower volatility alongside it.

Note that popular discussions of hedge fund underperformance, especially in the clickbait-dependent popular financial media, doesn’t discuss the subtlety of Sharpe ratios and risk-adjusted returns. But in the real world of financial professionals, understanding this is a requirement.