The concept of expected return is one that plays a vital role in just about every topic within the field of investing. Yet my (entirely anecdotal) experience suggests that many investors are unclear on what, exactly, “expected return” means.

**Expected return** is simply the sum of each of the possible outcomes, multiplied by its probability.

For example, when rolling a six-sided die, the expected return of a roll is a value of 3.5, calculated as follows:

(1/6 x 1) + (1/6 x 2) + (1/6 x 3) + (1/6 x 4) + (1/6 x 5) + (1/6 x 6) = 3.5.

### Expected Return in Investing

The expected return for an investment is calculated in precisely the same way: by summing {each outcome (i.e., possible return) multiplied by its probability}.

The trick, of course, is that *we don’t know* the probabilities of each outcome the way that we do when rolling a die. Therefore, in investing, the best we can do is estimate an expected return.

Often, past performance data is used as a stand-in for probabilities. In most cases this is better than nothing, but it still leaves a lot to be desired. For example, just because we have data that says that stocks have outperformed bonds in 77% of 5-year periods from 1928-2008, it’s inaccurate to say that there is a 77% probability that stocks will outperform bonds over any given 5-year period in the future.

### Don’t Expect the Expected Return

It’s important to remember that the expected return of an investment is simply one point (out of an infinite number of points) on the spectrum of possible returns. And, interestingly enough, with high-risk investments over short periods, we don’t actually expect to earn the expected return–or even anything particularly close to it.

Or, as Carl Richards puts it, “average is not normal.”

### Risk and *Expected* Return

The concept that risk and return are positively correlated is one of the most fundamental tenets of finance. What many people miss, however, is that it’s *expected* return that’s correlated with risk.

In other words, there’s no *knowing* that a high-risk investment is going to earn a greater return than a low-risk investment over a given period. All we can do is *expect* that it will. (There is, after all, a reason that it’s called “risk.”)

### The Role of Time

The longer the period we look at, the more likely it is that we’ll see a value close to the expected return.

That’s why, over short periods of time, stock returns are wildly unpredictable, yet over extended periods of time, inflation-adjusted stock returns tend to close in around a small range of values.

That’s also why, as we look at longer and longer periods, higher risk investments (i.e., stocks) become more and more likely to outperform lower risk investments (i.e., bonds).

### In Summary

Expected return frequently trips people up in two ways:

- It may have been estimated poorly in the first place (using poor estimates of the probability for each outcome), and
- Even if it
*was*calculated correctly, outcomes that are dramatically different from the expected return can still occur.

The most important things to remember are that the “expected” outcome becomes more and more likely over longer periods, and that–no matter how fancy our calculations–there’s no way to truly calculate the probability of any given outcome.

I find it’s useful to consider the expected value and the historical worst case for the given time period. I set my goals based on the more conservative worst case scenario. That way if I get the expected returns I can celebrate and if performance is terrible I’m still OK.

-Rick Francis