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:

1. It may have been estimated poorly in the first place (using poor estimates of the probability for each outcome), and
2. 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.

One benefit of Oblivious Investing is that you can take an “I don’t know, and I don’t care” attitude about market swings and short-term market results. It’s quite freeing when compared to investment strategies that put you at the mercy of the month-to-month whims of the investing public.

Long-term market returns, however, are another story. There’s simply no way to create an investment plan without using something as your projected rate of return.

In other words, while, “I really can’t say for sure.” is the most truthful market prediction anybody can give, it’s also entirely unhelpful.

Darn.

My best guess

The three primary determinants of market return are:

1. Dividend yield
2. Earnings growth, and
3. Shifts in market P/E ratios (caused by changes in the demand for stocks).

Historically, over periods of 30 years or more, the first two factors (the more predictable ones) have made up the bulk of the return, while the third factor (the unpredictable one) has performed a much smaller role–generally either increasing or decreasing the annual return by 1% or so.

At the moment, applying this formula indicates that we can expect a 30-year annualized return between 7.5% and 9.5%.

Where things get tricky

The problem, as Carl reminds us, is that you don’t pay your bills with percentages. You pay them with dollars. And while expected annual returns become fairly predictable over long periods, expected total return becomes less predictable.

The reason, of course, is that a slight change in annual return–when compounded over multiple decades–causes a dramatic change in ending value.

For example, if an investor plans on 40 years of 10% returns, and she gets 40 years of 9% returns, she’ll have only 76% as much money as she planned on having–even though her estimated annual return wasn’t too far off.

So what should we plan on?

Naturally, the prudent thing to do is plan on a conservative rate of return. For example, based on the “dividend yield + earnings growth” formula mentioned above (often called the “Gordon equation”), I’d currently plan on a 7.5% annual rate of return over the next few decades.

(And for any period shorter than a few decades, my answer is still a stubborn “I have no idea.”)

Ongoing (infrequent) monitoring

At least as important as what return you should plan on earning is the question of how to monitor the return you’re earning to see if it’s living up to your expectations. In my opinion, an annual checkup–done at the same time as your annual rebalancing–should be quite sufficient.

If, when looking at your portfolio’s 5-year or 10-year returns, it appears that you’re falling short of your estimates, it’s time to either step up your contributions or adjust your goals.

In a comment on a recent post, Ethan gave one of the best explanations I’ve seen for why long-term returns are predictable, and short-term returns are not.

Here’s my attempt at explaining the concept visually. It’s not exactly action-packed, but hopefully it’s easy to understand.

Long-Term and Short-Term Stock Market Returns from Mike Piper on Vimeo.

Summary of video in case you can’t watch it:

If a company’s P/E ratio stays constant over a given period, then the company’s share price must increase at precisely the same rate as its rate of earnings growth. Therefore, the total return on the stock would be equal to its dividend yield plus earnings growth.

And the same thing applies for the market as a whole: If the average market P/E ratio stays constant, the stock market’s return will be equal to the market’s dividend yield plus its earnings growth.

Of course, P/E ratios don’t stay constant. They move around. Sometimes the market is scared, and P/E ratios are low. Other times the market is confident, and P/E ratios are high.

Over short periods, changes in market confidence (as measured by P/E ratio) will determine market returns. But over long periods, changes in P/E ratios will mostly level out, and market return will be equal to earnings growth plus dividend yield.

Same takeaway as always: If you want predictable returns in the stock market, you must stay in the market for an extended period. None of this jumping in and out funny business.

In the world of investing, there’s so much data available that it’s essentially impossible to look at all of it. Instead, we have to examine only a small slice of history at a time. Unfortunately, by carefully selecting which slice of history to look at, people can “prove” just about anything they want.

For example, I’m reading a book right now that repeatedly uses statements like, “Look at how well this strategy did in 2001 and 2002!” Of course, there’s no mention of how well the strategy did in the 8 years before, or in the 2 years after. (The book was published in 2004.)

The way I see it, using statements like this is just cheating. It’s an easy way to “prove” a point without digging for any more substantial data. What significance does a 2-year return have? As far as I can tell, the only thing it’s useful for is telling us how well the strategy might do over 2-year periods in the future. (And even for that purpose, it’s only meaningful when combined with data from several other 2-year periods.)

Which ten years?

The problem isn’t just with people selecting time frames that are too short. A similar strategy can be used to mislead people using periods of any length.

For example, if you look at the 10 years ending in 2008, the S&P returned -1.36% per year. But if you shift that period backward one year, it returned 5.84%. A clever marketer could quote one statistic or the other, whichever is more beneficial for selling his product. (Or if he really wanted to show high returns, he could quote the 10 years ending in 1998, over which the S&P 500 earned over 19% per year.)

It’s not just about time periods, either.

If you’d invested in American Funds’ Capital Income Builder, which “invests in common stocks of large, established companies with proven records of increasing dividends” you would have earned a 3.76% annual return for the 10 years ending 2/28/09–not bad considering how poorly the market did overall during that period.

However, if you’d invested in Fidelity Equity Income Fund (which follows essentially the same strategy as Capital Income Builder), you would have lost 2.35% per year over that same period.

Want to prove that investing in stocks with a high dividend yield is a great strategy? Quote Capital Income Builder’s success relative to the market. Want to prove that it’s a poor strategy? Quote Fidelity Equity Income Fund’s results.

Who can you trust?

In an environment in which people can use real facts to back up just about any statement they want, it’s difficult to know who you can trust. To the extent possible, I recommend doing your own research before accepting somebody’s claims. Try changing the assumptions (about period of time, for instance) and see if you still reach the same conclusion.

Does anybody happen to have any idea where I might be able to find up-to-date info regarding long-term gold returns? I’ve been searching online for a few days now and have had very little success.

Something like an updated version of the data in Jeremy Siegel’s Stocks for the Long Run would be great. Best-case scenario would be year-by-year prices, so I could calculate standard deviation and other similar stats.

Any help would be greatly appreciated!

Update: Thanks to “Frank” from Bad Money Advice.

As you know, the whole point of this blog is to encourage people to focus on the basics of investing while ignoring everything else. So for today we have the two fundamental factors in determining investment return.

1. How much money is the investment expected to pay?
2. How predictable is the payout?

It really is quite simple, but a little explanation probably wouldn’t hurt.

How much will the investment pay?

We’re not talking about a rate of return here. We’re talking about an amount of money. For example, a bond might be expected to pay $500 every 6 months for the next 10 years.

Of course, with many investments, this is clearly an estimate. For example, we can see that a given stock is paying X dollars in dividends each quarter, but we then have to make guesses as to whether that amount will increase, stay the same, or decrease.

How predictable is the payout?

All else being equal, investors will pay more for an investment that will reliably pay $500 per year than they will for an investment that will perhaps-pay-somewhere-around $500 per year. And that makes perfect sense.

As a result, the investment with the reliable payout will have a lower rate of return. (Paying more for a given payout by definition means a lower rate of return.)

All the factors that might make the payout on an investment less predictable are what are known collectively as “risk” (according to the traditional technical definition).

How to take advantage of this knowledge

Here’s the most important part: When investors consider the predictability of an investment’s payout, they look almost exclusively at short-term predictability.

As a result, stocks (unpredictable over the short-run) end up being priced such that they have a greater rate of return than bonds (fairly predictable over the short-run) and a much greater rate of return than CDs (very predictable over the short-run).

What’s so great for long-term investors, though, is that long-term stock payouts (for big enough groups of stocks, anyway) are actually relatively predictable. And this “high return plus predictable payout” is precisely what makes stocks so great for long-term investors.

Hopefully, if we can keep in mind the fact that there are fundamental reasons why stocks will earn more than other investments over extended periods, we can do a better job of keeping our heads during down markets.