What Return can we Expect from Stocks?

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This article is intended for the educated layman. It was written as part of a continuing series of articles on a variety of investment topics.  To view all the articles in this series, click on “More by the same author” in the left margin.

The race is not always to the swift nor the battle to the strong—but that’s the way to bet.
Damon Runyon

Part 1: The question

A friend of mine who was studying the philosophy of science at Cambridge University told me that an eminent don in his department assumed that every question was necessarily a profound one.  If you asked him the simplest question, he would ponder awhile, and then slowly begin, “I think I see what you’re getting at…”

Some of my readers who thought that they already understood the basics of investing likely feel as if they’re in the presence of that don when they encounter my essays.  But I’m not imposing complications on investment questions where none would otherwise exist.  In investing, clarity of thought requires the careful dissection of concepts that are too often taken for obvious. And so, this essay begins with the exegesis of a seemingly simple, innocent question:

What return can we expect from stocks over the long term?

This sentence contains four problematic terms: “return,” “expect,” “stocks,” and “long term.”

Let’s consider each in turn. Only once we understand these terms can we begin to formulate an answer. The question itself is critical; without an answer, we’d be hard pressed to justify investing in stocks at all. True, the lack of a view on this doesn’t stop many investors from heedlessly risking their money in the market.  But why would you invest if you didn’t have a view on whether, say, stocks were likely to have a higher return than cash?

  1. Return. We’ve already covered the meanings of “return” in an earlier essay.1  In the context of this question, it means the total return, which is the sum of the return from income (the dividend that a stock pays out) plus the return from the change in price, that is, the capital gain or loss.  Also in this context, it means the annual rate of (total) return.  It doesn’t mean the cumulative change, as when I bought a painting for $100,000 in 1997 and sold it for $150,000 in 2007.  That’s a cumulative return of 50% over ten years, but the corresponding rate of return is just 4.1% per year.

    If you multiply that 4.1% by 10 years, you won’t get 50%.  That’s because the rate is a growth rate, and growth begets new dollars which beget even more growth. This is the essence of compounding, which we considered in another essay.2 Because of compounding, a small positive rate can produce a large cumulative return over time; in other words, the cumulative return (if positive) is always greater, sometimes much greater, than the rate of return times the number of years.

    Furthermore, the average of the one-year returns is not the same as the annual rate of return, though they both summarize the one-year returns. This is a subtle but significant distinction that is missed by almost everyone unfamiliar with the mathematics of investing. Unless the one-year returns are all the same, their average will always and necessarily be greater than the rate.  Tzo begin to see why, consider the fanciful example of the stock market dropping 50% in the first year, then going up 100% in the second year. The net result is no change in value (because your investment halved, then doubled), for an annual rate of return of 0%. But the average return was not 0%.

    We’ll spend most of this essay considering the annual rate of return. For brevity, I’ll sometimes write just “return” when I mean “rate of return,” but the context should make the meaning clear. Toward the end, we’ll consider the average annual return, because this is what you might think of as a typical return.

  2. Expect. What we expect to happen seldom does happen, at least, not exactly as we expected it.  But—I should hope—we don’t live our lives without regard to the future; rather, we act, and sometimes even plan, according to some sort of expectations.  “Expectation” or expected value has a precise meaning in the discipline of statistical analysis. It does not mean what we hope or fear will happen (at least, not necessarily). It also, more subtly, does not mean the one result from among all the possibilities that is most likely to happen. Rather, it denotes the average of the possibilities we see before us, but that average is adjusted to reflect their probabilities. The more likely results contribute more to the average.

    The expected return is not at all the same as the average return I described a moment ago.  That was the average of the year-by-year returns from the present into the future. The expected return, rather, is the average of all the possible rates of return that may have been realized between now and a specified time in the future, weighted according to their likelihood.

    That is to say that, although when we arrive in the future and look back, we will see only one sequence of year-by-year returns from our stock market investment, we don’t yet know what that sequence will be, and there is an infinitude of future possibilities.  From our current vantage point, there are possible sequences that could result in very high rates of return; there are possible sequences that could result in very low rates of return. Both extremes are unlikely.  Much more likely are the possible sequences of year-by-year returns that result in middling rates of return. The expected return is the average of all these possible rates, but biased toward the rates that correspond to the more likely future market developments.

    Don’t marvel that to come up with our expected value, we’ll have to calculate the infinite number of possible sequences of returns and their probabilities in order to calculate the average of the resulting rates.  We won’t, but the concept of expected value as an average will prove useful when we have to situate the expected return in the context of risk, as any reader of my essays will know that we inevitably must.

  3. Stocks. When I say “stocks,” I mean the entire stock market (for the purpose of this essay, the U.S. stock market).  You can expect a selection of stocks to have a different return from that of the market as a whole.  If you have only five stocks in your portfolio, the answer to our question won’t be the same as the answer to, “What return can we expect from your stocks over the long term?”  “Stocks” as the entire market is a sort of abstraction, an ideal rather than a practical investment.  But for the last few decades, you could, if you so wished, buy something very close to the entire market by buying into a mutual fund designed to replicate the S&P 500 or some other index intended to represent the entire U.S. stock market, and more recently, there have been exchange-traded funds (ETFs) that allow you to do the same thing.  There are costs associated with these investments that reduce the return in practice below the return in theory, but these costs are small, and so the differences between the practical and the theoretical returns are very small.  In answering the question, we’ll assume away all costs.

    “Stocks,” the ones that constitute the entire market, are not a static group over time. Companies have lives; they are founded, grow, become listed on stock exchanges, shrink, are taken private, or merge out of existence.  You might hold a portfolio of a few stocks that, if you’re lucky, will continue to exist over long spans of time. But the market as whole, in its composition, is in constant flux, as are the indices that track the market.
    Because we are considering total return, we have to assume that all the dividends you receive are immediately reinvested in the stock market. This is another way of saying, once again, that our question concerns the total return.  Our question, as I’ve framed it, does not address the practical question of what would happen to your investment in the stock market if you were to  live off the dividends, and you wanted to know the return on the stocks that were left behind. If you were to devour the dividends rather than to reinvest them so that they could themselves earn returns in the future, the resulting market return would be much less than the answer we’re seeking. It’s not a bad practical question if you want to know how to live off your investments, but it’s worth asking only after we know how much total return the market is capable of providing.

  4. Long term. Some uneducated pundits who hold forth on one of the pressing issues of our time, global climate change, are unable to distinguish between forecasting the climate and forecasting the weather, and therefore treat both as equally uncertain, which they’re not.  As weather is to climate, so is the short term to the long term, if we think of forming an outlook or forecast.  For example, one theory of climate may explain why regions near the poles tend to be colder than regions near the equator, and this is entirely distinct from a forecast of rain next week in Nairobi or of snow next week at Prudhoe Bay.  We may or may not be able to make weather forecasts reliably, but even if we can’t, that doesn’t vitiate our theory of climate that explains the overall temperature differentials across the globe. 3 (Then again, our climate theory will require refinement when we discover glaciers on Kilimanjaro, which is almost on the equator.)

    Similarly, some analysts develop theories of what the stock market may do over the next week, based on valuations, past movements, relationships with bonds, volatility, measurements of investor sentiment, and so forth, but unless you’re very, very gullible, you’ll deeply discount any short-term market forecast based on such a theory, however plausible or even reasonable.  With rather more justifiable confidence (though without arriving at a value precise to the first decimal place), we can attempt a long-term forecast for the stock market.  For one thing, we are pretty confident that the long-term return will be positive.  How long is the long term? It’s not infinite, because, long before the sun cools, swells, boils off the oceans, and expands beyond the earth’s orbit, returns will reliably drop 100% and then stay at 0% per year.  The long term is not one year, either.  But perhaps 100 years is a good long-term span, or 50 years, or even 25 years.  If you’re a young or middle-aged investor in good health, it might make sense to think of the rest of your life as the long term; if you’re an aged investor planning to pass on your estate, then perhaps 10 to 15 years is a good figure for the long term.

1. Peabody River Newsletter, issue 2, July 2008, “How to Think about Returns.”

2. Peabody River Newsletter, issue 7, April 2010, “How Much is that Investment Worth in Real Money?

3. It is beside the point that in my example, climate change is over space and not over time, whereas weather change is over time. I chose the example of climate change over space rather than over time in order to emphasize the distinction between climate and weather, and implicitly, to suggest that the reliability of forecasts of one is unrelated to the reliability of forecasts of the other.