Stock Market Math: Why Long-Term Returns will be Sub-Par

In the short-term, stock market returns are nearly impossible to forecast reliably; I have yet to come across anyone who can do this well on a consistent basis. Traders and speculators try to make short-term predictions; sometimes their calls are right, and sometimes their calls are wrong.  In the long-term, however, which I define as a ten year period, it is possible to make a pretty good forecast.  It requires applying stock market math concepts to determine probabilistically which markets are attractive and unattractive based on valuation and to even construct a crude forecast of average annual investment returns.

I have been making the case that U.S. stocks are a currently a high risk, low reward proposition for long-term investors, due largely to the fact that U.S. stocks are overvalued. While U.S. stocks are generally expensive, I am also coming across increasing evidence that U.S. small cap stocks, as measured by the Russell 2000 Index, are particularly expensive.

However, before I write any further about small-cap stocks, I want to discuss a question that a client asked me which got me thinking about stock market math.

Why I Love Talking to Clients

In our recent quarterly letter, we explained why U.S. stocks are overvalued and, as a result, likely to be a high-risk, low-return proposition for investors with a ten-year investment horizon.

After studiously reading the letter, one of my clients sent me an unsolicited email commenting on the letter.  He said, “The two charts comparing value and 10-year forward annual return correlate beautifully. As you caution, they suggest sub-par returns in the future.”

I copied and pasted the two charts to which he was referring just below.  They do indeed correlate beautifully.

While I agreed with his assessment, his comment suggested that the relationship between valuation and stock market returns might be a spurious one. As I considered how I might respond, it became apparent that we did a poor job of explaining why high stock market valuation levels lead to anemic 10-year equity returns going forward.

To put it simply, it’s all about the math.

Stock Market Math 101

I would suggest that your long-term investment returns from owning stocks will be approximately equal to the sum of the following three sources of investment return:

1.  Dividend yield, plus

2. Revenue growth, plus

3. Increase (decrease) in the cyclically adjusted Price/Earnings (CAPE) ratio

Each of these factors contributes to stock market returns, sometimes to a greater extent and sometimes to a lesser extent, depending on the period in question. While dividends and revenue growth are almost always positive contributors to stock market returns, with the CAPE ratio, valuation can become a positive or a negative contributor to investment returns. If you start out the year with the S&P 500 Index at a 20x CAPE ratio, and then you end the year with the S&P 500 Index at a 10x CAPE ratio, you just experienced a 50% stock market crash (without considering the impact of dividends or revenue growth).

From the long-term chart of the CAPE ratio below, you will see that an expansion of the CAPE ratio was a major contributor of the S&P 500 Index since the financial crisis in 2008.  The strong U.S. stock market has not been a function of strong revenue growth or a high dividend yield — it is simply a function of an expanded valuation as expressed through the CAPE ratio.

Likewise, you can see that a compression of the CAPE ratio was a significant driver of negative stock market returns between 2000 and 2009.  If you get anything else from this chart, it should be that changes in valuation are an important driver of overall stock market returns.

Applying Stock Market Math to 1982

To better understand how stock market math works, let’s apply these three investment return drivers retroactively to the S&P 500 Index in July 1982, which was right at the end of a sixteen-year bear market.

(As an aside, yes, it is indeed possible to generate a negative return from owning stocks for sixteen years.)

1. Dividend Yield: In 1982, the dividend yield was 6.2%. In other words, even if stocks stayed flat, as long as companies continued to pay out the same level of dividends, you were going to generate a 6.2% return owning the S&P 500 Index. Today, a 6.2% return from owning U.S. stocks would be lovely.
2. Revenue Growth: Between 1982 and 1992, the U.S. economy expanded at a nominal rate of almost 5% per year. Between the dividend yield and revenue growth, thus far we are already at a double digit return from owning the S&P 500 Index, but we are just getting started.
3. CAPE ratio: The cyclically adjusted P/E ratio was at a generational low in 1982. During the subsequent decade, the CAPE ratio expanded from 6.6x in July 1982 to over 20x in July 1992, which means that the stock market tripled from CAPE multiple expansion alone.

Between July 1982 and July 1992, an investment in the S&P 500 Index generated an annualized return of approximately 18% between 1982 and 1992. It was a great decade to own U.S. stocks.

As I said, this stock market math model is a bit crude, but it is simple and useful in illustrating why valuation matters to long-term stock market returns.

Applying Stock Market Math to 2017

Today, the economy and the stock market are in a different position. In 1982, investors were worried about inflation, whereas today investors are worried about deflation. Interest rates were near a generational high, whereas today interest rates are near a generational low. Importantly, in 1982, U.S. stocks were inexpensive, whereas today U.S. stocks are incredibly expensive.

Let’s break down the math for the 2017 stock market:

1. Dividend Yield: The dividend yield of the S&P 500 Index is currently 1.9%. If stocks stay flat, as long as companies continued to pay out the same level of dividends, you are going to generate a 1.9% return. This is about 25% of the dividend yield that U.S. stocks were generating for investors in 1982.
2. Revenue Growth: During the past five years, real growth has been 2.2% and nominal growth has been about 3.7%, but that was before productivity started to decline at the end of 2016. That said, inflation could accelerate. Let’s assume revenues grow at a nominal rate of 4% per annum during the next ten years.
3. CAPE ratio: The cyclically adjusted P/E ratio is at a multi-year high of 30.5x, which is 50% more expensive than the 20x CAPE ratio of 1992 and 460% more expensive than the 6.6x CAPE ratio of 1982. Let’s assume that the CAPE ratio declines over the next ten years to the 1992 CAPE ratio of 20x. Such a contraction of the CAPE ratio would generate an annualized negative return of -4.1%.

Putting it all together, albeit, with several simplifying assumptions, an investment in the S&P 500 Index is set to generate an annualized return of 1.8% between 2017 and 2027. That 1.8% figure is equal to a 1.9% of dividend yield, plus 4% from revenue growth, minus 4.1% from CAPE ratio contraction.

Your approximate return from owning the S&P 500 Index, under my assumptions, would be positive, but not by all that much. And if the CAPE ratio contracts to 15x, your return would be negative.

For a 1.8% return, plus or minus, my question is, why take the risk?

You have much better options to consider which reduce your risk, enhance your likely return, or both. For example, you could buy a ten-year Treasury note and earn 2.1% per annum over the next decade. Owning U.S. Treasuries, you would generate a commensurate retrun while taking less risk. Alternatively, you could invest in other countries like South Korea where there is certainly risk, but where the valuation is far more reasonable and your likely return will be more attractive.  Finally, you could selectively pick individual securities where the stock market math looks more appealing.