Over long periods of time, the S&P 500 outperforms most financial assets; but paradoxically, no one knows its proper price and therefore its projected rate of return.
Existing economics either assumes that the “equilibrium” quoted price is always right, and thus there are no markets; or that its proper price in fluctuating markets is unfathomable.
With one minor change in assumption, our research demonstrates it is possible to derive the proper price of the S&P 500, and thus its prospective rate of return, in real financial markets.
Horizon Capital Research, Inc.
“Valuation (and therefore investment rates of return) is the central concept of
finance. While investors believe that the process is difficult and fraught
with errors and assumptions…valuation (ought to be) approached with rigor
and care. Without methods to assess value, capital budgeting (investing) becomes
Portfolio Returns in Real Financial Markets
This discussion is about real financial markets, not a market conforming to a short-term theoretical statistical model nor to a state of equilibrium, with lots of algebra, but no markets. This discussion is about real portfolios in real markets, which offer people the opportunities to buy or sell according to their needs.
Value investor are concerned not with the short-term technical pattern of asset prices, but with the long-term value of their investments, which as we shall show, are best expressed by the rates of return of bonds and by the implicit rate of return of large, but riskier, portfolios of stocks. This analysis therefore ties the contingent cash flows of the S&P 500 stock market directly to the contractual cash flows of the bond markets and then shows the former ought to be regarded as a markup upon the latter.
Historical Difference Between Stocks and Bonds
In portfolio management, stocks and bonds have traditionally been regarded as separate entities. Stocks were for capital appreciation and bonds were for income. Stocks have therefore been endowed with a separate aura from the more traditional and staid bond markets. During the market crash of the 1929, the stock and bond markets exhibited the following behaviors:
Comparison of the Stock and Bond Markets
S&P Stock Index * Earnings/Share Corporate AAA Bond Rate **
Year (1941-1943=10) (adj. to index) P/E (Annual Average Yield to Maturity)
1928 24.35 1.38 17.64 4.55
1929 21.45 1.61 13.32 4.73
1930 15.34 .97 4.55
1931 8.12 .61 4.58
1932 6.89 .41 5.01
* “Standard & Poor’s Security Price Index Record”; 1992 ed.; p. 120.
** U.S. Census Bureau; Statistical Abstract of the United States 2003; No. HS-39.
If you were a bond investor you did well enough. If you were a stock investor…. It is also useful to note that the stock market crash between 1929-1932 was not caused by an egregiously high market valuation. It was caused by a failure of the entire international economic system after W.W. I.
Current Similarities Between Stocks and Bonds
The actual return of bonds held to maturity can be obtained directly from daily quotes in the bond market, since bond cash flows are fixed by contract. What makes the S&P 500, with a risk premium, nearly equivalent to a bond is the fact that it is diversified; and linked both to the Fed’s monetary policy and to models that trade between stocks and bonds.
Stocks consist of 50 % of the U.S. securities market; and the S&P 500 accounts for 79% of that. The index is diversified among eleven industry groups. The Fed’s administrative control of liquidity affects both the levels of the bond and stock markets – most timely at this 11/22 writing. Moreover, the commonly used Modern Portfolio Theory (MPT) model assumes stable average returns of stocks and bonds, in order to then reduce portfolio risk. Given the above, we can generally say that stock and bond returns are related.
Why do we choose the S&P 500? There is also a very practical reason. Provided its entry price is well chosen, (we are value investors), it is one of the best long-term investments around, partaking of long-term innovation in the economy. The 12th edition of Professor Burton Malkiel’s book, “A Random Walk Down Wall Street (2020),” contains the following table:
Percentage of Actively Managed Funds
Outperformed by Benchmarks *
One Year Five Years Fifteen Years
All Large-Cap Funds vs S&P 500 63.08 84.23 92.33
Global Funds vs. S&P Global 1200 50.21 77.71 82.47
* Malkiel (2020); p. 177.
The above table strongly suggests that over the long-term, index funds outperform managed funds. The above is particularly relevant if you are interested in other things besides markets and stocks. (We are fascinated by these, but that’s us.)
We think the long-term superiority of the index is simply due to its diversification among different industries, and thus tricky sector rotation is not necessary. Professor Malkiel writes, “Every time I do a revision of this book, the results are similar (to the above).…(but) What (Efficient Market Hypothesis) implies is that no one knows for sure if stock prices are too high or too low.” (p.p. 177,181) So what we have is a outperforming asset, whose realized returns and volatility (risk) are known, but whose price for a prospective required return is not.
It is possible to use the principles of corporate finance to derive this price for a single stock. It is also possible to use the same principles to derive the required price for the S&P 500, with just one minor change in assumption. It is then possible to compare the long-term returns of the S&P 500 at a current or required price with those of bonds, whose prices are always known, and to judge whether this is adequate for the future.
The Value of the Future
The MPT model assumes the future will be like the past, some kind of natural law of average asset returns and Gaussian volatility having been discovered.
The financial present value model values the future, in real markets. Neither model nor real market can be “right,” and it is up to the investor to decide whether the pricing available from real markets is reasonably right for him. The reason for this subjectivity is simple. Bond markets, and thus interest rates, vary all over the place; depending upon circumstances. Markets are sort of like the Grand Central Station, where all economic influences converge.
It is a great advantage for investors to be able to directly compare the return of bonds in actual markets to the return of the S&P 500, a portfolio of stocks. We suggest a simple assumption, applicable to large companies, that converts reported operating earnings according to GAAP into cash flow. The simple assumption is this: annual capital expenditures (a cost) approximately equals annual depreciation (an expense). This simple assumption converts earnings into cash flow, that can then be used to value the S&P 500.
S&P 500 Operating Earnings
Standard & Poors publishes detailed earnings estimates of the S&P 500, that is used in finance as a diversified reference portfolio. Crucial to this, that we show per S&P report, Table I, is the distinction between “operating” and “as reported” earnings. One would normally think of “operating earnings” as the direct costs on the factory floor of producing goods, excluding corporate overheads such as interest paid on debt, marketing costs, r&d and so on. However, the intent of the S&P definition is to exclude only extraordinary items such as fixed asset writedowns and gains or losses on the sale of assets. This enables the summation of diverse company results into a single figure, S&P 500 operating earnings that includes the cost of leverage.
For large companies, yearly capital expenditures approximately equals annual depreciation. Therefore S&P 500 operating earnings approximately equals S&P 500 cash flow available to shareholders. This emphasis on cash flow is crucial, because it also enables the assumptions of company level corporate finance to be applied to the valuation of the S&P 500. We can then simply capitalize annual S&P 500 operating earnings.
The Operating Earnings Yield Model
But how? Remember that the duration (payback) period of a stock is approximately 36+ years. This implies that in a fluctuating economy, one year earnings results, which we will also discuss later, are less accurate than some form of long-term average. In 1988, Yale economist Robert Shiller published “Stock Price, Earnings and Expected Dividends.” Campbell and Shiller found, “Long historical averages of real earnings help forecast present values of future real dividends (i.e. stock prices factoring out inflation).” This is the famous CAPE (cyclically adjusted price-to-earnings ratio model). Those who are further interested in how we derived the level of the S&P 500, or who would like to do the calculation themselves, click here.
The 8/22/22 level of the S&P 500 is 4138.
The calculated level of the S&P 500 a/o 8/22/22 for a 7% annual return: P = (10 year average operating earnings/annual return) X 1.33
Ps&p 500 = (137.78/.07) X 1.33 = 2617
As we shall see, a 7% annual rate of return is what is reasonably required to compensate investors for the long-term risk of investing in equities.
The Gordon Model
It is a tenet of corporate finance that the total value of the company to shareholders equals the present value of the stream of dividends it produces, discounted at the rate of return required by investors (a cost of equity capital to a company). For companies with a constant growth in dividends, the Gordon model discounts those dividends back to the present. Thus:
Ps&p 500 = __kE__ = .3573 X 220.53/(.07-.04) = 2626
( r – g)
P = price
k = the dividend payout ratio=.3573 per NYU Stern School S&P statistics 2000-2020.
E = S&P operating earnings=220.53 per S&P report, Table I. Calculated dividends = $71.64. Actual dividends = $64.80
r = the rate of return of the investment=7%
g = the rate of growth in dividends (earnings)=2% real + 2% inflation
We first encountered this model in a stock market course; it struck us as very difficult to implement because what do you assume for (r), what do you assume for (g), and where do you find (k)? What this model requires is an interpretation in context, and that context is the realities of real financial markets. As in the above, we assume for economic growth 2% real and 2% inflation and that investment rates of return should be a 1% markup over the 10 year bond rate of return.
At a 7% rate of return, the two models are within 0.34% of each other. We prefer the first model because it is not dependent upon current dividend statistics. The dividend may be cut, as it was in 2009, in the event of a severe recession. Both models show that the current 8/22/22 level of the S&P 500 = 4138 is very unrealistic.
The Context of Markets
Both present value models need to operate within the context of the economy and markets. On 8/22/22 here is how equity looks according to the first model:
Logical Expectation 8/22/22 Actual Market 8/22/22
2% Policy Rate 2.33%
2% 10 year treasury premium .70%
2% BAA corporate bond premium 2.24%
1%* Equity risk premium (S&P 500=4138) ( .85%)
In response to Fed policy rate increases, the 10 year treasury is beginning to invert; and market traders (and computers) are buying the dips. Markets are apparently assuming a return of the low interest rate, low inflation, low growth environment of the past. The Fed policy rate is currently way below the current 5.90% rate of inflation in the core CPI, that excludes food and energy.
The Effect of Inflation
Another advantage of a quantitative method to evaluate the S&P 500 is to analyze the effect of unanticipated inflation. If the central banks were to tolerate a 4% inflation, rather than a 2% inflation, the further effect of this upon the equilibrium value of the S&P 500 would, for most people, negate a substantial lifetime of work.
8/22/22 current level of the S&P 500 = 4138
Predicted level with a 2% inflation = 2617, 7% return.
Predicted level with a 4% inflation = 2036, 9% return.
A 9% return sounds great, if you neglect inflation, but the predicted level of the S&P must drop by another 22%; the factors ROC/R and LTG/R remain close to their former values.
From Keynes onward, it has been noted although stocks are clearly very long-term assets, with a payback duration of over 36 years, their pricing in markets is very short-term. If portfolios are structured for the long-term, then a longer-term view is necessary. That longer-term portfolio view, particularly for those interested in other things, is inflation protected income – stocks for long run inflation protection.
The bond markets, but not yet the stock market, are beginning to make it possible for a 50/50 portfolio to reach a cash return of around 4%, which can be either spent or saved. We are therefore now concerned with bond interest rather than stock market dividends, which presently refer to a different world. The 4% rule generally applies to portfolios managed in the U.S. or the U.K. which have similar economic systems. This article from the 5/8/15 NYT indicates that Bill Bengen, a former financial planner and M.I.T. aerospace graduate, has worked out the implications of this rule, with the provision that the future will be like the past. In dealing with the present, this 4/19/22 WSJ article writes that he is now mainly in cash. The rule-of-thumb is exactly equal to our assumption for long-term economic growth – 2% inflation and 2% real. Stated in terms of our model, the remaining balance of the portfolio (2% inflation and 2% real) should last a long time, provided the U.S. economic system does not fall apart due to great changes. Our 50/50 portfolio should eventually look like this:
Asset Cash Return Weight Portfolio Cash Return
Bond 5.5% 50% 2.75%
Stock 2.5% * 50% 1.25%
* S&P at 2617 a/o 8/22/22. In real markets, we may be a few
10ths of a percent off; and the S&P dividend level of $64.80
may be temporarily cut.
When to Buy and Hold
The following graph from Minack Advisors is really useful, for it charts the entire S&P 500 in terms of Professor Shiller’s cyclically adjusted earnings model. It shows that most of the time, say 90%, the conventional mantra of staying invested and adding to one’s stock investments is correct – when the cyclically adjusted P/E is less than 24. But when the CAPE P/E is greater than 24 (10% of the time, and provided the economy does not change drastically from the past) we would not add to our stock holdings and would think of trimming back; even though the market might be soaring. With inflation now out of control, we are now in the throes of a large market correction.
This study places the S&P 500 in the context of the bond markets, and thus its prospective rate of return to investors. We hope that this has been helpful to you.
We encourage you to speak with a qualified financial advisor about your specific situation.