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September 12, 2005

The S&P 500 as a Stream of Payments

John P. Hussman, Ph.D.
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As stock market investors, it's tempting to take on faith that there is a relationship between prices and fundamentals – between what you pay now and the stream of cash you'll get from your investment over time.

It's easier with bonds, at least default-free ones like Treasuries. In the bond market, what you see is what you get. The instant you buy a bond, you know with certainty the long-term return you will earn if you hold it to maturity. You know if you take all of the payments you'll get from the bond, discount them to present value at the prevailing yield to maturity, and add them up, the figure you'll get will be exactly the price of the bond.

With stocks, most of us sort of have it in our heads that we'll get something like 10% annually if we hold the S&P 500 over the very long term (though buy-and-hold investors usually like to think that this year or next year will be different, and that they'll get lucky and earn more than 10% this time around). So it's probably useful to have some idea of what level the S&P 500 would have to trade at in order to deliver a long-term return of 10%.

Discounted dividends

We know that if we hold the S&P 500 index this year, we'll get the dividends on the S&P 500, and the year-from-now value of the S&P 500. Hold it for a second year, and we'll have two years of dividends, and the two-year-from-now value of the S&P 500. Hold it for a third year, and we'll have three years of dividends, and so forth. Notice that we can repeat this exercise indefinitely, and since we know that the value of a dollar received in the infinite future is essentially zero, we can think of the S&P 500 as the discounted value of the future stream of dividends it will deliver over time. At every point in time, the value of the S&P 500 is the value of its stream of dividends from that point into the indefinite future*.

Suppose we look back over history, and at each date, add up all the dividends the S&P 500 actually delivered over the subsequent years, discounted at a long-term rate of return of 10%. We could literally check whether investors got what they paid for.

Of course, the more recent the date, the more we'd have to project some future dividends. But that's not a terribly difficult matter. As it turns out, the average dividend growth rate since 1900 has been about 5%, the average since 1940 has been 6%, and the highest growth rate for any 30-year period has been 6.4%. We also know that S&P 500 earnings growth has displayed a very, very durable 6% growth rate measured from peak-to-peak across economic cycles. So assuming anything between 6% to 7% long-term dividend growth will give us a very robust series of likely future dividends.

For most of our calculations, assumptions about the future don't matter too much. For instance, since dividends in the distant future are less valuable than dividends that arrive early on, the projected stream of dividends from 2005 onward represents just 3% of the 1940 valuation, so that value we calculate for 1940 is based almost entirely on the actual value of dividends that investors realized on an investment in the S&P 500 from that date to the present. By 1974, the dividends beyond 2005 still represented only about 30% of the total valuation, so 70% of what we calculate as “fair value” has already been realized through dividend payments.

The following chart presents the discounted value of realized and projected dividends on the S&P 500, discounted at a 10% rate of return (green line). The actual S&P 500 is depicted in blue. The calculations assume 6% future dividend growth after 2005. Unfortunately, it turns out that the fair value for S&P 500, based on a 10% required long-term rate of return is currently only about 585. The index closed on Friday at 1241.

The next chart is nearly identical, but assumes 7% future dividend growth (which exceeds the highest growth rate observed during any historical period of 30 years or longer). Again, stocks remain expensive here. The current fair value for S&P 500 based on a 10% required long-term rate of return is just 777.

The alternative way to state these conclusions, of course, is that stocks are priced to deliver probable long-term total returns well below 10% annually. It's axiomatic that given the current 1.8% dividend yield on the S&P 500, a long-term dividend growth rate of 8.2% would imply that the market is fairly valued here (1.8% yield + 8.2% growth = 10% total return at current prices). However, we've never seen multi-decade dividend growth anywhere near that level, and the assumption would imply that except for the late 1990's bubble, stocks were underpriced at every date in history since 1937, including the 1972 and 1987 market peaks. Suffice it to say that it requires a pure leap of unsubstantiated faith to expect 10% long-term total returns from the current level of the S&P 500.

As a measure of the S&P 500 level that would produce long-term returns of 10%, 777 (corresponding to 7% long-term dividend growth) seems most reasonable to me. Though even this would require a dividend growth rate that we've never seen historically, the assumption might actually be justified by the fact that the dividend payout ratio (the proportion of earnings paid out as dividends) is currently just 35%, compared to a historical norm closer to 55%. With S&P 500 earnings at a record, we have a great deal of historical evidence that a 6% peak-to-peak earnings growth rate is plausible. A 7% dividend growth rate, in that context, would imply that the dividend payout ratio will rise to more conventional levels over the coming decades. Against that logic, it's also true that the low payout ratio owes more to unusually elevated profit margins, rather than low dividends (which are reasonably in line with revenues, book values and so forth), but nobody wants to be a spoilsport.

Of course, there have been several periods in history where the S&P 500 traded well below the level that would deliver 10% long-term returns (a lower price implies that stocks are priced to deliver even higher returns). We can see that clearly at the extremely good buying points that existed in the 1940's, and also in 1974 and 1982.

Given these facts, investors looking for assurance that the S&P 500 could not decline below 777 in the coming years will find no such assurances in the data. If anything, the data suggest that we'll continue to observe periods where stocks are priced to deliver long-term returns both above and below 10%. At present, we're in one of those overvalued, below 10% phases. Long-term investors should firmly understand that this is, indeed, a phase.

Market Climate

As of last week, the Market Climate for stocks remained characterized by unusually unfavorable valuations and relatively neutral market action. The market at this point appears reasonably overbought. Though further progress can't be ruled out, the market at this point has reasonably discounted the possibility that the Fed will stand pat for at least one meeting, in order to allow more information to emerge in the wake of Katrina.

It's true that several Fed governors have kept the potential alive for a further rate hike at the next meeting, but it's definitely not Greenspan's style. Throughout his tenure, Greenspan has shown a very strong tendency to give the benefit of the doubt to uncertainty, which we certainly saw after the Asian crisis and blowout of Long-Term Capital Management, and throughout the post-bubble recession. With only a few months remaining in Greenspan's tenure, it would be surprising to see the Fed act on a further rate hike here without sufficient data. Yes, we'll get some hard inflation data next week, but the impact on employment, energy, shipping and other factors will take longer. So my guess, for what it's worth, is that the Fed will hold off for one meeting. That said, the markets have a tendency to buy the rumor and sell the news, so it wouldn't be a surprise to see the market sell off after a brief surge on the actual Fed statement.

In any event, the current condition of valuations and market action don't provide much support for a significant exposure to market fluctuations here, so the Strategic Growth Fund remains largely hedged here, tightening up our range of exposure to between 5-15% of the value of our stocks, with the remaining 85-95% of our stock holdings hedged against the impact of market fluctuations, depending on day-to-day conditions.

In bonds, the Market Climate was characterized last week by modestly unfavorable valuations and modestly favorable market action. Given underlying inflation pressures, even the potential for economic weakness is not presently enough to justify a substantial exposure to duration risk at the current, relatively low level of yields. When the yield curve is relatively low and flat, favorable market action has a tendency to play out until it doesn't. In other words, you can get modest further rallies in bond prices, and then get whacked on modest surprises in inflation or economic growth. That's a somewhat frustrating environment to be taking interest rate risk.

The Strategic Total Return Fund does have the majority of its assets invested in Treasury securities, particularly modest duration TIPS and shorter duration bills and notes, so we're definitely maintaining the income component of returns. But I don't view exposure to bond price fluctuations as having satisfactory potential for capital gains. Overall, I believe that our budget for risk remains better allocated to areas such as precious metals shares, where the Strategic Total Return Fund continues to have about a 20% exposure, accounting for most of the day-to-day fluctuations in the Fund.

* Geek's notes: As explained in the March 21, 2005 comment, stock repurchases are already factored into the calculation of the S&P 500 index, so they show up in the level and growth rate of per-share dividends, and don't need to be counted twice. As for terminal values, it's true that if the index was to permanently depart from fundamentals and grow at say, 11% annually, and we only discounted it at 10%, the terminal value wouldn't vanish. But that would also imply that stocks have infinite value. Economists call that a “violation of transversality.” Most people know it as a “bubble.” Finally, estimates of current value may vary by about 4% depending on timing assumptions. If one assumes a lump-sum 22.35 dividend for the coming year, rather than continuous growth and distribution, fair value for the S&P 500 at 6% and 7% dividend growth would be 559 and 745, respectively.


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