March 21, 2005
Don't Discount Discounted Dividends
Suppose that a broker approached you with this pitch: “In recent decades, U.S. Treasury bonds have provided investors with total returns of about 8% annually. Hey, 8% is a solid return for a default-free investment, so Treasuries are a great long-term investment here.”
Undoubtedly, your assessment of the broker's intelligence would drop to a range somewhere between Elmer Fudd and SpongeBob Squarepants, and you'd quickly excuse yourself to find another advisor. Clearly, the historical return delivered by an investment is determined by its past level of valuation. The future return on an investment is driven by the level of valuation when you actually invest. Presently, a 30-year zero-coupon Treasury bond is priced to deliver a yield-to-maturity of 4.67%.
[Of course, if it's a long-term security and you don't hold it to maturity, the level of valuation at the end of the holding period is also critical. The only way to get, say, 8% in that zero-coupon bond over the next decade is to hope for an increase in bond valuations that would allow you to sell it at a yield of 3.04% ten years from now… which gives you a modest idea of why we're not taking a lot of duration risk here.]
What's amazing is how many investors swallow the same pitch about stocks, confusing future returns with historical returns, without any questions. Analysts constantly quote historical returns on stocks as if they are somehow inherent in stocks themselves, rather than being a function of the price you pay.
I've focused heavily on valuations in recent comments, because valuations matter for future returns, and the financial security of our shareholders (and non-shareholders) relies on an understanding of that basic fact. The S&P 500 is currently priced to deliver annual total returns most probably in the neighborhood of 2-3% over the coming decade, a conclusion that is robust to a variety of analytical methods. Even if the market goes nowhere, it will undoubtedly do it in an interesting way, including both bull and bear markets of substantial amplitude. But in the end, stocks are not priced to deliver satisfactory returns to buy-and-hold investors in the major indices.
The trial and persecution of dividends
Since about 1995, the use of dividends as a valuation tool has fallen entirely out of favor. To some extent, this reflects the argument that share repurchases are a form of compensation to investors as well, since share repurchases concentrate a company's future cash flows into the hands of fewer investors.
Unfortunately, the knee-jerk rejection of dividends vastly overstates the value of repurchase activity to investors (much of which simply offsets the dilution from option grants and share issuance to executives and employees). More importantly, the rejection of dividends as a valuation tool overlooks the fact that repurchases are already taken into account because of the way that the S&P 500 index is calculated. That's the short answer to the criticism of dividend-based valuation. The long answer follows.
Since these updates are written for shareholders and financial advisors at a wide variety of analytical levels, I'm going to beg your indulgence for a few paragraphs, in hope that less mathematical readers will bear with me, or at least scroll down until we hit the chart. Better yet, grab a pad of paper and work through this. It's useful stuff, and I promise not to get too fancy.
The basic dividend discount model
Let's begin with a simple assumption that the market's level of valuation stays constant over time, as measured by the dividend yield (D/P). That means, by definition, that prices and dividends would grow at the same rate over time. Call that growth rate of dividends “g.” Since total return, call it “k,” is equal to the growth in prices plus the dividend yield, we can write total return as follows:
k = g + D/P
We can then rearrange this equation to solve for the stock price P:
P = D /(k-g)
For example, if a market index is expected to pay $20 in dividends this year, growing at 6% annually, and priced to deliver a 10% long-term return, the price of the index would be $20 / (.10 - .06) = 500. Notice the dividend yield would be 20/500 = 4%. Holding that dividend yield constant, annual total returns would then be: 6% growth + 4% dividend yield. Hey! 10%, just what we bargained for. Cool.
That's the basic dividend discount model. Notice that since the dividend yield is never negative, we always assume that k exceeds g. If they're equal, or dividends are zero, the model is simply undetermined. Notice also that stock yields work a lot like bond yields: the long-term return “k” is only accurate for short-term holding periods if valuations stay unchanged. If the dividend yield falls over the holding period (so prices grow faster than dividends), the total return over the holding period will be higher than the “k” initially assumed by the model. In contrast, if the dividend yield rises over the holding period (so prices grow slower than dividends), the total return over the holding period will be lower than the “k” initially assumed by the model. Notice finally that we can define k and g in either real or nominal terms, since the inflation rate cancels out.
[Geeks note: You can also derive the dividend discount model by actually discounting the future dividend stream to solve the infinite series: P = D/(1+k) + D(1+g)/(1+k)^2 + D(1+g)^2/(1+k)^3 …, but that puts people to sleep.]
Warning: The dividend discount model, as written above, can be wildly misused by analysts who choose unrealistic or counter-factual assumptions about k and g. For example, if you arbitrarily choose k and g so that the difference is a very small number, you can justify a virtually infinite level of stock prices. This was a common tactic during the advance toward the market's 2000 peak, and was the central trick to Glassman & Hassett's “Dow 36,000.”
Dividend discount with stock repurchases
Notice that if we interpret “g” to be the growth rate of total dividends paid by the company, and assume there are no stock repurchases, it's reasonable to expect stock prices to track the growth rate of dividends, and the dividend discount model makes sense.
On the other hand, if the company does use part of its retained earnings to repurchase stock, then we've got two choices:
a) Use a discounted free cash flow model. In this case, we change the numerator to “FCF” rather than D. Free cash flow includes all cash flows available to shareholders, including not only dividends but also amounts used for net repurchases (repurchases over and above those required to offset dilution from option and share grants to executives and employees). In this case, we still define “g” as the growth rate of total free cash flows at the company level.
b) Redefine “g” as the growth rate of per-share dividends. The math is awfully tedious, but you can prove that this small adjustment makes the dividend discount model equivalent to a discounted free cash flow model. [Geeks note: It turns out that the growth rate of per-share dividends g* = k – d (k – g) where d is the proportion of free cash flows paid out as dividends and g is the growth rate of total free cash flows at the company level.]
Putting the debate about repurchases to rest
It is extremely important that the dividend discount model is valid, even with share repurchases, provided that you use growth in per-share dividends.
This is big news, which easily escapes attention unless you go through the tedium of actually deriving it mathematically. It's big news because it turns out that the calculation of the S&P 500 index does result in a dividend figure that grows on a per-share basis. In other words, if you use index dividends and their associated growth rate, you don't NEED to factor in repurchases, because the index does it for you.
The easiest way to see this is to recognize that the divisor for the S&P 500 index is reduced in response to share repurchases, so the same aggregate level of dividends will, after a repurchase, result in a proportionally higher index dividend. To demonstrate it mathematically, notice that if the companies in the index were to repurchase 10% of their shares, the recalculated index divisor would be reduced by exactly 10%, so the same level of aggregate dividends from the component companies would be associated with an 11.11% increase in the dividend reported for the S&P 500 index. Of course, that's exactly how much per-share dividends have increased as a result of the repurchase.
In short, the index dividend for S&P 500 (and its associated growth rate) already captures the impact of net share repurchases. Further adjustments to the dividend discount model represent double-counting.
Back to long-term returns
With these observations, let's come back full circle and approach the problem of long-term returns from the standpoint of dividends (see recent weekly comments for alternative earnings-based analysis).
Over the long-term, it's no secret that stocks have provided long-term total returns, after inflation, of over 7% annually. In nominal terms, the long-term return has been over 10%. Since the following analysis uses very long-term data from 1871 to the present, we'll use real returns, in order to factor out variations in inflation over time and give us a well-behaved estimate of long-term dividend growth.
It turns out that growth in real, inflation-adjusted dividends has been very consistent over history. From 1871, per-share real dividend growth for the S&P 500 index has averaged 1.5% annually. There's been a modest amount of variation – for instance, real dividends grew at over 2% annually during the post-war period from 1945 to 1960 – but over extended periods, real dividend growth has averaged about 1.5%, plus or minus a few tenths of a percent.
Given the good behavior of real dividends over time, there are a few ways to think about “fair value” for stocks. One approach would be simply to assume that stocks should always be priced to deliver a particular real return, say 7% annually. That assumption leads to a simple conclusion: that the dividend yield on the S&P 500 should always be about 7% - 1.5% = 5.5% (which is just k – g). Though that was indeed the average dividend yield over much of the first half of the 1900's (which is largely why stocks, in fact, have provided a real return of over 7% since then), it's not a very satisfactory assumption, because it fails to closely track the actual behavior of stock prices over time.
An optimistic and slightly quirky assumption, but one that better fits the long-term data, comes from my former colleague at the University of Michigan, Robert Barsky, and economist Bradford DeLong. They observe that the volatilities of dividends and the economy have declined over the past century, and assume that investors have recognized that by reducing the risk premiums (and increasing the valuations) of stocks over time. Specifically, they assume that the real rate of return demanded by investors declines linearly with time. That formulation slightly strains credibility in that it ultimately implies that investors will be willing to hold stocks for no expected return at all. It's also something of a “bubble” model: assuming that k declines constantly over time is another way of assuming that prices grow forever at a faster rate than earnings or dividends. That said, it's a simple way of capturing the notion that economic risks have gradually declined, and it also captures the rising level of stock valuations in the historical data.
You can get a good fit to historical data using the assumption that real dividends grow at 1.5% annually, and that the real return demanded by investors begins at 7.5% annually in 1871, and declines linearly by 0.002% monthly. On that assumption, for example, investors in 1975 were willing to price stocks to deliver a long-term real return of 5%, and today's investors would be willing to accept a long-term real return of just 4.25%.
Granted, a real long-term return of just 4.25% seems improbably low (since it implies that even at fair value, investors would be comfortable with long-term nominal returns on stocks of only about 7%), but that's what you have to do even to come close to the data. The reason is that in recent decades, the portion of earnings paid out as dividends has dropped, yet per-share dividend growth hasn't notably increased. This implies that either earnings have been overstated, or buybacks have been offset by increased issuance of stock to corporate insiders through options and stock grants. In any case, the only way to fit the data is to allow for a persistent drop in expected returns over time. Yet even allowing for much lower future real returns, stocks still appear overvalued here.
The chart below tracks the actual S&P 500 index (blue) along with the fitted value (green) from this optimistic version of the dividend discount model. You can see the optimism in that even the 1929, 1972 and 1987 peaks were not profoundly above the fair value kicked out by the model. Overall, though, it's about as good a long-term fit as you'll find on the basis of a simple fundamental model. Moreover, deviations between the S&P 500 and the model tend to be corrected, and those deviations are fairly well correlated with subsequent multi-year (though not necessarily short-term) returns.
What is striking is the extent to which stocks became overvalued in 2000, and still appear overvalued at present. Specifically, for stocks to be priced for a 4.25% real return, the required dividend yield works out to be 2.75% (versus the actual value of just 1.80%). That implies a fair value of about 770 on the S&P 500 index, suggesting that stocks would have to decline by at least 35% in order to be appropriately priced. Unfortunately, the model can be tweaked to produce a fair value of 1200 for the S&P 500 only by assuming that stocks were profoundly undervalued at every point in history prior to 1998, including major peaks like 1929.
The 770 fair value figure for the S&P 500 is interesting, because it's very close to the estimate of fair value (725 on the S&P 500) recently published by Jeremy Grantham at GMO (one of the most astute value managers you'll find, next to Warren Buffett). Grantham arrives at this valuation using earnings-driven analysis that adjusts for abnormally high profit margins, differences between operating income and net income, and other factors. Grantham's recent analysis gets the issues exactly right, noting “you simply cannot look at unnormalized p/e ratios when dealing with the total market. In addition to adjusting for the profit cycle, you have to allow for write-downs of prior claimed earnings. In theory, operating income and net income should be the same, with unusual debits in the long run being offset by unusual credits. In real life there is a bias to unusual debits because of systematic overstatement of earnings. In the last 10 years, there has been an average of 14% net write-downs.” Grantham estimates that the probable real return on stocks over the coming decade is likely to be about –2.2%, with nominal returns averaging about –0.6% annually.
Using our optimistic version of the dividend discount model, if we assume that the current overvaluation is relieved gradually over a period of 10 years, and that the required return on stocks continues to decline (resulting in higher justified valuations) the probable real return over the coming decade still works out to roughly zero, and the probable nominal total return on the S&P 500 over the coming decade is approximately 2-3%. For readers of these weekly comments (e.g. February 22), that's starting to become a familiar range.
Given these prospects, what can investors do? Well, fortunately, the likelihood of weak long-term returns for the S&P 500 shouldn't create a major obstacle for investment approaches that are not tied to a buy-and-hold strategy on the broad market. As I frequently note, stocks may go nowhere over the coming decade, but they'll probably go there in an interesting way. For investors who respect value and have a willingness to vary their investment exposure based on market conditions, persistently rising stock prices are not essential to achieve satisfactory long-term returns.
As of last week, the Market Climate for stocks remains characterized by unusually unfavorable valuation, while the quality of market action has deteriorated to an extremely tenuous condition, but still not at the point that would justify a fully defensive investment stance. In practice, about 70% of the diversified stock portfolio of the Strategic Growth Fund is fully hedged against the impact of market fluctuations using matched long-put/short-call combinations (which act as interest bearing short sales on the S&P 100 and Russell 2000 indices). The remaining 30% of the portfolio is hedged with index put options that are now in-the-money.
The difference at this point between our current investment position and a fully hedged one, amounts to a modest amount of option premium that could be obtained by matching those long puts with short calls and moving to a fully hedged stance. We do not yet have the evidence to do this, however, and given the market's oversold position, there remains some potential for the market to recover in a way that sustains a generally constructive Market Climate. Suffice it to say that if the market continues lower, Fund returns are likely to be within less than one percent of what they would be if the Fund was, in fact, fully hedged. But the Fund does retain a modest amount of exposure to market fluctuations that would gradually become more meaningful (due to the curvature of option valuations) if the market was to rise substantially. In short, we continue to give the market a modest benefit of the doubt here, but not to an extent that would significantly impact returns or risk if market conditions deteriorate further.In bonds, the Market Climate remains characterized by unfavorable valuations and unfavorable market action. The mid-week rally in bonds last week brought yields back to the point where the prospect for further returns did not appear worth the duration risk. The Strategic Total Return Fund currently carries a duration of about 2 years, meaning that a 100 basis point move in bond yields would be expected to impact the Fund by about 2% on the basis of bond price fluctuations. The Market Climate for precious metals continues to be generally favorable on our measures, but I also slightly reduced our exposure to precious metals shares to about 18% of portfolio value, given recent strength in that sector. In all, the Fund remains generally defensive, with the bulk of its 2-year duration in Treasury Inflation Protected Securities, and most of the day-to-day volatility in the Fund likely to come from our moderate exposure to precious metals shares.
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