The Expected Return One-Step

After any particularly wrenching period in the markets, I usually get a few calls and messages in the following vein: "You saw how the Nasdaq just got cut off at the knees on no fundamental news… do you still believe that the market is efficient?" To which my stock reply is, "It’s efficient all right; it’s just not always rational."

Just how rational the markets appear depends on your time frame. Turn on CNBC and you’re faced with an asylum narrated by the Three Stooges. But look at market behavior over a 50-year horizon and you’ve got a well-manicured lawn, tended by Paul Samuelson and Bill Sharpe. As a practical matter, the more attention you pay to Samuelson and Sharpe and the less to the Three Stooges, the better off you are. The choice between focusing your attention on 30-year returns and one-year returns should be obvious, even if emotionally unsatisfying during market declines.

In November, I attended a conference on fixed-income investing sponsored by Grant’s Interest Rate Observer and found out that the vicissitudes of market exposure could be much, much worse—I could be a bond manager. For these benighted folks there is no long term, only a terrifying succession of Hobbsean quarters and years; lag the benchmark by more than a nanosecond and you’re on the phone to Momma asking about the condition of your old room. In addition, bond managers face a relatively recent, poorly-publicized demon peculiar to debentures—a liquidity crunch straight out of Kafka. You can almost always unload a modest amount of stock with little impact cost; that’s one benefit of the increasingly frenetic, highly liquid, equity trading of recent years. In contrast, following the derivatives-driven global financial crisis of 1998, trading in bonds has been as sleepy as the no-load fund desk at Merrill Lynch. One attendee estimated that there were "continuous-market" markets in the debt of only the 60 or so largest issuers. Everything else trades, euphemistically, "by appointment." Which means that if fund redemptions require bond sales, a devastating haircut may prove necessary. Or worse, it may not be possible to obtain a bid at any price.

All investors are faced with market (systematic) and specific security (nonsystematic) risk. Nowadays bond managers must also worry about "liquidity risk": the possibility that the market for an otherwise perfectly good bond may simply dry up. Could the same thing happen to equities? Presently, it seems unlikely. But prolonged bear markets usually feature lackadaisical trading, so I wouldn’t rule out the possibility.

But I digress. The conference attendees were rewarded by one speaker who did focus on the long term—Jim Bianco (Bianco Research) analyzed expected bond returns through a long lens, testing an intriguing hypothesis: that the primary determinant of bond yields is the growth of GDP and not supply, as is commonly supposed. In his words:

"Think of this measure as an asset valuation model with the asset being the entire economy. If the asset, as measured by nominal GDP, returns a rate higher than the prevailing interest rate (the five-year Treasury note), then it makes sense for a business to borrow and expand. One can make money in such an environment because the asset has a higher return than the cost of borrowing. This will cause an increase in the demand for credit thus putting upward pressure on the price of credit—interest rates. This will last as long as yields are below the year-over-year change in nominal GDP (or at least the perception that interest rates are below nominal GDP). On the flip side, if interest rates (five-year Treasury note) are higher than the returns provided by the economy (nominal GDP), then borrowing to "buy" is a money-losing proposition. In this case the demand for money will fall because the profit incentive is not present. This will drive the price of credit (interest rates) down so long as yields are above the growth rate, or perceived growth rate, of nominal GDP."

It’s not too difficult to nitpick this one. Why the five-year Treasury rate? Why not T-bills? Junk bonds? (After all, most unseasoned companies are not creditworthy, particularly these days.) Expected stock returns? You get the idea. But superior hypotheses are easily testable, and this one passes with flying colors. Here’s the data, reproduced with the kind permission of the author.

The below plot shows the raw data: the five-year Treasury and year-over-year GDP change:

The agreement between the two is good, but far from perfect, as you might expect given the fact that we’re looking at a frequent sampling interval. The below plot is the difference between them.

This plot certainly seems to mean-revert around the zero value. The last plot explains the short-term gap between theory and practice: a high rate of new debt issuance will cause interest rates to be higher than GDP growth, and vice versa:

But what is remarkable is that a supply of new Treasuries only temporarily perturbs the equivalency between GDP growth and interest rates; the fundamental relationship between the two persists. Bianco locks up his case with nearly identical data from Japan, the U.K., Canada, and Australia. The Japanese data are particularly powerful, as they explain their bizarrely low interest rates as a consequence of the zero economic growth of the past decade. The importance of this cannot be overstated. Most economists rank debt supply as the primary mover of interest rates, with economic growth exerting only a secondary effect, and not the other way around.

Now the punch line: the long-term equivalency of interest rates and GDP growth supplies us with a way of estimating the equity premium with breathtaking simplicity. This is because long-term corporate earnings and dividend growth must also be equivalent to GDP growth. And since long-term equity returns are closely approximated by the sum of dividend/earnings growth and the dividend rate, then the equity premium is simply the dividend rate. In other words, since in the long run it is approximately true that:

Treasury yield = GDP growth = Corporate dividend/earnings growth

And that:

Expected equity return = Corporate dividend/earnings growth + Corporate dividend rate

Then, it must be so that:

Stock return – Treasury yield = Equity premium = Corporate dividend rate

(For the purposes of this paper I’ve avoided the term "equity risk premium," as this properly refers to the stock return in excess of the risk-free T-bill rate.)

It’s just that simple. From 1926 to 1994 stocks returned 5% more than Treasury notes—almost exactly the average dividend rate for the period. And going forward, in the very long term, you’re gonna get all of a 1.3% excess return over bonds.

The problem is that on a day-to-day basis you get your return from multiple (PE) change—so-called "speculative" return in Bogle’s terminology. But over the ages your return is dividends plus growth, Bogle’s "fundamental" return. The trick is to think like Samuelson, Sharpe and Bogle, not like the Three Stooges. Is 1.3% an adequate reward for favoring stocks over bonds? You be the judge.

Copyright © 2001, William J. Bernstein. All rights reserved.

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