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July 11, 2005

Explaining isn't Justifying

John P. Hussman, Ph.D.
All rights reserved and actively enforced.

An old philosopher once said that there are two ways to be wrong. One way is to be just plain wrong. The other is to be wrong, but in an interesting way.*

Among the common bullish arguments these days is that price/earnings ratios deserve to be elevated because interest rates are so low. This argument is wrong in an interesting way, and we can learn a lot by asking why.

The more you focus on recent history, they more you can show in the data that, in fact, interest rates and stock valuations move together. The most popular version of this, of course, is the Fed model, which posits that the 10-year Treasury yield and the prospective earnings yield on the S&P 500 should always be equal.

Since the Fed Model is based only on data since about 1980, the entire period representing a long secular decline in interest rates, the statistical relationship is on somewhat shaky ground. Anytime you measure the statistical relationship between two variables that trend together, you'll get a very tight fit that may be entirely spurious. In order to have more confidence, you really want to see goodness-of-fit over several wide up-and-down cycles.

[Data Monkey's Note: Unfortunately the series of projected operating earnings only goes back a couple of decades, so you have to estimate past operating earnings in order to look further in history. It turns out that while the level of fitted operating earnings is a little higher than the series of peak earnings that I use to calculate price/peak-earnings multiples, the results are otherwise the same, so I'll use those below for simplicity and ease of replication].

Earnings yields and interest rates

If you examine the full historical record, you'll find that the relationship between S&P 500 earnings yields and 10-year Treasury yields (or other interest rates for that matter) isn't tight at all. The further you look back, the weaker the relationship. To a large extent, the relationship we do observe is linked to the single inflation-disinflation cycle that began in the mid-1960's, hit its peak about 1980, and then gradually reversed course over the next two decades.

Still, it's clear that during the past few decades, however one wishes to explain it, earnings yields and interest rates have had a stronger relationship than they have exhibited historically (though not nearly as strong as the Fed Model implies).

So why isn't it correct to say that lower interest rates justify today's elevated P/E ratios?

Well, that's where being wrong gets interesting.

Let's do some simple statistics. We'll use the S&P 500 earnings yield, the 10-year Treasury yield, and the 3-month Treasury bill yield in order to explain the subsequent 1-year total return on the S&P 500 index. It's important to notice here that the resulting figures are only a measure of what has occurred on average, not what can be relied on to occur in any particular instance. That said, here are the regression coefficients that fit those equations, for different starting points to the present.

Regression coefficients explaining the
1-year total return on the S&P 500

 

Constant

Earn_Yld

Long_Yld

Tbill_Yld

Since 1926

-14.54%

2.32

0.82

0.30

Since 1940

-11.48%

2.35

0.11

0.65

Since 1960

-9.58%

1.27

0.97

0.63

Since 1970

-14.74%

0.83

2.63

-0.08

For instance, suppose we choose some point where the price/peak-earnings ratio on the S&P 500 was at 14 (for a 7.14% earnings yield), 10-year yields were at 7%, and the 3-month Treasury yield was at 6%. Given the typical historical relationships in the data since 1960, you would have observed, on average, a total return on the S&P 500 over the following year of [-9.58% + 1.27*7.14 + 0.97*7.00 + 0.63*6.00 = ] 10.06%. That's not surprising. In fact, those are about the average values for all of these variables since 1960.

Stare at the table for a second. Notice that from about 1960 onward, the earnings yield has exerted a smaller (direct) impact on the subsequent 1-year return on the S&P 500, while the 10-year Treasury bill yield has exerted a larger impact on returns. Treasury bill yields have become nearly useless in explaining returns. To a large extent, what we're seeing in these statistics is the 10-year yield “picking up” the influence which earnings yields used to exert independently. That's because earnings yields have become something of a puppet to interest rate movements in recent decades (though the strings are still fairly loose).

In fact, if you were to run more studies, you would find that the 10-year Treasury yield has exerted substantially more effect on price/earnings multiples (or earnings yields) in recent decades than in the past. This is mostly a reflection of an extreme valuation swing that stocks experienced during the inflation-disinflation cycle that started in the mid-1960's. An exaggerated plunge to very low P/E ratios accompanied the rising interest rates of the 70's and early 80's (when the price/peak earnings ratio on the S&P 500 declined to just 7), and an exaggerated spike to very high P/E ratios accompanied the falling interest rates of the 90's (when the price/peak earnings ratio moved over 30 as the decade ended). There is emphatically no long historical tendency for P/E ratios to be high when interest rates are low. As I've noted before, if you look at the full record, it turns out that the average P/E ratio of the market does not increase even if you restrict the data to periods of low interest rates, say, under 5% (indeed, this restriction essentially filters out most of the data since 1965).

Still, if one focuses only on recent decades, it might seem at first glance that low 10-year Treasury yields do justify elevated valuations here. But it's in the meaning of the word “justify” where things get interesting. To most investors, a justified valuation is the level of prices that would still be likely to deliver a reasonable return. Unless that's true, being able to explain the price/earnings ratio is not enough to say that it's a justified valuation.

And that's where the rubber meets the road here. Notice that the 10-year bond yield has a coefficient of 2.63 since 1970 in the table above. That means that in the data since 1970, every 1% increase in the 10-year bond yield has been associated on average with a 2.63% increase in the S&P 500's total return over the following year (an additional effect is picked up by the coefficient on the earnings yield - the value would be even higher if one used the 10-year Treasury yield as the only variable). Similarly, every 1% decrease in the 10-year bond yield has been associated with S&P 500 total returns over the following year being 2.63% lower than they would otherwise have been. Similar results hold if you look at subsequent market returns over say, 2 years more.

So while it's true that lower yields have been associated with higher P/E ratios in recent decades, the meaning of that for investors isn't positive or even neutral, it's decidedly negative. What we're really seeing is that stocks since 1970 have been heavily sensitive, and possibly overly sensitive, to interest rate swings. While it's true that lower interest rates have supported higher P/E ratios, those lower rates and higher P/E ratios, in turn, have been associated with poorer subsequent stock market performance.

In short, if investors want to argue that low interest rates help to explain today's elevated P/E ratios, that's fine, as long as they also recognize that subsequent returns on stocks are likely to be dismal in the future as a result.

With the S&P 500 earnings yield about 5%, 10-year yields at 4% and 3-month Treasury yields at 3%, what do historical relationships have to say about the 1-year total return that investors would normally expect on the S&P 500?

Using the data since 1929, the fitted projection for the S&P 500 is 1.24%. Using the data since 1940, 2.64%. Since 1960, 2.55%, and since 1970 – the period that investors arguing the importance of interest rates are most likely to favor: -0.32%. The statistics for investment horizons of 2-10 years provide similarly weak expectations for future returns.

None of those should be relied upon as forecasts, but suffice it to say that explaining P/E multiples using interest rates is not nearly the same thing as justifying them.

Market Climate

As of last week, the Market Climate for stocks remained characterized by unusually unfavorable valuations and modestly unfavorable market action. The bright spot in the market here continues to be the action of the broad market, particularly on the basis of advances versus declines. However, we're observing a substantial weakening in the quality of that breadth when it comes to factors like trading volume, momentum, and (as Richard Russell has noted) the extent to which the broad market seems to be struggling against its currently overbought condition. Suffice it to say that conditions are mixed, but we're not yet observing any type of deterioration that suggests a substantial increase in the skittishness or risk-aversion of investors. The main difficulties here are in the underlying factors – valuations, sentiment, overbought status, weakening (though not sharply deteriorating) economic fundamentals and credit conditions, and so forth.

The big picture continues to suggest a market too elevated in valuation to deliver satisfactory long-term returns, with too much initial deterioration to warrant much speculative risk taking, but still not evidencing immediate risks. That's another way of saying that we remain defensive, but that our defensiveness should not be confused with any expectation that the market will or must decline abruptly. It's just that market conditions, at present, continue to suggest a relatively muted and possibly disappointing tradeoff to risk taking. That's a situation that makes exposure to market fluctuations relatively inefficient.

I clipped off our contingent call option positions in the Strategic Growth Fund on market strength last week, so the day-to-day fluctuations in the Fund at present can be interpreted primarily as the difference in performance between the stocks held by the Fund and the indices we use to hedge (primarily the S&P 500 and the Russell 2000 index). That performance differential will certainly fluctuate from day-to-day, and can certainly be down or up over consecutive days or weeks. Still, the performance of our stock holdings relative to the major indices has accounted for a substantial portion of the Strategic Growth Fund's returns since its inception. I am planning to include further detail on this in the upcoming annual report, which will be issued next month.

In bonds, the Market Climate remains characterized by moderately unfavorable valuations and relatively neutral market action. The Strategic Total Return Fund continues to carry a duration of just under 2 years (meaning a 100 basis point change in interest rates would be expected to impact the Fund by about 2% on the basis of bond price fluctuations). I would prefer our duration to be closer to 4-7 years, but at present, neither yield levels, spreads, or economic conditions provide such an opportunity. A recent stall in credit spreads also suggests caution here. If credit spreads were widening more rapidly, it would portend both the likelihood of economic weakness, and also an easing of inflation potential (credit weakness typically induces a decline in monetary velocity). For now, we continue to carry a fairly muted duration. The Strategic Total Return Fund continues to hold about 20% of assets in precious metals shares, and about 6% in select utility shares. Until there's enough evidence to increase our portfolio duration in bonds, those positions are likely to account for most of the day-to-day fluctuation in the Fund.

* Thanks to Mark Hulbert for the observation in the opening paragraph.


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