Long-Term Evidence on the Fed Model and Forward Operating P/E Ratios

(a discussion of useful recession indicators follows)

John P. Hussman, Ph.D.
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In recent years, price/earnings ratios based on "forward operating earnings" have been embraced by Wall Street as a replacement for valuations based on trailing net earnings. The beliefs of investors about what represents a "normal" P/E, however, have not changed - despite the change in the earnings measure being used. Meanwhile, the Fed Model - the notion that the earnings yield of the S&P 500 (based on forward operating earnings) should be equal to the 10-year Treasury bond yield, has been embraced as a simple and reliable method of valuing stocks.

It's likely that these beliefs will prove disastrous for investors. The assumed one-to-one correspondence between forward earnings yields and 10-year Treasury yields is a statistical artifact of the period from 1982 to the late 1990's, during which U.S. stocks moved from profound undervaluation (high earnings yields) to extreme overvaluation (depressed earnings yields). The Fed Model implicitly assumes that stocks experienced only a small change in "fair valuation" during this period (despite the fact that stocks achieved average annual returns of nearly 20% for 18 years), and attributes the change in earnings yields to a similar decline in 10-year Treasury yields over this period.

Unfortunately, there is nothing even close to a one-to-one relationship between earnings yields and interest rates in long-term historical data. Why doesn't Wall Street know this? Because data on forward operating earnings estimates has only been compiled since the early 1980's. There is no long-term historical data, and for this reason, the "normal" level of forward operating P/E ratios, as well as the long-term validity of the Fed Model, has remained untested.

While there are a variety of papers that debate the validity of the Fed Model based on its implications for how earnings growth and inflation are related, my objective here is to answer three questions: 1) Is there a reasonably robust way to estimate what forward operating earnings would have been historically? 2) Is the Fed Model valid in long-term historical data? and 3) What is the "normal" P/E multiple for the S&P 500 based on forward operating earnings?

For a bit of background, forward operating earnings are the estimates of Wall Street analysts for year-ahead earnings, excluding extraordinary charges and a variety of other factors that are otherwise responsible for earnings volatility over time. These "operating earnings" are not even defined under generally accepted accounting principles (GAAP) and are invariably much higher than actual subsequent net earnings. Still, this is not a wholesale criticism of operating earnings or analyst estimates, both of which can be useful, but only if they properly understood and interpreted.

Operating earnings are a "smooth" measure of earnings that, as it turns out, can be cleanly and accurately approximated using variables that are available historically - specifically, the highest level of S&P 500 (trailing net) earnings achieved to-date, the actual level of S&P 500 trailing net earnings, and the U.S. unemployment rate (which helps to capture business cycle fluctuations). The ISM Purchasing Managers Index provides slightly better accuracy than the unemployment rate, but has a shorter history. The results below are not very sensitive to the choice, so in the interest of data availability and to make it easy for others to replicate and verify these results, I've used the unemployment rate (our Data Page has links to earnings and unemployment data, and loads of other historical data series).

Estimating long-term historical data on forward operating earnings

We know that all measures of S&P 500 earnings are "co-integrated," in the sense that they move together over the long-term, and do not diverge from each other indefinitely. In order to properly estimate forward operating earnings, we can preserve that co-integration by modeling forward earnings as a variable (but non-exploding) "markup" to the maximum level of trailing net earnings achieved at any particular date.

Using the available data, we obtain the following relationship (skip to the next paragraph if math makes your eyes glaze over):

forward operating earnings = k * record trailing net earnings to-date

where

k = 1.2721 + 0.3115 (current trailing net earnings / record trailing net earnings - 1)
- 0.5011 (unemployment rate / 16-month average of unemployment rate - 1)
- 0.5985 ( (record trailing net / record trailing net 5 years prior) ^ (1/5) - 1)

IMPORTANT: I should emphasize that while this particular estimation provides a good fit, there is nothing magic or special about it. A variety of other versions provide equal or better fits (though with less available data), and perform well even if a holdout sample is used for testing. The indicators I'm using are very general measures of deviation from trend, nothing more - they have no magic to them - the essential point is that forward operating earnings are a very well-behaved markup to record earnings to-date, and can be accurately and simply modeled that way.

(If you want to interpret this particular equation, it just says that forward operating earnings tend to be about 20-some percent above the peak level of trailing earnings to-date, with a few intuitive adjustments: analysts use a smaller "markup" to record earnings if current earnings are less than their record level, if the economy is sluggish so that unemployment is above its recent average, and if the growth rate in that record level of earnings has been unusually strong in recent years).

To give you an idea of the goodness of fit, the chart below presents the S&P 500 earnings yield based on actual I/B/E/S forward operating earnings estimates versus the earnings yield based on estimated or "fitted" forward operating earnings.

(I/B/E/S data provided by our indispensable data source, Thomson Financial)

Having an accurate method of estimating what "forward operating earnings" would have been on a historical basis, we can now examine the data from a long-term historical perspective, to see whether the "Fed Model" actually works, and what the "normal" level is for a P/E based on forward operating earnings.

Below, I've calculated the fitted values for forward operating earnings historically, and have extended the earnings yield chart back to 1948. For reference, I've also included the earnings yield based on the highest level of S&P 500 earnings to-date, as well as the 10-year Treasury yield.

Chart: Earnings yields vs. 10-year Treasury yields

Several points are worth noting. First, the fitted series is well-behaved - there is a fairly stable relationship between the earnings yield based on fitted operating earnings and the actual earnings yield based on the highest level trailing earnings-to-date (if these two yields moved in wildly different directions, we would have to conclude that something in our estimation was amiss). The operating earnings yield is generally higher than the yield based on peak earnings, with the same normal range of variation that we've observed since the 1980's when "forward operating earnings" came into use. Since all earnings measures are co-integrated over time, we already know that our conclusions don't rely on our use of estimated forward earnings, but having good estimates does allow us to make apples-to-apples comparisons.

Just a note - it's difficult to see the original (green) IBES yield on this chart because the actual yield is virtually identical to the fitted one for the period since the early 1980's for which the actual forward operating earnings series is available.

The next observation is crucial. If you look at the relationship between earnings yields and Treasury yields, you'll notice that earnings yields and interest rates do not move tightly together. The notable exception is the period from about 1980 to 1998. During that period, you'll notice that the Treasury yield and the forward earnings yield moved lower together in an almost one-to-one fashion. It's that short but spurious one-to-one relationship that is the entire basis for the "Fed Model." The model is simply a statistical artifact based on that period. But Wall Street doesn't even know how bad an artifact it is because the forward operating earnings series isn't available historically.

The next chart is what Wall Street "knows" as an accepted truth. It presents data since the early 1980's, showing the percentage by which the S&P 500 would have to increase or decrease in order to bring the "forward earnings yield" to the same level as the 10-year Treasury yield.

The inference seems very strong - the Fed Model clearly indicates stocks as being overvalued and vulnerable in 1987, cheap at several points in the early 1990's, and extremely overvalued in 2000, just before the market tumbled. Subsequently, the model indicates that stocks were deeply undervalued in 2003, and remain very favorably priced today.

Chart: The "Fed Model" since the 1980's

Unfortunately, it turns out that 1987 and 2000 are the only two periods in which the Fed Model would ever have been significantly negative. Below is the sobering longer-term picture.

Chart: The Whole Truth - The Fed Model since 1948

The profile of actual market returns looks nothing like this. Rather, the profile of actual market returns - especially over 7-10 year horizons - looks much like the simple, humble, raw earnings yield, unadjusted for 10-year Treasury yields (which are too short in duration and in persistence to drive the valuation of stocks having far longer "durations").

On close inspection, the Fed Model has nearly insane implications. For example, the model implies that stocks were not even 20% undervalued at the generational 1982 lows, when the P/E on the S&P 500 was less than 7. Stocks followed with 20% annual returns, not just for one year, not just for 10 years, but for 18 years. Interestingly, the Fed Model also identifies the market as about 20% undervalued in 1972, just before the S&P 500 fell by half. And though it's not depicted in the above chart, if you go back even further in history, you'll find that the Fed Model implies that stocks were about as "undervalued" as it says stocks are today - right before the 1929 crash.

Yes, the low stock yields in 1987 and 2000 were unfavorable, but they were unfavorable without the misguided one-for-one "correction" for 10-year Treasury yields that is inherent in the Fed Model. It cannot be stressed enough that the Fed Model destroys the information that earnings yields provide about subsequent market returns.

Over time, Fed Model adherents are likely to observe behavior in this indicator that is much more like its behavior prior to the 1980's. Specifically, the Fed model will most probably creep to higher and higher levels of putative "undervaluation," which will be completely uninformative and uncorrelated with actual subsequent returns.

Historically, readings from the Fed Model explain just 3% of the variation in S&P 500 total returns over the following year, 2% of the variation in 7-year returns, and just 1% of the variation in subsequent 10-year returns.

In contrast, the simple raw operating earnings yield explains 8% of the variation in subsequent 1-year returns, 41% of the variation in 7-year returns, and fully 52% of the variation in subsequent 10-year returns.

The popularity of the Fed Model will end in tears. The Fed Model destroys useful information. It is a statistical artifact. It is bait for investors ignorant of history. It is a hook; a trap.

If I am passionate about fallacies like this, it is because I am certain that innocent, ordinary people will ultimately suffer from them. Is our profession really so lazy that we would advise people to risk their financial security based on tinker-toy models and pretty pictures that we don't even have the rigor to test historically?

16? Lower. 14? Lower.

Now, to the issue of P/E ratios based on forward operating earnings. As noted above, it's clear that forward operating earnings are generally much higher than the record level for trailing net earnings to-date, and of course, record earnings are always equal to or higher than raw trailing earnings.

Investors are used to the idea that "normal" P/E ratios are typically in the range of 14 to 16. But as Cliff Asness of AQR has repeatedly stressed, those norms are based on raw trailing earnings. If you calculate P/E ratios based on earnings figures that are higher, you clearly obtain lower P/E ratios.

As it happens, the long-term historical norm for the P/E ratio based on forward operating earnings would be about 12.

Chart: Historical Forward Operating P/E Ratios for the S&P 500

Of course, that average of 12 includes the heights of the late 1990's bubble. The historical average was just 10.6 prior to that point.

It gets worse. Currently, profit margins are at the highest level in history, which further reduces the P/E multiple we observe. If investors wish to use that observed P/E ratio as their standard of value without normalizing for profit margins, they should be aware that they are implicitly assuming that profit margins will remain at current levels indefinitely.

That assumption is hard to support. Historically, profit margins have been highly cyclical. But it's important to understand the argument here. I am not arguing that stocks are vulnerable because profit margins are going to come down, so earnings are going to come down, so stocks are going to follow earnings lower. No. There is virtually no correlation between year-over-year movements in earnings and year-over-year movements in stock prices. The argument isn't about the near term direction of earnings.

Rather, the argument is about the long-term valuation of stocks. If an investor is going to use the current level of earnings to determine the reasonable price to pay for a long-term asset, it had better be true that those earnings represent a normal and sustainable level of profit. You wouldn't buy a lemonade stand by extrapolating the profits it earns in August.

The following chart presents the ratio of forward operating earnings to S&P 500 revenues (net profit margins are even more volatile).

Chart: Historical Profit Margins (Forward Operating Earnings / Revenues)

You'll notice that prior to 1995, there were only a few instances when operating profit margins exceeded 8%. At those points, prior to the late-1990's bubble, the forward operating P/E for the S&P 500 averaged just 8. That's not a typo.

Investors appear eager to "scoop up" so-called "bargains" on the belief that stocks are "cheap relative to bonds." All of this is predicated on the belief that profit margins will remain at record highs, that the Fed Model is correct, and that P/E ratios based on extremely elevated measures of earnings should be evaluated based on norms for much more restrained measures of earnings.

That's not investing. It's speculation. And it's speculation that runs entirely counter to historical evidence. While an improvement in market internals might provide reason to speculate modestly on the basis of market action, there is no investment merit in current market valuations. Again, we do not need stocks to become "fairly valued" or undervalued in order to remove most or all of our hedges, but in the absence of reasonable valuation, we do need constructive market internals (short of extremely overbought or overbullish conditions).

Look at the composition of S&P 500 earnings. Financials currently make up about 25% of the S&P 500 market capitalization, but close to 40% of the earnings. Wages and salaries as a fraction of U.S. corporate profits have rarely been lower. Irresponsible lending and suppressed labor costs have been strong contributors to S&P 500 earnings in recent years thanks to a massive leveraging cycle - financial profits exploded, while wage demands stayed low because it was easy to spend out of home equity withdrawals and strong real-estate gains. But these are not permanent factors, and it is dangerous to value stocks as if recent profit margins will endure in perpetuity.

Based on daily closing prices, the S&P 500 has not even experienced a 10% correction, yet the recent decline has been characterized as if investors are acting "like the world is about to end." This is not the pinnacle of human irrationality, but in fact, quite a shallow selloff from a historical standpoint. The fact that Wall Street is branding it otherwise is evidence that investors have completely forgotten how deep the market's losses can periodically become.

Alpha versus Beta

Our investment objective is to achieve long-term capital appreciation, with added emphasis on the protection of capital during unfavorable market conditions. Preferably, to significantly outperform the S&P 500 over the full market cycle, with smaller periodic losses than a passive investment strategy. The Strategic Growth Fund set a fresh high little more than a week ago. Including reinvested distributions, the Fund has achieved a total return of over 120% since its inception in July 2000, while the S&P 500 has achieved a total return of less than 11%. The market may or may not have entered the "bear" portion of this cycle, but has not even declined 10% on a daily closing basis. It would be helpful to keep some portion of the prior bear market in memory until the current bull-bear cycle runs its course.

Achieving gains in a declining market does not require us to carry a significantly negative "beta." In extremely negative conditions, raising the strike prices on index put options side of our hedges can create a moderate negative beta and can help to avoid the impact of indiscriminate selling early in a bear market. But conditions that warrant these "staggered strike" positions are historically infrequent. Notably, our gains during the 2000-2002 market plunge were not due to net short positions or negative betas. Our gains were due to the slow accrual of "alpha," averaging less than a penny of net asset value per day. It is essential to understand the distinction.

"Beta" is a measure of the extent to which a particular security "participates" in a 1% movement in the market. A stock or mutual fund with a beta of 1.0 can be expected to gain 1% in response to a 1% market advance, on average, and to lose 1% in response to a 1% market decline, on average. Though a few stocks, such as precious metals shares, often have a slightly negative beta, several "bear funds" are available that take significant short positions in the market, and establish negative betas over the complete market cycle. These funds can be expected to predictably and continually gain as the market declines, and to predictably and continually lose as the market advances.

In contrast, "Alpha" is a measure of the extent to which a particular security advances, on average, independent of market movements. Alpha is not driven by fluctuations in the market, but "accrues" slowly over time. For example, suppose that the Strategic Growth Fund is fully hedged and has a beta of zero. In order to achieve a 15% total return over a period of a year, the Fund would have to achieve an average daily alpha amounting to slightly under a penny per day in NAV. It is important to understand that alpha does not accrue in response to a given day's market action. That's beta. It is not riskless. That's Treasury bill interest. Alpha involves at least some amount of risk (for us, it is the "basis risk" that our stocks could lag the market rather than outperform), it accrues almost unobservably on a day-to-day basis, but it has been responsible for the majority of the returns in the Strategic Growth Fund over time.

Simply put, the Fund does not establish big negative betas, though raising the strike prices of our index put options can create a moderate negative beta in a small percentage of historically extreme conditions. To position the Fund with a large and continuous negative beta, so that we can achieve a rapid gain on a market decline, would also be to position the Fund to suffer large and continuous losses on any sustained market advance. The "staggered strike" aspect of our hedge has certainly allowed us to experience some "giveback" during sharp rebounds after a market decline, and the Fund may experience losses even in a hedged investment position if our stocks underperform the indices we use to hedge or we experience net time decay on our option hedges. In any event, the dollar value of our hedges does not materially exceed the dollar value of our long stock holdings.

There are bear funds available for investors interested in carrying a large or persistently negative beta. The Strategic Growth Fund is not intended to do this. To the extent that the Fund has achieved gains during periods of market weakness, those gains have most often been attributable to the slow and often imperceptible accrual of alpha. For us, our alpha has generally been the result of holding favorably valued stocks with good sponsorship, that tend, on average, to very slightly outperform the market on a day-to-day basis. It's sometimes possible to observe the accrual of alpha over the course of a few months. It is nearly impossible to distinguish it from random noise on a day-to-day basis.

In any event, given that the Fund does not have much of a beta at present (I closed our "staggered strike" position during last Thursday's market decline, so the Fund now has a flat hedge), it will not be particularly helpful or informative to compare the Fund with the market on a day-to-day basis. The Fund is not positioned with a big negative beta that would achieve rapid gains on market declines, and rapid losses on market advances. Instead, we are positioned in the expectation of accruing alpha over time.

Market Climate

As of last week, the Market Climate for stocks remained characterized by unfavorable valuations and unfavorable market action. I closed our "staggered strike" configuration on Thursday's severe market weakness, so the Fund now carries a "flat" hedge, with matched short call / long put combinations at identical strike prices and expirations. I recognize that investors have a strong pull to "buy the dips," in hope of timing short-term rebounds, but we presently have no evidence to take an unhedged investment position. As I've noted recently, the quickest way to obtain such evidence would be for us to observe the type of market action that typically initiates sustained "clearing rallies" - a quick and sharp reversal from lopsided negative breadth to strongly positive breadth, accompanied by falling yield trends across a variety of maturities. Presently, we don't have sufficient evidence to accept a speculative exposure to market fluctuations here.

To the contrary, leadership has flipped from a significant number of stocks reaching new highs to a significant number reaching new lows. When you observe that sort of flip within a few weeks of a fresh market high, a persistent selloff of say, 5 consecutive down days (which we recently saw in the NYSE Composite) is typically followed by a halting recovery and then abrupt, and often deep further weakness. As usual, that's not a forecast, but until we observe evidence that has historically been associated with an acceptable return/risk profile, we'll have little interest in trying to "catch" short-term rebounds from oversold levels. That sort of evidence may very well appear shortly, but we don't observe it yet, and it is likely that we'll require much more lopsided internal weakness as a "setup" for a compelling breadth and leadership reversal. In any event, we'll remove a portion of our hedges if and when we observe evidence that is associated with a favorable average return/risk profile.

In bonds, the Market Climate was characterized last week by unfavorable yield levels and moderately positive market action. The Strategic Total Return Fund continues to carry a duration of about 2 years, mostly in TIPS, but we may moderately increase that duration if the bond market experiences weakness.

Aside from the cut in the discount rate, which remains above the Federal Funds rate (and which I again viewed as an appropriate but overrated action by the Fed), probably the most important development in the bond market last week was that the spread between 6-month commercial paper and 6-month Treasury bill yields has blown sharply wider. While this is largely because Treasury bill yields have declined, the historical evidence is that it is not material whether spreads widen due to rising commercial paper yields or falling Treasury bill yields. I've noted repeatedly that a blowout in this spread would probably be a precursor for any imminent recession risk.

A toolbox of useful indicators to gauge recession risk

We still don't have quite enough evidence to confidently anticipate a recession, but I think this is a good point to review the simple 4-indicator criteria set that has reliably preceded or accompanied the beginning of U.S. recessions. Most of the following is excerpted from my Brief Economics Primer:

1) The "credit spread" between corporate securities and default-free Treasury securities becomes wider than it was 6 months earlier. This spread is measured by the difference between 10-year corporate bond yields and 10-year U.S. Treasury bond yields (or alternatively, by 6-month commercial paper minus 6- month U.S. Treasury bill yields). This spread is primarily an indication of market perceptions regarding earnings risk and default risk, which generally rises during recessions.

2) The "maturity spread" between long-term and short-term interest rates falls to less than 2.5%, as measured by the difference between the 10-year Treasury bond yield and the 3-month Treasury bill yield. A narrow difference between these interest rates indicates that the financial markets expect slower economic growth ahead. If the other indicators are unfavorable, anything less than a very wide maturity spread indicates serious trouble, regardless of unemployment, inflation, or other data.

3) The stock market falls below where it was 6 months earlier, as measured by the S&P 500 Index. Stock prices are another important indicator of market perceptions toward credit risk and earnings expectations. While the economy does not always slow after a market decline, major economic downturns have tended to follow on the heels of a market drop. Stock markets tend to reach their highs when the economy "cannot get any better" -- unemployment is low and factories are operating at full capacity. The problem is that when things cannot get any better, they may be about to get worse.

4) The ISM Purchasing Managers Index declines below 50, indicating a contraction in manufacturing activity. This index is strongly related to GDP growth, and when combined with the previous three indicators, has signaled every recession in the past 40 years.

Presently, the first two of these conditions are in place, the third is borderline (depending on day-to-day market activity), and the fourth has not occurred yet.

The following are some additional early warning indicators of an oncoming recession:

A sudden widening in the "consumer confidence spread," with the "future expectations" index falling more sharply than the "present situation" index (currently in place). In general, a drop in consumer confidence by more than 20 points below its 12-month average has accompanied the beginning of recessions (not observed yet);

Low or negative real interest rates, measured by the difference between the 3-month Treasury bill yield and the year-over-year rate of CPI inflation. Last week, T-bill yields plunged to about the same level as CPI inflation, so this indicator is now unfavorable;

Falling factory capacity utilization from above 80% to below 80% has generally accompanied the beginning of recessions. This is not yet in place.

Slowing growth in employment and hours worked. The unemployment rate itself rarely turns sharply higher until well into recessions (and rarely turns down until well into economic recoveries). So while the unemployment rate is an indicator of economic health, it is not useful to wait for major increases in unemployment as the primary indicator of oncoming economic changes. As for employment-related data, slowing growth in employment and hours worked tend to accompany the beginning of recessions. Specifically, when non-farm payrolls have grown by less than 1% over a 12 month period, or less than 0.5% over a 6 month period, the economy has always been at the start of a recession. Similarly, the beginning of a recession is generally marked by a quarterly decline in aggregate hours worked. All of these indicators are slowing considerably, but they have not crossed to levels typically associated with imminent recession.

In short, the risk of recession is increasing, but we do not yet have the evidence to indicate that a recession is imminent or inevitable. Important data to monitor in the next few months will be the ISM figures, consumer confidence (especially a sharp drop), employment, hours worked, and capacity utilization.

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The foregoing comments represent the general investment analysis and economic views of the Advisor, and are provided solely for the purpose of information, instruction and discourse.

Prospectuses for the Hussman Strategic Growth Fund, the Hussman Strategic Total Return Fund, the Hussman Strategic International Fund, and the Hussman Strategic Dividend Value Fund, as well as Fund reports and other information, are available by clicking "The Funds" menu button from any page of this website.

Estimates of prospective return and risk for equities, bonds, and other financial markets are forward-looking statements based the analysis and reasonable beliefs of Hussman Strategic Advisors. They are not a guarantee of future performance, and are not indicative of the prospective returns of any of the Hussman Funds. Actual returns may differ substantially from the estimates provided. Estimates of prospective long-term returns for the S&P 500 reflect our standard valuation methodology, focusing on the relationship between current market prices and earnings, dividends and other fundamentals, adjusted for variability over the economic cycle (see for example Investment, Speculation, Valuation, and Tinker Bell, The Likely Range of Market Returns in the Coming Decade and Valuing the S&P 500 Using Forward Operating Earnings ).