The Speculator
We road-test
a rule of thumb
A lot of readers blanched at our prediction of a
15% rise in the S&P 500 this year. So we dug a little deeper into the Fed
model that produced it -- and we're still bullish
By Victor
Niederhoffer and Laurel Kenner
Posted 5/15/2003
Simple models often give the best
forecasts -- particularly in the financial markets.
Investors
can make good money comparison-shopping stocks and bonds -- specifically, by
considering whether a dollar's worth of next year's earnings is a better value
than the payout on the 10-year Treasury. Known widely as the Fed model, the
comparison gives a highly bullish forecast for stocks right now.
The Fed model has many of the virtues as well as the
defects of other simple formulas. On the plus side, it uses few variables, and
only one rate of change is considered. On the minus side, it leaves out many
important factors. It takes no account of risk, nor of investors acting quickly
on its signals, nor of the accuracy of the data used.
We used the Fed model last week to predict a 15%
return in the S&P 500 ($INX) this year, based on 40 years
of data. Alas, few readers showered us with gold coins in admiration. Our mail
-- usually about 20-to-1 positive -- was 20-to-1 negative. The following notes
give the flavor:
"You are total scam
artists. You know the market is very overvalued (30x EPS on S&P), yet you
are bullish. Give me a break.
"Whenever a fraud feels emboldened by a sucker rally, he reaches for some
justification for absurd overvaluation of 34x earnings. Why is it that the
model only goes back to 1962? Because when you apply it to the entire century,
it proves to be a phony model which doesn't work. It doesn't take a finalist in
'Jeopardy' to realize that our situation now is much more similar to the early
30s than at any time in the last 40 years.
"Again you have oversimplified and will be proved wrong."
Objections
fell into several broad categories:
Field testing
All of these objections sound good. But they’re the
kind of protests you hear around the water coolers and on the commuter trains
after every close sports game. Everybody knows it as Monday-morning
quarterbacking -- advice to the coach without the benefit of a real-world test.
Nobody is going to get it right all the time, but a
good tested idea improves your chances in any field. Without some
simplification, nothing would get done. If all things were always considered,
the surgeon would never make a cut; the pilot would never leave the ground; the
investor would never sell or buy.
Real-world testing is the reason that knowledge has
increased exponentially during the last 150 years in every field of human
endeavor. Every field, that is, except the stock market, where untested
hypotheses, myths and mumbo jumbo still hold sway. Steve Stigler, in his
classic scientific history, "Statistics on the Table: The History of
Statistical Concepts and Methods," writes: “If a serious question has been
raised, whether it be in science or society, then it is not enough merely to
assert an answer. Statistics must be put on the table.”
We subscribe so completely to that statement that
the whole of our book, "Practical Speculation," is based on it. The
value of stocks certainly qualifies as a serious question. We therefore will
present the numbers that support our view that the Fed model provides a
reasonably good forecast of future stock market returns.
Let us begin by explaining how the model works.
Although the relation between earnings and note
yields looks simple, it contains the essence of some very complex economic
conditions, interactions and investment theory. Usually, the yield of the
10-year note is higher than the earnings yield on stocks. That’s because
earnings, unlike fixed-income yields, have the potential to grow with
inflation. To keep up with the Joneses, fixed-income investors demand more
yield. Over the past 40 years, the differential has been some 2.6 percentage
points higher for notes, on average.
Slight changes in this relation are front-page news
to investors. If the earnings yield is above the 10-year note yield, it’s
bullish for stocks. If the earnings yield is unusually far below the 10-year
note yield, it’s bearish for stocks. Federal Reserve economists once mentioned
this seesawing in a 1997 report to Congress, and it has been known ever since
as the Fed model.
Big difference
With the S&P 500 at 879.82 at the end of last
year, analysts estimated total 2003 earnings for companies in the index at
$54.08 a share. Thus, the earnings yield was 6.1%. The 10-year note was only
3.8%, a full 2.3 percentage points below the earnings yield.
Why use estimated earnings rather than one of the
many varieties of trailing earnings such as GAAP, net, operating profit, core,
etc.? Because the stock market is a forward-looking creature; it trades on the
future, not the past.
Why not use corporate bond yields instead of 10-year
Treasury notes? We did so, using our 40 years of data, and found that the
relation has no predictive significance. (However, using only the past 10 years
of data, the predicted return based on corporate bond yields would be quite
high for 2003).
Now, let’s look at the five times in the last 40
years when the earnings yield was at its highest relative to the note yield.
High
earnings yield, low note yield
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The average S&P 500 return in years following
these conditions was 11.8%; the year was positive four times out of the five.
The flip side of the relation gives completely
different results. Here are the five years when the earnings yield was at its
lowest relative to the note yield.
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Low earnings yield, high note yield |
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In the following year, the market was up three times
out of five, with an average S&P 500 return of -4.1%.
(Note that the spreads in the tables reflect
vagaries in rounding.)
Thus, the five years of highest earnings yields
relative to note yields were followed by an average return of 12% the next year
in the S&P 500. The five years of lowest earnings yields relative to note
yields were followed by a dismal -4.1% return in the S&P 500, on average.
Estimating returns
Using regression analysis, it is possible to
estimate a quantitative relation between the yield differential and the
expected return in the market. The equation is:
Stock market return = 8.5% +
1.4 times yield differential
The
correlation between the predicted return and the actual return is 20%. A
correlation this high gives the investor about a 10% edge in predicting the
direction of the market.
The current yield differential is 2.33%. Putting
that number in the formula gives an expected return of 12% for the S&P 500
in 2003. (As we write on Tuesday morning, the S&P 500 is up 7% year to
date.)
This result differs from the 15% forecast we arrived
at last week, when we regressed the degree of overvaluation according to the
Fed model. No model is perfect.
Yet another way of approaching the problem is to
look at year-to-year changes in the differential. The equation that describes
the line of best fit for this relation is:
Stock market return = 8% +
1.3 times the change in differential
In 2002,
the earnings yield was 2.3 percentage points higher than the note yield. In
2001, the earnings yield was 2.88 percentage points lower than the note yield.
Therefore, the differential improved by 5.2 percentage points. And putting 5.2
into the equation gives an estimated return of 14.7% for the S&P 500 this
year:
8% + 1.3 x 5.21 = 14.7%
The Fed model is by no means the
be-all and end-all of forecasts. But it does seem to have validity when
subjected to tests with real numbers. No doubt there are many readers and
analysts out there who have better ways of calculating the components. Our own
tests, however, using the only operational data we could find, appear to show
that the model is quite bullish for this year.
Addendum
Just before publishing our conclusions on Wednesday,
we received demurrals from Cliff Asness, an award-winning scholar in this field
who is managing principal of AQR Capital Management, a widely respected money
management firm, and from Sam Eisenstadt, research director of Value Line. Both
argued that the Fed Model seems to work only because the market produces
stronger-than-average returns after P/Es drop to low levels. Interest rates
have little to do with the matter.
Recommended reading
It is rare that we can recommend a book as heartily
as we can "Ahead of the Market: The Zacks Method for Spotting Stocks Early
-- in Any Economy," by Mitch Zacks. This is a must-read for readers who
have heard of the excellent performance of the Zacks, Investment Business Daily
and Value Line rating systems and wish current documentation of the major
academic findings on income statement anomalies. It’s also good for anyone who
wants to know about the components of income statements and their impact on
price. More generally, anyone interested in the process of decision-making
under uncertainty will learn much. For us, the highlight was the discussion of
the estimation of earnings and the ratings process -- a meal for a lifetime for
all those who wish to develop an appreciation of what works on Wall Street.
"Ahead of the Market" contains some 100
graphs and tables showing the exact impact of how expectations, revisions,
ratings and forecasts work out in the real world. Chapter 12, “Valuation,
Earnings, Uncertainty and the Fed Model,” contains an excellent discussion of
the Fed model and includes scatter diagrams of its components and the other
variables discussed above. Particular attention should be paid to the Zacks
tables and contributions relating to the recency of earnings forecasts and the
effects of better- and worse-than-expected sales. The only reservation we have
in recommending "Ahead of the Market" is that the tables and systems
seem to assume that past relations will continue eternally. Such is not in concert
with the principle of ever-changing cycles. But as this objection applies to
almost everything written about the market, this should be taken merely as a
caution rather than a criticism. As a lagniappe, the book offers a method of
beating the Dow based on the uncertainty of earnings estimates for the
individual stocks. The less uncertain, the better. Highly recommended.
Final note
An excellent discussion of simplicity in science is
contained in "Simplicity, Inference and Modeling" by Arnold Zellner.
… Scatter diagrams and raw data for our Fed model studies are posted on our Web site. The
site also has an updated list and workout of stock buybacks. … We encourage and
answer all reader correspondence about the market; send it to us by e-mail.