Using The Fed Model To Understand This Market

The Fed Model provides a quantitative analysis of the basic investor decision: Buy stocks or buy bonds?

The following chart compares the S&P 500 to "fair value" as determined by the Fed Model, ending in 1998. It is presented on a log scale to facilitate comparisons over a long historical period.

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One can see the basic quality of the overall fit, but there are other important observations. In the Crash of '87, for example, one would not have wanted the model to track the S&P in the days preceding the crash. A valuation model should not be expected to trace the market exactly, but rather provide a warning of anomalies. The period around the first Gulf War provides a similar illustration.

One might ask why our analysis begins where it does. The reason is that we do not have a record of forward earnings before 1979. Anyone reading a Fed Model study that purports to go farther back in history should carefully read the footnotes to see if forward earnings are really being used.

If we had more data, what would or should we use? We'll take up this question in our overall review, but regular readers of "A Dash" know that we are extremely skeptical of very old data. Many big-name investment research firms use data going back to the Great Depression. One Fed Model critic found trailing earnings for a test going back to 1871, although we cannot imagine why! A good dividing line might be the invention of market derivatives like stock options and futures and the development of computer-based econometric models.

Let us now take a look at the Fed model including the next period, the Internet/Technology/Stock Market Bubble. This is a period that is now generally recognized as one that involved excessive stock valuations. Here is what the model shows:

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A prescriptive model should offer advice; the advice here is similar to the acclaimed work of Robert Shiller. It shows excessive valuations beginning in 1997 (was it time to sell?) and the big valuation gap at the bubble peak. Since we believe that is what actually happened, the model is also a good descriptive model. It accurately identified irrational exuberance and excessive stock valuation. Despite this performance, some critics alleged that the Fed Model "did not work" because it did not track actual market levels. One wonders whether these critics just write articles or actually invest. Most of us would be delighted to have wise counsel that investment in stocks was dangerous.

Anyone who is intrigued by the Fed Model performance from 1979 to 2001, and you should be, might wish to study the current chart.

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The key feature of the current chart is the persistent valuation gap. Stocks became under-valued in 2002 and have remained so for about four years. It may be helpful to consider "fair value" as a horizontal axis to emphasize the deviations. Here is a look at the same data using that approach. This view enables us to focus on the deviations over time.

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According to the model, we are in the longest sustained period of deviation from calculated fair value in the entire time period. This intriguing situation deserves further investigation.

Since interest rates and stock prices are known, the only remaining variable in the model is projected earnings. One could conjecture that the forward estimates are incorrect. Or one could argue that "things are different this time" and that the relationship between stocks and bonds no longer holds. Or one could argue that the model is leaving out important considerations that have had a special relevance in the last four years.

The next segment of this series will offer our analysis of this valuation gap. We will then turn to criticisms of the Fed Model. In the last of this series of short articles we will ask what stocks might be of special interest in the coming year.

Comments

[CHRIS.ZAPITIS:]

Dear Jeff,

I would be very much interested to know what actual data sources are you using in your modeling,
and also the exact form of the FED model implemented.

I am using the FED model to find the FAIR value for the S&P 500 with the Shiller datasheet,
with a FED model which takes into account Nominal Long Interest rates, 1 year forward inflation expectations and
an empirically computed 10-year moving average for the risk premium.

I am not sure that this approach is correct, but I would be very much interested in any comments or insight you may offer!!!!

I hope I hear from you soon


Regards,
C.

2007 Mar 16 04:17 PM

[Jeff Miller:]

Hi Chris,

The data I describe includes the forward earnings from Thomson and the rate for the ten-year note.

I understand the desire to tweak this with adjustments and more variables. You can make changes that create a better apparent fit with the last few years. To me, this is just like people who were changing their models to fit the "bubble era". I hope to write about some of the alternative approaches as I pursue this theme. The simple version of this model may not be the best, but it is a lot better than blindly discussing P/E without any mention of interest rates. We have learned to be cautious in making models more complex.

For now, let me make two brief observations. First, inflation expectations should be reflected in the ten-year rate, and the chained forward rates of other fixed income instruments (like eurodollars). The simple model I show is the choice faced by an investor. I do not see (at least not yet) a good reason for measuring inflation expectations in a different way, or adding another inflation variable.

Second, the "risk premium" might be zero. There are some studies showing little risk difference between stocks and bonds. It also depends on the holding period. If the gap implied by the Fed model were to close as a result of interest rates moving higher, the bond holder would suffer major losses. Stocks have a lot more upside and a better long-term record. When Dr. Ed Yardeni was working on this theme, I think that was his basic conclusion. What I have used in my charts is an extension of the time series he used to make publicly available.

Your questions and my two observations are current topics for papers and debate. As I read this work, I often find myself asking whether the modeler is reflecting a real process followed by the investor, or doing something fancy for "academic" purposes.

Thanks for the question.

2007 Mar 24 10:30 AM