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Fed Stock Model

One hundred years ago JP Morgan was asked, “When is a good time to buy stock?”

He replied, “When you have some money.”

The men and women of Wall Street will ALWAYS tell you to buy stock. Their wealth is dependent on the number of shares they can peddle to the children of Main Street. They want your money and they will say whatever is necessary to get it.

On Wall Street Week on Jan. 4, 2002 Abby Joseph-Cohen proclaimed that US stocks were 10-20% under-valued, even though P/E ratios had never been higher.

When stocks are under-valued, prudent investors buy and vice versa. If you understand the relationship between interest rates and corporate earnings, then it will help you determine if it really is a good time to buy.

Realize that when most analysts speak of selling stocks to buy bonds and vice versa they are NOT recommending liquidation of one in favor of the other. They are simply recommending increasing or decreasing exposure by some, generally small, pre determined amount because something happened to change valuation levels. The problem is no one can determine, with absolute precision, that stocks and/or bonds are either cheap or dear. However, relative to historic norms, one can determine if stocks relative to bonds are cheap or dear.

Frequently columnists and commentators will refer to the Fed’s model when comparing relative valuation levels. The Fed and others use stock and bond valuation models to determine stock and bond valuation levels. This paper will describe how they do it. Recognize that many stocks in any stock market will unexpectedly out-perform and many others will unexpectedly under-perform. The same can be said for the entire market: At times it will be incredibly over-valued or under-valued; several months or years later it may be even more over-valued or under-valued. Recognize that as a fact of investment life and try to be emotionally and financially prepared to deal with it. Let’s have a little review before we get started:

Question
What are the subjective drivers of stock market performance?
Answer
Fear and Greed

Question
Can Fear and Greed be quantified?
Answer
Maybe, but not with a high degree of precision

Question
What are the objective drivers of stock market performance?
Answer
Stock Market earnings vs. Fixed Income returns

Question
Can Stock Market earnings vs. Fixed Income returns be quantified?
Answer
Yes

It may be helpful to review some definitions:

S&P 500 earnings:
The amount of money earned by one hypothetical share of the index e.g., for the year ending 12/31/01 the index earned $28.24 and it closed at $1148.08

Earnings yield:
Earnings divided by the Index Value
Example
Earnings = $28.24
Index closing price = $1148.08
Earnings yield = $28.24 / $1148.08 = 2.46%

P/E ratio:
Index Value divided by Earnings
Example
P/E Ratio = $1148.08 / $28.24 = 40.65
Or, P/E Ratio = the inverse of the earning’s yield
P/E Ratio = 1 / 2.46% = 40.65

Dividend yield:
Dividend ($15.59 for the year ending 12/31/01) divided by the Index Value
Example
Dividend yield = $15.59 / $1148.08 = 1.36%

T Note Yield:
Current Annual Interest on Treasury Notes

Question
On average, what is the earnings yield of the S&P 500?
Answer
The earnings yield of the S&P 500 over the last fifty years has averaged 7% and varied from a high of almost 14% in 1979, which was the beginning of the greatest bull market in US history, to less than 2.5%. Note that the inverse of the earnings yield is the P/E ratio: 1 / Yield = P/E ratio.

Example:
1 / 14% = 7.14 (This is a Great P/E ratio i.e., Lower is Better)

Example:
1 / 7% = 14.28 (This is an Average P/E Ratio)

Example:
1 / 2.5% = 40.00 (This is a Terrible P/E ratio i.e., Lower is Better)

Question
How can the P/E ratio be improved?
Answer
Earnings can rise and/or stock prices can fall.

Question
How much do earnings normally grow in one year?
Answer
Earning’s growth rates have averaged about 9% a year with an 18% standard deviation from 1945 thru 2004. What this means is that earnings have about a 1% chance of increasing or decreasing by about 54% relative to the 9% average over the following year. In fact, the most they increased was 49% in 2004. The most they decreased was 47% in 2001. Many contemporary investors believe earnings are being managed or controlled by auditors and accountants. If that were true, then one would reasonably expect earnings to be less volatile than they were in the past. In fact, earnings have been considerably more volatile over the thirty-year period ending with 2004 than they were over the thirty-year period following WW2

During 2008, earnings decreased by 78%, and during 2009, earnings increased by 243%. These two years changed everything, meaning the average earning's growth rate is now 10.8% and its standard deviation as of 2009 is 37%. That also means that the earning's fall of 2008 was a six sigma event. Let us all hope it doesn't happen again anytime soon.

Some history:
Before 1958 it was relatively easy to determine if stocks were under or over-valued: If the dividend yield on the S&P 500 approached the yield of the long term treasury bond most investors believed stocks were getting pricey i.e., stocks are riskier than bonds; ergo, stocks should pay more: In 1957 the dividend yield on the S&P 500 was 4.6%; the 30-year T Bond yield was 3.3%

Question
What happened in 1958?
Answer
The dividend yield fell below the long bond yield

In 1958 the dividend yield on the S&P 500 was 3.2%; the 30-year T Bond yield was 3.8%

Questions
What’s the dividend yield on stocks now?
What’s the long bond yield?
Answers
On 12/31/2001 the dividend yield was 1.4%; the 30-year T Bond yield was 5.5%

According to the consensus opinion, in 1958 stocks were over-valued with a P/E ratio under 20

According to Abby Joseph-Cohen stocks were under-valued at the end of 2001 with a P/E ratio over 40

Question
Why were stocks over-valued then, and why are they under-valued now?
Answer
This stuff only works if you believe we’re in a new era. The fact is that we have been in a new era for more than fifty years. The real question is: Are we going to stay in the new era or are we going to go back to the bad old days when dividends were what mattered? Nobody knows. Very few folks today are saying investing is easy.

The Fed Stock Model uses the Ten-year Treasury Note Yield (hereafter called the T Note Yield) and the S&P 500 Earning’s Yield to determine if the S&P 500 is over, under, or fairly valued:

If the T Note Yield is equal to the S&P 500 Earning’s Yield, then stocks are fairly valued.

Make absolutely certain you understand the preceding statement because it is the assumption from which all else is derived. Note that you don’t have to agree with it, but if you want to understand the model, then you must understand the assumption.

Definition:

The T Note Premium is the difference between the T Note Yield and the S&P 500 Earning’s Yield

Expressed in absolute terms:
T Note Premium = T Note Yield – S&P 500 Earning’s Yield

Expressed as a ratio:
T Note Premium = (T Note Yield – S&P 500 Earning’s Yield) / S&P 500 Earning’s Yield

When the T Note Premium is zero stocks are fairly valued

When the T Note Premium is positive stocks are over-valued

When the T Note Premium is negative stocks are under-valued

Note that this is a SIMPLE valuation model. Many more factors can be used to create a far more complex model, but there is very little evidence that the forecasting ability of the model increases when more factors are used.

As far as I'm concerned, this model is useful only as a benchmark to show relative valuation levels. That is, since 1994 the valuation levels, based on forecasted operating earnings, have ranged from a high of 70% overvalued during 1999Q4 to a low of 65% undervalued during 2008Q4 and 2010Q3.

The biggest problem with this model is that it relies on forecasted earnings. It is reasonably well known that forecasted earnings are nine parts wishful and one part analytical. That means that if the wishful part of the equation comes true, then the model will function as designed.

Example:

The Ten-year Treasury Note Yield at the end of 2001 was 5.2%
The S&P 500 Reported Earning’s Yield at the end of 2001 was 2.5%%
Find the T Note Premium at the end of 2001

Expressed as a ratio:
T Note Premium = (T Note Yield – S&P 500 Earning’s Yield) / S&P 500 Earning’s Yield
T Note Premium = (5.2 – 2.5) / 2.5 = 1.08s were 108% over-valued based on the S&P 500 Reported Earning’s Yield

However, most contemporary analysts use forecasted earnings when attempting to value stock because most analysts agree one pays for FUTURE earnings when one buys stock

Earnings were depressed at the end of 2001 because of the terrorists, the war effort, deficit spending, corporate scandals, etc. Earnings were bound to grow at a much, much higher rate than normal, after Gee Dubya’s tax cut and corporate re-structuring took effect.

Let’s assume earnings are going to grow as much as they have ever grown over the next year.

If earnings grow a rate of 50% over the next year, then in one year the earnings yield will be:

1.50 X 2.5% = 3.75%

T Note Premium = (T Note Yield – S&P 500 Earning’s Yield) / S&P 500 Earning’s Yield

T Note Premium = (5.2 – 3.75) / 3.75 = 0.39
OR
Stocks were 39% over-valued based on the most optimistic S&P 500 Forecasted Earning’s Yield

Note that a 50% earnings growth rate in one year has never been achieved so Ms. Joseph-Cohen’s contention that stocks were under-valued at the beginning of 2002 was wildly optimistic, but understandable: All the gods and goddesses of Wall Street are paid to be optimistic about the future. It is worth mentioning that NOT one of her contemporaries on Wall Street Week expressed pessimism about the market during 2000, 2001, and 2002. During this period the S&P 500 lost more than 37% of its value. In 1999 Gail Dudack, a former Wall Street Week regular, expressed concern about valuation levels, so Lou Rukeyser fired her: Pessimism is NOT permitted on Wall Street

Question
How much did earnings really grow during 2002?
Answer
Earnings grew by about 45% during 2002

Question
What was the return of the S&P 500 during 2002?
Answer
Earnings did not grow enough to satisfy investors so the S&P 500 lost more than 22% during 2002

Fortunately the folks at Standard and Poor's share their forecasts so you and I don’t have to make any guesses about the future. Let’s apply the methodology discussed above to the S&P data available at the end of 2002

There are two ways of tracking earnings on Wall St. "Bottom up" projections are based on analysts' estimates for individual companies while "top down" forecasts are made by strategists and economists using economic and industry figures to estimate overall earnings growth.

Traditionally, the "bottom up" and "top down" projections vary widely early in the year, with industry analysts more optimistic than market strategists. But as the year progresses, the two forecasts get closer, usually with the bottom up analysts reducing their forecasts. The critical question is not whether the industry analysts lower their numbers, but will they lower them more than normal.

Calculations for the period ending 12/27/2002:

Current Actual top down Reported S&P 500 EPS yield = 3.62% (Used in Case 1 below)

Current Estimated top down Reported S&P 500 EPS yield = 4.51% (Used in Case 2 below)

Current Estimated bottom up Operating S&P 500 EPS yield = 6.36% (Used in Case 3 below)

10-Year T Note yield: 3.83% (Used in all cases)

Case 1

Based on Current Actual top down Reported S&P 500 EPS yield:

T Note Premium = (T Note Yield – EPS Yield) / EPS Yield

T Note Premium = (3.83-3.62) / 3.62 = 5.8%

Or, based on current actual reported earnings the market is currently 5.8% OVER-valued

Case 2

Based on Current Estimated top down Reported S&P 500 EPS yield:

T Note Premium = (T Note Yield – EPS Yield) / EPS Yield

T Note Premium = (3.83-4.51) / 4.51 = -15.16%

Or, based on current estimated reported earnings the market is currently 15.16% UNDER-valued

Case 3

Based on Current Estimated bottom up Operating S&P 500 EPS yield:

T Note Premium = (T Note Yield – EPS Yield) / EPS Yield

T Note Premium = (3.83-6.36) / 6.36 = -39.78%

Or, based on current estimated bottom up operating earnings the market is currently 39.78% UNDER-valued

Analysis of Case 1

The S&P 500 is currently 5.8% over-valued based on actual current reported earnings. Most investors believe that you should be prepared to pay for future earnings when you buy equities. If you believe earnings are going to stay where they are for at least another year, OR, if you believe that interest rates are going to rise commensurately with earnings, then use Case 1 to determine stock valuation levels.

Analysis of Case 2 and 3

The S&P 500 is currently 15.16% under-valued based on estimated top down future reported earnings and 39.78% under-valued based on estimated bottom up future operating earnings. Go to Standard and Poor’s website for their definition of reported and operating earnings. Most investors believe that you should be prepared to pay for future earnings when you buy equities. If you agree that future earnings should be considered when pricing stocks, then you may want to use either Case 2 or 3 to determine stock valuation levels.

How can this information be used?

Any intelligent investor should be able to make compelling arguments for or against any of the above cases. To be sure, it is certainly troubling that there are huge differences between reported and operating earnings but very few folks are now saying, “Investing is easy”.

Let’s assume you’re an extremely conservative investor and you’re not buying into the forecasts. Obviously you’re a candidate for Case 1 which suggests stocks are moderately i.e., 5.8% over-valued relative to bonds. If you have a neutral stock allocation goal, then this suggests that you should under-weight your neutral stock allocation by 5.8%. Your neutral stock allocation is the allocation you have assigned to stocks and bonds in your portfolio. A great deal has been written about stock-bond allocations and this paper assumes you have a neutral stock-bond allocation. If you maintain your neutral allocation regardless of underlying market fundamentals, then this is not for you. If, on the other hand, you believe that changing interest rates imply changes in stock-bond allocations, then you may be interested in what follows.

Example 1 for Case 1

Stock allocation for an extremely conservative investor who doesn’t believe S&P forecasts

T Note Premium = 5.8%

Neutral Stock Allocation = 50% (or whatever else you want as a neutral allocation)

Stock portion of Portfolio = (1 minus T Note Premium) multiplied by Neutral Stock Allocation

Stock portion of Portfolio = (1 - .058) X (50%) = .94 X 50%

Stock portion of Portfolio = 47%

Example 2 for Case 2

Stock allocation for a conservative investor who believes that investors should pay for future REPORTED earnings when they buy stocks.
Go to Standard and Poor’s websites for a detailed explanation of the differences between REPORTED and OPERATING earnings.

T Note Premium = minus 15.16%

Neutral Stock Allocation = 50% (or whatever else you want as a neutral allocation)

Stock portion of Portfolio = (1 minus T Note Premium) multiplied by Neutral Stock Allocation

Stock portion of Portfolio = (1 - (-0.1516)) X (50%) = 1.1516 X 50%

Stock portion of Portfolio = 58%

Example 3 for Case 3

Stock allocation for a moderately aggressive investor who believes that investors should pay for future OPERATING earnings when they buy stocks.
Go to Standard and Poor’s websites for a detailed explanation of the differences between REPORTED and OPERATING earnings.

T Note Premium = minus 39.78%

Neutral Stock Allocation = 50% (or whatever else you want as a neutral allocation)

Stock portion of Portfolio = (1 minus T Note Premium) multiplied by Neutral Stock Allocation

Stock portion of Portfolio = (1 - (-0.3978)) X (50%) = 1.3978 X 50%

Stock portion of Portfolio = 70%

Summary

The Fed Model showed stocks were over-valued by 39% at the end of 2001 and the S&P 500 lost more than 22% during 2002. At the end of 2002, the model showed stocks were under-valued by 40%, and the S&P 500 returned more than 28% during 2003. It doesn’t always work that well, but I back tested it to 1994, and concluded it is worth the effort.

 I have also been using it on the asset allocation model I maintain on this website since June 30, 2001, but both timed models were discontinued during January 2016.

The timed models added to the absolute return of the 50-50 models because they generally had a stock component greater than 50%, but they were also more volatile. My final evaluation of the timed strategy showed that the risk adjusted return difference wasn't great enough to continue the effort.

However, the primary reason the timed models were discontinued is that timed models imply an ability to predict an uptrend or a downtrend. Neither I nor anyone else has that ability. If anyone tells you otherwise, they are either delusional or they are liars. You would do well to remember that John Kenneth Galbraith once said, "The only function of economic forecasting is to make astrologers look respectable".

Forecasters are especially bad at predicting downturns, and that's obviously when the investor could really use some help. The Economist analyzed the forecasts of the International Monetary Fund (IMF) from 1999 to 2014. Over that period there were 220 instances in which an economy grew in one year before shrinking in the next. In its April forecasts for the next year, the IMF never once predicted the contraction. Even in October of the year during which a recession began, the IMF predicted the recession had begun only half  the time i.e., flip a coin.

You can go to Asset Allocation to see how well a portfolio with a neutral 50-50 stock-bond allocation is working. Portfolios that restrict themselves to the US, and Global Portfolios are both shown on the Asset Allocation page.