Fed Stock and Bond Valuation 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
$1148.08 / $28.24 = 40.65
Or the inverse of the earning’s yield
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 which is a great P/E ratio.
Example:
1 / 7% = 14.28 which is the average P/E ratio of the S&P 500.
Example:
1 / 2.5% = 40.00 which is a terrible P/E ratio.

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.

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 for the first time in US history!

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

Question
What’s the dividend yield on stocks now? What’s the long bond yield?
Answer
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 almost 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

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)
divided by the S&P 500 Earning’s Yield

T Note Premium = (5.2 – 2.5) / 2.5 = 1.08

Stocks 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)
divided by 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 Ruckeyser 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 Poors 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.