Deutsche Bank - Asset Valuation Allocation Models 2002.pdf - economy - Kaktusik123

Research

Asset Valuation & Allocation

Models

July 30, 2002

Dr. Edward Yardeni

(212) 778-2646

ed_yardeni@prusec.com

Amalia F. Quintana

(212) 778-3201

mali_quintana@prusec.com

- Introduction -

I. Fed’s Stock Valuation Model

How can we judge whether stock prices are too high, too low, or just right? The purpose

of this weekly report is to track a stock valuation model that attempts to answer this

question. While the model is very simple, it has been quite accurate and can also be used

as a stocks-versus-bonds asset allocation tool. I started to study the model in 1997, after

reading that the folks at the Federal Reserve have been using it. If it is good enough for

them, it’s good enough for me. I dubbed it the Fed’s Stock Valuation Model (FSVM),

though no one at the Fed ever officially endorsed it.

On December 5, 1996, Alan Greenspan, Chairman of the Federal Reserve Board,

famously worried out loud for the first time about “irrational exuberance” in the stock

market. He didn’t actually say that stock prices were too high. Rather he asked the

question: “But how do we know when irrational exuberance has unduly escalated asset

values, which then become subject to unexpected and prolonged contractions….” 1 He did

it again on February 26, 1997. 2 2 He probably instructed his staff to devise a stock market

valuation model to help him evaluate the extent of the market’s exuberance. Apparently,

they did so and it was made public, though buried, in the Fed’s Monetary Policy Report

to the Congress, which accompanied Mr. Greenspan’s Humphrey-Hawkins testimony on

July 22, 1997. 3

The Fed model was summed up in one paragraph and one chart on page 24 of the 25-

page document (see following table). The chart shows a strong correlation between the

S&P 500 forward earnings yield (FEY)—i.e., the ratio of expected operating earnings (E)

to the price index for the S&P 500 companies (P), using 12- month-ahead consensus

earnings estimates compiled by Thomson Financial First Call.—and the 10-year Treasury

bond yield (TBY). The average spread between the forward earnings yield and the

Treasury yield (i.e., FEY-TBY) is 29 basis points since 1979. This near-zero average

implies that the market is fairly valued when the two are identical:

1) FEY = TBY

Of course, in the investment community, we tend to follow the price-to-earnings ratio

more than the earnings yield. The ratio of the S&P 500 price index to expected earnings

(P/E) is highly correlated with the reciprocal of the 10-year bond yield, and on average

the two have been nearly identical. In other words, the “fair value” price for the S&P 500

(FVP) is equal to expected earnings divided by the bond yield in the Fed’s valuation

model:

2) FVP = E/TBY

1 http://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm

2 “We have not been able, as yet, to provide a satisfying answer to this question, but there are reasons in the

current environment to keep this question on the table.”

http://www.federalreserve.gov/boarddocs/hh/1997/february/testimony.htm

3 http://www.federalreserve.gov/boarddocs/hh/1997/july/ReportSection2.htm

Page 2 / July 30, 2002 / Prudential Securities Asset Valuation & Allocation Models

E xcerpt from Fed’s July 1997 Monetary Policy Report:

The run-up in stock prices in the spring was bolstered by unexpectedly strong

corporate profits for the first quarter. Still, the ratio of prices in the S&P 500 to

consensus estimates of earnings over the coming twelve months has risen

further from levels that were already unusually high. Changes in this ratio have

often been inversely related to changes in long-term Treasury yields, but this

year’s stock price gains were not matched by a significant net decline in interest

rates. As a result, the yield on ten-year Treasury notes now exceeds the ratio of

twelve-month-ahead earnings to prices by the largest amount since 1991, when

earnings were depressed by the economic slowdown. One important factor

behind the increase in stock prices this year appears to be a further rise in

analysts’ reported expectations of earnings growth over the next three to five

years. The average of these expectations has risen fairly steadily since early

1995 and currently stands at a level not seen since the steep recession of the

early 1980s, when earnings were expected to bounce back from levels that were

quite low.

The ratio of the actual S&P 500 price index to the fair value price shows the degree of

overvaluation or undervaluation. History shows that markets can stay overvalued and

become even more overvalued for a while. But eventually, overvaluation is corrected in

three ways: 1) falling interest rates, 2) higher earnings expectations, and of course, 3)

falling stock prices—the old fashioned way to decrease values. Undervaluation can be

corrected by rising yields, lower earnings expectations, or higher stock prices.

The Fed’s Stock Valuation Model worked quite well in the past. It identified when stock

prices were excessively overvalued or undervalued, and likely to fall or rise:

1) The market was extremely undervalued from 1979 through 1982, setting the stage

for a powerful rally that lasted through the summer of 1987.

2) Stock prices crashed after the market rose to a record 34% overvaluation peak during

September 1987.

3) Then the market was undervalued in the late 1980s, and stock prices rose.

4) In the early 1990s, it was moderately overvalued and stock values advanced at a

lackluster pace.

5) Stock prices were mostly undervalued during the mid-1990s, and a great bull market

started in late 1994.

6) Ironically, the market was actually fairly valued during December 1996 when the

Fed Chairman worried out loud about irrational exuberance.

Prudential Securities Asset Valuation & Allocation Models / July 30, 2002 / Page 3

7) During both the summers of 1997 and 1998, overvaluation conditions were corrected

by a sharp drop in prices.

8) Then a two- month undervaluation condition during September and October 1998

was quickly reversed as stock prices soared to a remarkable record 70%

overvaluation reading during January 2000. This bubble was led by the Nasdaq and

technology stocks, which crashed over the rest of the year, bringing the market closer

to fair value

II. New Improved Model

The FSVM is missing a variable reflecting that the forward earnings yield is riskier than

the government bond yield. How should we measure risk in the model? An obvious

choice is to use the spread between corporate bond yields and Treasury bond yields. This

spread measures the market’s assessment of the risk that some corporations might be

forced to default on their bonds. Of course, such events are very unusual, especially for

companies included in the S&P 500. However, the spread is only likely to widen during

periods of economic distress, when bond investors tend to worry that profits won’t be

sufficient to meet the debt-servicing obligations of some companies. Most companies

won’t have this problem, but their earnings would most likely be depressed during such

periods. The FSVM is also missing a variable for long-term earnings growth. My New

Improved Model includes these variables as follows:

3) FEY = CBY – b · · LTEG

where CBY is Moody’s A-rated corporate bond yield. LTEG is long-term expected

earnings growth, which is measured using consensus five- year earnings growth

projections. I/B/E/S International compiles these monthly. The “b” coefficient is the

weight that the market gives to long-term earnings projections. It can be derived as -

[FEY-CBY]/LTEG. Since the start of the data in 1985, this “earnings growth coefficient”

averaged 0.1.

Equation 3 can be rearranged to produce the following:

4) FVP = E ¸ ¸ [CBY – b · · LTEG]

FVP is the fair value price of the S&P 500 index. Exhibit 10 shows three fair value price

series using the actual data for E, CBY, and LTEG with b = 0.1, b = 0.2, and b = 0.25.

The market was fairly valued during 1999 and the first half of 2000 based on the

consensus forecast that earnings could grow more than 16% per year over the next five

years and that this variable should be weighted by 0.25, or two and a half times more than

the average historical weight.

III. Back To Basics

With the benefit of hindsight, it seems that these assumptions were too optimistic. But,

Page 4 / July 30, 2002 / Prudential Securities Asset Valuation & Allocation Models

this is exactly the added value of the New Improved FSVM. It can be used to make

explicit the implicit assumptions in the stock market about the weight given to long-term

earnings growth. The simple version has worked so well historically because the long-

term growth component has been offset on average by the risk variable in the corporate

bond market.

IV. Stocks Versus Bonds

The FSVM is a very simple stock valuation model. It should be used along with other

stock valuation tools, including the New Improved version of the model. Of course, there

are numerous other more sophisticated and complex models. The Fed model is not a

market-timing tool. As noted above, an overvalued (undervalued) market can become

even more overvalued (undervalued). However, the Fed model does have a good track

record of showing whether stocks are cheap or expensive. Investors are likely to earn

below (above) average returns over the next 12-24 months when the market is overvalued

(undervalued).

The next logical step is to convert the FSVM into a simple asset allocation model

(Exhibit 1). I’ve done so by subjectively associating the “right” stock/bond asset mixes

with the degree of over/under valuation as shown in the table below. For example,

whenever stocks are 10% to 20% overvalued, I would recommend that a moderately

aggressive investor should have a mix of 60% in stocks and 40% in bonds in their

portfolio.

Bonds/Stocks Asset Allocation Model

More than 30% overvalued

70% bonds, 30% stocks

20% to 30% overvalued

50% bonds, 50% stocks

10% to 20% overvalued

40% bonds, 60% stocks

10% undervalued to 10% overvalued

30% bonds, 70% stocks

10% to 15% undervalued

20% bonds, 80% stocks

More than 15% undervalued

10% bonds, 90% stocks

Prudential Securities Asset Valuation & Allocation Models / July 30, 2002 / Page 5

Deutsche Bank - Asset Valuation Allocation Models 2002.pdf

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