The Sharp Model
                   A Stock Valuation Program
  (C) Copyright, 1983 American Association of Individual Investors

   In the March, 1983 issue of the AAII Journal Mr. Robert Sharp,
of Spokane Washington, wrote about a stock valuation model he had
developed for his own use. Many AAII members felt that the model
might be useful in their own analysis of stocks, and have asked
if we could provide a program for the model. So here it is. The
model is not difficult to program; it is written in a subset of
the full BASIC language, and should run on most microcomputers
without modification. We will summarize Mr. Sharp's development
of the model as we prodeed. However, for a full understanding of
the model and it's use for stock valuation, you should read the
original article.

   First, Mr. Sharp assumes that an "average" stock should behave
similarly, in terms of price behavior, to a market index, such as
the Dow Jones Industrial Average or Standard and Poor's 500
index. Thus, the first equation:

(1)    V = E x M

equates value (V) to earnings (E) times the price/earnings
multiple (M) of a stock index average. (He uses the the Dow Jones
industrial average as the stock index.) 

   Next, he develops a relationship between the the earnings
yield (E/P) for the DJIA (The earnings yield is simply the
reciprocal of the price/earnings multiplier (P/E).) and the
risk-free rate of return. (The risk-free rate of return is the
rate one can earn without risk of loss. Many articles have been
written regarding which actual interest rate should be used to
represent the risk-free rate.) Mr. Sharp uses the annualized
inflation rate (Consumer Price Index rate) plus 3 percent, which
he assumes is the real rate of interest. (The real rate of
interest is the actual return to the investor after discounting
for the effects of inflation.) Based on yearly data for the past
16 years, Mr. Sharp developed the following estimating equation
by using lest squares regression.

(2)    (E/P) = 1.22 + 0.85(I+3)

where (E/P) is the earnings yield, 1.22 is the regression
constant, 0.85 is the coeficiant of change, I is the inflation
rate and 3 is the assumed constant real rate of return.

   (At this point we need to digress a little. The real rate of
return has historically been measured as being in the range of
2.5 to 4.5 percent, although currently it is higher, perhaps in
the range of 5.5 to 6.5 percent. It may be the case that Mr.
Sharp wanted to average the real rate of return and picked 3
percent as a constant average value. Unfortunately in so doing,
he has eliminated the contribution of the real rate of return to
the regression estimate, i.e., the coeficiant of change. In
effect, Mr. Sharp has really estimated a direct relation between
earnings yield and inflation, not earnings yield and the risk
free interest rate. I have restimated the corrected regession
equation; it appears as equation 2a.

(2a)   (E/P) = 3.77 + 0.85(I)

The explanatory power of this equation is the same as the
previous one.)

   Given that the price/earnings multiplier (P/E) is the
reciprocal of the earnings yield, on a per dollar basis, the
(P/E) ratio is given by:

(3)   (P/E) = 100/(3.77 + 0.85(I)) 

Substituting (P/E) for (M) in equation (1) gives:

(4)   V = E x 100/(3.77 + 0.85(I))

This is an estimating equation for an "average" stocks value,
given an estimate of the next year's earnings (E) for the stock.

   Mr. Sharp then incorporates a stock's "beta" into the
estimating equation. (As many of you know, beta is an index of
market risk for a stock. A stock with a beta greater than 1 is
expected to have a rate of return greater than the market rate of
return in a rising market. Beta is also interpreted as the
expected change in return for a stock with respect to a given
change in return for the market.) The incorporation of beta into
the valuation equation is an attempt to allow for differences in
projected value for non-average stocks. The final valuation
equation is:

(5)   V = E x B x 100/(3.77 + 0.85(I))

This is the valuation equation that we use in the program. Mr.
Sharp simplifies this equation for his own use, he uses:

(5a)    V = E x B x 100/(I+3)

for his personal stock evaluations.

   Valuations are made by comparing actual stock prices (SP) with
the value determined by the model (V).  The proportion (SP/V)
is an indicator of under- or over- valuation. Overvalued stocks
will have indicators greater than 1, while undervalued stocks
will have indicators less than 1.

   Mr. Sharp suggests, and I agree, that you should first assess
a stocks fundamentals before applying this method of valuation.
The model gives an indication of value relative to past market
performance, as represented by a market index; it is certainly not
infallible. Given the performance of the market since October,
1982, the model will tend to show valuations considerably above
prior years.

   You may want to try and improve upon the model. For example,
it could be reestimated using quarterly data, using data for more
recent time periods. You might also want to experiment with using
a "risk free" interest rate instead of the inflation rate. Any
linear regression program could be used for experimentation.

   The program listing is straight-forward. First, you are asked
to enter the necessary data. Then, in line 140, the valuation is
computed. Lines 170 through 190 are routines for displaying
values to 2 decimal places. Finally, at the end of the program,
you are asked if you want to run it again. As the program is
written it will only accept capital letters as input here. Also,
if your version of BASIC does not support alphabetic strings, you
can write the program so as to ask for a numeric value instead.

   In using the program, you would input an earnings estimate,
the current stock price, the stock's beta and the current
inflation rate (on an annual basis.) Stock selection would be on
the basis of choosing those stocks that are undervalued relative
to the rest of the stocks under consideration. Stocks under
consideration should have been examined for their fundamentals
before using the valuation model.

   As we previously stated, you should read Mr. Sharp,s original
article before using the model for valuation or experimenting
with the valuation model, as he outlines his approach in detail
in the original article.