# Relative P/R, a novel valuation tool

In order to address the question of market valuation, we should consider what is meant by "value". Investors purchase stocks in order to make money. The more money the investor makes from a stock, the more that stock was worth when she bought it. There are two ways in which an investor can make money from a stock. One is by collecting dividend payments from the stock. The other is by selling the stock to someone else at a higher price than what one paid for it. The value of a stock, then, is simply the present value of the two sources of money: future dividends and the proceeds from a future sale of the stock. By present value we mean the quantity of cash that if invested at a particular rate of return called the discount rate, would generate the same amount of money as the stock will. For example, suppose the stock will pay a dividend of $1 next year. To generate this dollar next year we would need to invest $0.91 at a 10% rate of return right now. Thus, we say the present value of the $1 dividend next year with a 10% discount rate is $0.91. The present value for a series of n dividend payments made over n years is given by the following formula:

1) PV_{DIV} = S div_{j} / (1 + r)^{j} for
j = 1 to n

Here PV_{DIV} refers to the present value of the future
dividend stream, div_{j}, is the dividend j years in the
future and r is the discount rate. The present value (PV_{SALE})
of the future sale price (P_{SALE}) is the quantity of
money invested today at the discount rate of return that will yield
the future sale price and is given by:

2) PV_{SALE} = P_{SALE} / (1 + r)^{j}

The value of the stock is the sum of PV_{DIV} and PV_{SALE}.
These equations are perfectly valid, but not very useful, as they
require knowledge of the future price and dividend payments of
the stock of interest, which, of course, we do not know. We can
use these to calculate the present value of the *historical* stock
market (or more precisely, a market index) based on future returns
(which we know for markets of the past). We could call this discounted
value the "true value" of the historical market based
on future returns. To do this, I constructed a series of average
monthly price levels for a representative index of stocks for the
period 1802-1999, which includes the S&P 500 index for the
years 1937-1999, the Cowles Index for 1871-1937 and a compilation
of indices for the years before 1871. Jeremy Siegel, in his excellent
book *Stocks for the Long Term*, presents essentially the
same index.

Figure 1. The price to true value for the stock index 1802-1969

Dividends of 6.4% were assumed for the 1802-1871 period, based
on the average for the 1870's as described by Siegel. Dividends
after 1871 were obtained from the Cowles and S&P500 data provided
by Shiller.
I chose a rather long period of 30 years for the investment time
(n = 30) in order to minimize the effects of the business cycle
on dividends and stock prices. P_{SALE} was simply the
annual average index value 30 years in the future. The long term
return on stocks (in constant dollars) over the entire period has
been 6.9%. Thus, the discount rate used was 6.9% plus the prevailing
inflation rate over the thirty year investment period. The 30-year
discounted true value of the stock market was calculated as the
sum of PV_{DIV} and PV_{SALE}, using equations
1 and 2, for all the years from 1802 to 1969. The actual value
of the market index was divided by the true value and the resulting
ratio plotted in the above figure. Examination of Figure 1 shows
that the market rarely prices stocks "right". At times,
such as the 1940's, the market underprices stocks. Long term investments
in stocks made at these times will yield average real returns higher
than 6.9%. Other times, such as the late 1920's and mid 1960's,
the stock market overprices stocks. Long term investments made
during these times will yield average real returns lower than 6.9%.
The propensity for the market to over or under price stocks is
a consequence of the tendency of the stock market to move in lengthy *trends*,
the secular bull and bear markets. Although this tendency as always
been present in the market, it seems to have grown more extreme
in the twentieth century as compared to the nineteenth.

Figure 2. Price to True Value compared to P/E for the period 1871-1999

A question naturally arises. Is there some way to estimate what
the true value of the market is today? To use equations 1 and 2
directly we would have to wait thirty years to obtain future dividends
and stock prices. One way to get around this would be to find some
sort of valuation method that can be calculated today that correlates
with the true value. An obvious (and very traditional) choice is
the price to earnings ratio (P/E). Figure 2 shows the price to
true value ratio compared to the P/E for the S&P500 and its
predecessors for the period since 1871. As you can see, the P/E
in the year 1999 was at an all-time high. What is also evident
is that the P/E was also quite high in the mid 1890's, during which
the stock market was not overpricing stocks, and again in 1921,
when the market was actually *underpricing* stocks. The general
correspondence between the P/E trend and the price/true value trend
is also quite poor. These observations suggest that the P/E of
the S&P500 is a poor estimator of long-term market value.

Figure 3. Price to True Value compared to relative P/R for the
period 1802-2000

In an earlier article, the
concept of the price to business resources (P/R) was introduced.
In that article it was used simply as part of a technical tool
to identify secular market trends. In this paper, we try to use
this concept as a market valuation method. Figure 3 shows the *relative* P/R
value (i.e. the present value of P/R divided by its average value
over the preceding stock cycle). The correspondence between the
price to true value and the relative P/R is excellent. Peak values
in one correspond to peak values in the other. Of interest is that
relative P/R in 1929 was higher than at any other market peak before
1970, and the price to true value was highest in 1929. Note that
relative P/R was at its second highest pre-1970 value in 1966,
and the price to true value was likewise at its second highest
value then. Furthermore, the relative P/R method strongly suggests
that the price to true value in the early 1980's was much less
than one, indicating that stocks at that time were underpriced
relative to their future 30 year performance. The enormous bull
market since then is strong evidence that this was so.

Another interesting observation is to compare the market in 1929
versus 1987. Both years were similar in that a massive bull market
driven by disinflation was terminated by a stock market crash.
The market was similarly valued in terms of P/E in both years (see
Figure 2). In terms of relative P/R, the 1929 market was super-overvalued
yet 1987 was actually *undervalued*. In actual fact, the 1929
market was extremely overvalued, as evidenced by the 25 year period
required for the market to recover its precrash highs. The performance
of the stock market since 1987 strongly suggests that the 1987
market was not overvalued like in 1929, although we will not be
able to determine a definitive answer to this question until 2017.
Nevertheless, had one employed the relative P/R as a market value
proxy one would have known to sell after the 1929 crash, but to
hold after the 1987 crash, which as it turned out, were the correct
strategies for the long term investor.

Authors note: This paper was originally written in 1999. I have updated it, making the terminology consistent with that I use in my book and adding some additional post 1999 data. In 1999 I had pointed out that the level of relative P/R was higher than ever before, implying that stocks were more overvalued relative to their future prospects. Since then we all know that the stock market peaked in March 2000 and has begun a serious bear market correction. The Stock Cycle analysis suggests that this was the end of the secular bull market that began in 1982. After the discovery and characterization of the stock cycle in 1997, it remained a curiosity, a simple technical tool of unproved worth. In October 1999, I happened upon the Longwaves site and learned about the Kondratiev Cycle or K-cycle. In short order I learned that the stock cycle was directly dependent on the Kondratiev Cycle. Having found an explanation for secular trends, I wrote a book called Stock Cycles: Why stocks won't outperform money markets over the next twenty years.

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