Are Bull Markets Supported
By Rational Growth in Stock Valuations?

John Ruda



            “The rich get richer” is a frequently heard adage in the United States, a country quickly associated with capitalism.  US financial markets make headline news on a daily basis, so people are well aware when the domestic stock market’s indices rise or fall.  Given the widespread distribution of information on the stock market’s performance, much excitement can easily be generated during a bull market, broadly defined as a trend during which stock prices are climbing.  Does the publicity and excitement surrounding a bull market further perpetuate rising stock prices?

A look at historic daily closing values for the S&P 500 index from January 2, 1997 to December 31, 1999 reveals overall growth of 99.35%[i], which on average indicates similar growth in the stock prices of the companies included in the index.  Clearly, this three year period falls within a bull market, since the S&P 500 is commonly utilized to represent average performance of the stock market on the whole.  A return of 99.35% on an investment is excellent and far exceeds the general return on “risk-free” investments like FDIC insured savings accounts or Treasury bills.

[i] Percent change calculation derived from widely published market data


Examination of Common Stock Valuation to Account for Rising Share Prices

            Like most economic evaluations, the decision to purchase a share of a company’s stock is based on an individual’s willingness to pay versus the current selling price of the share.  Fundamentally, the willingness to pay is determined by a valuation of that share of stock.  For a given share of common stock, the willingness to pay is, or should be, linked to the present value of the stream of future cash flows that the investor will receive from expected dividends and through any expected capital gain for selling the share at a higher price than at which it was purchased.[i]  Thus, there are three main factors the affect the valuation of a share of common stock: future dividends, future market price of the share, and the discount rate used.

[i] Fundamentals of Financial Management, Eugene F. Brigham & Joel F. Houston, Harcourt College Publishers: Forth Worth, 2001. (p. 409)


Future Dividends

             In order to receive dividends on a share of common stock, a company must generate positive earnings, since dividends are pain out the retained earnings account that appears on the balance sheet.  In principle, a share of common stock is a claim on the company’s net income (and the amount of the claim is dependent upon the number of shares of common stock issued).[i]  

             Since dividends are claims on net income, a rational investor examines and predicts the company’s ability to generate earnings into the future.  It is common to look at earnings on a per share basis to analyze the amount of income that is attributed to a single share, which represents the absolute maximum potential dividend that the shareholder may receive (if the company pays out one hundred percent of earnings as dividends). 

[i] The economics of Money, Banking, and Financial Markets, Frederic S. Mishkin, Addison Wesley: Boston, 2002. (p. 23)


During the referenced January 2, 1997 to December 31, 1999 period, the calendar year earnings per share of a sample of seven of the leading companies (in terms of market capitalization, not stock performance) that make up the S&P 500 index rose 43.97% on average.[i],[ii] Although an investor’s willingness to pay for a share of common stock is dependent on, amongst other factors, the company’s future earnings, the S&P 500’s value grew more than twice as much as the earnings of the sample of the most widely-held companies.  As a result, price to earnings multiples close to doubled during the period, suggesting investors attributed more value to each share of stock.

[i] Sample includes General Electric, Pfizer, Wal-Mart, Proctor & Gamble, Coca Cola, International Business Machines, Johnson & Johnson

[ii] Percent change calculation derived from historic calendar year earnings obtained through Thomson Financial’s First Call software


Future Market Price

            The present value of a stock is also linked to the present value of the capital gain or loss that an investor anticipates based on the change in market price from the time of purchase to the time the investor chooses to sell the share.  Since market price is linked to the overall willingness to pay for a share of the company’s stock amongst all investors in the stock market, and potential new investors, the future market price analysis is dependent on an evaluation of the behavior of other investors.  Such analysis requires the assumption that other investors will behave rationally, performing a calculation of the present value of anticipated future cash flows.  If a single investor believes that the overall market expectation of a company’s ability to generate future income is low, the investor would expect the stock price to rise as the market’s other investors become enlightened. 

The estimation of future market price cannot rationally cause a substantial short-term increase in the present value of a share of common stock.  Given the rationale that all investors are in theory performing the similar present value calculations to value the share of common stock, all else equal, the future market price of the stock should not increase dramatically unless the majority of investors have been consistently underestimating the company’s ability to generate future earnings and pay dividends.  The principle of future cash flow estimation is based upon the expectation of the cash flow in period t + 1 (where t represents today), which is based on the cash flow of period t + 2, and so on.  It is not debated that there will not be a change in estimations long-term cash flows as the periods become closer to the present, but in theory, there should not be a large change in the expectations in the short run unless the company consistently reports dramatic earnings surprises on the upside.


Of course, there is a general expectation that on average stock prices will rise over the long-term, because otherwise there would be no economic incentive to invest in equity.[i]  However, the overall upward trend should be somewhat in line with overall economic growth (represented by, for example, growth in GDP).  There was not enough growth in GDP over the 3-year sample period to justify the remaining portion of the increase in stock prices after allowing for the growth due to higher earnings per share.  Thus, if increased estimate of future stock prices is to account for the higher valuation, the investors must be anticipating speculation.[ii]  Since speculation is defined as “assumption of unusual business risk in hopes of obtaining commensurate gain,” it may explain an unusual rise in stock prices.[iii]  While speculation does not necessarily constitute rational economic behavior since it lacks valid fundamental analysis, it is rational for an investor to include potential speculation by others into his/her valuation.


[i] The Equity Risk Premium: The Long-Run Future of the Stock Market, Bradford Cornell, John Wiley & Sons: New York, 1999. (p. 159)

[ii] The Equity Risk Premium: The Long-Run Future of the Stock Market, Bradford Cornell, John Wiley & Sons: New York, 1999. (p. 165)

[iii] Merriam-Webster Online <>


Discount Rate

            After estimating the future cash flows from dividends and capital gains, a discount rate must be applied to develop a present valuation.  Having been unable to arrive at a complete rational explanation for the rise in stock prices from January, 1997 through December, 1999 thus far, there is the possibility that the discount rates used by investors may have decreased during the 3-year period.  The question then is whether a continuous decrease in the discount rate during the sample period can be rationalized.  To answer the question, one must understand that the discount rate that is used in theory to value the anticipated future cash flows of a share of stock to the present involves several factors.

Risk-Free Rate

            The risk-free rate is understood to be the return on your investment that you could earn securely if the money were to be put into a “risk-free” investment.  In general, the guideline for the risk-free rate is the rate on US Government “T-Bills”.  By examining the historic rates for 30-year US Treasury Bills, it is observed that between the start and end of the sample period, the yield on the T-Bills declined 20 basis points from 6.83% to 6.63%.[i]  However, in October of 1998, it had declined to the low of the period, 5.01%.[ii]  The overall decline in the yield of the “risk-free” Treasury Bill contributes to a reduction in the overall discount rate applied to common stock valuations.  This case is similar to the bull market in the 1980’s where, in the first half of the bull run, P/E ratio expansion was rational due to falling interest rates, but as the fall in interest rates ended, P/E multiples continued to grow and then were corrected by the crash of 1987.[iii]  Furthermore, the more dramatic mid-period decline in the yield may have accelerated growth in stock prices, which may have prompted a decline in another discount rate component: the equity risk premium.

[i] Federal Reserve Statistical Release H.15 <>

[ii] Federal Reserve Statistical Release H.15 <>

[iii] “P/E Ratios, Interest Rates, Inflation, Estimate Revisions, and the Great Crash of ‘87”, Stanley Levine & Dirk van Dijk, Handbook of Security Analyst Forecasting and Asset Allocation, JAI Press: Greenwich, CT, 1993.



Equity Risk Premium

            Bradford Cornell argues that “if changes in the discount rate are to explain a dramatic increase in stock prices on the order of magnitude of that observed in the 1990’s, it must be due to a drop in the equity risk premium.”[i]  The equity risk premium portion of the discount rate for stock valuations if defined as “The extra return that the overall stock market or a particular stock must provide over the rate on Treasury Bills to compensate for market risk.”[ii]  Since the higher the discount rate, the lower the present valuation of a share of stock, it is necessary to pinpoint a rational decline in the equity risk premium in order to explain the rising stock prices.

One factor to examine to determine the equity risk premium is the volatility of returns of the stock market.[iii]  If the market is more volatile, an investor will assess a higher equity risk premium, lowering stock valuations.  Conversely, if the market is perceived to be less volatile, the risk premium will decline and can explain higher stock prices.  However, studies conducted in the past cannot link a decrease in volatility of market returns with the sharply rising stock prices in the 1990’s.[iv]

The bull market of the 1990’s had a relatively long run.  It is reasonable to think that new investors may have perceived the stock market to be less risky due to its consistent high returns during the recent past.[v]  Thus, new assets would flow into the stock market as a result of a perceived decline in equity risk premium by new investors.  The new investors and assets would naturally lead to an expansion of stock prices and P/E multiples, assuming the inflow of new assets was greater than the value of any new shares of stock issued by companies.  The opposite view is that, the longer a bull market lasts, the more likely it is to collapse.[vi]

[i] The Equity Risk Premium: The Long-Run Future of the Stock Market, Bradford Cornell, John Wiley & Sons: New York, 1999. (p. 165)

[ii] <>

[iii] The Equity Risk Premium: The Long-Run Future of the Stock Market, Bradford Cornell, John Wiley & Sons: New York, 1999. (p. 168)

[iv] The Equity Risk Premium: The Long-Run Future of the Stock Market, Bradford Cornell, John Wiley & Sons: New York, 1999. (p. 170)

[v] “Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets”, Asger Lunde & Allan G. Timmermann, January 30, 2000. (p.7) <>

[vi] “Duration Dependence in Stock Prices: An Analysis of Bull and Bear Markets”, Asger Lunde & Allan G. Timmermann, January 30, 2000. (p.7) <>




            The rising stock prices that are produced during the sample 1997 - 1999 bull market analyzed cannot be explained merely by a fundamental rise in the valuations of stocks by seasoned investors.  Therefore, the growth of a bull market is partially attributed to speculation by new investors who, after seeing the beginning of a bull market (which may be tied to a rational increase in stock valuations), have perceived the stock market as an easy way to earn a high return on their investment.  Eventually, more professional investors who rely on fundamental analysis become wary of the P/E expansion that the speculation yields during a bull market, and a correction in share values occurs.  However, it is economically rational for stock prices to rise gradually over the long terms as more investors enter the stock market and the confidence in the market’s ability to generate good returns grows, decreasing the equity risk premium.[i] 

[i] The Equity Risk Premium: The Long-Run Future of the Stock Market, Bradford Cornell, John Wiley & Sons: New York, 1999. (p. 173-175) 





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