The Market Crash in October 1987
Can an event such as the October 1987 market crash be explained by rational considerations, or does such a rapid and significant change in market valuations prove the dominance of psychological rather than logical factors in understanding the stock market? Behaviorists would say that a one-third drop in market prices, which occurred early in October 1987, cannot be explained by rational considerations. The basic elements of the valuation equation do not, according to the behavioral view, change rapidly enough to produce such a substantial change in rationally determined market prices. It is impossible to rule out the existence of behavioral or psychological influences on stock-market pricing. Nevertheless, it may be useful to review the several logical considerations that could explain a sharp change in market valuations during the first weeks of October 1987.
As a frame of reference we should recall that common stocks are rationally priced as the present or discounted value of the future stream of dividends expected from them. For a long-term holder of stocks, this rational principle of valuation translates to a simple formula:
Rate of Return to Stockholder = Dividend Yield + Long-run Dividend Growth Rate.
In symbols we can write the basic valuation equation as r= D/P + g, where r is the rate of return, D/P is the yield (dividend divided by price), and g is the long-term growth rate. Using this equation, it is easy to show how sensitive share prices can be as a result of rational responses to small changes in interest rates and risk perceptions. This equation can also throw the “Monday meltdown” (October 19, 1987) into a more logical setting.
I believe there were very good reasons to think that investors should rationally have changed their views about the proper values of common stocks during October 1987. Specifically, a number of factors tended to increase the “r” – the rate of return required by stock investors – in the equation above. First, there had been a substantial increase in interest rates in the previous two months. Yields on long-term Treasury bonds increased from about 9 percent to almost 10 1/2 percent just before the crash. In addition, a number of events created significantly increased risk perceptions in the market. In early October, Congress threatened to impose a “merger tax” that would have made merger activity prohibitively expensive and could well have ended the merger boom. It is significant to note that the stocks that went down the most in the week preceding October 19 were the stocks of companies that were the subject of takeover attempts. The risk that merger activity might be curtailed increased risks throughout the stock market by weakening the discipline over corporate management that potential takeovers provide. Also, James Baker, then secretary of the Treasury, had threatened in October to encourage a further fall in the price of the dollar, increasing risks for all foreign investors and thereby frightening domestic investors as well.
A numerical illustration will show how sensitive share prices can be as a result of rational responses to small changes in interest rates and risk perceptions. Recalling our previous equation of rational present-value pricing of common stocks, r=D/P + g, we will consider r to be the rate of return for the market as a whole and P to be the market price index, such as the price of one of the broad stock-market averages. Suppose initially that the “riskless” rate of interest on government bonds is 9 percent and that the required additional risk premium for equity investors is 2 percent. In this case r, the appropriate rate of return for equity holders (or, equivalently, the proper discount rate for common stocks), will be 11 percent (0.09 + 0.02 = 0.11). If a typical stock’s expected growth rate, g, is 6 percent and if the dividend is $5 per share, we can solve for the appropriate price of the stock index (P), obtaining 0.11= $5/P + 0.06 P = $100.
Now assume that yields on government bonds rise from 9 to 10 1/2 percent with no increase in expected inflation (which might increase so that stock market investors now demande a premium of 2 1/2 percentage points instead of the 2 points in the previous example. The appropriate rate of return or discount rate for stocks, r, rises then from 11 percent to 13 percent (0.105 + 0.025), and the price of our stock index falls from $100 to $71.43:
0.13 = $5/P + 0.06 P = $71.43.
The price must fall to raise the dividend yield from 5 to 7 percent so as to raise the total return by the required 2 percentage points. It is clear that no irrationality is required for share prices to suffer quite dramatic declines with the sorts of changes in interest rates and risk perceptions that occurred in October 1987. Of course, even a very small decline in anticipated growth would have magnified these declines in warranted share valuations.
This is not to say that purely psychological factors were irrelevant in explaining the sharp correction of market prices. I am sure that they, too, played a role in the decline. Moreover, the swiftness of the decline was probably accelerated by new trading techniques such as “portfolio insurance,” which dictated that some institutional investors should increase their selling as share prices declined. In addition, “program training,” a technique whereby an entire basket of securities can be sold or purchased using computerized generation of orders, enables changes in the market sentiment (as well as any discrepancies between the value of any stock indices, which trade mainly in Chicago, and the value of the component stocks) to affect the prices of shares with extraordinary speed. But it would be a mistake to dismiss the significant change in the external environment, which can provide a rational explanation of the need for a significant decline in the appropriate values for common stocks.
Burton G. Malkiel. A Random Walk Down Wall Street, including a life-cycle guide to personal investing. First edition, 1973, by W.W. Norton and company, Inc.