The Volatility of the Stock Market

A Random Walk?

In his famous book, "A Random Walk Down Wall Street," Burton Malkiel explains the Random Walk Theory, "In essence, the random walk theory espouses the belief that future stock prices cannot be predicted. It says that a blindfolded monkey throwing darts at the newspaper's financial pages could select a portfolio that would do just as well as one carefully selected by the experts." (Malkiel, 1973) He describes the investing in the Stock Market as being "a gamble whose success depends on an ability to predict the future." The intrigue, therefore, is just that. There is a great deal of uncertainty involved however the payoff is can be very great. Malkiel divides the approaches to "predicting the future" into two categories: "The firm-foundation Theory" and the "castle-in-the-air theory," and these theories appear to be mutually exclusive.

An Introduction to the Firm Foundation Theory

This theory argues that each common stock (representative of a certificate of part ownership of a corporation) has a firm anchor of something called intrinsic value, which can be determined by careful analysis of the firm's current position and future prospects. (Malkiel, 1973) Market prices’ falling below this firm foundation of intrinsic value means a buying opportunity, because, according to the theory, price fluctuation is eventually corrected. Conversely, with prices’ rising above this value comes a selling opportunity. This technique, developed in large part by John B. Williams, appears quite simple. Williams presented a formula for determining the intrinsic value which was based on dividend income. He utilized the idea of "discounting" which, as Malkiel describes it, basically involves looking at income backwards.

Discounting looks at the desired future return on an investment and determines the present value corresponding to that return. This present value thus depends on the interest rate. If future returns (dividends) are viewed in real terms, we take the real interest rate and perform the following calculations:

Jean-Paul wants a $27,500 payment at the end of one year. The real interest, r, is 10% How much does Jean-Paul have to invest now in order to get the return that he wants?

Let Jean-Paul's investment amount (present value) = x Therefore Jean-Paul's return amount at the end of one year is the principal plus interest gained That is,

    Return payment = x(1 + r)
                   = x(1 + 0.1)
                   = x(1.1)

So we have,

            x(1.1) = 27,500

Therefore,

            x = 27,500/(1.1)
              = 25,000

So Jean-Paul needs to invest $25,000 today if he wants to have $27,500 at the end of one year. That is,

 The present value of $27,500 is $25,000.

Williams said that the intrinsic value of a stock was equal to the present (or discounted) value of all its future dividends. However this way of valuating stock prices encounters problems of its own: one must attempt to forecast the extent and duration of future growth which, in Malkiel's opinion, is a tricky and treacherous business.

An Introduction to the Castle-in-the-Air Theory

This theory concentrates on "psychic values" as opposed to intrinsic values. (Malkiel) Lord Keynes, a famous economist and outstandingly successful investor, developed the theory, arguing that intrinsic values were too difficult to calculate. Keynes was more interested in how investors are likely to behave in the future and how, in times of optimism, they tend to "build their hopes into castles in the air" (Malkiel, 1973) Keynes focus was therefore more on investor psychology rather than on financial evaluation.

Keynes described "playing" the stock market as "being analogous to entering a newspaper beauty-judging contest in which you have to select the six prettiest faces out of 100 photographs. The prize goes to the person whose selections most nearly conform to those of the group as a whole. The smart player recognizes that his personal criteria of beauty are irrelevant in determining the contest winner. A better strategy is to select those faces the other players are likely to fancy. This logic tends to snowball. After all, the other contestants are no fools and they are likely to play the game with at least as keen a perception. Thus the optimal strategy is not to pick those faces the player thinks are prettiest, or even those he may believe the other players are likely to fancy, but rather to predict what the average opinion is likely to think the average opinion will be or to proceed even further with this sequence. So much for British beauty contests." (Malkiel, 1973) Now as difficult as this may seem, Keynes also proposed, in Malkiel's words, the "greater-fool theory" in which, "It's perfectly alright to pay three times what a stock is worth as long as later on you can find some innocent to pay five times what it's worth."
Today, there are many other developments in Behavioral Finance since Keynes' time that are discussed later.