Cootner, The Random Character of Stock Market Prices, V

Today I conclude my series of posts on Paul Cootner’s classic book with some excerpts from his brief introduction to Part IV, “The Statistical Analysis of Option Prices.” Don’t forget that the articles in this section were written before the Black-Scholes pricing model was developed (1973).

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“The richest field of application of the random walk theory of stock prices has been in the determination of the value of such derivative assets as puts, calls, and warrants and convertible bonds.” (p. 373)

“The second paper by Kruizenga and the one by A. J. Boness, both deal with the ‘rationality’ of put and call prices. … If both the buyer and the seller of such options could estimate, without error, the parameters of the distribution of stock prices, and if they each hoped to maximize their mathematical expectation of wealth, options would be so priced as to leave each without profit from repeated transactions. To test the correspondence between this view of option pricing and actual prices, Kruizenga examines hypothetical transactions at prices submitted to the Securities and Exchange Commission in the period 1948-1956. Boness looks at actual transactions during a shorter, and different, period (1958-1960). Kruizenga finds option purchasing to be mildly profitable; Boness finds it highly unprofitable. … Yet another study, by Richard Katz (1963, 1964), covering a slightly longer and different period, finds intermediate results: both purchases and sales of options are slightly unprofitable, these losses arising from the commissions paid to intermediaries.

“The general lack of agreement in these studies is not likely to fill the reader with confidence about the results. Still, some conclusions are probably safe. Option premiums are relatively more stable than rates of increase of stock market averages, so that when stock prices are generally rising rapidly results of call option buying will seem more attractive than in periods of relative price stability. This is not inconsistent with a random walk model of stock prices, in which expectations of future price changes remain constant at some long run average drift, because recent post rates of changes are no predictors of future changes.” (pp. 373-74)

“The final two papers address themselves to a different aspect of option trading—attitudes toward risk. If options are priced such that they offer consistent opportunities for profit to either buyer or seller, it can imply that such buyers and sellers either have consistently erred in their expectations about the future, or that they have attitudes toward risk which make them willing to buy or sell such options at prices different from their mathematical expectation.” (p. 374)

“A paper by Rosett (1964), to be published elsewhere, investigates a slightly more complex hypothesis. Rosett conjectures that buyers of puts and calls may have cubic utility functions, implying that they may be averse to increased variance in asset prices but that they may prefer assets that have positively skewed probability distributions; i.e., have greater likelihood of gain than loss. Using data on actual put and call transactions and exercise of those options, Rosett confirms this hypothesis.” (p. 375)