Implications for Stock & Futures Price Volatility

An Analysis of the Implications for Stock and

Futures Price Volatility of Program Trading

The introduction of futures and options markets in stock indexes is strongly associated with the use of programmed trading strategies. Such strategies are used for spot/futures arbitrage, market timing, and portfolio insurance. It is this last use of programmed trading strategies that raises fascinating theoretical questions, the answers to which may have practical importance for understanding the impact of such strategies on the volatility of stock and futures prices.

Recent advances in financial theory have created an understanding of the environments in which a real security can be synthesized by a dynamic trading strategy in a risk free asset and other securities (The seminal contribution is the Black-Scholes [1973] option pricing approach, whereby it is shown how a dynamic trading strategy in a stock and risk free asset can reproduce a European call or put option on the stock). The proliferation of new securities has been made possible, in part, by this theoretical work. The issuer of a new security can price the security based on its ability to synthesize the returns stream of the new security using a dynamic trading strategy in existing securities, futures and options. This use of dynamic trading strategies has been extended even further by eliminating the "new" security altogether and just selling the dynamic hedging st

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till be able to achieve the same outcome (or close to it), by using a dynamic trading strategy to synthesize the desired security (See Cox and Rubenstein [1985] for an exposition of dynamic trading strategies which synthesize options and other contingent claims). Consider the following very simple example. Suppose that the stock price is $10 at date 1, and at date 2 it either rises or falls from its date 1 level by 10%. Suppose further that the at date 3 the stock price can either rise of fall from its date 2 level by 10%. Thus there are three possible date 3 prices: $8.1, $9.9, and $12.1. Let the investor start with 100 shares, and assume that the risk free interest rate is 0%. Suppose that the investor's preferences are such that he wants to get the highest expected date 3 wealth subject to the constraints that: (a) his date 3 wealth is no lower than $900, and (b) he is allowed to invest no more than his total wealth in the risky asset. If the expected return on the stock is higher than that of the risk free asset, then it can be shown that the optimal trading strategy for the investor is to (i) invest all of his date 1 wealth in the risky asset (i.e., buy 100 shares at date 1); (ii) if the price at date 2 is $9, then he se

Category: Economics - I