Dedicated stock portfolios

Abstract

T he Markowitz portfolio model introduced in 1952 expressed the optimal relationship between portfolio volatility and expected return. While tlie procedure was quite capable of providing perfectly accurate answers to questions such as, “Given a population of securities, what single combination would have had the lowest volatility in monthly return over the preceding period?”, the computing power of the times limited its application. A decade later, Sharpe introduced the singleindex model [1963]. In essence, Sharpe’s model replaced the exact, but cumbersome, Markowitz formula for portfolio volatility with a simplified approximation that assumed all the interrelationships among security returns could be attributed to the fact that they all respond differentially to the pull of the single index. Sharpe represented his single index by the returns to the market itself, but others (King [1966], for example) soon provided evidence that other common forces were pulling security returns as well. King at the time noted industry-related factors, but since then attention has shifted from aggregate stock marketor industry-related portfolios to more generalized economic factors. In some models the factors are real (economic variables such as unexpected changes in inflation, industrial production, and term and default premiums in bond yields see Chen, Roll, and Ross [1986]), while in others they are portfolios, derived from factor analysis (Chen [1983]). The factor analytic portfolios allegedly mimic the behavior of the underlying economic variables actually responsible for the correlations between security returns. Index models that initially were regarded as routes to a simplified expression for portfolio volatility eventually became widely accepted as ways to track targets such as the S&P 500. But times have changed since 1952. There have been significant advances in computing hardware and in the algorithms to compute portfolio volatility (Von Holhenbalken (19751). Analysts are now fully capable of obtaining Markowitz solutions for several hundred securities at a time, which makes the relative computational simplicity of index models less valuable. The latest advances in hardware and software now make it possible to construct dedicated stock portfolios based on all the information in the full covariance matrix of security returns. These portfolios are dedicated to a mission of risk management such as hedging against inflation or against unexpected changes in interest rates that may dramatically increase the present value of the liabilities of pension funds. Just as the Markowitz model provides the reactively accurate answer to the minimum volatility question posed above, it also provides the more accurate answer to the question, “Which combination of securities would have achieved the greatest degree of tracking power in the past?” While the relative predictive power of the Markowitz and index models remains an open question (and one that obviously