Isabelle Bajeux-Besnainou

Categorical Thinking in Stock Portfolio Management: A Puzzle?

Puzzles have become a popular way to question financial concepts. Many scholars, who are in Paul Samuelson’s line of thinking, have advanced knowledge in Finance and Economics by proposing and explaining interesting paradoxes. Here we introduce a puzzle linked to categorical thinking in stock portfolio management. Institutional investors, such as pension funds and university endowments, use investment consultants for establishing investment policies and guidelines, strategic asset allocation decisions, active vs. passive investment decisions, selection of active managers, and performance measurement. To this end, they look for guidance on how to allocate the fund’s assets among various asset classes, and select individual manager styles for each class. This approach leads to categorical portfolio allocation, whereby money managers are labeled depending on their specific investment style. On the domestic stock side, a categorical approach or multi-layered structure might include such asset subclasses (styles) as large-, mid-, and small-cap with additional categories for the value and growth styles. On the fixed income side, the choices usually include U.S. Treasuries, high-yield bonds, emerging market debt, and callable bonds such as mortgage-backed securities. We concentrate on the stock portfolio allocation process after the strategic asset allocation has been determined between Stocks and Bonds. The puzzle appears with the methodology of selecting different layers for stock portfolio allocation. In fact, as the two-fund separation theorem states, every ‘rational’ investor should allocate his/her wealth between the money market fund for the risk-free allocation and the market portfolio for the risky allocation. In practice, institutional investors apply these theoretical results as they use mean-variance optimizers to select the optimal portfolio allocation. They understand that low correlation between layers creates more efficient portfolios in the risk-return space and use this argument to justify a layer approach for their asset allocation decisions. Moreover, they prefer the industry to introduce new “layers” with low correlation with the prevailing layers to increase the financial efficiency of the overall portfolio. In this context, why would the institutional investors not conform completely to the theory and select directly an index fund, which by definition would not only provide the largest diversification effect but should also be the most cost-efficient? In summary, institutional investors are using the mean-variance framework as a benchmark model but not using its basics conclusions. This is the inconsistency or puzzle that we are addressing here. What are the explanations for this puzzle? The first potential explanation is the “search for positive alphas.” The goal of any active management mandate is the generation of positive alpha for the overall portfolio. Institutional investors are looking for active portfolio managers, who are themselves trying to obtain positive alphas in their respective opportunity sets, depending on their respective benchmarks. In particular, the ‘stock-picking’ approach to investing, usually justified by extensive fundamental research of the companies is a very popular technique. There are also ‘quant shops’ that would implement mathematical and statistical techniques in order to generate consistent excess returns over the given benchmark. In addition to managers with the fundamental approach and the quantitative managers with state-of-the-art information processing skills, there has been a surge of a new set of managers who hope to capitalize on behavioral biases. Behavioral managers believe that perception-induced biases result in significant inefficiencies with a potential for positive alpha generation. Despite numerous studies, empirical evidence does not allow to conclude whether active managers have the ability to generate positive alpha in a consistent manner. Consequently, attempts in selecting individual active managers will not result in consistent positive alphas and the quest for positive alpha is not a convincing explanation of the puzzle. The second potential explanation goes along the lines of some recent academic research in behavioral finance. In particular, investors may use categorical thinking as a framework to decide on the asset allocation process. Indeed, even the father of normative portfolio theory, Harry Markowitz, made the following comment when asked how he was allocating his retirement money: “My intention is to minimize my future regret. So, I split my contribution 50-50 between bonds and stocks.” What he did was basically to use the “1/n heuristic” rule in the case of two categories. This rule is The Journal of Behavioral Finance 2003, Vol. 4, No. 3, 118–120 Copyright

Pricing stock and bond derivatives with a multi-factor Gaussian model

The martingale approach to pricing contingent claims can be applied in a multiple state variable model. The idea is used to derive the prices of derivative securities (futures on stock and bond futures, options on stocks, bonds and futures) given a continuous time Gaussian multi-factor model of the returns of stocks and bonds. The bond market is similar to Langetiegs multi-factor model, which has closed-form solutions. This model is a generalization of Vasiceks model, where the term structure depends on state variables following correlated mean reverting processes. The stock market is affected by systematic and unsystematic risk.

Optimal portfolio allocations with tracking error volatility and stochastic hedging constraints

The performance of mutual fund or pension fund managers is often evaluated by comparing the returns of managed portfolios with those of a benchmark. As most portfolio managers use dynamic rules for rebalancing their portfolios, we use a dynamic framework to study the optimization of the tracking error–return trade-off. Following these observations, we assume that the manager minimizes the tracking error under an expected return goal (or, equivalently, maximizes the information ratio). Moreover, we assume that he/she complies with a stochastic hedging constraint whereby the terminal value of the portfolio is (almost surely) higher than a given stochastic payoff. This general setting includes the case of a minimum wealth level at the horizon date and the case of a performance constraint on terminal wealth as measured by the benchmark (i.e. terminal portfolio wealth should be at least equal to a given proportion of the index). When the manager cares about absolute returns and relative returns as well, the risk–return trade-off acquires an extra dimension since risk comprises two components. This extra risk dimension substantially modifies the characteristics of portfolio strategies. The optimal solutions involve pricing and duplication of spread options. Optimal terminal wealth profiles are derived in a general setting, and optimal strategies are determined when security prices follow geometric Brownian motions and interest rates remain constant. A numerical example illustrates the type of strategies generated by the model.