Implementation Efficiency

An analysis of risk, covariance, and correlation is used to measure the implementation losses that arise as a result of transaction costs and investment constraints. Losses are measured relative to an ideal, costless, and unconstrained implementation. The figure of merit is mean-variance expected utility expressed as portfolio alpha minus penalties for active variance and transaction costs. In a general setting, before-cost results are found that define the opportunity loss and identify its sources. In a specific case, after-cost results are found that enable prediction of how expected utility and information ratios are influenced by the investment process, information turnover, risk aversion, and transaction costs. The efficient management of investment portfolios requires an ability to understand, measure, forecast, and manage risk, return, and costs. In this article, I demonstrate how the tools of portfolio analysis—namely, analysis of risk, covariance, and correlation—can be used to understand, measure, and forecast the implementation losses that arise because of transaction costs and investment restrictions.An ideal, costless and unconstrained, implementation strategy is established as a benchmark; then, any actual implementation is measured relative to that ideal. The figure of merit is mean-variance expected utility expressed as portfolio alpha minus penalties for active variance and transaction costs. The difference between where we would like to be (the ideal) and where we are is called the “backlog.” The backlog is the basket trade that would move us to an ideal holding. The loss in expected utility for any implementation is equal to the variance penalty for that backlog position. The correlation of the actual and ideal implementations is the transfer coefficient; the information ratio of any implementation is equal to the information ratio of the ideal implementation multiplied by the transfer coefficient. Moreover, the ratio of the objective values (before costs) for the actual and ideal implementations is bounded above by the transfer coefficient squared. Thus, a transfer coefficient of 0.7 indicates that we are getting less than 50 percent of the potential utility. This analysis lets me demonstrate, through an example, a general procedure for allocating the utility loss to constraints and costs.I consider a specific model that provides after-cost results in a simple analytic form. This model has four drivers: the power of our information, the half-life (shelf life) of our information, our risk aversion, and a model of transaction costs. These four factors determine, in a relatively simple way, the resulting nature of the investment in terms of active risk level, expected alpha, and expected transaction costs per year. The model is used to demonstrate the sensitivity of after-cost investment performance to changes in the half-life of the investment insights and to various levels of transaction costs.