A Dynamic Model of Portfolio Management

Richard Grinold

Volume 4, Number 2, Second Quarter 2006

This paper presents a simplified model of dynamic active portfolio management. It is designed to answer questions about product design and provide a guide to better implementation. The model has four inputs: an information ratio that measures the anticipated ability to add value, a risk aversion parameter, a speed of decay of our information called the half-life, and finally a measure of transactions costs. With this structure and some assumptions we can derive relatively simple algebraic expressions for the annualized alpha, risk and transactions costs of the strategy. This allows us to construct both pre-and post-cost measures of implementation efficiency.

The model can be used in many ways. First establishing sensitivity of outputs to inputs. This sensitivity can be an aid in the allocation of research effort. Second, measuring the effect of increased assets under management on the ability to deliver post-cost results. Third, investigating the cost of parameter errors; if we think transactions costs are X but they really are 2*X, what are the implications. Fourth, weighting multiple signals.