A simple algorithm to incorporate transactions costs in quadratic optimisation

Quantitative fund management invariably involves portfolio performance being measured in terms of a quadratic objective function (due to the inclusion of variance terms as a measure of risk). Periodically, the constituents of the fund are adjusted to improve performance. This adjustment incurs a transaction cost which is a modulus function of the changes in holdings. Thus the fund manager wishes to minimise a combined quadratic and modulus function. This paper presents a new approach to deal with the minimisation of this hybrid function, using a well tried quadratic programming algorithm. The new algorithm is demonstrated using a tactical asset allocation problem and an equity index tracking fund.