Construction of Risk-Averse Enhanced Index Funds

Abstract

We propose a partial replication strategy to construct risk-averse enhanced index funds. Our model takes into account the parameter estimation risk by defining the asset returns and the return covariance terms as random variables. The variance of the index fund return is forced to be below a low-risk threshold with a large probability, thereby limiting the market risk exposure of the investors and the moral hazard associated with the wage structure of fund managers. The resulting stochastic integer problem is reformulated through the derivation of a deterministic equivalent for the risk constraint and the use of a block decomposition technique. We develop an exact outer approximation method based on the relaxation of some binary restrictions and the reformulation of the cardinality constraint. The method provides a hierarchical organization of the computations with expanding sets of integer-restricted variables and outperforms the Bonmin and the Cplex 12.1 solvers. The method can solve very large (up to 1000 securities) instances, converges fast, scales well, and is general enough to be applicable to problems with buy-in threshold constraints. Cross-validation tests show that the constructed funds track closely and are consistently less risky than the benchmark on the out-of-sample period.

Portfolio Optimisation: Models and Solution Approaches

“…Here we have assumed zero transaction cost. Note here that Equations (17) and (19) together imply that N i=1 w i = 1 (as in Equation (3)). In time period t we get a return associated with the index, R t = log e (I t /I t−1 ), where we define return using continuous time.…”

“…Recent work, other than that discussed above, dealing with enhanced indexation can be found in Lejeune [18], Lejeune and Samatli-Pac [19], and Li et al [21]. The idea here is to construct a portfolio of assets that gives a return independent of that of a benchmark market index, as the underlying index rises and falls (varies).…”

Complex portfolio selection via convex mixed‐integer quadratic programming: a survey

“…Moreover, the mean‐variance approach considers only the first‐ and second‐order moments of the probability distribution of the returns: consequently, in specific situations, this approach might lead to counterintuitive or even paradoxical solutions (Copeland and Weston, ). However, this approach gives rise to different possible applications (see, for instance, the recent papers: Lejeune and Smatlı‐Paç, ; Ji and Lejeune, ; Vinel and Krokhmal, ).…”

Price and Earnings Momentum, Transaction Costs, and an Innovative Practitioner Technique

“…Note that an extra 92 bps per annum attained in a tax‐deferred retirement savings scheme improves the ending value of a lump sum deposit by about half as much again over a 45‐year horizon. Many conservative active quantitative funds (sometimes called ‘enhanced index funds’ or ‘alpha tilt index funds’) are looking for no more than a couple of hundred bps of outperformance on a benchmark per annum from a combination of perhaps 5–10 strategies (Grinold and Kahn , chapter 5; Loftus , exhibit 2; Chincarini and Kim , chapter 9; Lejeune and Samatli‐Paç ). So, getting in excess of 90 bps from a paired strategy is very attractive.…”