Information Horizon, Portfolio Turnover, and Optimal Alpha Models

Abstract

T he bottom-line value of an active investment process has two parts: the theoretical value of the alpha skill (the gross paper profit), minus the cost of implementation. The higher the former and the lower the latter, the happier the investor is. Clearly total assets under management (AUM) influence the latter. A strategy might be profitable with a low level of assets under management but unprofitable with more assets-as asset amounts grow, so do transaction costs.Kahn and Shaffer [2005] note that one approach to remedy the size problem is to reduce portfolio turnover. While this is a sensible suggestion, Kahn and Shaffer's work is based on a hypothetical relation between turnover and expected alpha that might be too general to be applicable. In reality, any relation between turnover and expected alpha is not exogenous. It depends on alpha factors, their weights in an alpha model, and the rebalance horizon.We propose an analytic framework for integrating alpha models with portfolio turnover. In practice, many alpha models are not constructed in such an integrated framework. Typically, managers first develop an alpha model (giving little consideration to turnover), and then throw the alpha model into an optimizer, setting turnover constraints to handle the transaction costs. There are two drawbacks to this two-step process: 1) It makes it hard to know the true effectiveness of the alpha model; and 2) it does not let managers adjust the alpha model along the way as AUM grow.To integrate an alpha model with portfolio turnover, we extend work by Qian and Hua [2004] and Sorensen et al. [2004] that provides an optimal solution for Information Horizon, Portfolio Turnover, and Optimal Alpha Models

Multi-period portfolio optimisation with alpha decay

“…Consider the Information Coefficient (IC) (see Qian et al [13]) of the short-term and the long-term alpha signals which at t is defined as the correlation between the alpha signal at the start of period t and the realized returns at the end of period t. Similarly, we define the lagged IC as the correlation between the alpha signal at the beginning of period t and the realized returns at a future period say t + l where l > 0. The IC measures the strength of the alpha-signal in predicting returns, while the lagged IC measures how this predictive power decays over time.…”

“…They test their heuristic on a realistic example and a simulated example with promising results. Grinold [8,9], Qian et al [13], and Sneddon [14] each solve a static auxiliary problem that trades-off signal strength and time decay to determine the signal weights. These weights are then used in a single-period model to generate the portfolio holdings.…”

Evaluating fund capacity: issues and methods

“…Both Kahn and Shaffer (2005), and Serbin et al (2009) extend Perold andSalomon (1991) by modelling capacity in a mean-variance framework that aligns with the 'fundamental law of active management' (Sneddon, 2005(Sneddon, , 2008Grinold, 2007;Qian et al, 2007). These authors maximise net alpha conditional on the following: alpha prior to costs, active risk relative to the benchmark, an expression for transaction costs and FUM.…”

“…However, these survey results only represent perceptions, albeit informed. Qian et al (2007) introduce the concept of 'information horizon' as a method for characterising the profile over which a signal decays. They define the 'lagged information coefficient (IC)' as the correlation between a (factor-based) signal and returns over each future period, and 'horizon IC' as the correlation between the signal and the accumulation of returns over various horizons.…”

Evaluating Fund Capacity: Issues and Methods

“…35 A number of authors present similar models to Coppejans and Madhavan (2007) based on the fundamental law of active management, e.g. Grinold (2007), Qian et al (2007), Sneddon (2005Sneddon ( , 2008. These models generate optimal portfolios and turnover allowing for transaction costs, and are derived under conditions where the horizon of an investment signal is profiled by either the autocorrelation of the signal, or the correlation between the signal and returns over a forecast horizon.…”