**Factor Investing And Risk Allocation: From Traditional To Alternative Risk Premia Harvesting**

**Introduction**

Academic research (see Ang (2014) for a synthetic overview) has highlighted that risk and allocation decisions could be best expressed in terms of rewarded risk factors, as opposed to standard asset class decompositions, which can be somewhat arbitrary. For example, convertible bond returns are subject to equity risk, volatility risk, interest rate risk and credit risk. As a consequence, analyzing the optimal allocation to such hybrid securities as part of a broad bond portfolio is not likely to lead to particularly useful insights. Conversely, a seemingly well-diversified allocation to many asset classes that essentially load on the same risk factor (e.g., equity risk) can eventually generate a portfolio with very concentrated risk exposure. More generally, given that security and asset class returns can be explained by their exposure to pervasive systematic risk factors, looking through the asset class decomposition level to focus on the underlying factor decomposition level appears to be a perfectly legitimate approach, which is also supported by standard asset pricing models relying on equilibrium arguments (the Intertemporal CAPM from Merton (1973)) or arbitrage arguments (the Arbitrage Pricing Theory from Ross (1976)).

In a recent paper, Martellini and Milhau (2015) provide further justification for the factor investing paradigm by formally showing that the most meaningful way for grouping individual securities is by forming replicating portfolios for asset pricing factors that can collectively be regarded as linear proxies for the unobservable stochastic discount factor, as opposed to forming arbitrary asset class indices. Building on this insight and a number of associated formal statistical tests, they provide a detailed empirical analysis of the relative efficiency of various forms of implementation of the factor investing paradigm and analyze the robustness of these findings with respect to a number of implementation choices, including the use of long-only versus long-short factor indices, the use of cap-weighted versus optimized factor indices, and the use of multi-asset factor indices versus asset class factor indices.

From a practical perspective, two main benefits can be expected from shifting to a representation expressed in terms of risk factors, as opposed to asset classes. On the one hand, allocating to risk factors may provide a cheaper, as well as more liquid and transparent, access to underlying sources of returns in markets where the value added by existing active investment vehicles has been put in question. For example, Ang, Goetzmann, and Schaefer (2009) argue in favor of replicating mutual fund returns with suitably designed portfolios of factor exposures such as the value, small cap and momentum factors. In the same vein, Hasanhodzic and Lo (2007) argue in favor of the passive replication of hedge fund vehicles, even though Amenc et al. (2008, 2010) found that the ability of linear factor models to replicate hedge fund performance is modest at best. On the other hand, allocating to risk factors should provide a better risk management mechanism, in that it allows investors to achieve an ex-ante control of the factor exposure of their portfolios, as opposed to merely relying on ex-post measures of such exposures.

Given the increasing interest in risk premia harvesting, and the desire to enhance the diversification of their portfolio, large sophisticated asset owners investors are turning their attention to so-called alternative risk premia, loosely defined as risk premia that can be earned above and beyond the reward obtained from standard long-only stock and bond exposure (see Section 2 for a tentative taxonomy of alternative risk premia). These alternative risk factors are empirically documented sources of return that can be systematically harvested typically through dynamic long/short strategies, which have been found to have explanatory power for some hedge fund strategies (see for example Fung and Hsieh (1997a,b, 2002, 2004, 2007) or Agarwal and Naik (2004, 2005)).

More precisely this paper aims at analyzing what the best possible approach would be for harvesting alternative risk premia. To answer this question, we empirically analyse whether systematic rule-based strategies based on investable versions of alternative (and traditional) factors allow for the satisfactory in-sample and also out-of-sample replication of hedge fund performance, or whether it is instead the case that properly harvesting alternative risk premia, which are more complex to extract and trade compared to traditional risk premia, requires active managers’ skills.

As such, our project is related to the stream of research on hedge fund replication (see Hasanhodzic and Lo (2007), Amenc et al. (2008, 2010), among many others), which we extend in the following two main directions. In a first step, in contrast to some of the previous research that has analysed the replication of global hedge fund indices, which are often dominated by long/short equity strategies that are arguably the easiest to replicate, our focus will be on replicating hedge fund strategy indices (see Asness et al. (2015) for a recent reference). It is in fact one of the goals of the research project to identify which strategies are easiest/ hardest to replicate using alternative risk premia and possibly conditional models that may capture changes in hedge fund exposures by exploiting information from relatively high frequency conditioning variables (see Kazemi et al. (2008) for an analysis of conditional properties of hedge fund return distributions). Finally, we consider the possible improvement allowed for by the introduction of a specific set of factors for each strategy, as opposed to using a single set of systematic factors for all funds. Given the concern over data mining that would arise from a statistical search of the best factors, we have constrained ourselves to a purely economic selection of factors. In a second step, we shift the perspective from hedge fund replication to hedge fund substitution, and investigate whether suitably designed risk allocation strategies may provide a cost-efficient way for investors to get an attractive exposure to alternative factors, regardless of whether or not they can be regarded as proxies for any particular hedge fund strategy.

The rest of the paper is organized as follows. In Section 2, we first attempt to provide a definition for the rather loosely defined alternative risk factors as well as a list of the main alternative risk factors that have been analyzed in the academic and practitioner literature. In Section 3, we analyze the explanatory power of various statistical model that can be used for the replication of hedge fund returns with (traditional and) alternative risk factors. In Section 4, we extend the analysis to the construction of investment strategies with attractive risk-adjusted performance based on these alternative risk premia. We present our conclusions and suggestions for further research in Section 5, while technical details are relegated to a dedicated appendix.

**Table 1: List of risk factors**

This table summarises in the first three columns the whole set of the traditional and alternative risk factors considered in our empirical analysis, their proxies and their sources. The other columns indicate the bespoke economic subset of factors used for each strategy in our empirical analysis. CA refers to Convertible Arbitrage, CTA to CTA Global, DS to Distressed Securities, EM to Emerging Markets, EMN to Equity Market Neutral, ED to Event Driven, FIA to Fixed Income Arbitrage, GM to Global Macro, LSE to Long Short Equity, MA to Merger Arbitrage, RV to Relative Value, SS to