Optimal style allocation incorporating return predictability

Empirical finance documents the evidence of time-varying expected returns with predictable components across styles. The important implication of such return predictability is that active investors may wish to engage style rotation strategies to enhance returns. To model expected returns, traditional finance generally links expected returns with the condition risk premium by previous observable information set. One of the popular approaches to model the time-varying expected return patterns is to allow the information set to contain some economic pervasive variables that have been identified as return predictors by previous research6_{. Campbell and Viceira (2005)} argue that the stock return predictability can have a strong impact on the variance and covariance structures of asset returns which is relevant for buy-and-hold investors with fixed investment horizons. Brant (2010) observes that following the recent empirical evidence of such predictable time-varying return distributions, optimal portfolio selection problems has once again been in the forefront of financial research. For example, Kandel and Stambaugh (1996) show that from an ex ante perspective variables predicting the distributions of the moments of stock return exert significant impact on a tactical portfolio allocation. Brennan and Schwartz (1996), Brennan et al. (1997) and Barberis (2000) examine the impact of predictability to the myopic versus dynamic portfolio choice problems. Ferson and Siege (2001) derive the optimal portfolio weights for mean-variance

6 _{Solnik (1993) argues there are three approaches to model expected returns: the}

first is to contain past returns in the information set. The second is to contain the first and second moments in the information set, and the third is to use economic variables like yld, def, term and div as discussed in previous sections. Studies such as Harvey (1991) show the strong explanatory power of such variables to both U.S. and none U.S. equity risk premia.

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investors assuming that the moments of stock returns are known functions of state variables. More recently, Avramov and Chordia (2006a, 2006b) find that a real time optimising investor benefits from incorporating business cycle information to the asset allocation between stocks and cash, and investment strategies such as ‘fund of mutual funds’ can also benefit from capitalising on the predictable time-varying dynamics over the business cycles.

Asset allocation is the key factor in determining the performance of long-term investments. Brinson et al. (1986) show that the decision of how to allocate assets accounts for about 90% of the performance variations for large pension funds. Likewise, the prominent study of Sharpe (1992) suggests that 90% of the performance of equity funds is due to the overall style of the fund, while the remaining 10% is due to the individual characteristics of the specific securities hold. From a money manager’s perspective, for a solid strategy to decide an appropriate asset allocation, it requires first to consider on which level, tactical or strategic.

There is fundamental difference between tactical asset allocation and strategic asset allocation framework. Strategic asset allocation is mainly driven by the long-term return-risk assumptions for various asset classes. It specifies the overall weight of various styles in a portfolio to satisfy investor’s risk-return preference in a lengthy investment period. However, the change of investor’s life style will eventually impact the underlying risk tolerance and in turn his strategic asset allocation decision. Hence the risk-return profile for strategic asset allocation should be evaluated periodically once the investment landscape experience fundamental change. Unlike strategic framework, tactical asset allocation takes into account the

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short-term market conditions and is therefore designed to identify the possibility to tilt strategic asset allocations according to the changes in the investment opportunity set. Hence the underlying drivers for tactical asset allocation are valuation, momentum or contrarian, investor’s sentiment and business cycle effect etc. Overall, the strategic asset allocation is the establishment of a long-term investment objective, while the tactical asset allocation determines how to adjust strategic asset allocation by exploiting inefficiencies in equilibrium values among asset classes. A solid investment strategy must highlight the role of both frameworks from the very beginning.

The optimal strategic and tactical asset allocations are perhaps most relevant for delegated asset management. As mentioned previously, institutional investors like pension funds and endowment funds act as fiduciaries and generally accept substantial responsibilities and assume significant liabilities. van Binsbergen et al. (2008) argue that the asset allocation of such investors are mainly structured around asset classes. As a result the fund’s Chief Investment Officer (CIO), who acts in the best interest of his beneficiaries, would pick asset manager who is specialised in a single style or delegates the portfolio decision to such specialists. Therefore the asset allocation decisions are made in two stages, namely CIO’s strategic allocation to different styles represented by different style managers and the individual style manager’s tactical allocation within his style7_{. The CIO usually} has long-term investment horizon and his objective is to minimise the utility cost from the misalignments of incentives induced by the above two-step allocations by optimising the investment weights to

7 _{The reason why the CIO in the asset management firm should hire such multi-}

style managers can be justified by Sharp (1981) who argues that the decision to employ different managers is to exploit their specialisation or to diversify among managers (i.e. style diversifications).

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different style managers in a mean-variance framework. In contrast, the individual style manager, however, is motived to maximise his remuneration on a relatively short horizons. van Binsbergen et al. (2008) argue that if asset returns are predictable, the CIO’s optimal style manager choice problem depends on his investment horizon and requires being tactically optimised. This introduces the hedging demands from the difference between the strategic and tactical style portfolio weights in response to changes in the future investment opportunity set.

A variety of theoretical solutions have been explored in the literature to solve the optimal portfolio choice problem incorporating return predictability. Brandt and Santa-Clara (2006) point out that most techniques are out of reach for ordinary investors since close-form solutions are not always available. Over the years the mean-variance paradigm of Markowitz (1952) is the major workhorse of portfolio optimisation. When solving the optimal portfolio choice problem, prior studies generally first estimate the conditional moments with state variables and then apply traditional Markowitz approach. This methodology raise concerns such as rigid assumptions between moments of returns and state variables to safeguard covariance matrix and massive number of parameters be estimated. Michaud (1989) argues this will inevitably results in notoriously noisy and unstable test results. Recently, Brandt (1999) develops a framework to bypass the procedure of estimating the joint distributions of conditional stock return but directly estimate the optimal portfolio weights based on the state variables. Ait-Sahalia and Brandt (2001) argue that the predictability of expected returns and the covariance structure is difficult to be translated into portfolio selection advice because the two moments may be predicted by different variables.

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Moreover, a variable may be both significant for predicting the variations of expected return and variance but such variations offset therefore it is not useful for determining optimal portfolio weights. Based on that, Brandt and Santa-Clara (2006) propose an approximation to solve the CIO’s problem by introducing managed and timing portfolios in the asset space. This approach is easy to apply by investors in the traditional static Markowitz paradigm.

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