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W hile the modern paradigm of asset pricing is to represent an asset's expected return as a combination of one or more systematic risk factors (Sharpe [1964], Lintner [1965], and Ross [1976]), the process of portfolio allocation has generally been to directly decide on the optimal holdings of asset classes--rather than on the factors that drive assets' expected returns. Part of this disconnect is that there is no standard procedure for mapping factors to assets. In fact, financial models are usually built to go in the opposite direction: to decompose asset returns into systematic factors, with the remainder being idiosyncratic risk.
In this article, we develop a methodology that performs a mapping from a given set of factors to a set of asset classes. Because there are usually fewer factors than asset classes, this mapping is not unique. Our contribution is to show that we can express a given set of factor exposures to a particular combination of assets that have approximately the same factor exposures but reflect real-world relevant investor constraints such as the following: leverage, minimum and maximum asset class positions, illiquid versus liquid proportions, active risk, turnover, and other constraints. Formally, we find the set of asset classes with the minimum distance in terms of factor exposures from the desired set, subject to these constraints. It is actually the constraints that pin down the unique asset class portfolio.
There are several advantages of working directly with factors, compared to directly specifying asset classes. Factor investing illuminates portfolio positions and the key drivers of risk and return. During 2008 and 2009, many investors did not anticipate losses because viewing their portfolio in asset classes masked the underlying risks (see Ang [2014]). Working in factors also provides greater freedom in asset allocation and manager selection. Whereas an endowment model treats public and private equity separately, factor investing recognizes that growth risk, for example, is an important driver of both. Mapping growth to both of these asset classes allows investors to allocate to both of them consistently. With a mapping of factors to assets, investors can focus their allocation process on selecting which factor risks they are willing to bear in order to harvest long-term risk premiums.
Among academic studies, our approach is related to...