University of Washington - Department of Statistics
The general Fund-of-Funds (GFoF) class of investment organizations includes fund-of-hedge funds (FoHF), family offices, endowments, pension plans and asset management companies. GFoF portfolios are characterized by two important types of returns problems among others. The first is that the returns histories of the portfolio assets are unequal, sometimes quite short and often contain multiple frequencies, resulting in structured missing data problems. The second is that the returns have fat-tailed and skewed distributions to varying degrees. To date there are no well-established statistical methods for accurate risk assessment and optimization of GFoF portfolios whose returns pose such data difficulties. In order to solve this problem we introduce a very general new class of factor model Monte Carlo (FMMC) methods for portfolio construction and risk management. These methods are based on constructing a good factor model for each portfolio asset using a relatively small number of factors that have long histories, coupled with selection of appropriate distribution models for the risk factors and the residuals and simulation from the fitted models. The factor models can be of any known type, and various combinations of fat-tailed and skewed distributions can be used for the risk factors and the residuals. As such FMMC is based on a class of conditional-plus-marginal definition of multivariate distribution models that can be either parametric or semi-parametric. We demonstrate that relative to using only the asset returns themselves the FMMC methods achieve significantly increased accuracy for estimating risk and performance measures such as volatility, information ratio, value-at-risk (VaR) and expected tail loss (ETL). The FMMC approach also delivers effective portfolio construction that is superior to naÃ¯ve methods that discard useful information by truncating the returns histories to the longest common history. Empirical results indicate that FMMC based risk estimates are as good as or better than multiple back-fill/imputation methods with respect to estimation error. We also discuss several related methodologies and topics, including choice of sample size for FMMC, the use of partial influence functions to obtain large sample variances, the connection between FMMC and maximum entropy updating, and clarification of missing data frameworks and their implication.