Estimating Asset Allocation Inputs
A number of different techniques are also used to improve the estimates of future asset class returns, standard deviations, correlations, and other inputs that are used by various asset allocation methodologies. Of these variables, future returns are the hardest to predict. One approach to improving return forecasts is to use a model containing a small number of common factors to estimate future returns on a larger number of asset classes. In some models, these factors are economic and financial variables, such as the market/book ratio, industrial production, or the difference between long- and short-term interest rates. Perhaps the best known factor model is the CAPM (capital asset pricing model). This is based on the assumption that, in equilibrium, the return on an asset will be equal to the risk-free rate of interest, plus a risk premium that is proportional to the asset’s riskiness relative to the overall market portfolio. Although they simplify the estimation of asset returns, factor models also have some limitations, including the need to forecast the variables they use accurately and their assumption that markets are usually in a state of equilibrium.
The latter assumption lies at the heart of another approach to return estimation, known as the Black–Litterman (BL) model. Assuming that markets are in equilibrium enables one to use current asset class market capitalizations to infer expectations of future returns. BL then combines these with an investor’s own subjective views (in a consistent manner) to arrive at a final return estimate. More broadly, BL is an example of a so-called shrinkage estimation technique, whereby more extreme estimates (for example, the highest and lowest expected returns) are shrunk toward a more central value (for example, the average return forecast across all asset classes, or BL’s equilibrium market implied returns). At a still higher level, shrinkage is but one version of model averaging, which has been shown to increase forecast accuracy in multiple domains. An example of this could be return estimates that are based on the combination of historical data and the outputs from a forecasting model.
When it comes to improving estimates of standard deviation (volatility) and correlations, one finds similar techniques employed, including factor and shrinkage models. In addition, a number of traditional (for example, moving averages and exponential smoothing) and advanced (for example, GARCH and neural network models) time-series forecasting techniques have been used as investors search for better ways to forecast volatility, correlations, and more complicated relationships between the returns on different assets. Finally, copula functions have been employed with varying degrees of success to model nonlinear dependencies between different return series.
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