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Cointegration and Long-Run Asset Allocation

Risks facing a short-run and long-run investor can be quite different. While at very short horizons, the contribution of cash-flow news to the variance of return may be small, as the investment horizon increases, cash-flow fluctuations become the dominant source of return variability. Hence, understanding and modeling the behavior of asset returns, especially at long horizons, depend critically on understanding and modeling the dynamics of their cash flows. In this paper we argue that deviations between cash-flow levels and aggregate consumption (the error-correction term) contain important information about means and variances of future cash-flow growth rates and, consequently, returns.

Incorporating this cointegration restriction in return dynamics yields interesting implications for the term-structure of expected returns and risks and, hence, asset allocations at various investment horizons. In particular, we show that the error correction mechanism significantly alters the risk-return trade off and the shape of optimal portfolio rules implied by models where the long-run adjustment of cash flows is ignored.

Our motivation for including the error-correction mechanism is based on the ideas of long-run risks developed in Bansal and Yaron (2004), Hansen, Heaton, and Li (2005), Bansal, Dittmar, and Lundblad (2005), and Bansal, Dittmar, and Kiku (2009). These papers, both theoretically and empirically, highlight the importance of the long-run relation between cash flows and aggregate consumption for understanding the magnitude of the risk premium and its cross-sectional variation. Built on this evidence, our paper aims to explore the effect of long-run properties of asset cash flows on the optimal portfolio mix at various investment horizons.

Intuitively, if the long-run dynamics of asset dividends are described by a cointegrating relation with aggregate consumption, then current deviations between their levels should forecast future dividend growth rates (see Engle and Granger (1987)). Further, as risks in long-horizon returns are dominated by cash-flow news, predictability of asset dividends emanating from the error-correction mechanism may significantly alter the future dynamics of multi-horizon returns and their volatilities. This suggests that the error-correction channel may be very important for determining the optimal asset allocation at intermediate and long investment horizons.

Cointegration and Long-Run Asset Allocation