Many years ago Samuelson (1969) and Merton (1969, 1971) derived the conditions under which optimal portfolio decisions of long-term investors would not be different from those of short-term investors. One important condition is that the investment opportunity set remains constant over time. Among other things this implies that excess returns are not predictable. Interest in long-term portfolio management has been revived now that a growing body of empirical research has documented predictability for various asset returns. Excess stock returns appear related to valuation ratios like the dividend yield, price earnings ratio, and also to inflation and interest rates. Similarly, the term spread is a well-known predictor of excess bond returns.
A growing number of studies explores the implications of the changing investment opportunity set for long-term investors. As an insightful exploratory tool Campbell and Viceira (2005) introduce a ”term structure of the risk-return trade-off”. They use this term structure to show why time-varying expected returns lead to portfolios that depend on the investment horizon. They focus on a long-term investor who has a choice between stocks and long- and short-term bonds.
Typically these studies focus on an individual investor, who either is concerned about final wealth or who solves a life-cycle consumption problem. In this paper we will focus on the strategic asset allocation problem of an institutional investor, especially a pension fund. We therefore extend the existing models to an asset and liability portfolio optimization framework and expand the investment universe with assets that are nowadays part of the pension fund investment portfolios. We explicitly include risky liabilities in the optimal portfolio choice. Liabilities are a predetermined portfolio component in the institutional investor’s portfolio with a negative portfolio weight and with a return that is subject to real interest rate risk and inflation risk. The optimal portfolio for an institutional investor can therefore be different from the portfolio of an individual investor. Assets that hedge against long-term liabilities risk are valuable components for an institutional investor.
Second, we study the risk characteristics of other assets than stocks, bonds and cash at various investment horizons. In this way we extend the term structure of the risk-return trade-off of Campbell and Viceira (2005) for assets like credits, commodities, real estate and hedge funds. We consider these assets in an ”asset-only” context and also investigate if these asset categories are a hedge against inflation and real rate risk at different investment horizons. This gives insights into whether there is more than stocks and bonds in the universe that is interesting for strategic asset allocation. Which asset classes have a ”term structure of risk” that is markedly different from that of stocks and bonds?
The remainder of this paper is organized as follows. Section 3 describes our model and presents the estimation results. Like Campbell and Viceira (2005) we consider a vector autoregression model to describe the time series properties of returns jointly with those of macro-economic variables. Since we include more assets the dimension of our VAR is larger. A large part of the section deals with parsimony of the model and with the problem of handling asset classes for which we have a short time series of returns. Section 3 explores the risk and hedging qualities of the asset classes at different horizons using the dynamics implied by the vector autoregression. In section 4 we will derive optimal portfolios both in an ”asset-only” and an ”asset-liability” context. We also use a certainty equivalent calculation to estimate the costs of sub-optimal asset allocations that ignore either liabilities or the alternative asset classes. Section 5 concludes.
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Strategic Asset Allocation with Liabilities: Beyond Stocks and Bonds
