A weakness in this resolution of the asset allocation puzzle is that it assumes that long-term bonds are indexed, or equivalently, that there is no inflation uncertainty The portfolio allocations to nominal bonds in Table 8 do not correspond well with popular investment advice. In order to rationalize the popular investment advice for long-term nominal bonds, one must assume that future interest rates will be generated by a different process than the one estimated in 1952-96, a process with less uncertainty about future inflation. Interestingly, we have estimated just such a process over the Volcker-Greenspan sample period 1983-96. Table 9 repeats Table 8 using our 1983-96 estimates and finds that even when only nominal bonds are available, aggressive long-term investors should hold stocks, while conservative ones should hold primarily long-term nominal bonds along with small quantities of stocks.14 These results support the conventional wisdom about optimal portfolio choice for long-term investors.
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In this paper we have shown that investors may hold long-term bonds for two reasons. First, if long-term bonds offer a term premium then investors may hold them for speculative purposes, to increase their expected portfolio return even at the cost of some extra short-term risk. This “myopic demand” for long-term bonds can be large when risk aversion is small, because long-term bonds have attractive Sharpe ratios.
Second, long-term investors may hold long-term bonds for hedging purposes. Longterm bonds can finance a stable long-run consumption stream even in the face of time-varying short-term interest rates, and this is attractive to risk-averse long-term investors. In the extreme cases where there is no term premium, or where investors are infinitely risk-averse, the myopic demand for long-term bonds is zero and all bond demand is accounted for by the hedging demand.
We have shown that indexed bonds are particularly suitable for hedging purposes, because they do not impose extraneous inflation risk on long-term investors seeking a stable real consumption path. When long-term indexed bonds are available, an infinitely risk-averse long-term investor with zero intertemporal elasticity of substitution holds a bond portfolio that is equivalent to an indexed perpetuity. The indexed perpetuity is the riskless asset for a long-term investor, since it finances a constant consumption stream forever. When only nominal bonds are available, highly risk-averse investors shorten their bond portfolios in order to reduce their exposure to inflation risk. Less risk-averse investors hold long-term nominal bonds for speculative purposes if there is a positive inflation risk premium.
We have extended our approach to solve the intertemporal portfolio choice problem imposing short-sale and borrowing constraints. This is possible because our solution takes the same form as the solution to a static portfolio choice problem for which standard mean-variance analysis is appropriate. Therefore we can solve our constrained problem using methods that have been developed to solve static problems with portfolio constraints.