Monthly Archives: February 2015


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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Bond Demand in the Presence of Equities

The realism of the preceding analysis is limited by the fact that we have not allowed investors to hold equities. We now consider a scenario in which both bonds and equities are available to the investor. Table 8 reports optimal demands for equities and for 10-year indexed or nominal bonds by investors who are unconstrained (in panel A) or subject to borrowing and short-sales constraints (in panel B). For simplicity we do not allow investors to hold equities and both types of long-term bonds simultaneously.
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In a world with full indexation, the unconstrained demand for both long-term indexed bonds and equities is positive and often above 100%, implying that the investor optimally borrows to finance purchases of equities and indexed bonds. The portfolio share of indexed bonds exceeds that of equities, despite the higher Sharpe ratio of equities, because indexed bonds are much less risky than equities. As the coefficient of relative risk aversion increases, the demands for both long-term indexed bonds and equities fall, but the share of equities falls faster.

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Comparing the first two panels of Table 7, we see that bond indexation can have substantial benefits to investors. Investors with low risk aversion benefit because indexed bonds have higher Sharpe ratios than nominal bonds, while more conservative investors benefit because indexation eliminates an unwelcome source of risk. The effects on welfare can be substantial; when their portfolio choice is unconstrained, for many investors the value function is more than twice as high in a fully indexed environment than in a purely nominal environment. Such investors would be willing to pay more than half their wealth to enjoy the benefits of indexation. The only investors who lose from indexation are investors with low risk aversion who are subject to borrowing and short-sales constraints. These investors prefer to hold nominal bonds, despite their low Sharpe ratios, as a way to increase risk and expected return without using leverage.
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These findings are in strong contrast with the claim of Viard (1993) that indexation has only minor welfare effects. Viard models indexation as elimination of the inflation risk in a one-period asset, and studies the benefits to one-period investors. Since there is little risk in inflation over one period, Viard’s result is not surprising. We get much larger benefits of indexation because we model indexation as elimination of the inflation risk in long-term assets, and study the benefits to long-term investors.

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