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.
An apparently paradoxical result is that for some investors welfare is higher when only indexed bonds are available (in the top panel) than when both nominal and indexed bonds are available (in the third panel). The explanation is that in the top panel the short-term bond is indexed, whereas in the bottom panel it is nominal. The small benefits of short-term indexation in the top panel are enough to outweigh the small benefits of the additional long-term nominal asset that is available in the third panel.
The case where two long-term nominal bonds and one short-term nominal bond are available is illustrated in the bottom panel of Table 7. This asset menu delivers the highest welfare for investors with low or moderate risk aversion, but is much less satisfactory for investors with high risk aversion (above 10 or so). Such investors have a strong demand for the consumption insurance provided by long-term indexed bonds.
Advocates of bond indexation have sometimes argued that the availability of indexed assets will stimulate saving. However this effect depends on the elasticity of intertemporal substitution, ф. If ф = 1, then the consumption-wealth ratio is constant regardless of the available asset menu. If ф is close to zero, as many empirical estimates suggest, then the consumption-wealth ratio approximately equals the value function. Thus the welfare benefit of indexation is accompanied by an increase in consumption and a decline in saving. This point can be appreciated by comparing the average consumption-wealth ratios in Table 5 with the welfare measures in Table 7.
Finally, we note that welfare calculations for the 1983-96 sample period, not reported here, deliver qualitatively similar results but considerably smaller welfare benefits of bond indexation. The Volcker-Greenspan monetary regime has greatly reduced long-run uncertainty about inflation, and has correspondingly reduced the benefits of eliminating inflation risk entirely.