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| Research Paper 5 | |
| | Who Should Buy Long-Term Bonds?
Winner
of the 1999 FAME Research Prize
Authors
John
Y. CAMPBELL - Harvard University
Luis VICEIRA - Harvard Business School
Date
October
1998
This paper has now been published and is no longer available as
a part of our Research Paper Series. The reference to this paper is:
Campbell,
J., Viceira, L., "Who should buy Long-Term Bonds", in American Economic Review, vol. 91, issue
1, March 2001, pp.99-127.
Abstract
According
to conventional wisdom, long-term bonds are appropriate for long-term investors who value stability
of income. We develop a model of optimal consumption and portfolio choice for infinitely-lived investors
facing stochastic interest rates, solve it using an approximate analytical method, and evaluate the
conventional wisdom. We show that the demand for long-term bonds has both a myopic component and an
intertemporal hedging component. As risk aversion increases, the myopic component shrinks to zero but
the hedging component does not. An infinitely risk-averse investor who is infinitely unwilling to substitute
consumption intertemporally should hold a portfolio of long-term indexed bonds that is equivalent to
an indexed perpetuity. This portfolio finances a riskless consumption stream and in this sense provides
a stable income. We calibrate our model to postwar US data and compare consumption and portfolio rules
with and without bond indexation, portfolio constraints, and the possibility of investment in equities.
We find that when indexed bonds are not available, inflation risk leads investors to shorten their bond
portfolios and increase their precautionary savings. This has serious welfare costs for conservative
investors, who are much better off when they have the opportunity to buy indexed bonds. We also find
that the ratio of bonds to equities in the optimal portfolio increases with the coefficient of relative
risk aversion, which is consistent with conventional portfolio advice but inconsistent with the mutual
fund theorem of static portfolio analysis. Our results illustrate the general point that static portfolio
choice models should not be used to study the dynamic problems facing long-term investors.
Executive
Summary
According to conventional wisdom, long-term bonds are appropriate
for long-term investors who value stability of income. We develop a model of optimal consumption and
portfolio choice for infinitely-lived investors facing stochastic interest rates, solve it using an
approximate analytical method, and evaluate the conventional wisdom.
We
show 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.
Long-term 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
show 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
extend 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.
Our
constrained solution enables us to study the welfare effects of bond indexation in a realistic framework.
When portfolio constraints are in place, and both nominal and indexed bonds are available to investors,
more conservative investors hold in their portfolios relatively more indexed bonds than nominal bonds.
These investors benefit substantially from the consumption insurance provided by long-term indexed bonds.
We
also study the demand for bonds when equities are available as an alternative investment. We find that
the ratio of bonds to stocks in the optimal portfolio increases with risk aversion, very much in line
with popular investment advice but contrary to the mutual fund theorem of static portfolio analysis.
However the demand for long-term bonds is only large when these bonds are indexed, or when inflation
uncertainty is low as it has been in the Volcker-Greenspan monetary policy regime since 1983.
Our
analysis also has interesting implications for the design of pension plans and annuities. Our results
suggest that conservative investors should favor indexed defined-benefit plans, while more risk-tolerant
investors may be willing to accept some inflation or equity risk in their retirement income in exchange
for higher average payments.
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