because modern portfolio theory was established when the academic
profession believed in the random walk theory of security prices. As
noted earlier, under a random walk, the relativerisk of various securities
does not change for different holding periods, so portfolio allocations do
not depend on how long one holds the asset. The holding period be-
comes a crucial issue in portfolio theory when the data reveal the mean
reversion of stock returns.^8INFLATION-INDEXED BONDS
Until the last decade, there was no U.S. government bond whose re-
turn was guaranteed against changes in the price level. But in January
1997, the U.S. Treasury issued the first government-guaranteed infla-
tion-indexed bond. The coupons and principal repayment of this
inflation-protected bond are automatically increased when the price
level rises, so bondholders suffer no loss of purchasing power when
they receive the coupons or final principal. Since any and all inflation
is compensated, the interest rate on this bond is a real, or inflation-
adjusted, interest rate.
When these bonds were first issued, their real yields were about 3^1 ⁄ 2
percent, and they rose to over 4 percent at the height of the 2000 bull
market. However, these yields have declined markedly since 2001, and
at the end of 2006, their real yields fell to about 2 percent, less than one-
third the historical return on equity. Nevertheless, these bonds may be
an attractive alternative for investors who do not want to assume the
short-term risks of stocks but fear loss of purchasing power in bonds. In
20 percent of all 10-year periods from 1926, stocks have fallen short of a
2.0 percent real return. For most long-term investors, inflation-indexed
bonds should dominate nominal bonds in a portfolio.CHAPTER 2 Risk, Return, and Portfolio Allocation 35
(^8) For an excellent review of this literature see Luis M. Viceira and John Y. Campbell, Strategic Asset
Allocation: Portfolio Choice for Long-Term Investors, New York: Oxford University Press, 2002. Also see
Nicholas Barberis, “Investing for the Long Run When Returns Are Predictable,” Journal of Finance,
vol. 55 (2000), pp. 225–264. Paul Samuelson has shown that mean reversion will increase equity
holdings if investors have a risk aversion coefficient greater than unity, which most researchers find
is the case. See Paul Samuelson, “Long-Run Risk Tolerance When Equity Returns Are Mean Re-
gressing: Pseudoparadoxes and Vindications of ‘Businessmen’s Risk’” in W. C. Brainard, W. D.
Nordhaus, and H. W. Watts, eds., Money, Macroeconomics, and Public Policy, Cambridge: MIT Press,
1991, pp. 181–200. See also Zvi Bodie, Robert Merton, and William Samuelson, “Labor Supply Flex-
ibility and Portfolio Choice in a Lifecycle Model,”Journal of Economic Dynamics and Control, vol. 16,
no. 3 (July–October 1992), pp. 427–450. Bodie, Merton, and Samuelson have shown that equity hold-
ings can vary with age because stock returns can be correlated with labor income.