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Economic
Research & Data 
Publications
Economic Letter
FRBSF Economic Letter
96-19; June 28, 1996
Stocks and bonds have very different risk-return characteristics. In
general, while stocks are more volatile than bonds, over the long run,
stocks are expected to yield higher returns than bonds. By varying the
mix of stocks and bonds in a portfolio, an investor can achieve her desired
level of risk exposure. However, the level of risk in a portfolio depends
not only on the risks of individual assets, but also on the comovements
of the individual assets in the portfolio. For example, if prices of two
hypothetical assets tend to move in opposite directions, investing in
a portfolio of these two assets would be less risky than investing in
each individual asset alone, because a decline in one asset's price would
be partially offset by a rise in the other asset's price, and vice versa.
Recently, however, stock prices and bond prices appear to have been moving
together more closely than in the past, suggesting that the risk of a
portfolio of stocks and bonds may have increased, even though the mix
of stocks and bonds in the portfolio remains the same.
To help understand how stock and bond prices move, this Economic Letterlooks
at the recent research on this issue. The emphasis in this research is
to distinguish first the economic forces that drive the prices of stocks
as well as those that drive the prices of bonds, and then to study the
comovement between the prices within the context of those economic forces.
The relationship between stock and bond prices will be developed further
in the next issue of the Economic Letter. The discussion there
will focus on the relation between stock and bond prices not at the aggregate
level but at the firm level.
The present value model is a framework for understanding how the prices
of stocks and bonds are determined. Both stocks and bonds are claims of
future cash flows. According to the present value model, their current
prices should be equal to the present value of future cash flows, subject
to the appropriate discount rates, which consist of the real interest
rate, inflation expectations, and a premium for holding a risky asset.
Other things being equal, an increase (decrease) in the expected future
discount rates for both stocks and bonds should cause both stock prices
and long-term bond prices to fall (rise), resulting in a positive correlation
between returns on outstanding stocks and long-term bonds.
But other things are not always equal. For example, the discount rate
for stocks may be different from the discount rate for bonds. This would
be the case if their risk premiums were different. Furthermore, the dividend
stream that is discounted for a stock is fundamentally different from
the coupon stream that is discounted for a long-term bond, and that also
can lead to differences in their prices. One difference relates to the
effect of inflation. An inflation shock would affect bond prices much
more than stock prices: Because the nominal value of the coupon is fixed,
an inflation shock would dampen the real value of the bond's coupon stream;
the nominal value of the stock dividend stream, in contrast, rises in
response to an inflation shock, leaving the real value of the dividend
stream fairly stable. Another difference relates to the sources of interest
rate changes. Suppose interest rates fall because the market gets information
that future economic activity, and therefore corporate profits, are going
to be on the low side. That information also would drive stock prices
down, because it would imply eventually lower dividends. The effect on
bond prices would be just the opposite: Bond prices would rise because
the fixed coupon stream is discounted at a lower rate. Thus, the relation
between stocks and bonds depends on what underlying economic variables
are driving asset prices.
A study by Shiller and Beltratti (1992) examines whether the observed
relation between changes in stock and long-term bond returns is consistent
with the implications of the present value model. Time-series econometric
methods were used to forecast future discount rates and future dividend
growth rates. The forecasted values of discount rates and dividend growth
rates are substituted into the present value model to infer the "theoretical"
prices for stocks and bonds if prices were set according to the present
value relationship. Using annual data for the U.S. during the period 1948
to 1989, they estimated that the present value model implies only a small
positive comovement between stock and bond returns. They found that the
theoretical correlation between stock and long-term bond returns under
the premise of the present value model is a mere 0.06. The low theoretical
correlation suggests that the discount rates for stocks and bonds do not
move in tandem, so neither do the expected future cashflows for stocks
and bonds. Interestingly, the observed correlation between stock and long-term
bond returns is 0.37--quite small in economic terms, but higher than what
the present value model implies.
One interpretation of this difference between the theoretical and observed
correlation is that the stock market "overreacts" to the bond
market, or vice versa. But an "overreaction" would imply that
there is something "irrational" in the behavior of financial
markets. Rather than asserting that the financial market exhibits irrational
behavior, an alternative interpretation is that a somewhat different approach
to implementing the present value model is needed. Specifically, one could
refine the methodology in order to look more closely at the forces that
drive stock and bond prices and their dynamics. Once these forces are
better identified, one can then study the relation between stocks and
bonds by appealing to the underlying economic forces.
Campbell and Ammer (1993) studied what moves stock and bond markets using
monthly data for the period 1952 to 1987. They focused on the excess returns
earned in holding stocks and bonds, that is, the returns over what would
have been earned if people had invested their money in a highly liquid,
virtually risk-free instrument like the one-month T-Bill. They recast
the present value model in a dynamic accounting framework and used time-series
econometric methods to break excess returns into components associated
with "news" about future cash flows, which refer to dividends
for stocks and coupons for bonds, and "news" about future discount
rates, which consist of the real interest rate, inflation expectations,
and the risk premiums for holding stocks or bonds. The term "news"
refers to surprises, or more formally, the unexpected component. This
method allows them to study the relative importance of the effects of
the different components on the historical behavior of individual asset
returns and, hence, the comovement between stocks and bonds.
Campbell and Ammer found that about 70 percent of the variance of excess
stock returns was attributable to the "news" about future risk
premiums for holding stocks and about 15 percent of the stock return variance
was attributable to "news" about future dividends; real interest
rates were found to play a relatively minor role in the variation of stock
returns, and inflation expectations even less of a role. (They found similar
results using raw returns, rather than excess returns.) It is interesting
to note that these results also suggest that U.S. stocks display "excess
volatility," in the sense that returns have a standard deviation
much greater than the standard deviation of news about future dividend
growth. However, it remains unclear what economic forces drive expected
future stock returns.
Regarding bonds, during the period 1952 to 1979, almost all the variation
in bond returns can be accounted for by news about future inflation. When
the data for the 1980s also were included, in addition to inflation news,
news about future risk premiums for holding bonds were equally important
in accounting for variations in bond returns. However, their findings
indicate that when investors learn that long-run inflation will be higher
than they expected, they also tend to learn that risk premiums for holding
bonds will be lower than they expected. (That is, news about future risk
premiums for holding bonds and news about future inflation are found to
be negatively correlated.) Therefore, the two types of news tend to have
offsetting effects on bond price variability because the capital loss
from higher expected inflation is partly offset by a capital gain from
lower expected future bond returns. As a result, the additional source
of variation due to future bond returns does not increase the overall
variation of long-term bond returns. Real interest rates again were found
to play a minor role in the variation in bond returns.
As for the comovement between stocks and bonds, while Campbell and Ammer
reported that stock and bond returns are always positively correlated,
the correlation was tiny--only 0.082 for the period 1952 to 1972, increasing
to 0.26 for the period 1973 to 1987. Over the full sample, the two asset
returns had a modest positive correlation of 0.20. The low correlation
is due to the balance among several offsetting factors. First, stock and
bond returns tend to move in opposite directions when expected future
inflation varies. An increase in long-run expected inflation is bad news
for the bond market but good news for the stock market. This effect by
itself would lead to large negative comovement between bond and stock
returns. Second, during the period 1973 to 1987, real interest rate changes
tended to result in stock and bond returns moving in the same direction.
Third, stock and bond returns move in the same direction when expected
future risk premiums for holding stocks and bonds change. This effect
by itself would lead to a large positive comovement between stock and
bond returns. Combining all three effects accounts for the small positive
correlation between stock and bond returns. The correlation increases
from the earlier time period to the later one when the real interest rate
and expected future asset return effects become stronger relative to the
inflation effect.
It is far from clear how stock and bond prices move together. The present
value model suggests that by holding other things constant, a change in
the discount rate for both stocks and bonds would result in a positive
comovement between these long-term assets. However, other things are not
constant: As Shiller and Beltratti showed, the theoretical correlation
between stock and bond returns under the present value relationship should
be only slightly positive. Campbell and Ammer also found that the correlation
between stock returns and bond returns in general is small, but it seems
to be increasing over time. In distinguishing more asset return components
than do Shiller and Beltratti, they were able to explain the modest correlation
between stock and bond returns, as well as why the observed correlation
is increasing over time. Depending on what underlying economic forces
are driving asset prices, stocks and bonds may or may not move in synchronization.
Investors should be mindful of the time-varying comovement between stocks
and bonds in implementing their investment strategies. Nevertheless, there
are still a lot of unanswered questions about which economic forces are
driving asset returns at what time. The next Economic Letterwill
discuss the relation between stocks and bonds at the microeconomic level,
that is, the comovement between individual stocks and bonds that are issued
by the same firm.
Simon Kwan
Economist
Campbell, John Y., and John Ammer. 1993. "What Moves the Stock and
Bond Markets? A Variance Decomposition for Long-Term Asset Returns."
Journal of Finance48, pp. 3-37.
Shiller, Robert J., and Andrea E. Beltratti. 1992. "Stock Prices
and Bond Yields - Can their Comovements be Explained in Terms of Present
Value Models?" Journal of Monetary Economics30, pp. 25-46.
Opinions expressed in this newsletter do not necessarily reflect
the views of the management of the Federal Reserve Bank of San Francisco,
or of the Board of Governors of the Federal Reserve System. Editorial
comments may be addressed to the editor or to the author. Mail comments
to
Research Department
Federal Reserve Bank of San Francisco
P.O. Box 7702
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