1996-19

June 28, 1996

On the Relation between Stocks and Bonds – Part I

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

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.

What moves stocks and bonds?

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.

Conclusion

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

References

Campbell, John Y., and John Ammer. 1993. “What Moves the Stock and Bond Markets? A Variance Decomposition for Long-Term Asset Returns.” Journal of Finance 48, 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 Economics 30, pp. 25-46.

Opinions expressed in FRBSF Economic Letter 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. This publication is edited by Sam Zuckerman and Anita Todd. Permission to reprint must be obtained in writing.

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