Matched-long term maturity stock and bond returns in international markets.

Cakici, Nusret ; Kellman, Mitchell ; Kraizberg, Elli 等

1. Introduction

Most studies in Finance employ ex-post bond and stock returns to analyze two different, though interrelated, issues. The first issue focuses on the driving forces, underlying stock and bond realized returns and is based on the assumption that bond and stock returns are driven by some specific underlying process. Then, given the underlying process, the ex-ante expected returns could be derived. The second issue is related to the notion of equilibrium in ex-ante or expected returns, based on market required risk premium, irrespective of a particular underlying process. Specifically, equilibrium models demonstrate that market risk premium should be a positive linear function of conditional market variance (CAPM) or that inter-temporal variation in the market risk premium can be explained by time-varying co-variances with priced risk factors (Merton's ICAPM 1973). In this context, long term government bond returns serve as a key variable in setting risk premium, and as suggested by Merton, serve as a proxy for s hifts in the investment opportunity set.

A link between these two issues could be the assumption that stocks and bonds rates of return follow a random walk. More specifically, one, who uses the actual ex-post rates of returns and the expost parameters of the process that drives these returns in order to derive an ex-ante model, must make a set of restrictive assumptions, such as that the coefficient of relative risk aversion is inter-temporally constant, and the conditional second moments are time-varying; and that realized simple excess returns on stock and bond portfolios are unbiased proxies for the unobserved time-varying risk premia (See Scruggs and Glabadanidis (2001) for a summary of these conditions).

This paper focuses on the first issue. Initially, starting in the late seventies the research objective that has been related to this issue was the negative relationship found between stock and bond returns (e.g. Bodie (1976), Jaffe and Mandelker (1976), Nelson (1976), Fama and Schwert (1977), Breen, Glosten, and Jagannathan (1989), Ferson (1989), and Campbell and Ammer (1993)). Fama (1981) argued that such negative correlations are merely spurious. Shiller (1982) in an intuitive model of time varying discount rates implied that the returns on bonds should co-vary positively with stock returns, since both of these competing assets are driven by a common underlying discount factor. Furthermore, a rational expectations explanation according to which movements in long-term interest rates might be related to information about the future dividend stream on stocks might also provide a theoretical explanation countering the negative relationship between stock prices and bond yields on stocks. This could happen if a n increase in long term interest rates is interpreted as resulting from positive information about the outlook for corporate profits (Shiller and Beltratti 1992, p 26.).

The second issue, mentioned above was extensively analyzed as well. (1) The theoretical answer to the second issue is obviously that, ex-ante, one should observe a positive risk-return relationship or a positive relation between the market risk premium and time-varying market volatility. Most studies, however, have reported a non-positive ex-post relationship.

In the late eighties these issues were generalized a bit. Studies that employed long-term government bond returns, as a risk factor, managed to explain cross-sectional variation in portfolio risk premia (See Chen, Roll and Ross (1986), Shanken (1990), Keim and Stambaugh (1986), Campbell (1987), and Fama and French (1989)). At the same time, focusing on the second issue, specified above, new intertemporal models, allowing time-varying risk premia, managed to explain the predictable variation in stock and bonds excess returns (See Bolleerslev, Engle, and Wooldrige (1988), Harvey (1989), Ng (1991), Bodurtha and Mark (1991), Chen Karolyi and Stulz (1992) and Evans (1994). Harrison and Zhang (1999) aiming to analyze the second issue (ex-ante intertemoral equilibrium) found an ex-post significant positive risk and return relationship at long holding intervals. This finding supports the finding of Campbell and Hentschel (1992). However, most studies found the opposite relationship (See Fama and Schwert (1977), Camp bell (1987), Breen, Glosten, and Jagannathan (1989), Glosten, Jagannathan, and Runkle (1993), and Bekert and Wu (2000)). Scruggs and Glabadanidis (2001) find that conditional bond variance responds symmetrically to bond return shocks but is virtually unaffected by stock return shocks, while conditional stock variance responds asymmetrically to both stock and bond return shocks. Additionally, they argue that models which impose a constant correlation restriction on the covariance matrix between stock and bond returns are strongly rejected.

In the nineties, following Fama and French (1989) and Fama and French (1996) the first issue in its original version has returned to attract attention. They found that many interest rate-related instrumental variables (e.g., term spreads, quality spreads, short-term T-Bill yields, etc.) have forecasting power for time series of stock and bond returns. Hence, these support the hypothesis that stock returns do not follow a pure random walk process. Further support for returns not following a pure random walk is offered by Fleming and Remolona (1997), Glare and Thomas(1992), Campbell and Hamao (1989), and Keim and Stambaugh (1986). Aburachis and Kish (1999) offer additional support for the view that stock and bond returns do not follow a pure random walk. They quantify the relationship between stock returns and bond yields for nine industrial countries during the period 1984-1994.

This paper, Aburachis and Kish (1999) and Harrison and Zhang (1999), provides several innovations:

(i) It is more appropriate to compare bond and stock return which are affected by the same source of uncertainty, and therefore the paper carefully match the stock return horizons with the bond yields. (2) This study provides an analysis of co-movement of the volatilities of bond and stock returns as well. The results clearly demonstrate that the volatility of long term real stock returns is closely related to the volatility of long term real bond yields.

(ii) This study tests these relationships for 16 countries and finds that the results applicable to the US are supported in each single market analyzed.

(iii) This study finds that the sensitivity of the real stock returns to bond returns is negatively related to the average rate of inflation and the coefficient of variation for the inflation variable.

The main results of the paper are summarized as follows. First, we find a strong positive relationship between long term real bond returns and matchedmaturity bond yields for every country in our sample. Second, the volatility of long term real stock returns is closely related to the volatility of long term real bond yields. Third, the sensitivity of the real stock returns to bond returns is negatively related to the average rate of inflation and the coefficient of variation for the inflation variable.

The rest of the paper is organized as follows. The next section describes the data. The empirical estimation and the results are explained in section 3. Section 4 analyzes cross-sectional variation of the betas. The summary and conclusion are provided in Section 5.

2. The Data

We utilize monthly observations on stock market indices for the 16 countries for which reasonably complete coverage is available. The stock market price index used is International Monetary Fund's International Financial Statistics (IFS) Series 62. These indices relate to common shares of companies traded on national or overseas stock exchanges. Monthly indices are obtained as simple arithmetic averages of the daily or weekly indices, although in some cases, mid-month or end-of-month quotations are included. All reported indices are adjusted for changes in quoted nominal capital of companies. In general, these indices are base-weighted arithmetic averages with market values of outstanding shares as weights. The coverage is very broad in each of the country markets. For example, the series for Germany refers to the average of daily quotations covering approximately 95 percent of common shares of industrial companies with headquarters in Germany. The period covered is from January 1957 to July 1997--a total of 487 observations. The long-term interest rate series was IFS Series 61--Long-Term Government Bond Yield. In most cases, this is the 10 year yield though sometimes the maturity is not defined. For our purposes, this variable is assumed to be the 10-year yield. The consumer price index used CPI values from IFS series 64.

3. The Empirical Estimation (3)

We estimated the following equation:

[r.sub.t,t+n] = [alpha] + [beta][y.sub.t,t+n] + [u.sub.t] (1)

where [r.sub.t.t+n] is the ex post continuously compounded real return to holding stock from time t to time t+n, [y.sub.t,t+n] is the continuously compounded real return to holding an n-period bond from t to t+n, and [u.sub.t,t+n] is a stochastic innovation in the stock return. If the excess-returns hypothesis is true, then, [beta] = 1. The results are given below in Table 1.

First, considering that we used a different data source than did Zhou (1998), and examined a somewhat different time period (our data end in July 1997), and tested a longer maturity time-horizon, the results obtained for the United States are notably (if not remarkably) similar to his. Our 10-year maturity results for the U.S. (a coefficient of 1.34) is almost identical to Zhou's 3 year coefficient (Zhou Table 4, page 19). Substantively, our findings strongly support his findings of a clearly significantly positive relationship between long term returns in the stock and bond markets for the United States.

Second, we find the same (significantly positive) relationship to apply in the case of each and every of the sixteen countries tested. We thus find broad, international support for the proposition that over long time periods, when maturities are properly accounted for, a positive relationship is found between the returns of holding stocks, and those obtained from owning (similarly long term) debt. As noted earlier, this finding supports Fama's (1981) observation dismissing the commonly found negative relationships as spurious. It further indirectly supports the proposition forwarded by Zhou (1988) that the source of the spurious negative correlations is a misspecification resulting from a failure to match maturities.

Third, the volatility of long term real stock returns is closely related to the volatility of the long-term real bond yields. This result is very important because it indicates that the fluctuations of long term real stock returns are related to real variables such as long-term real bond yields in the economy. For the U.S., [R.sup.2] is 0.70, which says that 70% of the fluctuations in long term real stock returns can be explained by the fluctuations in long term real bond yields. The average [R.sup.2] for all countries is 0.43.

The More Recent Period

It may be argued a priori that when one includes other stock markets in the analysis, some of which are relatively smaller in size, the time period covered in our analysis (1957-1997) does not constitute a stationary state. This is because in the period preceding the 1980s, many institutional differences characterized the operations of these markets. In particular, the fixed foreign exchange rate regime of the pre-1973 period involved quite different risk elements (and hence different risk premia) due to the prevalence of the large exchange disequilibria (and hence "crises") which typified this earlier period. Perhaps more critical is the fact that most pre1980 asset markets outside those of the United States and United Kingdom included relatively effective restrictions on foreign exchange, foreign ownership, and on short sales.

It was only from the early 1980s that powerful liberalization swept most markets, creating a more global environment in the world capital markets. It is therefore interesting to inquire whether the positive correlations summarized in Table 1 above apply to the more homogeneous period of the 1980s and 1990s. Equation [1] was therefore reestimated for data restricted to the period January 1980-July 1997. The results are in Table 2 below.

The results summarized in Table 2 support the robustness of the original results. In each of the sixteen countries, the relationship between stock and bond returns was found to be significantly positive. On the average, the size of the beta coefficient decreased from an average of 1.36 for the original longer period coverage, to 1.20 for the more recent subperiod summarized in Table 2.

4. A Cross-Section Analysis

In order to further analyze the relationship between the long term real stock returns and the long term real bond yields for each country, we calculate the average long term real stock returns and bond returns. Then we estimate the following regression:

[r.sub.i] = [alpha] + [beta][y.sub.i] + [u.sub.i] (2)

where [r.sub.i] and [y.sub.i] are the average real stock return and the average long term real bond yield for country i, respectively, and [u.sub.i] is a random error term. The results are presented in Table 3. The beta coefficient for the full sample is 1.09, and for the subperiod it is 0.90. Based on these results we cannot reject the hypothesis that there is a one-to-one relationship between the long term real stock returns and the long term real bond yields.

Though all of the relevant betas in Tables 1 and 2 are significantly positive in all sixteen national markets, they tend to exhibit a somewhat broad dispersion. In Table 2, these values range from a minimum of (still significantly positive) 0.21 for Korea to a maximum of 3.73 for Austria. (4) This raises an interesting question: what country characteristics are associated with relatively high (or alternatively low) values for beta? In other words, what country characteristics affect the responsiveness of long-horizon stock returns to changes in long-maturity bond yields? As noted, it is precisely this relationship that has been the center of a major controversy over the past several years in the finance literature. The great majority of studies in this area depend solely on time series relationships. It is for this reason that the following cross country analysis is of special interest.

The hypothesis we explore is that the investing public will tend to be more sensitive to changes in real bond returns, the lower is the rate of inflation and the lower is the degree of fluctuation or variability in inflation. The logic underlying these propositions is straightforward. An investor living in an environment of high and highly variable rates of inflation will come to expect rapid changes in real rates of return on debt instruments (and will incorporate premiums for this increased level of uncertainty). In such a circumstance, a relatively larger change in real interest would be required to elicit a given change (in the same direction) in required real stock returns. In terms of our estimated model, such a situation would be characterized by a smaller beta.

A cursory examination of Table 4 below indicates that the values of the betas are indeed inversely associated with the mean inflation experience of each country. For example, countries like Pakistan, Italy, Spain and Korea, which have experienced the highest mean inflation rates in the sample, also have some of the smaller betas. On the other hand, countries with relatively low mean inflation rates, such as Germany, Japan, and the Netherlands, have large betas. In short, the countries which tended to experience higher rates of inflation tended to demonstrate lower levels of (real) stock return sensitivity to long-term bond rates. This intuitive negative relationship is clearly illustrated by the scatter diagram in Figure 1. This supports our hypothesis, though there are clearly other possible explanations for this finding. (5) It is of interest to note that no obvious outliers appear in the scatter diagram. This would suggest that the inflation sensitivity of stockbond return patterns is not systematically di fferent in high versus low inflation countries, or in rich industrialized versus poor developing countries.

In order to examine whether both difference in country rates of inflation, and the degree of variability within each country around the mean inflation experience might (both) lead to country differences in the propensity of share gains to react to long-term debt rates, the following regression model was estimated:

[[beta].sub.i] = [b.sub.0] + [b.sub.1][[pi].sub.i] + [b.sub.2][CV.sub.1] + [u.sub.i] (3)

where [[beta].sub.i] is the regression coefficient for country i from Table 2, [[pi].sub.i] is the average rate of inflation, [CV.sub.i], is the coefficient of variation for the inflation and [u.sub.i] is a random error term. The results are reported in Table 5. The results support the hypothesis and shed an interesting light on the issue of the relationship between stock and bond returns over long-term horizons. Both mean country inflation and the coefficient of variation of country inflation have a significantly negative regression coefficient. That indicates that in the context of this regression model, long-horizon stock returns tend to react to a greater extent to a given change in long-term bond returns in those countries with lower rates of inflation, and in countries in which the annual rates of inflation tend to be relatively stable over time. This last finding is in agreement with the existence of hysteresis in the expectation pattern of investors such that any change in the inflation trend is viewed with some surprise, representing news which casts doubt on the information content of observed ex-post bond returns, and therefore leading to a smaller response in the stock market.

5. Conclusion

In this paper we empirically examine the relationship between real stock returns and matched-maturity long term bond yields for 16 countries. Our findings can be summed up as follows. First, there is a strong positive correlation between real stock returns and corresponding matched-maturity long term bond returns for every country in the sample. Second, the findings indicate that the volatility of long term real stock returns is closely related to the volatility of long term real bond yields. Finally, an additional cross-sectional analysis indicated that the sensitivity of real stock returns to real bond yields in each country is negatively related to the average rate of inflation and the coefficient of variation of these inflation rates.

We believe these results are quite interesting since the conventional wisdom in this field, supported by most previous studies using short term stock returns and bond yields, find a negative relationship.

TABLE 1

The Ex-Post Relation beween Real Stock Returns and Real Bond Yields
(1957-1997)

Regressions of ten-year real stock returns on matched-maturity real bond
yields: [r.sub.t,t+n] = [alpha] + [beta][y.sub.t,t+n] + [u.sub.t] where
[r.sub.t,t+n] is the ten-year real stock returns, [y.sub.t,t+n] is the
ten-year bond returns, and [u.sub.t] is is a random error term. Standard
errors and t-statistics are reported in parenthesis () and [],
respectively. They have been computed using the Newey-West (1987)
adjustment procedure.

Country [beta] [R.sup.2]

Average 1.36 0.43
United States 1.34 (0.103) [12.96] 0.70
Austria 3.73 (0.243) [15.35] 0.68
Canada 0.41 (0.094) [4.42] 0.19
Denmark 0.52 (0.124) [4.18] 0.25
France 1.34 (0.059) [22.79] 0.64
Germany 1.98 (0.338) [5.86] 0.40
Italy 0.86 (0.115) [7.51] 0.26
Japan 1.02 (0.130) [7.88] 0.25
Korea 0.21 (0.121) [1.76] 0.08
Netherlands 2.20 (0.121) [18.12] 0.85
Norway 1.56 (0.110) [14.19] 0.64
Pakistan 0.90 (0.105) [8.56] 0.35
Spain 0.31 (0.147) [2.08] 0.07
Sweden 1.17 (0.166) [7.06] 0.30
Switzerland 2.86 (0.501) [5.70] 0.35
United Kingdom 1.42 (0.062) [22.98] 0.83

TABLE 2

The Ex-Post Relation between Real Stock Returns and Real Bond Yields
(1980-1997)

Regressions of ten-year real stock returns on matched-maturity real bond
yields: [r.sub.t,t+n] = [alpha] + [beta][y.sub.t,t+n] + [u.sub.t] where
[r.sub.t,t+n] is the ten-year real stock returns, [y.sub.t,t+n] is the
ten-year bond returns, and [u.sub.t] is a random error term. Standard
errors and t-statistics are reported in parenthesis () and [],
respectively. They have been computed using the Newey-West (1987)
adjustment procedure.

Country [beta] [R.sup.2]

Average 1.20 0.38
United States 1.20 (0.098) [12.24] 0.76
Austria 3.73 (0.243) [15.35] 0.68
Canada 0.24 (0.098) [2.45] 0.12
Denmark 0.38 (0.146) [2.59] 0.14
France 1.13 (0.111) [10.20] 0.61
Germany 1.98 (0.338) [5.86] 0.40
Italy 0.59 (0.112) [5.25] 0.22
Japan 1.16 (0.168) [6.89] 0.22
Korea 0.21 (0.121) [1.76] 0.08
Netherlands 2.34 (0.166) [14.13] 0.82
Norway 1.34 (0.142) [9.41] 0.60
Pakistan 0.77 (0.144) [5.31] 0.22
Spain 0.31 (0.147) [2.08] 0.07
Sweden 0.72 (0.160) [4.48] 0.22
Switzerland 1.95 (0.944) [2.07] 0.10
United Kingdom 1.29 (0.053) [24.38] 0.87

TABLE 3

Cross-sectional relationship between the average real stock returns and
average real bond yields

Regression of the average long term real stock returns on the average
long term real bond yields: [r.sub.t] = [alpha] + [beta][y.sub.t] +
[u.sub.t], where [r.sub.t] and [y.sub.t] is the average long term real
stock return and the average long term real bond yield for country i,
respectively, and [u.sub.t] is a random error term. Standard errors and
t-statistics are reported in parenthesis () and [], respectively. They
have been computed using the Newey-West (1987) adjustment procedure.

Sample Period: 1957-1997

[alpha] [beta] [R.sup.2]

 -0.62 1.09
 (0.53) (0.07) 0.70
[-1.16] [15.39]

Sample Period: 1980-1997

[alpha] [beta] [R.sup.2]

 0.85 0.90
 (0.71) (0.11) 0.52
 [1.19] [8.19]

TABLE 4

The betas, mean inflation and the coefficient of variation of inflation
rates for 16 countries 1980-1996

The betas are from Table 2. The mean inflation rates, and the
coefficients of variantion were calculated from annual CPI values from
IFS Series 62. *

 Mean Coefficient
 Inflation of for
Country beta rate inflation

United States 1.20 4.12 48.34
Austria 3.73 3.33 45.63
Canada 0.24 4.54 70.91
Denmark 0.39 4.46 67.10
France 1.13 4.80 78.38
Germany 1.98 2.85 63.06
Italy 0.59 7.89 57.83
Japan 1.16 1.73 79.05
Korea 0.07 6.25 72.98
Netherlands 2.34 2.52 74.09
Norway 1.34 5.62 64.61
Pakistan 0.77 8.51 33.88
Spain 0.31 7.68 46.72
Sweden 0.72 6.10 55.10
Switzerland 1.95 3.18 59.40
United Kingdom 1.29 5.34 53.23

* Though the betas were calculated from monthly data, they reflect
annualized returns on stocks and bonds. It was felt that for the cross
section analysis, the use of annual inflation data would better avoid
white noise and therefore would most clearly differentiate the countries
in terms of the underlying inflation trend, and the degree of inter-year
variability around this trend.

TABLE 5

Cross-sectional relationship between the betas and inflation statistics

Regression of te betas on the average inflation rate and the coefficient
of variation for the inflation: [beta] = [b.sub.0] + [b.sub.1]
[[pi].sub.i] + [b.sub.2] [CV.sub.i] + [u.sub.i] where [beta].sub.i] is
the regression coefficient for country i from Table 2, [[pi].sub.i], is
the average rate of inflation, [CV.sub.1] is the coefficient of
variation for the inflation. and [u.sub.i] is a random error term.
Standard errors, and t-statistics are reported in parenthesis () and [],
respectively. They have been computed using the Newey-West (1987)
adjustment procedure.

Sample Period: 1980-1997

[b.sub.0] [b.sub.1] [b.sub.2] [R.sup.2]

 5.81 -0.415 -0.042
(1.38) (0.10) (0.017) 0.53
[4.21] [-4.30] [-2.541

Notes

(1.) Campbell (1987), French, Schwert and Stambaugh (1987), Harvey (1989), Turner, Startz and Nelson (1989), Pagan and Hong (1989), Baillie and DeGennaro (1990), Nelson (1991), Campbell and Hentschel (1992), and Glosten, Jagannathan and Runkle (1993), Whitelaw (1994), Chauvet and Potter (1998), Mayfield (1999), and Whitelaw (2000).

(2.) A similar approach was exercised by Zhou in the late i 990s and produced comparable results for the United States. Unfortunately, efforts to get his permission for citation were unsuccessful.

(3.) The theoretical underpinnings of this specification, and its relationship to the excess returns hypothesis are in Zhou (1998).

(4.) Though country specific (probably asset market institutional) factors are reflected in a range of betas, it is notable that the cross sectional average of the betas was very close to unity (1.20). Since such an average abstracts from the country institutional peculiarities, it may be seen as supporting Zhou's excess-returns hypothesis.

(5.) For example, it may be that the full effects of expected inflation are not completely or satisfactorily being accounted for in the calculation of "real" values. This could happen, for example, because of the use of an improper price deflator (in our case, CPI).

References

Aburachis, A. T. and Richard J. Kish, "International Evidence on the Co-Movements Between Bond Yields and Stock Returns: 1984-1994" Journal of Financial and Strategic Decisions, Volume 12 Number 2 Fall 1999 pp. 1-41.

Baillie, R. T. and R. P. DeGennaro. "Stock Returns and Volatility." Journal of Financial and Quantitative Analysis, 25, (1990), 203-214.

Balvers, R., Cosimano, T. and B. McDonald, "Predicting Stock Returns in an Efficient Market," Journal of Finance 45(4), 1990, pp. 1109-1128.

Bekaert, G. and G. Wu. "Asymmetric Volatility and Risk in Equity Markets." Review of Financial Studies, 13 (2000), 1-41.

Black, F. (1992), "Estimating expected returns," Financial Analysts Journal, 49, 36-38.

Bossserts P. and P. Hillion, (1999), "Implementing statistical criteria to select return forecasting models: what do we learn?," Review of Financial Studies, 12 (2), 405-428.

Bodie, Z. (1976), "Common stocks as a hedge against inflation," Journal of Finance 31, 459-470.

Breen, W., L. R. Glosten, and R. Jagannatban (1989), "Economic Significance of predictable variations in stock market returns," Journal of Finance 44, 1177-1190

Campbell, J. Y. "Stock Returns and the Term Structure." Journal of Financial Economics, 18 (1987), 373-399.

Campbell, John Y. and John Ammer, "What Moves the Stock and Bond Markets? A Variance Decomposition for Long-term of Present Value Models," Journal of Monetary Economics 30, 1992, pp. 25-46.

Campbell, John Y. and Yasushi Hamao, "Predictable Bond and Stock Returns in the United States and Japan: A Study of Long-Term Capital Market Integration," Journal of Finance 47(1), 1989, pp. 43-70.

Campbell, J. Y and N. G. Mankiw, "Permanent and Transitory Components in Macroeconomic Fluctuations," American Economic Review 77, 1987, pp. 111-117.

Chauvet, M. and S. Potter. "Nonlinear Risk." Working paper, University of California, Riverside (1998).

Clare, A. D. and S. H. Thomas, "International Evidence for the Predictability of Bond and Stock Returns," Economic Letters 40, 1992, pp. 105-112.

Cremers, M. (2000), "Stock return predictability: A Bayesian model selection perspective," NYU Stern Business School, Working Paper.

Evans, M. D. D. "Expected Returns, Time-Varying Risk, and Risk Premia" Journal of Finance, 49 (1994), 655-679.

Fama, E. F. and K. R. French. "Dividend Yields and Expected Stock Returns." Journal of Financial Economics, 22 (1988), 3-25.

Fama, E. F. and K. R. French. "Business Conditions and Expected Returns on Stocks and Bonds." Journal of Financial Economics, 25 (1989), 23-49.

Fama, E. F. and K. R. French. "Common Risk Factors in the Returns on Stocks and Bonds." Journal of Financial Economics, 33 (1993), 3-56.

Fama, E. F., and J. MacBeth, (1973), "Risk, return, and equilibrium: Empirical tests," Journal of Political Economy 81, 607-636

Fama, E. F. and G. W. Schwert. "Asset Returns and Inflation." Journal of Financial Economics, 5 (1977), 115-146.

Ferson, W. and C. Harvey, "The Risk and Predictability of International Equity Returns," Review of Financial Studies 6(3), 1993, pp. 527-566.

Ferson, W. and C. Harvey, "Sources of Predictability in Portfolio Returns," Financial Analysts Journal 47(3), 1991, pp. 49-56.

Fleming, Michael J. and Eli M. Remolona, "What Moves the Bond Market?" Economic Policy Review 3(4), 1997, pp. 3 1-50.

French, K. R., G. W. Schwert and R. F. Stambaugh. "Expected Stock Returns and Volatility." Journal of Financial Economics, 19 (1987), 3-29.

Glosten, L. R., R. Jagannathan, and D. E. Runkle. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks." Journal of Finance, 48 (1993), 1779-1801.

Goetzmann, William N. and Jorion Philippe, "Testing the Predictive Power of Dividend Yields," Journal of Finance 48(2), 1993, pp. 663-679.

Harrison, P. and H. H. Zhang. "An Investigation of the Risk and Return Relation at Long Horizons." Review of Economics and Statistics, 81 (1999), 399-408.

Jaffe, J., and G. Mandelker (1976), "The Fisher Effect for risky assets: An empirical investigation," Journal of Finance 31, 447-458

Jegadeesh, N, "Evidence of Predictable Behavior of Security Returns," Journal of Finance 45(3), 1990, pp. 881-898.

Keim, Donald B. and Robert F. Stambaugh, "Predicting Returns in the Stock and Bond Markets," Journal of Financial Economics 17, 1986, pp. 357-390.

Lo, A. and A. MacKinlay, "Stock Prices Do Not Follow Random Walk," Review of Financial Studies 1(1), 1988, pp. 41-66.

Merton, R. C. "An Intertemporal Asset Pricing Model." Econometrica 41 (1973), 867-887.

Nelson, D. B. "Conditional Heteroskedasticity in Asset Returns: A New Approach." Econometrica, 59 (1991), 347-370.

Nelson, C. (1976), "Inflation and rates of return on common stock," Journal of Finance 31, 471-483.

Scruggs J. T. and P. Glabadanidis, "Risk Premia and the Dynamic Covariance Between Stock and Bond Returns" Working paper, Washington University in St. Louis John M. Olin School of Business (1999).

Shiller, R. J. (1982), "Consumption, asset markets, and macroeconomic fluctuations," Carnegie Rochester Conference Series on Public Policy 17, 203-238.

Shiller, R. and A. Beltratti "Stock prices and bond yields," Journal of Monetary Economics 30, 25-46.

Veronesi, P. "How Does Information Quality Affect Stock Returns?" Journal of Finance, 55 (2000), 807-837.

Wainscott, Craig B., "The Stock-Bond Correlation and Its Implications for Asset Allocation," Financial Analysts Journal July-August 1990, pp. 55-60.

Whitelaw, R. F. "Stock Market Risk and Return: An Equilibrium Approach." Review of Financial Studies, 13 (2000), 521-547.

Nusret Cakici *, Mitchell Kellman **, and Elli Kraizberg ***

The authors are Professors in the Economics Department at CCNY, and the Graduate Center of CUNY *,** and Bar Ilan University ***. We wish to thank the Schwager Fund for assistance. Please address all correspondence to: Prof. Mitchell Kellman, Department of Economics, The City College and Graduate Center of the City University of New York, Convent Ave. at 138th Street, New York, NY 10031. Tel: (212) 650-6203. E-mail: tiger998@hotmail.com