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).
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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