Page 1
A Critical Analysis of the Impact of Macroeconomic Conditions on the
Relationship between Stock and Bond Returns: An Empirical Study
Module: Finance Research Methods
Group Members: Tian Liu (1402592)
Seki Park (1402997)
Josselin Williams (1403248)
Albert Wilson (1204785)
Date: June 5, 2015
Page 2
Abstract
This study investigates the relationship between stock and bond returns with evidence from the
UK market. As this relationship is influenced by macroeconomic factors, this study also included
the influence of GDP growth, expected inflation, changes in the money supply, and changes in
sovereign bond yields. The paper finds that there is a positive correlation between bond and
stock returns. Furthermore, GDP has a positive impact on stock returns, but not on bond returns.
Also, changes in the money supply does not influence stock and bond returns. In addition,
expected inflation negatively influences bond returns but do not influence stock returns. Finally,
changes in sovereign bond yields have an influence on stock returns but not on bond returns. Our
results are similar to previous studies.
1.0 Introduction
Understanding the intrinsic relationship amongst financial assets is critical when implementing
effective investment strategies. One particular relationship that has been a focal point for finance
literature for years is the relationship between the returns of stocks and bonds. The general
consensus is that there is an inverse relationship between the returns of stocks and bonds which
is subject to the influence of macroeconomic factors such as economic growth, expected
inflation, and the money supply. Implicit in this notion is the tendency of investors to adjust their
asset allocations, relative to stocks and bonds, based on macroeconomic and microeconomic
conditions. Given the dynamic nature of macroeconomic factors, the relationship between stocks
and bonds remains ambiguous.
This paper critically analyses the impact of macroeconomic conditions on the relationship
between stocks and bonds. The remainder of this paper is divided into four sections. Section two
reviews of the existing literature regarding the relationship between stocks and bonds. Section
three explains the data and section four presents the methodology used in this study. In section
five, the findings are presented. Section six offers a brief conclusion and a discussion.
Page 3
2.0 Literature Review
The intrinsic relationship between stock and bond returns was first examined by Benjamin
Graham in The Intelligent Investor, published in the 1950’s, who concluded that stock and bond
returns are negatively correlated (Barksby, 1989). However, Graham’s analysis lacked empirical
support (Barksby, 1989). Markowitz (1952), in his theory on Portfolio Selection, confirmed that
assets returns are fundamentally correlated. This discovery induced a new field of enquiry into
the causal relationship between stock and bond returns.
In analysing the variability of stock prices, Shiller (1982) concluded that there is no
significant correlation between stock and bond prices. However, his analysis was limited due to
insufficient data. As such, Shiller’s conclusion (1982) was challenged by Summers (1983) who
analysed the relationship between the interest rate and the stock market during 1973 - 1980.
Summers (1983) suggested that there is a negative correlation between stock and bond prices
subject to interest rates. In other words, lower interest rates induce an increase in bond prices and
an associated decline in stock prices.
According to Barksby (1989), the relationship between stocks and bonds is determined
by macroeconomic conditions such as productivity growth and market risk, which ultimately
influence the profits of firms and the real interest rate. As such, Barksby concurs that bonds and
stocks are negatively correlated. This concept was further augmented by Gulko (2002) who
concluded that financial distress also affects the relationship between stock and bond returns. Li
(2002) examined the effects of inflation and the real interest rate on the relationship between
bond and stock returns and concluded that uncertainty regarding long-term expected inflation
causes significant negative correlation between bond and stock returns. Andersson et al (2008)
concluded that the relationship between bond and stock returns varies over time, subject to
uncertainty. This gave credence to the notion of a dynamic relationship between stock and bond
returns, which explains why understanding this particular asset relationship remains elusive.
This discussion accentuates the significance of macroeconomic factors on the relationship
between stock and bond returns.
Page 4
3.0 Data
3.1 Variable Selection
Based the above discussion, the three primary variables observed in this study are GDP, expected
inflation, and the money supply (M4). Needless to say, this set of variables are not
comprehensive as there are other macroeconomic factors such as unemployment and savings and
investment which may also influence the relationship between the returns of stocks and bonds.
The intuition for using GDP to test the relationship between the returns of stocks and
bonds is that both stock and bond returns are influenced by GDP. Relative to stocks, changes in
stock prices reflect the expectations of investors regarding future corporate earnings, which is
influenced by economic growth. Bond yields are also affected by GDP as economic growth
influences the demand for corporate bonds and the equilibrium between the supply and demand
for corporate bonds determines the bond yield. In this study, UK GPD growth is used which was
calculated by dividing the difference of the total GDP at market prices for each quarter, as shown
in the following formula:
GDP Growth = ln(GDPt/ GDPt-1).
Furthermore, expected inflation (CPI) is also used to examine the relationship between
the returns of stocks and bonds. There is a general consensus that expected inflation impacts the
returns of stocks either positively or negatively. Relative to bonds, rising inflation depletes the
real rate of interest, which is significant because nominal interest rates are usually fixed upon
issue. In this study, expected inflation is assumed to be equal to the prevailing rate for simplicity.
Since the data collected was non-stationary, the difference in the inflation for each month was
calculated using the following formula:
Inflation Rate = ln(Inflation Ratet/ Inflation Ratet-1).
In addition, the money supply is also presumed to influence the relationship between
stocks and bonds. In a general equilibrium analysis, an increase in the money supply should
increase consumption and consequentially increase savings and investment. However, financial
intermediation can impede an increase in the money supply as banks may simply increase their
reserves following injections of money by central banks (Joyce, et al., 2012). As such, the
Page 5
optimum indicator for the money supply is M4 which the most comprehensive measure of the
money supply and includes the following: notes and coins, short and long-term deposits, bonds
and similar instruments, claims from repos, and estimated holdings of sterling bank bills
(Hussain and Gilhooly, 2010). Similar to inflation, since the data collected was non-stationary,
the difference in M4 for each month was calculated using the following formula:
M4 = ln(M4t / M4t-1).
To account for the preferences of investors relative to the yield curve, this study also
analyses the effect of the risk-free rate on the relationship between the returns of stocks and
bonds. This study uses the yield of 3-Month or 90-Day Sovereign Bonds traded in the UK. Since
the data collected was the annual yield, it had to be adjusted to a monthly yield in order to be
used in our analysis. The data was also non-stationary, so the difference in the sovereign bond
yields for each month was calculated using the following formula:
Yield = ln(Yieldt/ Yieldt-1).
3.2 Sample
The sample for stocks and bonds is based on the UK corporate securities market. Relative to
stocks, the data was obtained from an index produced by Reuters, which included all UK traded
shares. As for bonds, the data was obtained from an index produced by iBoxx, which contained
all UK traded corporate bonds of all maturities. To make the data stationary, the following
formula was used:
Return = ln(Pricet/ Pricet-1).
All data in this study are collected using DataStream from a number of sources including
the Office for National Statistics, the OECD, Reuters, and iBoxx. The time period observed in
this study is May 2000 - May 2015, which is selected to account for the recession in 2008.
4.0 Methodology
In testing the relationship between the returns of stocks and bonds, we employed multiple linear
regressions supplemented with descriptive statistics, mean comparison, and correlation tests.
Page 6
First, a primary analysis was conducted where we tested the impact of stock and bond
returns on each other. The linear regression takes the following forms:
RE = α + βRB + e
RB = α + βRE + e
Where, RE is stock returns, RB is bond returns, α is the constant, β is the sensitivity of the
dependent variable to the independent variable, and e is the regression error.
We then introduced each macroeconomic factor into the multiple linear regressions
individually to observe their impact on the relationship between stock and bond returns in
isolation. The multiple linear regressions take the following forms:
RE = α + βRB + β1F1 + e
RB = α + βRE + β1F1 + e
Where RE is stock returns, RB is bond returns, α is the constant, β is the sensitivity of the
dependent variable to the independent variable, β1 is the sensitivity of the dependent variable to
the macroeconomic factor, F1 is the specific macroeconomic factor, and e is the regression error.
5.0 Findings
In analysing the impact of macroeconomic factors on the relationship between stock and bond
returns, we have found varying results, which can be found in detail in the Appendix.
In conducting our primary analysis, we found insightful results. The average stock return
was 0.152% and the average bond return was 0.089%. In terms of skewness, both returns were
skew to the left, which indicates that most of the returns of stocks and bonds are on the lower
range. As for kurtosis, the distribution pattern of stock returns is significantly more peaked than
that of bond returns. No significant difference was found in in the average returns of stocks and
bonds, which suggests that there was little or no arbitrage opportunity. There was also significant
positive correlation between bond and stock returns. We also found that the sensitivity of stock
returns to bond returns is 0.681, meaning that for every 1-unit increase in bond returns, stock
Page 7
returns increased by 0.681. On the other hand, the sensitivity of bond returns to stock returns is
0.086, meaning that for every 1-unit increase in stock returns, bond returns increased by 0.086.
Next, we observed the influence of GDP growth on the relationship between bond and
stock returns. The average GDP growth was 0.991%, which reflects the 2008 recession. In terms
of skewness, GDP growth was also skew to the left. On the kurtosis measure, GDP growth
followed a normal distribution pattern (below three). Furthermore, there was significant
correlation between stock returns and GDP growth, but there was no significant correlation
between bond returns and GDP growth. We also found that the sensitivity of stock returns to
GDP growth is 2.551. This suggests that GDP growth significantly influences stock returns
through its direct impact on the future earnings of the firm. On the other hand, we found that
bond returns are not influenced by GDP growth. Introducing GDP growth into the model did not
significantly increase the sensitivity of stock returns to bond returns. However, with GDP growth
in the model, the sensitivity of bond returns to stock returns increased to 0.109.
As for the money supply, we also found insightful results. The average change in the
money supply was 0.511%. Relative to skewness, the change in the money supply was skew to
the right, which reflects expansionary monetary policies. As for kurtosis, the distribution pattern
of changes in the money supply was significantly peaked. Furthermore, there was no significant
correlation between the money supply and stock returns. However, at an 89.1% confidence
interval, there is significant negative correlation between the money supply and bond returns.
Though this is an inadequate confidence interval, it suggests that the money supply negatively
influences bond prices. After conducting the multiple linear regressions, we found that at a 95%
confidence interval, changes in the money supply had no significant impact on the returns of
stocks and bonds or on the relationship between stock and bond returns. A possible explanation
for this is that banks increased their reserve ratios and reduced their lending which hindered the
effectiveness of the expansionary monetary policy.
We then observed the influence of inflation on the relationship between stock and bond
returns. The average inflation rate was 2.204%, which is slightly above the inflation target of the
Bank of England. As for skewness, the inflation rate was skew to the right, which reflects
moderate levels of inflation. In terms of kurtosis, the distribution pattern of the inflation rate had
a very low peak, which confirms the previous intuition. Furthermore, there was no significant
Page 8
correlation between the inflation rate and stock returns. However, at a 95% confidence interval,
the inflation rate and bond returns were positively correlated. After conducting the multiple
linear regressions, we found that the inflation rate had no significant influence on stock returns.
On the other hand, the inflation rate negatively influences bond returns, as the sensitivity of bond
returns to the inflation rate is -0.003. Introducing inflation into the model reduces the sensitivity
of stock returns to bond returns to 0.673.
Finally, we introduced the yield of sovereign bonds as an ancillary factor. The average
change in sovereign bond yields was 1.481%. Furthermore, the change in sovereign bong yields
was skewed to the left, indicating that the change in yield was mostly low. As for the kurtosis,
the distribution pattern of the change sovereign bond yields had a very high peak. In addition,
there was positive correlation between stock returns and the change in sovereign bond yields, but
there was no correlation between bond returns and changes in the yield. The sensitivity of stock
returns to changes in sovereign bond yields was 0.086. Also, introducing changes in sovereign
bond yields into the model had no influence on the relationship between stocks and bonds.
6.0 Conclusion
In summary, there is an inherent relationship between stock and bond returns. Unlike the general
consensus, our results show that stock and bond returns are positively correlated. The intuition
behind this is that previous studies examined the short-term relationship between stocks and
bonds, and the negative correlation reflects fluctuations in investor preferences and temporary
economic conditions. Whereas, our study examined the long-term relationship between stocks
and bonds, where these fluctuations are smoothened. Of the primary macroeconomic factors
examined in this study, only GDP growth and the inflation rate influenced stock and bond returns
and relationship between stocks and bonds returns.
Relative to future research, further analyses should be done on the announcement effects
of expansionary monetary policy on the relationship between stock and bond returns. In addition,
investors’ preferences should also be quantified and added to the analysis.
Page 9
References
Andersson M., Krylova, E., and Vähämaa, S., 2008. Why Does the Correlation between Stock and Bond
Returns Vary over Time?,Applied Financial Economics, 18(2), pp.139-151.
Barsky, R. B., 1989. Why Don’t the Prices of Stocks and Bonds Move Together?,American Economic
Review, 79, pp.1132-1145.
Giilhooly, R., and Hussain, F., 2014.Seasonal adjustment of M4 excluding intermediate OFCs (M4ex) - an
update, Monetary & Financial Statistics, Bank of England.
Gulko, L., 2002. Decoupling, Journal of Portfolio Management, 28(3), pp.59-66.
Joyce, M., Miles, D., Scott, A., and Vayanos, D., 2012.Quantitative Easing and Unconventional Monetary
Policy - An Introduction, The Economic Journal, 122 (November), pp.271-289.
Li, L., 2002. Macroeconomic Factors and the Correlation of Stock and Bond Returns. Yale ICF Working
Paper No. 02-26.
Markowitz, H.M., 1952, Portfolio Selection, Journal of Finance, 7(1), pp.77-91.
Shiller, R., 1982. Consumption, Asset Markets, and Macroeconomic Fluctuations, Carnegie Rochester
Conference Series on Public Policy, (Autumn 1982)17, pp.203-238.
Summers, L., The Nonadjustment of Nominal Interest Rates: A Study of the Fisher Effect in J. Tobin, ed.,
Macroeconomic Prices and Quantities: Essays in Memory of Arthur Okun, Washington: The Brookings
Institution, 1983.
Page 10
Appendix
1.0 Primary Analysis
1.1 Descriptive Statistics of Stock and Bond Returns
Descriptive Statistics
N Minimum Maximum Mean
Std.
Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic
Std.
Error Statistic
Std.
Error
RE 179 -.2783 .09979 .0014927 .049435 -1.596 .182 5.687 .361
RB 179 -.0733 .07027 .0004447 .017436 -.431 .182 3.226 .361
Valid N
(listwise) 179
1.2 Independent Sample Test Relative to Stock and Bond Returns
Independent Samples Test
Levene's Test
for Equality of
Variances t-test for Equality of Means
F Sig. t df
Sig.
(2-
tailed)
Mean
Difference
Std. Error
Difference
95% Confidence Interval of
the Difference
Lower Upper
Returns Equal
variances
assumed
66.873 .000 .315 358 .753 .0012295 .003899 -.006439 .008898
Equal
variances
not assumed
.315 223.472 .753 .001229 .003899 -.006454 .008913
For the test with equal variances assumed, the significant figure (0.00) is less than 0.05, so we
disregard this line. For the test with equal variances not assumed, the significant figure (0.753) is
greater than 0.05 so we accept the H0 and conclude that there is no significant difference in the
average returns of stocks and bonds.
Page 11
1.3 Correlation between Stock and Bond Returns
Correlations
RE RB
RE Pearson Correlation 1 .242**
Sig. (2-tailed) .001
N 180 180
RB Pearson Correlation .242** 1
Sig. (2-tailed) .001
N 180 180
**. Correlation is significant at the 0.01 level (2-tailed).
The significant figure (0.001) is less than 0.05, so we reject the H0 and conclude that there is
positive correlation between stock and bond returns.
1.4 Linear Regression with Stock Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .242a .059 .053
.04796702733946
7
a. Predictors: (Constant), RB
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .001 .004 .370 .712
RB .681 .205 .242 3.328 .001
a. Dependent Variable: RE
The significant figure (0.001) is less than 0.05, so we reject the H0 and conclude that the
sensitivity of stock returns to bonds returns is 0.681.
Page 12
1.5 Linear Regression with Bond Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .242a .059 .053
.01704033105541
7
a. Predictors: (Constant), RE
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .000 .001 .125 .901
RE .086 .026 .242 3.328 .001
a. Dependent Variable: RB
The significant figure (0.001) is less than 0.05, so we reject the H0 and conclude that the
sensitivity of bond returns to stock returns is 0.086.
2.0 Analysis of the Influence of GDP Growth on the Relationship between Stock and Bond
Returns
2.1 Descriptive Statistics
Descriptive Statistics
N Minimum Maximum Mean
Std.
Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic
Std.
Error Statistic
Std.
Error
RGDP 58 -.02263 .028419 .0099 .0091 -1.040 .314 2.217 .618
Valid N
(listwise) 58
Page 13
2.2 Correlation amongst Stock Returns, Bond Returns, and GDP Growth
Correlations
RE RB RGDP
RE Pearson Correlation 1 .321* .335*
Sig. (2-tailed) .014 .010
N 58 58 58
RB Pearson Correlation .321* 1 .204
Sig. (2-tailed) .014 .125
N 58 58 58
RGDP Pearson Correlation .335* .204 1
Sig. (2-tailed) .010 .125
N 58 58 58
*. Correlation is significant at the 0.05 level (2-tailed).
Relative to stock returns and GDP growth, the significant figure (0.010) is less than 0.05, so we
reject the H0 and conclude that there is positive correlation between stock returns and GDP
growth. As for bond returns and GDP growth, the significant figure (0.125) is greater than 0.05,
so we accept the H0 and conclude that there is no correlation between bond returns and GDP
growth.
2.3 Multiple Linear Regressions with Stock Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .423a .179 .149
.0767242747899
76
a. Predictors: (Constant), RGDP, RB
Page 14
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) -.022 .015 -1.468 .148
RB .686 .325 .264 2.112 .039
RGDP 2.551 1.131 .282 2.256 .028
a. Dependent Variable: RE
Relative to bond returns, the significant figure (0.039) is less than 0.05, so we reject the H0 and
conclude that the sensitivity of stock returns to bonds returns is 0.686. As for GDP growth, the
significant figure (0.028) is less than 0.05, so we reject the H0 and conclude that the sensitivity of
stock returns to GDP growth is 2.551.
2.4 Multiple Linear Regressions with Bond Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .337a .114 .081
.0306495997979
45
a. Predictors: (Constant), RGDP, RE
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) -.004 .006 -.573 .569
RE .109 .052 .285 2.112 .039
RGDP .378 .469 .109 .806 .424
a. Dependent Variable: RB
Page 15
Relative to stock returns the significant figure (0.039) is less than 0.05, so we reject the H0 and
conclude that the sensitivity of bonds returns to stock returns is 0.109. As for GDP growth, the
significant figure (0.424) is less than 0.05, so we accept the H0 and conclude that bond returns
are not influenced by stock returns
3.0 Analysis of the Influence of Changes in the Money Supply on the Relationship between
Stock and Bond Returns
3.1 Descriptive Statistics of Changes in the Money Supply
Descriptive Statistics
N Minimum Maximum Mean
Std.
Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic
Std.
Error Statistic
Std.
Error
RE 178 -.278 .09979 .00147 .04957 -1.591 .182 5.637 .362
RB 178 -.0733 .070274 .00048 .017477 -.437 .182 3.207 .362
RM4 178 -.0237 .080995 .0051 .00945 2.668 .182 22.980 .362
Valid N
(listwise) 178
3.2 Correlation amongst Stock Returns, Bond Returns, and Changes in the Money Supply
Correlations
RE RB RM4
RE Pearson Correlation 1 .245** -.059
Sig. (2-tailed) .001 .430
N 178 178 178
RB Pearson Correlation .245** 1 -.121
Sig. (2-tailed) .001 .109
N 178 178 178
RM4 Pearson Correlation -.059 -.121 1
Sig. (2-tailed) .430 .109
N 178 178 178
**. Correlation is significant at the 0.01 level (2-tailed).
Page 16
Relative to stock returns, the significant figure (0.430) is greater than 0.05 so we accept the H0
and conclude that there is no correlation between stock returns and changes in the money supply.
As for bond returns, the significant figure (0.109) is greater than 0.05 so we accept the H0 and
conclude that there is no correlation between bond returns and changes in the money supply.
3.3 Multiple Linear Regressions with Stock Returns as the Dependent Variable
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .026 2 .013 5.673 .004b
Residual .409 175 .002
Total .435 177
a. Dependent Variable: RE
b. Predictors: (Constant), RM4, RB
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .002 .004 .473 .637
RB .684 .209 .241 3.269 .001
RM4 -.159 .387 -.030 -.412 .681
a. Dependent Variable: RE
As for stock returns, the significant figure (0.681) is greater than 0.05 so we accept the H0 and
conclude that changes in the money supply do not influence stock returns.
Page 17
3.4 Multiple Linear Regressions with Bond Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .267a .071 .061
.016939201994
093
a. Predictors: (Constant), RM4, RE
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .004 2 .002 6.714 .002b
Residual .050 175 .000
Total .054 177
a. Dependent Variable: RB
b. Predictors: (Constant), RM4, RE
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .001 .001 .945 .346
RE .084 .026 .239 3.269 .001
RM4 -.197 .135 -.106 -1.458 .147
a. Dependent Variable: RB
Relative to bond returns, as suggested by the correlation test, the significant figure (0.147) is
greater than 0.05 so we accept the H0 and conclude that changes in the money supply do not
influence bond returns.
Page 18
4.0 Analysis of the Influence of the Inflation Rate on the Relationship between Stock and
Bond Returns
4.1 Descriptive Statistics of the Inflation Rate
Descriptive Statistics
N Minimum Maximum Mean
Std.
Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic
Std.
Error Statistic
Std.
Error
RE 179 -.2783 .09979 .00149 .0494 -1.596 .182 5.687 .361
RB 179 -.0733 .07027 .0004447 .01743 -.431 .182 3.226 .361
RCPI 179 -.10000 5.2000 2.20391 1.09889 .626 .182 .043 .361
Valid N
(listwise) 179
4.2 Correlation amongst Stock Returns, Bond Returns, and the Inflation Rate
Correlations
RE RB RCPI
RE Pearson Correlation 1 .245** -.084
Sig. (2-tailed) .001 .266
N 179 179 179
RB Pearson Correlation .245** 1 -.212**
Sig. (2-tailed) .001 .004
N 179 179 179
RCPI Pearson Correlation -.084 -.212** 1
Sig. (2-tailed) .266 .004
N 179 179 179
**. Correlation is significant at the 0.01 level (2-tailed).
Relative to bond returns and inflation rates, the significant figure (0.001) is less than 0.05, so we
reject the H0 and conclude that there is positive correlation between returns of inflation and bond
returns, but not between stock returns and inflation. The result shows that there is significant and
negative relation between them.
Page 19
4.3 Multiple Linear Regressions with Stock Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .247a .061 .050
.0481782335121
59
a. Predictors: (Constant), RCPI, RB
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .026 2 .013 5.705 .004b
Residual .409 176 .002
Total .435 178
a. Dependent Variable: RE
b. Predictors: (Constant), RCPI, RB
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .004 .008 .544 .587
RB .673 .212 .238 3.178 .002
RCPI -.001 .003 -.033 -.445 .657
a. Dependent Variable: RE
Relative to stock returns, the significant figure (0.657) is greater than 0.05 so we reject the H0
and conclude that the inflation rate does not influence stock returns.
Page 20
4.4 Multiple Linear Regressions with Bond Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .311a .097 .087
.0166648805494
13
a. Predictors: (Constant), RCPI, RE
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .005 2 .003 9.433 .000b
Residual .049 176 .000
Total .054 178
a. Dependent Variable: RB
b. Predictors: (Constant), RCPI, RE
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .007 .003 2.519 .013
RE .081 .025 .228 3.178 .002
RCPI -.003 .001 -.193 -2.685 .008
a. Dependent Variable: RB
Relative to bond returns, the significant figure (0.008) is less than 0.05, so we reject the H0 and
conclude that the inflation rate influences bond returns. The sensitivity of bond returns to the
inflation rate is -0.003. However, the adjusted R square is only 0.087 that means 8.7% of bond
returns can be explained by stock returns and inflation.
Page 21
5.0 Analysis of the Influence of Changes in Sovereign Bond Yields on the Relationship
between Stock and Bond Returns
5.1 Descriptive Statistics of Changes in Sovereign Bond Yields
Descriptive Statistics
N Minimum Maximum Mean
Std.
Deviation Skewness Kurtosis
Statistic Statistic Statistic Statistic Statistic Statistic
Std.
Error Statistic
Std.
Error
RE 179 -.27832 .09979 .00149 .0494 -1.596 .182 5.687 .361
RB 179 -.07333 .07027 .00044 .0174 -.431 .182 3.226 .361
RT 179 -.74533 .40546 -.0148 .1189 -1.376 .182 11.326 .361
Valid N
(listwise) 179
5.2 Correlation amongst Stock Returns, Bond Returns, and Changes in Sovereign Bond Yields
Correlations
RE RB RT
RE Pearson Correlation 1 .245** .204**
Sig. (2-tailed) .001 .006
N 179 179 179
RB Pearson Correlation .245** 1 -.014
Sig. (2-tailed) .001 .851
N 179 179 179
RT Pearson Correlation .204** -.014 1
Sig. (2-tailed) .006 .851
N 179 179 179
**. Correlation is significant at the 0.01 level (2-tailed).
Relative to stock returns and sovereign bond yields, the significant figure (0.006) is less than
0.05, so we reject the H0 and conclude that there is positive correlation between returns of T-bill
and stock returns. As for bond returns and sovereign bond yields, the significant figure (0.851) is
Page 22
greater than 0.05 so we accept the H0 and conclude that there is no correlation between bond
returns and sovereign bond yields.
5.3 Multiple Linear Regressions with Bond Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .253a .064 .053
.0169638157892
95
a. Predictors: (Constant), RE, RT
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .003 2 .002 6.030 .003b
Residual .051 176 .000
Total .054 178
a. Dependent Variable: RB
b. Predictors: (Constant), RE, RT
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .000 .001 .128 .899
RT -.010 .011 -.067 -.899 .370
RE .091 .026 .258 3.467 .001
a. Dependent Variable: RB
As for bond returns, the significant figure is (0.370) so we accept the H0 and conclude that
sovereign bond yields do not influence bond returns.
Page 23
5.4 Multiple Linear Regressions with Stock Returns as the Dependent Variable
Model Summary
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate
1 .321a .103 .093
.0470839964763
20
a. Predictors: (Constant), RB, RT
ANOVAa
Model Sum of Squares df Mean Square F Sig.
1 Regression .045 2 .022 10.111 .000b
Residual .390 176 .002
Total .435 178
a. Dependent Variable: RE
b. Predictors: (Constant), RB, RT
Coefficientsa
Model
Unstandardized Coefficients
Standardized
Coefficients
t Sig. B Std. Error Beta
1 (Constant) .002 .004 .694 .489
RT .086 .030 .208 2.913 .004
RB .702 .202 .248 3.467 .001
a. Dependent Variable: RE
As for stock returns, the significant figure (0.004) is less than 0.05 so we reject H0 and conclude
that sovereign bond yields have an influence on stock returns. The sensitivity of stock returns to
bond returns is 0.086. Both bond returns and T-bill have a positive relation with stock returns,
i.e., stock and bond returns, and T-bill move the same direction. However, the adjusted R square
is only 0.093, which means 9.3% of stock returns can be explained by bond returns and changes
in the sovereign bond yields.