Easerling 1
Are the movements of stocks, bonds, and housing linked?
Zachary D Easterling
1140324
Department of Economics
The University of Akron
One of the key ideas in monetary economics is that the prices of
investments tend to move in the opposite direction as interest rates. Does this
hold for different types of investments, ie: stocks, bonds, housing, gold, and other
investment media. Is there a direct correlation between stocks, bonds and
housing prices, and do they move in the same direction?
Can an economist predict the movement of one by looking at the
aggregate of the others in relation to interest rates? Using linear regression this
short work will focus on any positive or negative correlation between the federal
funds rate and investment media. The three types of investments that will be
touched upon in this paper will be stocks, represented by the Standard and
Poor’s 500; bonds, represented by the risk free rate of investment normally
associated with a one year treasury bill; and housing, given in a seasonally
adjusted average price index.
Easerling 2
Introduction: “As you know, the financial stress has not been confined to mortgage
markets,” said Ben Burnanke, the president of the Federal Reserve Bank, in his address to the
Federal Reserve Bank of Kansas City. “The markets for asset-backed commercial paper and for
lower-rated unsecured commercial paper market also have suffered from pronounced declines in
investor demand, and the associated flight to quality has contributed to surges in the demand for
short-dated Treasury bills, pushing T-bill rates down sharply on some days. Swings in stock
prices have been sharp, with implied price volatilities rising to about twice the levels seen in the
spring.” However, this speech was not given last week, last month, or even one year ago.
On August 31, 2007, Burnanke issued this statement in his nearly 20 minute speech on
the history of mortgages in the United States. It seems that Bernanke, even if by anecdotal
evidence alone, proved that least bond prices move in the opposite direction as their yield rates.
But is it possible for an economist to look at aggregate data from investment markets, and make
a determination about where other investments may be headed; specifically that instruments
yield.
Theoretical Overview: According to Mishkin (2004 pp.86-87) items such as bonds,
stocks, and housing are considered assets; because of their store of value. The prices of these
assets are determined in their respective markets by three general rules. First, the expected
return on a particular asset relative to other assets should have a positive correlation on the price
of that asset. An increase in the asset’s expected return relative to the return of an alternative
asset should increase the demand for that asset, and consequently raise the price. Second, the
risk level of an asset is negatively related to the price of the asset. If the risk level of stocks rises
in relation to bonds or housing, the demand for stocks should decrease, thus reducing the price.
Lastly, the liquidity of an asset plays an important role in determining the demand for that asset.
If housing suddenly became as liquid as stocks or bonds, the change in desirability to investors
would increase the demand for housing and cause prices to rise accordingly.
Methodology: Using Mishkin’s explanation of the Theory of Asset Demand, it should be
possible to determine if there exists any correlation between the prices of stocks, bonds, and
housing, by addressing their expected returns, risk, and liquidity. In the context of this paper all
price increases or decreases will be in percentage terms. This paper will specifically focus on an
asset’s expected return while holding risk and liquidity constant.
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
Data: Visual inspection of the movement in the prices of stocks, bonds, and housing
shows a wide variety of return levels. Bonds have historically provided ‘risk free investment
returns’ while
both stocks and
12.00
One Year Security
housing have
Two Year Security
provided erratic
10.00
Three Year
returns. Using
Security
Five Year Security
SAS linear
regression, it can
8.00
Seven Year
Security
be shown that
Ten Year Security
there is a
Twenty Year
6.00
Security
relationship
State/Local AAA
between the
Bonds
State/Local BBB
4.00
price of a one
Bonds
Municipal Bonds
year security and
Standard & Poors
the federal funds
2.00
High-Grade
rate as set by
Corporate AAA
the Federal
Corpporate BBB
0.00
Reserve Bank.
Corporate
(Moodys)
SAS output
provides the
Figure 1: Bond yields from 1990-2006
Easerling 3
following information for the analysis of the correlation between a one year treasury bill and the
federal funds rate.
The REG Procedure
Model: MODEL1
Dependent Variable: OneYrSec: One Year Treasury Security
Number of Observations Read
Number of Observations Used
204
204
Analysis of Variance
DF
Sum of
Squares
Mean
Square
1
202
203
3.67725
0.39120
4.06845
3.67725
0.00194
Root MSE
Dependent Mean
Coeff Var
0.04401
0.37696
11.67424
Source
Model
Error
Corrected Total
R-Square
Adj R-Sq
F Value
Pr > F
1898.77
<.0001
0.9038
0.9034
Parameter Estimates
Variable
|t|
Label
Intercept
<.0001
MnthFundsRate
<.0001
Intercept
DF
Parameter
Estimate
Standard
Error
t Value
1
0.06615
0.00777
8.51
1
0.07150
0.00164
43.57
Fed Funds Rate
Pr >
SAS uses a null hypothesis and alternative hypothesis to test for a relationship between
the price of the one year treasury security and the federal funds rate.
H0: The monthly federal funds rate is not useful to predict the movement of the one year treasury
security.
Ha: The monthly federal funds rate is useful to predict the movement of the one year treasury
security.
The small p-value returned by the SAS
regression analysis indicates there is
strong evidence against the null
hypothesis. Consequently we would
reject the idea that the federal funds rate
is not useful to predict the movement of
the one year treasury security and
conclude that it is.
The regression line shows a strong
correlation between the one year
treasury security and the federal funds
rate. SAS’s analysis of the variance
provides indicates this is an acceptable
model to use; and the R-squared value
indicates that the federal funds rate
provides a large portion of the one year
Figure 2: Regression Analysis Output from SAS
Easerling 4
security rate. The exact same analysis was carried out on the relationship between the federal
funds rate and the return of the stocks on Standard and Poor’s 500. The results showed mixed
Figure 3: Percentage movement of the S&P 500 from 1990 to 2006
15
10
5
-10
2006-06
2005-09
2004-12
2004-03
2003-06
2002-09
2001-12
2001-03
2000-06
1999-09
1998-12
1998-03
1997-06
1996-09
1995-12
1995-03
1994-06
1993-09
1992-12
1992-03
1991-06
1990-09
-5
TimePeriod
0
-15
-20
results, most likely stemming from the volatility in the stock market in regards to risk (which is
held constant in these models).
The REG Procedure
Model: MODEL1
Dependent Variable: OneYrSec OneYrSec
Number of Observations Read
Number of Observations Used
204
204
Analysis of Variance
DF
Sum of
Squares
Mean
Square
1
202
203
0.01338
4.05507
4.06845
0.01338
0.02007
Root MSE
Dependent Mean
Coeff Var
0.14168
0.37696
37.58612
Source
Model
Error
Corrected Total
R-Square
Adj R-Sq
F Value
Pr > F
0.67
0.4153
0.0033
-0.0016
Parameter Estimates
Variable
Label
Intercept
PctChng
Intercept
PctChng
DF
Parameter
Estimate
Standard
Error
t Value
Pr > |t|
1
1
0.37542
0.00202
0.01010
0.00248
37.18
0.82
<.0001
0.4153
Like with the previous regression analysis, SAS creates two hypotheses and tests the relationship
between the federal funds rate and the percentage change in the S&P 500.
Easerling 5
H0: The monthly federal funds rate is not useful to predict the movement of the Standard and
Poor’s 500.
Ha: The monthly federal funds rate is useful to predict the movement of the Standard and Poor’s
500.
The extremely large p-value returned by SAS is an indicator that there is very strong evidence for
the null hypothesis, and accordingly suggests that the null hypothesis be accepted, concluding
that the federal funds rate is in fact not useful to predict the movement of the S&P 500. The
regression line in
this output clearly
shows that there is
no correlation
between the federal
funds rate and the
S&P 500. The
scattered cloud of
data is also
indicative of the
randomness of the
stock market. This
is in fact a very
good sample of
observations for this
test.
The last test
performed was to
see if housing
prices were
predictable using
the federal funds
rate. This output is
the most interesting
of the three, due to
the fact that there is a small p-value indicating that there is a strong eveidence against the null
hypothesis as set forth by SAS and the low R-squared value as produced by SAS. These two
pieces of evidence seem to be counter-intuitive for on the one hand SAS has indicated that there
is a correlation between the federal funds rate and housing prices yet concludes that the
movement in the housing prices is not significantly due to the federal funds rate.
Figure 4: Price movement of the average home sold in the United States from 1990 - 2008
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
-0.60
2005-09
2004-12
2004-03
2003-06
2002-09
2001-12
2001-03
2000-06
1999-09
1998-12
1998-03
1997-06
1996-09
1995-12
1995-03
1994-06
1993-09
1992-12
1992-03
1991-06
1990-09
-0.40
TimePeriod
0.00
-0.20
Easerling 6
The REG Procedure
Model: MODEL1
Dependent Variable: AvgAdjPctChng AvgAdjPctChng
Number of Observations Read
Number of Observations Used
Number of Observations with Missing Values
204
192
12
Analysis of Variance
DF
Sum of
Squares
Mean
Square
1
190
191
2.27214
21.10825
23.38039
2.27214
0.11110
Root MSE
Dependent Mean
Coeff Var
0.33331
0.41530
80.25689
Source
Model
Error
Corrected Total
R-Square
Adj R-Sq
F Value
Pr > F
20.45
<.0001
0.0972
0.0924
Parameter Estimates
DF
Parameter
Estimate
Standard
Error
t Value
Intercept
1
0.68234
0.06376
10.70
MnthFundsRate
1
-0.06494
0.01436
-4.52
Variable
|t|
Label
Intercept
<.0001
MnthFundsRate
<.0001
Pr >
As with the previous regressions, The SAS null and alternative hypotheses are as follows.
H0: The monthly federal funds rate is not useful to predict the movement of the average price of a
home sold in the United States.
Ha: The monthly federal funds rate is useful to predict the movement of the average price of a
home sold in the United States.
Pearson Correlation Coefficients,
Treasury Security and Housing compared
WITH Federal Funds Rate
Prob > |r| under H0: Rho=0
FED FundsRate
FED FundsRate
Average Home
Selling
0.95071
<.0001
OneYrSec
-0.31174
<.0001
Pearson Correlation Coefficients,
Treasury Security and S&P 500 compared
WITH Federal Funds Rate
Prob > |r| under H0: Rho=0
FED FundsRate
FED FundsRate
OneYrSec
0.95071
<.0001
S&P 500
0.03844
0.5852
Results: The running of certain
Correlation Procedures in SAS also provided
evidence that there is indeed a relationship
between the federal funds rate and the one year
treasury security and that there is a partial
relationship between the federal funds rate and
the average price of a home sold in the United
States. Finally the results of the correlation test in
SAS confirmed that there is very little if any
relationship between the federal funds rate and
the S&P 500.
The correlation procedure was also run on each
variable in relation to the others, in hopes of
ferreting out a trend in the assets themselves.
Some of the results provided by SAS
seemed to indicate that there was a weak
negative correlation between the movement of
Easerling 7
stock prices and the movement of housing prices, and a stronger negative correlation between
the movements of bond prices when compared
Pearson Correlation Coefficients,
to housing prices. These results would require
Treasury Security and S&P 500 compared
further analysis using multiple-linear regression
WITH Average Home selling Price in the
or perhaps some other type of dynamic
United States
regression model.
Prob > |r| under H0: Rho=0
Summary: Thus, by using simple
procedures such as linear regression and
AVG H.Price
-0.34934
-0.12571
correlation it can be shown that the one year
AVG H.Price
<.0001
0.0823
treasury security follows the direction of the
federal funds rate, that the average selling price
of a home in the United States loosely follows the federal funds rate, and the Standard and Poor’s
500 do not follow the trends in the federal funds rate. And while it would be very interesting to
see how the aggregate of the three assets follows the federal funds rate that is unfortunately left
for another time.
OneYrSec
S&P 500
Data Sources
Bureau of Labor Statistics. Consumer Price Index - All Urban Consumers. US Department of
Labor.
http://data.bls.gov/servlet/SurveyOutputServlet?data_tool=latest_numbers&series_id=CUSR0000
SA0&output_view=pct_1mth (10 November 2008).
Office of Federal Housing Enterprise Oversight. Housing Prices Indexes.
http://www.ofheo.gov/media/hpi/MonthlyIndex_to_1991.xls (8 November 2008).
The Federal Reserve Board. H.15 Selected Interest Rates . Federal Reserve Bank.
https://www.federalreserve.gov/datadownload/Download.aspx?rel=H15&series=40afb80a445c59
03ca2c4888e40f3f1f&filetype=csv&label=include&layout=seriescolumn&from=01/01/1990&to=12/
31/2008 (10 November 2008).
The National Data Book. Banking, Finance, & Insurance: Money Stock, Interest Rates, Bond
Yields. US Census Bureau. http://www.census.gov/compendia/statab/tables/08s1167.xls (10
November 2008).
Yahoo! Finance. S&P 500 Historical Index.
http://finance.yahoo.com/q/hp?s=%5EGSPC&a=00&b=1&c=1990&d=11&e=31&f=2006&g=m (16
November 2008).
References
Bernanke, Ben S. Housing, Housing Finance, and Monetary Policy. Speech: At the Federal
Reserve Bank of Kansas City's Economic Symposium, Jackson Hole, Wyoming. August 31,
2007.
Campbella, Sean D., Morris A. Davisb, Joshua Gallina, and Robert F. Martina. "What Moves
Housing Markets: A Variance Decomposition of the Rent-Price Ratio."Federal Reserve
Board and b University of Wisconsin-Madison, October, 2008.
DeBondt, W. F. M. "Does the Stock Market Overreact." The Journal of Finance 40, no. 3 (1985):
793.
Easerling 8
Liu, C. H. "The Integration of the Real Estate Market and the Stock Market." The Journal of Real
Estate Finance and Economics 3, no. 3 (1990).
Piazzesi, Monika. "Housing, Consumption and Asset Pricing." Journal of Financial Economics 83,
no. 3 (2007): 531.
Mishkin, Frederic S., ed. The Economics of Money, Banking, and Financial MarketsPearson
Addison Wesley, 2004.