Are the Movements of Stocks, Bonds, and Housing Linked

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.

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 8.00 Seven Year regression, it can Security Ten Year Security be shown that there is a 6.00 Twenty Year Security relationship State/Local AAA Bonds between the 4.00 State/Local BBB Bonds price of a one Municipal Bonds year security and 2.00 Standard & Poors the federal funds High-Grade Corporate AAA rate as set by the Federal 0.00 Corpporate BBB 1 2 3 6 7 8 3 0 4 5 9 0 1 2 4 5 6 Corporate Reserve Bank. 9 9 9 9 9 9 0 9 9 9 9 0 0 0 0 0 0

9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 (Moodys) SAS output 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 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 204 Number of Observations Used 204

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 1 3.67725 3.67725 1898.77 <.0001 Error 202 0.39120 0.00194 Corrected Total 203 4.06845

Root MSE 0.04401 R-Square 0.9038 Dependent Mean 0.37696 Adj R-Sq 0.9034 Coeff Var 11.67424

Parameter Estimates

Parameter Standard Variable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 0.06615 0.00777 8.51 <.0001 MnthFundsRate Fed Funds Rate 1 0.07150 0.00164 43.57 <.0001

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

0 d 9 6 3 2 9 6 3 2 9 6 3 2 9 6 3 2 9 6 3 2 9 6 o 0 0 0 0 1 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 i ------r 0 2 3 5 5 7 8 0 1 3 4 1 2 4 6 8 9 1 2 4 5 6 -5 e 9 9 9 9 9 9 9 0 0 0 0 9 9 9 9 9 9 0 0 0 0 0 P 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 0 e 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 m -10 i T

-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 204 Number of Observations Used 204

Model 1 0.01338 0.01338 0.67 0.4153 Error 202 4.05507 0.02007 Corrected Total 203 4.06845

Root MSE 0.14168 R-Square 0.0033 Dependent Mean 0.37696 Adj R-Sq -0.0016 Coeff Var 37.58612

Parameter Estimates

Intercept Intercept 1 0.37542 0.01010 37.18 <.0001 PctChng PctChng 1 0.00202 0.00248 0.82 0.4153 Easerling 5

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.

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. Easerling 6

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 d 9 3 2 3 2 3 2 3 6 3 0.00 6 9 6 9 6 9 6 2 9 2 9 o i 0 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1 0 r ------

-0.20 e 0 1 2 2 3 4 5 5 6 7 8 8 9 0 1 1 2 3 4 4 5 P 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 e -0.40 9 9 9 9 9 9 9 9 9 9 9 9 9 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 m

-0.60 i T

Easerling 7

The REG Procedure Model: MODEL1 Dependent Variable: AvgAdjPctChng AvgAdjPctChng

Number of Observations Read 204 Number of Observations Used 192 Number of Observations with Missing Values 12

Model 1 2.27214 2.27214 20.45 <.0001 Error 190 21.10825 0.11110 Corrected Total 191 23.38039

Root MSE 0.33331 R-Square 0.0972 Dependent Mean 0.41530 Adj R-Sq 0.0924 Coeff Var 80.25689

Parameter Estimates

Intercept Intercept 1 0.68234 0.06376 10.70 <.0001 MnthFundsRate MnthFundsRate 1 -0.06494 0.01436 -4.52 <.0001

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 Results: The running of certain WITH Federal Funds Rate Correlation Procedures in SAS also provided evidence that there is indeed a relationship Prob > |r| under H0: Rho=0 between the federal funds rate and the one year treasury security and that there is a partial Average Home OneYrSec relationship between the federal funds rate and Selling the average price of a home sold in the United FED FundsRate 0.95071 -0.31174 States. Finally the results of the correlation test in FED FundsRate <.0001 <.0001 SAS confirmed that there is very little if any relationship between the federal funds rate and Pearson Correlation Coefficients, the S&P 500. Treasury Security and S&P 500 compared WITH Federal Funds Rate The correlation procedure was also run on each Prob > |r| under H0: Rho=0 variable in relation to the others, in hopes of ferreting out a trend in the assets themselves. OneYrSec S&P 500 FED FundsRate 0.95071 0.03844 FED FundsRate <.0001 0.5852 Some of the results provided by SAS seemed to indicate that there was a weak negative correlation between the movement of stock prices and the movement of housing prices, and a Easerling 8 stronger negative correlation between the movements of bond prices when compared to housing prices. These results would require further Pearson Correlation Coefficients, analysis using multiple-linear regression or Treasury Security and S&P 500 compared perhaps some other type of dynamic regression WITH Average Home selling Price in the United States model. Prob > |r| under H0: Rho=0 Summary: Thus, by using simple OneYrSec S&P 500 procedures such as linear regression and correlation it can be shown that the one year AVG H.Price -0.34934 -0.12571 treasury security follows the direction of the AVG H.Price <.0001 0.0823 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.

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=CUSR0000SA0&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=40afb80a445c5903ca2c4888e40f3f1f&filetype=csv&label=include&layout=series column&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 9

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.