Using Simple Regression Model to Explain the Relationship Between 3-Month T-Bill Rate and Dow-Jones Index

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Using the simple regression model to explain the relationship between 3-Month T-bill rate and Dow Jones Index

Index
1. Introduction………………………………………………3

2. Modeling the relationship between the 3-Month T-bill
rates and Dow Jones Index (First Model)……………………3

3. Hypothesis and Testing…………………………………...4

4. Empirical Analysis………………………………………...5

5. Further Comparison………………………………………5
6. Conclusion…………………………………………………7

7. Appendix……………………………………………………8

8. Reference…………………………………………………..10

1. Introduction

The 3-month T-bill rates and Dow Jones index are really close to the whole economic environment; the 3-month T-Bill rates are the preeminent default-risk-free rates in the US money market that is often used by researchers to proxy the risk-free asset whose existence is assumed by much conventional finance theory. Given their importance and visibility, it is not surprising that these interest rates has been studied extensively in economic and finance. Dow Jones Index, undoubtedly, is one of the most important economic indicators of the global financial market, This paper investigates the relationship between these two important economic data. In order to cover the business circle, the data which I choose is from 2001/01/01-2010/12/31, including the subprime lending crisis period. I use SAS and excel to get the information which indicates the relationship between these two representing data.

2. Modeling the relationship between the 3-Month T-bill rates and Dow Jones Index (First Model)

In order to present the relationship between the 3-Month T-Bill rates and Dow Jones index by our SAS output result, I constructed a single regression model: Y=β0+β1X
(β0 = the intercept of 3-Month T-bill rate)
(β1 = the slope of Dow Jones Index)

3-Month T-Bill rate=-0.04883+0.00000670*Dow Jones Index

This means that when the Dow Jones Index increased by one point, the 3-Month T-bill rates will increase by 0.00067%. According to the graph below, we can see the lower3-Month T-bill rate in accordance with the lower Dow Jones Index. However, this model cannot explain all situations, because as the above formula indicated,3-Month T-Bill rate can only be positive when Dow Jones Index is higher than 7,288 points.

3. Hypothesis and testing
First, I assumed that the 3-Month T-bill rate is negatively related to the Dow Jones Index, I constructed the null hypothesis and alternative hypothesis.

H0=β0≤0 (3-Month T-bill is negative related to the DJI)
HA=β0>0 (3-Month T-bill is positive related to the DJI)

As the SAS output showed that P-Value is below 0.05 , I can 95% confidently reject our null hypothesis that 3-Month T-bill rate is negative related to the Dow Jones Index and accept our alternative hypothesis that 3-Month T-bill rate is related to the Dow Jones Index.

4. Empirical Analysis

According to the SAS output result, the R-Square indicated more than 30%, the reasonable explanation is that when economic conditions are down, the investors are willing to transfer their portfolio from high-risk products into risk-free products such as T-bill. With money centralized to the T-bill, the 3-Month T-bill rate will decrease. When the 3-Month T-bill rate starts to decrease, it means that the investors and the investment institutions will start to sell their risk assets and then buy the American short-term debt to avoid the investment risk. Investors and the investment institutions tend to averse the risk. In other words, money flows out from the stock market and inflow to the bond market. With stock markets continuing facing selling pressure, that is why the Dow Jones Index easily fell and has difficulty regaining. We found that during the subprime lending crisis period, the 3-month T-bill rate was even lower than 0.001. At the same time, the Dow Jones Index was lower than 8,500 points. This result is proof of my view above.

5. Further comparison
5.1(Second Model)
Y=β0+β1X
(β0...
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