Federal Bond Yields
______________________________________________________________________
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
______________________________________________________________________ I. Introduction The Federal Open Market Committee raised the federal funds target interest rate from the historically low 1% to 1.25% at its meeting in June 2004. Macroeconomic theory tells us that long-term interest rates tend to move in the same direction, and generally in concert with, shortterm interest rates (Abel 2005). So, we would expect the yield on a long-term asset like the10year Treasury bond, which moves directly with interest rates, to move up when a short-term rate like the federal funds rate moves up. However, a cursory …show more content…
reading of financial news sources since the FOMC began its rate hike policy, through January 2005, show that the yield on the 10- year has actually fallen. This study will develop a predictive model to describe this direct influence and conclude that the federal funds rate directly influences the 10-year Treasury bond yield. This study will not try to predict what factors could be holding the yields down in any quantifiable way. The 10year Treasury bond yield is a benchmark rate, important to bond investors looking for future indicators of inflation, and to areas such as housing and other loans; a predictive model will allow investors to more adequately gauge investment risk and loan officers to judge what interest rates to charge Section II will present a brief review of the literature concerning these issues while helping to describe some decisions made in the current study. Section III will present the results of the data collection and analysis used to support our conclusions. The regression model will be described, and the predictions explained, with supporting evidence from the actual data. Section
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
1
IV will be a conclusion reestablishing our conclusions and also pointing out some of the aspects of the current study that caused some concern and that may warrant further investigation.
II. Review of the Issue There is some writing in the literature concerning how monetary policy affects asset prices, namely stocks and bonds. There are also studies that suggest the federal funds futures contract, the rate that people speculate the federal funds target rate will move to in the near term, is an indicator of monetary policy and the financial market’s reaction to such information. Fleming and Remolona (1997) use high frequency, intraday price activity to look at how announcements of events like the federal funds rate target, the employment numbers, the producer price index, and the consumer price index affect and contribute to price shocks and trading volume in the bond market. They found the federal funds rate target to be significant in their regressions, and that of the 25 greatest price shocks between 1993 and 1994, three of them were direct results of an announcement of a new federal funds target rate. Even with the strength of these results, their study of the federal funds target rate and its affect on bond prices had not been discussed in the literature up to that point. The study by Gulley and Sultan (2003) examines the federal funds futures contract as an indicator of monetary policy. They find that positive and negative changes in the federal funds rate have symmetric effects on the bond market, which supports my assertion that the federal funds rate has a direct effect on the 10- year Treasury bond yield. Further, they suggest that their findings are consistent with the expectation that an increase in the federal funds rate translates into lower bond prices, or higher bond yields which move inversely to prices.
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
2
Fleming and Remolona (1997) reference studies in the early 1980’s that show the impact of money supply announcements were significant in explaining market behavior. However, similar studies done in the mid 1980’s show a diminishing significance of these announcements. Gulley and Sultan (2003) suggest that there is a mixed review in the literature of how monetary policy aggregates, like the federal funds rate, affect long-term interest rates. Tarhan (1993) states that monetary policy may be an important factor in asset return volatility, and that the interaction of monetary policy, like the federal funds rate, and asset prices, like the yield on the 10-year Treasury bond, needs to be examined more fully. Based on this economic literature it is obvious that the relationship between the federal funds rate and the yield on the long term Treasury bond warrants further study. The preceding literature does not say anything directly about the actual federal funds rate. This paper makes the contribution of using the actual federal funds rate available to the banks, which carry out the Federal Reserve’s mo netary policy, as a contributor of the long-term bond yield.
III. Analytical Content – Empirical Results Anecdotally, why do we believe the federal funds rate will influence the Treasury bond yield? It is because this rate has become the Federal Reserves primary monetary policy tool used to effect its conclusions about the state of the economy. The Federal Reserve has built up a large supply of credibility over the years, so if it believes this country is headed for higher inflation, then most investors believe this. Also, it is the shortest-term interest rate on the market, lasting only a matter of hours when in use. But, it is also the quickest to be passed along to the general public in the form of higher interest loans and banking fees. It is no surprise that this short-term
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
3
benchmark rate would eventually have some influence on the long-term benchmark rate, the 10year Treasury bond yield. This study utilizes a multiple regression analysis to adequately determine the effect of the federal funds rate on the 10-year Treasury bond yield. A histogram of the residuals showed that the data followed a normal distribution, allowing us to use standard t and F tests to analyze the results. A White’s test was used to prove that the data were homoscedastic. Our high F test statistic and R-square values, along with highly significant coefficients from our explanatory variables, allowed us to conclude that there were no problems with multicollinearity. A DurbinWatson test did reveal that there was positive autocorrelation among the error terms. This required the use of a first-order autoregressive data transformation and the method of generalized least squares to help account for the autocorrelation and to derive our coefficients. Data gathered for this study was from the periods January 1990 through May 2004, a large enough period of time to include a variety of economic events – the early 1990’s recession, the stability of the mind 1990’s, the boom years of the late 1990’s, and the uncertainty of the recent past. Although this study is primarily concerned with the effect of the non-seasonally adjusted federal funds rate, using only this single variable to explain our yield would be inappropriate and would also violate our properly specified model assumption. Several other explanatory variables were included as controls to help specify the model and to distill the true effect of the federal funds rate. The findings of Fleming and Remolona (1997) show that employment, and the federal funds rate announcements were the number 1, and 4 most important in affecting bond price volatility, respectively. Accordingly, the non-farm, urban, non-seasonally adjusted unemployment rate is included as explanatory variable in our model. To arrive at a better
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
4
measure of the overall level of inflation anxiety and activity in the economy, the non-seasonally adjusted producer price index was included as an explanatory variable. All of these data were gathered from the Federal Reserve Bank of St. Louis’s FRED II database. Some of the early research into this subject suggested that exchange rates might play a part in the determination of the bond yield. Tarhan (1993) asserts that sterilized intervention policy, the way a country might manage their currency value by purchasing foreign debt, might be an important factor in asset return volatility. Miller (2005) provides a concrete example of this with the description of Asian central banks buying huge amounts of United States dollars, with the majority of this currency subsequently invested in 10- year Treasury bonds. The goal of this policy is to keep the dollar strong against currencies reliant on continued U.S. demand for imports. In order to account for the possibility that exchange rates might play a role in determining the yield, the trade weighted exchange index - a weighted average of the foreign exchange value of the U.S. dollar against the currencies of a broad group of major U.S. trading partners – was included as an explanatory variable. The data for the PPI and unemployment rates were only available in a monthly format, which required the use of monthly average rate data for the exchange rate and our two most important variables, the federal funds rate and the 10- year Treasury yield. According to Fleming and Remolona (1997), price shocks in the bond market occurred within 15 to 70 minutes of any news announcement. This is a remarkably quick time, certainly within the range of the daily data our study planned to use, and quick enough to lead us to believe that using monthly data would pick up the interaction between our explanatory variables and the yield. To further test that using monthly average data would not negatively affect the regression, two test models were created. The first regressed the daily federal funds rate against the daily yield rates, the second
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
5
regressed the monthly federal funds rate against the monthly yield rate. The results were nearly identical, providing convincing evidence that the use of monthly data would be sufficient to properly specify the model. To avoid problems with causality, that is, regressing the explanatory variable data against the yield data from the same month, we used lagged explanatory data. The unemployment rate, PPI, and exchange rate data are each one- month behind the corresponding yield rate. In testing different lag combinations to account for the autocorrelation problem and the causality situation, it was found that using the federal funds rate lagged one and two months behind the yield rate were significant in the regression. These are shown in the regression equation as FFR1 and FFR2. Research by Fleming and Remolona (1997) suggest that there might be a seasonality aspect to the markets behavior. So the last technique used to design the correct regression model was to use dummy variables, one for each month except December, the baseline month. The final regression equation, minus the dummy variables, looks like this:
Yi = B0 + B1FFR1 + B2FFR2 + B3UNEMP + B4PPI + B5EX + ui
Table 1 – Regression Statistics
Intercept FFR1 FFR2 UNEMP PPI EX R Square F stat Significance F Observations
Coefficients 8.4652 0.9912 -0.6171 0.0205 -0.0207 -0.0259 0.8460 52.1973 2.3117 E-53 169
Standard Error 2.1788 0.2562 0.2310 0.1442 0.0100 0.0080
t Stat 3.8853 3.8690 -2.6817 1.4221 -2.5950 -3.2199
P-value 0.0002 0.0002 0.0081 0.1570 0.0412 0.0016
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
6
We can use standard hypothesis testing techniques to determine the significance of our two federal funds rate coefficients.
The calculated t-stats of 3.8690 and –2.6817, compared to statistical tables, show that our coefficients are significant in the model at a 95% and 99% level. Further, the calculated P-values show that if the null hypothesis of these coefficients being statistically the same as zero, and thus not having an influence on the model, were true, the probability of obtaining these t-stats is 0.0002, and .0081, respectively. We can be quite confident that our federal funds rate coefficients are significant and have a strong influence over the Treasury yield. An interval estimation construction shows that the federal funds rate (FFR1) coefficient would be somewhere between .4890 and 1.4934 with 95% certainty, and the federal funds rate (FFR2) coefficient would be between –1.0700 and –1.6430 with 95% certainty. Since the null- hypothesized value of zero is not included in either range, we can again reject the hypotheses that we have committed a Type-I error with 95% confidence. T tests show that all the explanatory variables are individually significant in the model at at least the 95% confidence level. However, we do want to test the overall significance of our estimated regression model to ensure that we have not incorrectly specified the equation and to attest to the strength of our predictive model. Judging by the significant F statistic value of 2.3117 E-53, or essentially zero, we can reject the hypothesis that the federal funds rate, unemployment rate, PPI, and our exchange rate basket, together have no effect on the 10-year Treasury yield. This gives us a high level of confidence that our model is correctly specified. Such a significant F statistic also allows us to conclude that our R2 value is highly significant as well; that indeed 84.60% of the total variability in the Treasury yield data is explained by our model. Since all of our data is
a rate of some kind, we can speak in terms of basis point movements. It would be improper to isolate our one federal funds rate variable and say that a
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
7
100 basis point move in the FFR1 causes a 99 basis point move up in the Treasury yield. It is more proper to look at both federal funds rate variables and say that we can subtract the FFR1 and FFR2 rates to arrive at the conclusion that a 100 basis point move in the federal funds rate causes a 37 basis point move up in the Treasury yield. This is a far stronger influence than any other variable in the model. By this reasoning we would expect that by October or November of 2004 the yield would have risen around 37 basis points. The data show that the yield actually fell by 60 basis points. However, we cannot draw a direct prediction on the yield based solely on the federal funds rate due to the significant influence of the other variables. If we use our regression equation to predict the Treasury yield in the months since May of 2004 through January of 2005, the time when the FOMC has steadily increased the federal funds target rate, we get these results: Estimated June July August September October November December January 3.87 4.02 4.22 4.18 4.21 4.23 4.38 4.54 Actual 4.73 4.50 4.28 4.13 4.10 4.19 4.23 4.22
The estimated results show the general trend of an increasing yield, as we would expect. We cannot say that the actual yield is incorrect, because that is what the market determined price for this investment truly was. However, Miller (2005) suggests that some investors believe the yield on the 10-year Treasury to be as much as 50 basis points lower than it should be, so there is some traction to the theory that the market is operating somewhat inefficiently. Also, looking at the estimated data shows that the yield should have increased 21 basis points in the four months
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
8
since July and 36 basis points in the 5 months since July. This puts us in a position to reliably say how much influence the federal funds rate has on the yield, or at least close in on a range over time. Taking some random samples from the data imply that our estimate of 37 basis points per 100 basis points of the federal funds rate might be accurate. Between September 1993 and September 1996 the federal funds rate increased 219 basis points. This would predict an 81 basis point rise in the yield. The actual yield increased 123 basis points in this time. From February 1996 to February 2000 the federal funds rate increased only 11 basis points, while the yield increased 71 basis points. Finally, from May 2000 to May 2002 the federal funds rate decreased 428 basis points, with a predicted drop of 158 basis points in the yield. The yield declined 128 basis points. These results show that the yield tends to increase more than the increase in the federal funds rate, and tends to decrease less quickly as the federal funds rate declines. There appears to be a direct relationship between these two rates, exactly as predicted. Looking at the other variables in our model with a mind towards what could be keeping the yield low as the federal funds rate increases shows that the unemployment rate is the next most influential coefficient at .205. This seems to make sense since the unemployment numbers are one of the most widely watched numbers in all of economics and finance. This gives us an indication of the real economy, what real employers are doing and what everyday people are faced with in their lives. These situations affect how much people can spend and might provide some measure of the productivity required by employers and businesses to accomplish their production goals. The exchange rate is a very significant indicator in the model and would be a good candidate for future study all on its own. This would probably be best done as a group of
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
9
individual currencies rather than a basket, with a focus on watching out for currencies that are pegged to the dollar and which are known to be large buyers of Treasury securities.
IV. Conclusion Investors and institutions need to be able to rely on some degree of certainty when trying to establish future policies and investment decisions. One of the most important and unavoidable components of this decision making process is interest rates. What the government of the United States is doing with its monetary policy, and how this and other factors affect the debt of the U.S. has a direct effect on interest rates. This study focused on maybe the single most important benchmark interest rate in the world, the 10-year Treasury bond yield. Gaining an understanding of the influences of this rate, and the dynamics involved in determining or predicting it go a long way in the financial world. This study, however cursory, is one of only a very few to touch on the relationship between this interest rate and the federal funds rate. That is one of the most surprising aspects of this endeavor. Our original conclusion, that the federal funds rate has a strong and direct influence on the 10-year Treasury yield, has been firmly established. We were able to derive a fairly accurate equation based on a linear regression, which was used to perform some predictions of where the Treasury yield ought to be given the actions of the Federal Open Market Committee. Several issues are open for further study. Although it was shown that monthly data was appropriate for this study, an examination of daily data, which might have more va riability in it than the smoothed monthly data, would hopefully produce some results supporting the conclusions made here. This daily data might also alleviate the problem of autocorrelation found in the current study. Also, since many institutions look to make investment decisions over
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
10
several years, using more lagged variables, possibly even a years worth, might prove fertile ground for analysis. We might also keep this study in mind for the next year or more to see if our results have an accurate effect going into the future. It seemed that over the long term this predictive model had positive results; however, we have only had eight months for prediction in this model.
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
11
Bibliography
Abel, A and Bernanke, B (2005) Macroeconomics, Pearson Addison Wesley publishing. Fleming, M and Remolona, E (1997) What moves the bond market? Federal Reserve Bank of New York Research Paper No. 9706. Gulley, D and Sultan, J (2003) The link between monetary policy and stock and bond markets: evidence from the federal funds futures contract, Applied Financial Economics, 13, 199209. Miller, Rich (2005) The Mystery of the Sleeping Long Bonds, BusinessWeek, January 31, 2005, 29. Tarhan, V. (1993) Policy and volatility of asset returns, Journal of Economics and Business 43, 269-283.
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
12
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
______________________________________________________________________ I. Introduction The Federal Open Market Committee raised the federal funds target interest rate from the historically low 1% to 1.25% at its meeting in June 2004. Macroeconomic theory tells us that long-term interest rates tend to move in the same direction, and generally in concert with, shortterm interest rates (Abel 2005). So, we would expect the yield on a long-term asset like the10year Treasury bond, which moves directly with interest rates, to move up when a short-term rate like the federal funds rate moves up. However, a cursory …show more content…
reading of financial news sources since the FOMC began its rate hike policy, through January 2005, show that the yield on the 10- year has actually fallen. This study will develop a predictive model to describe this direct influence and conclude that the federal funds rate directly influences the 10-year Treasury bond yield. This study will not try to predict what factors could be holding the yields down in any quantifiable way. The 10year Treasury bond yield is a benchmark rate, important to bond investors looking for future indicators of inflation, and to areas such as housing and other loans; a predictive model will allow investors to more adequately gauge investment risk and loan officers to judge what interest rates to charge Section II will present a brief review of the literature concerning these issues while helping to describe some decisions made in the current study. Section III will present the results of the data collection and analysis used to support our conclusions. The regression model will be described, and the predictions explained, with supporting evidence from the actual data. Section
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
1
IV will be a conclusion reestablishing our conclusions and also pointing out some of the aspects of the current study that caused some concern and that may warrant further investigation.
II. Review of the Issue There is some writing in the literature concerning how monetary policy affects asset prices, namely stocks and bonds. There are also studies that suggest the federal funds futures contract, the rate that people speculate the federal funds target rate will move to in the near term, is an indicator of monetary policy and the financial market’s reaction to such information. Fleming and Remolona (1997) use high frequency, intraday price activity to look at how announcements of events like the federal funds rate target, the employment numbers, the producer price index, and the consumer price index affect and contribute to price shocks and trading volume in the bond market. They found the federal funds rate target to be significant in their regressions, and that of the 25 greatest price shocks between 1993 and 1994, three of them were direct results of an announcement of a new federal funds target rate. Even with the strength of these results, their study of the federal funds target rate and its affect on bond prices had not been discussed in the literature up to that point. The study by Gulley and Sultan (2003) examines the federal funds futures contract as an indicator of monetary policy. They find that positive and negative changes in the federal funds rate have symmetric effects on the bond market, which supports my assertion that the federal funds rate has a direct effect on the 10- year Treasury bond yield. Further, they suggest that their findings are consistent with the expectation that an increase in the federal funds rate translates into lower bond prices, or higher bond yields which move inversely to prices.
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
2
Fleming and Remolona (1997) reference studies in the early 1980’s that show the impact of money supply announcements were significant in explaining market behavior. However, similar studies done in the mid 1980’s show a diminishing significance of these announcements. Gulley and Sultan (2003) suggest that there is a mixed review in the literature of how monetary policy aggregates, like the federal funds rate, affect long-term interest rates. Tarhan (1993) states that monetary policy may be an important factor in asset return volatility, and that the interaction of monetary policy, like the federal funds rate, and asset prices, like the yield on the 10-year Treasury bond, needs to be examined more fully. Based on this economic literature it is obvious that the relationship between the federal funds rate and the yield on the long term Treasury bond warrants further study. The preceding literature does not say anything directly about the actual federal funds rate. This paper makes the contribution of using the actual federal funds rate available to the banks, which carry out the Federal Reserve’s mo netary policy, as a contributor of the long-term bond yield.
III. Analytical Content – Empirical Results Anecdotally, why do we believe the federal funds rate will influence the Treasury bond yield? It is because this rate has become the Federal Reserves primary monetary policy tool used to effect its conclusions about the state of the economy. The Federal Reserve has built up a large supply of credibility over the years, so if it believes this country is headed for higher inflation, then most investors believe this. Also, it is the shortest-term interest rate on the market, lasting only a matter of hours when in use. But, it is also the quickest to be passed along to the general public in the form of higher interest loans and banking fees. It is no surprise that this short-term
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
3
benchmark rate would eventually have some influence on the long-term benchmark rate, the 10year Treasury bond yield. This study utilizes a multiple regression analysis to adequately determine the effect of the federal funds rate on the 10-year Treasury bond yield. A histogram of the residuals showed that the data followed a normal distribution, allowing us to use standard t and F tests to analyze the results. A White’s test was used to prove that the data were homoscedastic. Our high F test statistic and R-square values, along with highly significant coefficients from our explanatory variables, allowed us to conclude that there were no problems with multicollinearity. A DurbinWatson test did reveal that there was positive autocorrelation among the error terms. This required the use of a first-order autoregressive data transformation and the method of generalized least squares to help account for the autocorrelation and to derive our coefficients. Data gathered for this study was from the periods January 1990 through May 2004, a large enough period of time to include a variety of economic events – the early 1990’s recession, the stability of the mind 1990’s, the boom years of the late 1990’s, and the uncertainty of the recent past. Although this study is primarily concerned with the effect of the non-seasonally adjusted federal funds rate, using only this single variable to explain our yield would be inappropriate and would also violate our properly specified model assumption. Several other explanatory variables were included as controls to help specify the model and to distill the true effect of the federal funds rate. The findings of Fleming and Remolona (1997) show that employment, and the federal funds rate announcements were the number 1, and 4 most important in affecting bond price volatility, respectively. Accordingly, the non-farm, urban, non-seasonally adjusted unemployment rate is included as explanatory variable in our model. To arrive at a better
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
4
measure of the overall level of inflation anxiety and activity in the economy, the non-seasonally adjusted producer price index was included as an explanatory variable. All of these data were gathered from the Federal Reserve Bank of St. Louis’s FRED II database. Some of the early research into this subject suggested that exchange rates might play a part in the determination of the bond yield. Tarhan (1993) asserts that sterilized intervention policy, the way a country might manage their currency value by purchasing foreign debt, might be an important factor in asset return volatility. Miller (2005) provides a concrete example of this with the description of Asian central banks buying huge amounts of United States dollars, with the majority of this currency subsequently invested in 10- year Treasury bonds. The goal of this policy is to keep the dollar strong against currencies reliant on continued U.S. demand for imports. In order to account for the possibility that exchange rates might play a role in determining the yield, the trade weighted exchange index - a weighted average of the foreign exchange value of the U.S. dollar against the currencies of a broad group of major U.S. trading partners – was included as an explanatory variable. The data for the PPI and unemployment rates were only available in a monthly format, which required the use of monthly average rate data for the exchange rate and our two most important variables, the federal funds rate and the 10- year Treasury yield. According to Fleming and Remolona (1997), price shocks in the bond market occurred within 15 to 70 minutes of any news announcement. This is a remarkably quick time, certainly within the range of the daily data our study planned to use, and quick enough to lead us to believe that using monthly data would pick up the interaction between our explanatory variables and the yield. To further test that using monthly average data would not negatively affect the regression, two test models were created. The first regressed the daily federal funds rate against the daily yield rates, the second
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
5
regressed the monthly federal funds rate against the monthly yield rate. The results were nearly identical, providing convincing evidence that the use of monthly data would be sufficient to properly specify the model. To avoid problems with causality, that is, regressing the explanatory variable data against the yield data from the same month, we used lagged explanatory data. The unemployment rate, PPI, and exchange rate data are each one- month behind the corresponding yield rate. In testing different lag combinations to account for the autocorrelation problem and the causality situation, it was found that using the federal funds rate lagged one and two months behind the yield rate were significant in the regression. These are shown in the regression equation as FFR1 and FFR2. Research by Fleming and Remolona (1997) suggest that there might be a seasonality aspect to the markets behavior. So the last technique used to design the correct regression model was to use dummy variables, one for each month except December, the baseline month. The final regression equation, minus the dummy variables, looks like this:
Yi = B0 + B1FFR1 + B2FFR2 + B3UNEMP + B4PPI + B5EX + ui
Table 1 – Regression Statistics
Intercept FFR1 FFR2 UNEMP PPI EX R Square F stat Significance F Observations
Coefficients 8.4652 0.9912 -0.6171 0.0205 -0.0207 -0.0259 0.8460 52.1973 2.3117 E-53 169
Standard Error 2.1788 0.2562 0.2310 0.1442 0.0100 0.0080
t Stat 3.8853 3.8690 -2.6817 1.4221 -2.5950 -3.2199
P-value 0.0002 0.0002 0.0081 0.1570 0.0412 0.0016
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
6
We can use standard hypothesis testing techniques to determine the significance of our two federal funds rate coefficients.
The calculated t-stats of 3.8690 and –2.6817, compared to statistical tables, show that our coefficients are significant in the model at a 95% and 99% level. Further, the calculated P-values show that if the null hypothesis of these coefficients being statistically the same as zero, and thus not having an influence on the model, were true, the probability of obtaining these t-stats is 0.0002, and .0081, respectively. We can be quite confident that our federal funds rate coefficients are significant and have a strong influence over the Treasury yield. An interval estimation construction shows that the federal funds rate (FFR1) coefficient would be somewhere between .4890 and 1.4934 with 95% certainty, and the federal funds rate (FFR2) coefficient would be between –1.0700 and –1.6430 with 95% certainty. Since the null- hypothesized value of zero is not included in either range, we can again reject the hypotheses that we have committed a Type-I error with 95% confidence. T tests show that all the explanatory variables are individually significant in the model at at least the 95% confidence level. However, we do want to test the overall significance of our estimated regression model to ensure that we have not incorrectly specified the equation and to attest to the strength of our predictive model. Judging by the significant F statistic value of 2.3117 E-53, or essentially zero, we can reject the hypothesis that the federal funds rate, unemployment rate, PPI, and our exchange rate basket, together have no effect on the 10-year Treasury yield. This gives us a high level of confidence that our model is correctly specified. Such a significant F statistic also allows us to conclude that our R2 value is highly significant as well; that indeed 84.60% of the total variability in the Treasury yield data is explained by our model. Since all of our data is
a rate of some kind, we can speak in terms of basis point movements. It would be improper to isolate our one federal funds rate variable and say that a
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
7
100 basis point move in the FFR1 causes a 99 basis point move up in the Treasury yield. It is more proper to look at both federal funds rate variables and say that we can subtract the FFR1 and FFR2 rates to arrive at the conclusion that a 100 basis point move in the federal funds rate causes a 37 basis point move up in the Treasury yield. This is a far stronger influence than any other variable in the model. By this reasoning we would expect that by October or November of 2004 the yield would have risen around 37 basis points. The data show that the yield actually fell by 60 basis points. However, we cannot draw a direct prediction on the yield based solely on the federal funds rate due to the significant influence of the other variables. If we use our regression equation to predict the Treasury yield in the months since May of 2004 through January of 2005, the time when the FOMC has steadily increased the federal funds target rate, we get these results: Estimated June July August September October November December January 3.87 4.02 4.22 4.18 4.21 4.23 4.38 4.54 Actual 4.73 4.50 4.28 4.13 4.10 4.19 4.23 4.22
The estimated results show the general trend of an increasing yield, as we would expect. We cannot say that the actual yield is incorrect, because that is what the market determined price for this investment truly was. However, Miller (2005) suggests that some investors believe the yield on the 10-year Treasury to be as much as 50 basis points lower than it should be, so there is some traction to the theory that the market is operating somewhat inefficiently. Also, looking at the estimated data shows that the yield should have increased 21 basis points in the four months
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
8
since July and 36 basis points in the 5 months since July. This puts us in a position to reliably say how much influence the federal funds rate has on the yield, or at least close in on a range over time. Taking some random samples from the data imply that our estimate of 37 basis points per 100 basis points of the federal funds rate might be accurate. Between September 1993 and September 1996 the federal funds rate increased 219 basis points. This would predict an 81 basis point rise in the yield. The actual yield increased 123 basis points in this time. From February 1996 to February 2000 the federal funds rate increased only 11 basis points, while the yield increased 71 basis points. Finally, from May 2000 to May 2002 the federal funds rate decreased 428 basis points, with a predicted drop of 158 basis points in the yield. The yield declined 128 basis points. These results show that the yield tends to increase more than the increase in the federal funds rate, and tends to decrease less quickly as the federal funds rate declines. There appears to be a direct relationship between these two rates, exactly as predicted. Looking at the other variables in our model with a mind towards what could be keeping the yield low as the federal funds rate increases shows that the unemployment rate is the next most influential coefficient at .205. This seems to make sense since the unemployment numbers are one of the most widely watched numbers in all of economics and finance. This gives us an indication of the real economy, what real employers are doing and what everyday people are faced with in their lives. These situations affect how much people can spend and might provide some measure of the productivity required by employers and businesses to accomplish their production goals. The exchange rate is a very significant indicator in the model and would be a good candidate for future study all on its own. This would probably be best done as a group of
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
9
individual currencies rather than a basket, with a focus on watching out for currencies that are pegged to the dollar and which are known to be large buyers of Treasury securities.
IV. Conclusion Investors and institutions need to be able to rely on some degree of certainty when trying to establish future policies and investment decisions. One of the most important and unavoidable components of this decision making process is interest rates. What the government of the United States is doing with its monetary policy, and how this and other factors affect the debt of the U.S. has a direct effect on interest rates. This study focused on maybe the single most important benchmark interest rate in the world, the 10-year Treasury bond yield. Gaining an understanding of the influences of this rate, and the dynamics involved in determining or predicting it go a long way in the financial world. This study, however cursory, is one of only a very few to touch on the relationship between this interest rate and the federal funds rate. That is one of the most surprising aspects of this endeavor. Our original conclusion, that the federal funds rate has a strong and direct influence on the 10-year Treasury yield, has been firmly established. We were able to derive a fairly accurate equation based on a linear regression, which was used to perform some predictions of where the Treasury yield ought to be given the actions of the Federal Open Market Committee. Several issues are open for further study. Although it was shown that monthly data was appropriate for this study, an examination of daily data, which might have more va riability in it than the smoothed monthly data, would hopefully produce some results supporting the conclusions made here. This daily data might also alleviate the problem of autocorrelation found in the current study. Also, since many institutions look to make investment decisions over
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields Kane Snyder 5/2/2005
10
several years, using more lagged variables, possibly even a years worth, might prove fertile ground for analysis. We might also keep this study in mind for the next year or more to see if our results have an accurate effect going into the future. It seemed that over the long term this predictive model had positive results; however, we have only had eight months for prediction in this model.
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
11
Bibliography
Abel, A and Bernanke, B (2005) Macroeconomics, Pearson Addison Wesley publishing. Fleming, M and Remolona, E (1997) What moves the bond market? Federal Reserve Bank of New York Research Paper No. 9706. Gulley, D and Sultan, J (2003) The link between monetary policy and stock and bond markets: evidence from the federal funds futures contract, Applied Financial Economics, 13, 199209. Miller, Rich (2005) The Mystery of the Sleeping Long Bonds, BusinessWeek, January 31, 2005, 29. Tarhan, V. (1993) Policy and volatility of asset returns, Journal of Economics and Business 43, 269-283.
How the Federal Funds Rate Affects 10 Year Treasury Bond Yields
Kane Snyder
5/2/2005
12