# «Daniel Domb An honors thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Science Undergraduate College Leonard ...»

Through my research I had two main goals. The first goal is to use economic indicators in conjunction with consumers’ choices to describe current fixed mortgage rates. Now that I have developed a model that describes over 98% of the uncertainty of the fixed mortgage rate, I will move onto my second main objective. My second main

using not only economic indicators, but those indicators combined with the choices of the median consumer when they purchase a home. I believe that the general population can make inferences based on the average homebuyer and how their actions change based on their perceptions of future interest rates.

When borrowers purchase a home there is typically a 30-90 day escrow period.

Borrowers make many choices when they purchase a home, some of those choices are made when they sign an agreement of sale and other choices are made between the time they sign the agreement and settlement. Usually borrowers lock there interest rates within 45 days of closing, or they may have to pay an additional locking fee. Borrowers make choices like the type of financing, either adjustable or a fixed rate, the length of the financing, the amount of financing, and the amount they are actually paying for the home.

Accept for the last choice, the others occur during the 30-90 day escrow period. To go further with my analysis we have to agree on a couple of assumptions. First, borrowers want the best deal possible, and don’t want to waste money. Second, if borrowers can invest their money somewhere else and make more they will make that choice.

Understanding the choices a borrower must make, one can see that borrowers do their best to predict what they think of interest rates in the future, in order to save them as much money as possible.

Out of the 11 independent variables entered into my first model, seven of the variables are directly based on the choices that consumers make in a given month. The

indicators that are not directly connected to consumers’ choices. To test the validity of my claim I ran several regressions to try and prove that borrowers as a whole have a very good understanding of the interest rate market, and have the ability to predict future rates.

However, before I can attempt to predict rates, I need to develop a benchmark to test my results against to see if there is any substance to my model.

To test if borrowers’ choices can predict interest rates that are 30 days in the future, I will start with my benchmark regression between the fixed rate of this month as the independent variable and next month’s fixed rate as the dependent variable. This simple regression will show the predictability of future rates by only looking at what current rates are to predict the next month’s rates. Exhibit 27 displays the regression equation and residuals, which are very significant with an f-statistic of almost 8,323 and an R-sq of 98.1%. These results are not surprising, because it usually takes more than a couple months to drastically change, and usually with any cyclical measure, they run in trends, several months in a row go up, and then several months in a row go own. The residual plot from this regression tells an interesting story. Clearly one can see when rates were the most volatile on a month to month basis. For example, in 1994-1995 rates first dropped, then increased, and then dropped again by over 200 basis points.

The true test if borrowers can predict interest rates 30 days in the future would mean that by using borrowers’ choices when purchasing a home, they can better describe future rates than current rates can. The first multi-linear regression I ran included all 11

variable. This regression yields an R-sq of 98.5% and an R-sq adjusted of 98.4 %.

Already we can see that there is value in this model because the R-sq adjusted has increased from 98.1% to 98.4%. However, interestingly, there is clearly one data point with an unusually high residual value at 3.19. Exhibit 28 shows a graphical representation of the residuals and it is difficult not to see the outlier at first glance.

Again this point is located at data point number 124, April 2000. I have already described the reason for this point not conforming to the model, and in this circumstance I decided to re-run the regression without this point to test the effect on the overall model.

In addition to removing data point 124, I also decided to remove the “peak to trough” variable because the p-value of this variable was so high at.8 and I knew that the removal of this variable would not affect the R-sq but would increase the f-statistic of the model.

The resulting model improved noticeably. The residual plot in Exhibit 29 is much tighter than the plot in Exhibit 28 and the R-sq increased by.1% to 98.6%, with an R-sq adjusted of 98.5%. The resulting model has a very good predictability of future interest rates.

To further investigate my hypothesis I decided to test this months fixed rate combined with the 7 independent variables that are decided based directly on consumers’ choices and used them to describe the dependent variable of the next months fixed mortgage rate. For this regression I added back in the outlier that was removed in the previous regression, because it may not be a problem in this analysis. This regression will prove if consumers’ choices play a role into helping decipher future interest rates,

statistically significant with an R-sq equaled to the R-sq adjusted at 98.5%. Out of the 8 variables “term to maturity” had a very high p-value at.588, so I decided to remove this variable from the model to increase my f-statistic, and hopefully keep the R-sq at 98.5%.

As I predicted Exhibit 30 displays the final regression and the R-sq has remained at 98.5%, which is significantly higher than the 98.1% R-sq without consumers’ choices in the model. Attempting to remove any further variables from the current model decreases the R-sq adjusted for the model, hence my final regression stands with 6 consumer choices and the fixed rate of the previous month.

My next goal is to see if consumers have the same predictive power over a 60 day period. Again I will use a benchmark of the current fixed rate against the fixed rate plus two months. Remembering back to the 30 day prediction model with only the fixed rate, the R-sq was 98.1%, however the extra 30 days drastically changes the model to 93.9%.

A detailed analysis of the fixed rate as the independent variables and the fixed rate plus 2 months as the dependent variable can be found in Exhibit 31. The fixed rate regression equation puts a lot more emphasis on the constant than the previous model. The implications of this regression show that although month to month changes are usually fairly predictable, adding a single month changes the predictability drastically, and it is difficult without other variables to accurately predict where interest rates are going with only the current month’s fixed mortgage rates.

against the fixed rate plus two months as the dependent variable. This regression was statistically significant with an R-sq of 96.8% and an R-sq adjusted 96.5%. Since there is a large gap between the R-sq and the R-sq adjusted, I removed data point 124 again, because similarly to the earlier residual plot, it was an obvious outlier with a residual value at just above 3. In addition to removing the data point from April 2000, I also removed “arm share” from independent variables because the after testing the removal of all of the independent variables with high p-values, it was the only removal that made a positive difference. The p-value for “arm share” was the highest of all of the variables at.774. The new regression with only 10 independent variables, which is displayed in Exhibit 32, has an R-sq of 97% and an R-sq adjusted of 96.8%. This final model has great predictive power for interest rates that are 60 days away compared with the benchmark R-sq of 93.9%.

To look further into the predictability of fixed rates two months in advance through consumers choices alone from economic indicators, I ran a regression between the current fixed rate and the 7 independent variables controlled directly from consumers choices against the fixed rate plus two months as the dependent variable. Again I put the outlier back into the model, in addition, “arm share’ was included in the multi-linear regression. The new regression output, which is in Exhibit 33, has an R-sq of 95.1% and an R-sq adjusted of 94.9%, which is an entire percentage point higher than without consumers choices factored into the model. Using the median consumers’ choices one

advance.

Although consumers may be able to predict interest rates a year in advance, the furthest applicable time period for the purpose of my research is 90 days in advance.

Again, before I attempted to build a model using the median consumers, I ran a simple regression between the fixed mortgage rate as the independent variable and the fixed rate plus three months as the dependent variable. If the last two benchmark regressions are any indication of what this regression will show, I expected the amount of uncertainty that the model can predict to drop further than the last regression. Not surprisingly, in Exhibit 34, one can see that the R-sq of the fixed rate against the fixed rate plus three months has dropped to 89%. The lower R-sq further implies that the more time between the fixed rates from different months the more emphasis is placed on other factors that describe the actual future rate. Although I did not run a regression that lagged the fixed rate by four or five months, I can only suspect that the R-sq from these simple regressions would get progressively worse.

My first multi-linear regression with all 11 independent variables against the fixed rate plus three months as the dependent variable yielded an R-sq of 93.9% and an R-sq adjusted of 93.5%. Although this regression already is a better indicator than the benchmark regression, the model can be improved by refining the variables. Exhibit 35 displays my final regression. My final regression only contains 8 of the original 11 independent variables. I eliminated the refinance index, investment to loan ratio and arm

all 11 variables of 93.9%, but the R-sq adjusted increased to 93.6%, and with the subtraction of variables without decreasing the statistical significance of the model, the fstatistic increased in the final model. Again I have been successful in showing that consumers in conjunction with the use of economic indicators have predictive power over future fixed mortgage rates. It is worth noting that out of the three multi-linear regressions I ran in this fashion, only this regression with the lagged 90 day regression did not have any outliers removed from the model. For some unexplainable reason that data point 124 or April 2000, was no longer an outlier in this regression.

In addition, to their existing predictive powers with the examination of consumers choices with economic indicators, I hypothesize that there is power in looking at consumers choices alone, isolated from economic indicators. To test this hypothesis I will take the benchmark simple regression and transform it into a multi-linear regression by adding the seven independent variables that are directly related to the choices that the general population of consumers makes during a given month. The resulting regression is represented in Exhibit 36. Consumers’ choices in combination with the current fixed rate do more accurately predict fixed mortgage rates that are 90 days in the future better than the benchmark regression. The regression has an R-sq of 91.1% and the R-sq adjusted is 90.7%. This final regression does not include “mortgage originations” as that is the only variable that improves the model when it is removed from the equation.

Another worthwhile observation with this regression refers to the residual plot also featured in Exhibit 36. The residual plot clearly shows an underlying pattern, which was

out, the longer the time frame the more clearly an underlying pattern appears in the residual plots that do not include any economic indicators. The implication of this finding is that consumers do a good job predicting interest rates as long as macro economic effects are kept to a minimum, but the longer the time frame, the more that other economic indicators must be taken into account with consumers choices to accurately predict interest rates.

## ANALYSIS OF RESULTS:

I have developed 7 final regressions. 6 out of the 7 regressions, according to the regression analysis, do a good job describing most of the uncertainty of a fixed rate mortgage. Interestingly, the model that includes the median consumer information and the economic indicators does a better job predicating interest rates that are 30 days away than it does at describing current rates. Still, most of the models describe over 98% of the uncertainty in a fixed rate. However, to truly check the validity of my models I must use the models to describe rates that are outside of my data set. Since my data set concludes with August of 2003, I will use information for the rest of 2003 and into 2003 to further test the usefulness of my model. Exhibit 37 shows the resulting data when applying each of the 7 regressions to the six month period, compared with the actual fixed rate across the last row of the chart. None of the models accurately predict or explain the fixed mortgage rate perfectly. To examine if there is a graphical relationship between the modeled explained fixed rate and the actual, I constructed a line graph of all 7 regressions and the actual fixed rate in Exhibit 38. Looking at the graph, it is difficultthis graph one can question if these multi-linear regressions have shed any light on future mortgage rates, other than providing a close estimation to the actual fixed mortgage rate.