Thursday, October 6, 2016

Modeling the impact of interest rates on stock prices

Initial thoughts on the impact of interest rates on six stock ETFs

In a previous post published in my finance blog I strongly suggested that six extremely popular Stock ETS are overpriced at the end of September 2016. 



The previous post presented a bleak general assessment of the investment environment.   By contrast, this post asks a very specific question.

What is the potential impact of an increase in interest rates on the six popular broad-based stock ETFs presented in the previous post?

Assignment:    Collect daily close stock market data for six stock ETFs – VTI (total Stock market), VB (Small Cap Stocks), VV (Large Cap Stocks), VUG (growth stocks), VDC (consumer stocks) and VIG (Dividend Stocks) – over the period starting the first market day in 2014 to September 30, 2016.   Use the data to estimate a distributed lag model of the log of the daily stock price change on the 10-year risk-free interest rate.  

Comment on the estimated impact of an increase in interest rates on the price of these six conservative stock ETFs.

Discuss the limitations of these distributed lag results.

Suggest refinements to this empirical work that would lead to a better understanding of the impact of interest rate changes on ETF prices.

A Note on data and the Model:  The data used in this paper was downloaded from yahoo finance.  The model was estimated with 545 closing price and closing 10-year ETF interest rate observations starting from the beginning of 2014 to September 30 2016.

The dependent variable in this analysis is the log of the price of the ETF.  The independent variables are the lag of the dependent variable and the log of the 10-year Treasury interest rate.


Results:   The table below contains the estimated regression coefficients and the p-value for the test that the coefficient is zero for the lagged dependent variable and the 10-year interest rate variable.


Results of Distributed Lag Model of Stock Price on Ten-Year Interest Rate
Fund
VTI
VB
VV
VUG
VDC
VIG
Fund  Description
Total Stock Market
Small-  Cap Stocks
Large Cap Stocks
Growth Socks
Consumer Stocks
Dividend Stocks
Lag Dependent Variable Coeff
0.969
0.972
0.969
0.972
0.972
0.96
p-value
0
0
0
0
0
0
Ten Year  Interest rate
Coeff.
-0.0074
-0.0045
-0.0077
-0.0077
-0.015
-0.0065
p-value
0.01
0.08
0.01
0.02
0
0.01
Sample size
545
545
545
545
545
545
R2
97.8
96.8
98
98.1
99.4
96.6
MSE
0.00867
0.00966
0.00859
0.00924
0.0075
0.0078


Discussion of Results:


The estimated coefficient of the interest rate variable is negative for all 6 stock ETF models.   The p-value is near 0.01 for 5 of the six coefficients.  The relationship between interest rates and stock prices appears significant at conventional levels of significance.

Interest rates appear to have the largest impact on consumer stocks and the smallest impact on small-cap stocks.


The lagged dependent variable is very close to 1.0 suggesting that the long-term effect of a change in interest rates is larger than the short-term effect.   (However, please see the comment below on this point.)


Comments and Caveats:


The long-term effect of the change of interest rates on the log of the stock price is interest rate coefff/ ( 1- lagged dependent variable coefficient).   I did not correct for first-order serial correlation in these regression models.   This ordinary least squares estimation method may have resulted in a biased estimate of the lagged dependent variable coefficient if the first-order AR term is correlated with the lagged dependent variable.   Future work will correct for this problem.

I believe that the relationship between interest rates and stock prices varies with economic conditions.   Right now economic growth remains slow but the economy is near full employment defined by the traditional unemployment rate and interest rates remain near historic lows.  Stock prices are high and some would say the stock market is in a bubble.   Under these circumstances I am not surprised that the relationship between interest rates and stock prices is negative.

Under different economic circumstances the relationship between interest rates and stock prices might be positive.  For example, the drop in interest rates during the 2008 financial crisis coincided with a drop in stock prices because both events were caused by the decrease in aggregate demand.

Concluding Thoughts:  The impact of interest rates on stock prices is a timely issue given that interest rates are near their historic lows, stock prices are very high and interest rate policy at the Fed and the market reaction to factors impacting interest rates may soon change.  

This essay is my first attempt to model the impact of interest rates on stock prices. The results presented here suggest that the major stock ETFs will fall in value should interest rates begin to rise.  These results reinforce my pessimistic view of the investment environment discussed in the finance post cited at the beginning of this article.

The model used here is admittedly simple.  The model would not consistently predict stock price changes over a long period where many economic variables changed.   However, parsimonious models of this type are often effective when used to assess short-term changes.

Future work will consider more complex models and measures of interest exposure starting with the comments and caveats listed above.  





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