Regression Analysis

 

The following independent variables were used for the regression model (34 monthly observations, November 1998-September 2001):
 

·         % Change in Fed Funds rate

·         % Change in Month-Average Temperature, Southern Region of US

·         % Change in Natural Gas Prices (Henry Hub)

·         % Change S&P 500 Index Price

·         Weather Factor Index

 

The data resulted in the following regression model:

 r_i = .071 + .711(%DFedFunds)+1.058(%DSP500)-.186(%DNaturalGas)+.19(%DTemperature)+.029(WeatherFactor)+.17

Interpretation of Coefficients:

 

B₀ = .071 represents the average monthly return on LD stock if the independent variables were 0.  This represents the slope intercept.

 

Independent variable coefficients:  r_i changes by b_i for each unit change in X, all else constant.  For example:  For each percent change in the Fed Funds rate, the monthly return on LD stock will change by .711%, if all other independent variables remain constant.

 

E = .17, the amount in which the observations of LD rate of return deviates from the estimated values.

 

Interpretation of other regression output:

 

Regression Statistics
Multiple R	0.490340722
R Square	0.240434023
Adjusted R Square	0.104797242
Standard Error	0.17668101
Observations	34

 

R Squared: 24% of the variation in the return on LD observations can be explained by the linear relationship with the independent variables.  The adjusted R squared takes into consideration the sample size and makes adjustments for small or large amount of observations.

 

ANOVA
	df	SS	MS	F	Significance F
Regression	5	0.276673905	0.055335	1.772631	0.15107
Residual	28	0.874053023	0.031216
Total	33	1.150726929

 

The ANOVA output shows the variation of the rate of return on LD stock that is explain by the variation of independent variables is .276 (SS-Reg).  Consequently, the unexplained variation is .87 (SS-Res).  In summary, this favors the idea that there is not a strong relationship between the variation in the independent variables and the rate of return on LD stock.

 

	Coefficients	Standard Error	P-value
Intercept	0.070948411	0.032681711	0.038572
%DFedFunds	0.711703658	0.71189488	0.326002
%DSP500	1.057716564	0.64815377	0.1139
%DNatGas	-0.186316448	0.159877285	0.253701
%DWeather	0.190093133	0.24924214	0.452029
Weather Factor	0.028730755	0.012829416	0.033251

 

Looking at the independent variables on an individual bases, some observations can be made.  The coefficients, as discussed in the model above,  determine the rate of change in the dependent variable, rate of return on LD stock, for a given change in the independent variable.  The standard error gives the amount in which the estimated Y value (dependent variable – r of LD stock) deviates from the actual sample.  The P-Value is used to determine the marginal contribution of the independent variable in predicting the dependent variable.  The lower the P-value, the more that particular variable’s variance contributed to the variance of the rate of return on LD stock.

 

Overall Summary

 

Louis Dreyfus Natural Gas Corp. has significant exposure to interest rate changes, natural gas price changes, and changes in weather (as a major factor of natural gas price demand changes).  To hedge against these exposures, the company enters into various derivative contracts resulting in an offset of potential asset value or cash flow fluctuations.  Although LD hedges less than half of it’s significant commodity and interest rate risks, my regression analysis did not show that the independent variables were strong predictors of rate of return on LD stock.  This phenomenon may be attributed to a delayed price impact, a non-linear relationship between risk factors and the stock price, or the existence of collinearity in the supplied data.

Works Sited

 

Historical Stock Data

www.dailystocks.com

 

Fed Funds Rate Data

www.econmagic.com

 

Temperature Data

http://www.nws.noaa.gov/

 

Louis Dreyfus Natural Gas Financial Information

2000 Annual Report

Form 10-k Fiscal Year Ended December 31, 2000