Econometric Analysis of Utility Sector

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Overview

The objective of this project is to study the evolution of the Utilities return and measure the

risk associated with it.

The data we are using for this analysis is the monthly data across the time period between January 1990 to November 2014. The returns we are using to run the regressions are excess returns i.e. return on the stocks excess of the risk-free interest.

The utilities sector is a category of stocks for utilities such as gas and power among others. The sector contains companies such as electric, gas and water firms, and integrated providers. Because utilities require significant infrastructure, these firms often carry large amounts of debt; with a high debt load. As a high-yielding equity investment, utilities companies become sensitive to changes in the interest rate [1].

Part 1:  LINEAR REGRESSION

1. CAPM Model vs FAMA French Model:

CAPM Model: The CAPM model assumes a linear relationship between the expected return in a risky asset and its β and further assumes that β is an applicable and sufficient measure of risks that captures the cross section of average returns, that is, the model assumes that assets can only earn a high average return if they have a high market β. In its simplest form the CAPM is defined by the following equation [2]:

Ra = Rf + β x (Rm – Rf)

• Ra = Returns of the stock
• Rf = The intercept (The risk-free rate)
• β = The sensitivity to the market
• (Rm – Rf) = The excess return of the market

After performing the regression of the CAPM model for the utilities data set. These are results which are obtained.

R-squared: 0.193, Adjusted R-Squared 0.19. The estimates of the coefficients are below:

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FAMA FRENCH MODEL: The Fama-French Three-Factor Model is a method for explaining the risk and return of stocks. It is an extension to the CAPM Model that uses a single factor, beta, to compare a portfolio with the market. The other two factors in the Fama-French model are ‘Size’ – the extra risk in small company stocks and the ‘Value’ – the value in owning out-of-favor stocks that have attractive valuations [3].

The results of the Fama-French model regression for the utilities data set are as below:

R-squared: 0.35, Adjusted R-Squared 0.344. The estimates of the coefficients are below:

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Based on the results obtained from testing the two models; the CAPM Model and the Fama French Model. An analysis is conducted of the R2 and the Adjusted R2 values to select which model is a better fir for the Utilities Dataset. The values for the same are as follows:

• CAPM Model

Ordinary R2 – 0.1926

Adjusted R2 – 0.1899

• Fama-French Model

Ordinary R2 – 0.35

Adjusted R2 – 0.34

Since the R2  and Adjusted R2  values for the Fama-French Model are higher, the model is a better fit to the actual data. Therefore, Fama-French Model is chosen over the CAPM Model for further analysis of the given data.

1.  Hypothesis Testing

After finding that Fama-French is a better fit than CAPM model, we are interpreting the coefficients and carrying out the hypothesis testing on the estimates.

From the estimates obtained from the regression, we find from the p value and t statistics that the Mkt, SMB & HML are statistically significant or different from zero because the p values are smaller than the significance level of 0.05. The intercept though is not statistically significant or different form zero because of the higher p value (0.28) than 0.05.  

The estimated value of β1 (Mkt) is 0.5142, which states that the excess returns of the utilities industry will be nearly half the excess returns of the market excess returns. The estimated value of the β2 (SMB) is -0.0015722 which is very small, but the returns vary in the opposite way of the small cap performance. The estimated value of the β3 (HML) is 0.0045525 which is very small, but the returns vary the same way as the stocks with a high value stocks.

We are testing the null hypothesis that β3 (HML) is 0.005

• Null Hypothesis (H0): HML = 0.005

Obtained p-value  = 0.2694

Since the p-value is not smaller than the significance level of 0.05, the null hypothesis (H0) cannot be rejected. Also, the 95% confidence interval for β3 (HML) is [0.0033,0.0058] which states that 0.005 is in the 95% confidence interval of β3.

That is HML value is statistically not different form 0.005.

 The second hypothesis we are testing is both β1 = 0.5, β3 = 0.005

• Null Hypothesis (H0): β1 = 0.5, β3  = 0.005

Obtained p-value = 0.7123,

Obtained F statistic = 0.3396

Again, since the p-value is not small, the null hypothesis (H0) cannot be rejected. Also, the F statistic is less than the critical value which is why (H0) the null hypothesis cannot be rejected.

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