Question

QUESTION 2

Howard Golub, CFA, is preparing to write a research report on Stellar Energy Corp. common stock. One of the worlds largest companies, Stellar is in the business of refining and marketing oil. As part of his analysis, Golub wants to evaluate the sensitivity of the stocks returns to various economic factors. For example, a client recently asked Golub whether the price of Stellar Energy Corporation stock has tended to rise following increases in retail energy prices. Golub believes the association between the two variables to be negative, but he does not know the strength of the association. Golub directs his assistant, Jill Batten, to study the relationships between Stellar monthly common stock returns versus the previous months percent change in the U.S. Consumer Price Index for Energy (CPIENG), and Stellar monthly common stock returns versus the previous months percent change in the U.S. Producer Price Index for Crude Energy Materials (PPICEM). Golub wants Batten to run both a correlation and a linear regression analysis. In response, Batten compiles the summary statistics shown in Exhibit 1 for the 248 months between January 1980 and August 2000. All of the data are in decimal form, where 0.01 indicates a 1 percent return. Batten also runs a regression analysis using Stellar monthly returns as the dependent variable and the monthly change in CPIENG as the independent variable. Exhibit 2 displays the results of this regression model.

EXHIBIT 1 - Descriptive Statistics

	Monthly Return Stellar Common Stock	Lagged Monthly Change CPIENG                   PPICEM
Mean Standard Deviation Covariance, Stellar vs. CPIENG Covariance, Stellar vs. PPICEM Covariance,CPIENG vs. PPICEM Correlation, Stellar vs. CPIENG	0.0123 0.0717 -0.00017 -0.00048 0.00044 -0.14524	0.0023 0.0160	0.0042 0.0534

EXHIBIT 2 - Regression Analysis with CPIENG

Regression Statistics Multiple R                                                           0.1452 R−squared                                                          0.0211 Standard error of the estimate 0.0710 Observations 248 Coefficients Standard Error t−Statistic Intercept                                                             0.0138                   0.0046                   3.0275 Slope coefficient                                              -0.6486 0.2818                   -2.3014

(2.1) Batten wants to determine whether the sample correlation between the two variables, namely the Stellar and CPIENG variables (-0.1452) is statistically significant. The critical value for the test statistic at the 0.05 level of significance is approximately 1.96. Batten should conclude that the statistical relationship between Stellar and CPIENG is

1. not significant, because the calculated test statistic has a higher absolute value than the critical value for the test statistic.

2. not significant, because the calculated test statistic has a lower absolute value than the critical value for the test statistic.

3. significant, because the calculated test statistic has a lower absolute value than the critical value for the test statistic.

4. significant, because the calculated test statistic has a higher absolute value than the critical value for the test statistic.

(2.2) Based on the regression, which used data in decimal form, if the CPIENG decreases by 1.0 percent, what is the expected return on Stellar common stock during the next period?

1. 0.0203 (2.03 percent)

2. 0.0138 (1.38 percent)

3. 0.0073 (0.73 percent)

4. 0.0065 (0.65 percent)

(2.3) Based on Batten’s regression model, the coefficient of determination indicates that

1. Stellar’s returns explain 14.52 percent of the variability in CPIENG.

2. Stellar’s returns explain 2.11 percent of the variability in CPIENG.

3. Changes in CPIENG explain 14.52 percent of the variability in Stellar’s returns.

4. Changes in CPIENG explain 2.11 percent of the variability in Stellar’s returns.

(2.4) For Batten’s regression model, the standard error of the estimate shows that the standard deviation of

1. the residuals from the regression is 0.0710.

2. values estimated from the regression is 0.0710.

3. Stellar’s observed common stock returns is 0.0710.

4. the intercept estimate from the regression is 0.0710.

(2.5) For the analysis run by Batten, which of the following is an incorrect conclusion from the regression output?

1. Viewed in combination, the slope and intercept coefficients from Batten’s regression are not statistically significant at the 0.05 level.

2. In the month after the CPIENG declines, Stellar’s common stock is expected to exhibit a positive return.

3. The estimated intercept coefficient from Batten’s regression is statistically significant at the 0.05 level.

4. In the month after no change occurs in the CPIENG, Stellar’s common stock is expected to exhibit a positive return.

Answer 1

(2.1) right choice is

4. significant, because the calculated test statistic has a higher absolute value than the critical value for the test statistic.

here we use t-test and t =r/sqrt[(1—r²)/(n—2)]=-0.1452/sqrt((1-(-0.1452)*(-0.1452)/(248-2))=-2.3 with n-2=248-2=246 df

(2.2) right choice is 4. 0.0065 (0.65 percent)

here the slope coefficient is -0.6486 (equivalently 0.65, two decimal place approximation) and slope is change in dependent variable Stellar’s returns. when unit change is done in independent variable CPIENG .

(2.3) 4. Changes in CPIENG explain 2.11 percent of the variability in Stellar’s returns.

here the R2=(-0.1452)*(-0.1452)=0.0211 is amount of variation in dependent variable Stellar’s return explained by independent variable CPIENG

(2.4) 1. the residuals from the regression is 0.0710.

(2.5) 1. Viewed in combination, the slope and intercept coefficients from Batten’s regression are not statistically significant at the 0.05 level.

both intercept and slope are significant as the absolute t-value is more than critical value 1.96