TLB EXHIBIT 1

SUMMARY OUTPUT

Regression Statistics
Multiple R 0.397871332
R Square 0.158301597
Adjusted R Square 0.146771482
Standard Error 0.099101922
Observations 75

ANOVA
df SS MS F Significance F
Regression 1 0.134839089 0.134839089 13.72940301 0.000407887
Residual 73 0.716946939 0.009821191
Total 74 0.851786028

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.012199246 0.011491282 1.061608746 0.291912927 -0.010702847 0.035101338
Rm 1.222767145 0.330003035 3.705320905 0.000407887 0.565072054 1.880462236


PRG
SUMMARY OUTPUT

Regression Statistics
Multiple R 0.24432461
R Square 0.059694515
Adjusted R Square 0.046813618
Standard Error 0.03658517
Observations 75

ANOVA
df SS MS F Significance F
Regression 1 0.006202953 0.006202953 4.63434453 0.03464324
Residual 73 0.097708651 0.001338475
Total 74 0.103911604

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 0.008975806 0.004242203 2.115835815 0.037770035 0.000521107 0.017430505
Rm 0.262261834 0.121826267 2.15275278 0.03464324 0.019462438 0.50506123

Exhibit 1 shows two regression outputs, one for the company identified as “TLB”, the other for company identified as “PRG”. Each output was obtained by regressing the respective company’s monthly returns on the monthly returns of the S&P 500 Index. The time period covered is January 1, 2002 to April 1, 2008. In Exhibit 1, the label “Rm” stands for the “Returns on the market portfolio”, in our case, the S&P 500 Index.

Please base your answers to this question on information provided in Exhibit 1. Assume that there is nothing “unusual” about the time period spanned, and assume that the S&P 500 Index is the appropriate market proxy.
A) Which of the two firms, “TLB” or “PRG”, appears to have the higher UNSYTEMATIC risk? Cite specific evidence to support your answer.
B) In the CAPM context (i.e. one in which everyone holds a well-diversified portfolio), which of the two firms has the higher relevant risk? Explain.
C) Based on the regression output, how confident can we be that there IS a relationship between the returns for the company and the returns on the market? Make a statement for each company, and cite evidence.
D) One of the companies in Exhibit 1 is a leader in the Home Construction business, while the other is a leader in the Household Supplies sector (diapers, detergent, etc.). Based on the output, match the company name (TLB/PRG) with the appropriate sector (Home Construction/Household Supplies), and provide a reason for your choice.

http://www.webopedia.com/TERM/T/TLB.html

A) To determine which company has higher unsystematic risk, we can look at the standard error in the regression output. The standard error measures the variability of the actual returns around the predicted returns. The higher the standard error, the higher the unsystematic risk.

In Exhibit 1, the standard error for TLB is 0.099101922, while the standard error for PRG is 0.03658517. Since TLB has a higher standard error, it suggests that TLB has higher unsystematic risk compared to PRG.

B) In the CAPM context, the relevant risk for a company is measured by its beta coefficient. The beta coefficient measures the sensitivity of a stock's returns to overall market returns. A higher beta indicates higher relevant risk.

In Exhibit 1, the coefficient for Rm (returns on the market portfolio) for TLB is 1.222767145, while the coefficient for PRG is 0.262261834. Since TLB has a higher beta coefficient, it suggests that TLB has higher relevant risk in the CAPM context compared to PRG.

C) To determine the relationship between the returns for each company and the returns on the market, we can look at the p-value associated with the coefficient for Rm. The p-value measures the statistical significance of the relationship. A small p-value (below a certain significance level, typically 0.05) indicates a strong evidence for a relationship.

In Exhibit 1, the p-value for TLB is 0.000407887, which is below the 0.05 significance level. So, we can be confident that there is a relationship between the returns for TLB and the returns on the market.

For PRG, the p-value is 0.03464324, which is also below the 0.05 significance level. So, we can be confident that there is a relationship between the returns for PRG and the returns on the market.

D) Based on the provided information, we can match TLB with the Home Construction sector and PRG with the Household Supplies sector. The reason for this choice is not explicitly mentioned in the provided regression output. However, the context provided mentions that one company is a leader in the Home Construction business, while the other is a leader in the Household Supplies sector.