Question C2

Ken is a junior stock analyst for an investment firm. He believes that stock returns are highly determined by the value, leverage and profitability of a company. With that, he decides to conduct a cross-sectional regression on the following variables.

Ri = stock returns for stock i BMi = book-to-market ratio for stock i DEi = debt-to-equity ratio for stock i ROEi = return on equity for stock i

The table below shows the output extract of the multiple linear regression for a cross- section of 20 randomly selected stocks on the local stock exchange.

ANOVA

Regression Residual Total

Intercept 0.2822 BM -0.0931 DE -0.0559 ROE 0.2271

df

3 16 19

Coefficients

SS

0.1778 0.0180 0.1958

Standard Error

0.0432 0.0256 0.0156 0.1148

C38FF

Required:

1. (a) Based on Kens regression output, construct the multiple regression equation using

   the notations given.

2. (b) What is the expected stock return for a company with a book-to-market ratio of 0.9,

   debt-to-equity ratio of 0.8 and a return on equity of 0.1?

3. (c) Explain how each of the independent variables is related to stock returns. (3 marks)

4. (d) Calculate the coefficient of determination and interpret this figure.

5. (e) Calculate the standard error of the estimate.

6. (f) Determine the 95% confidence interval for the coefficient of the debt-to-equity ratio.

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(4 marks) (4 marks)

(4 marks) (3 marks) (6 marks)

(g) Calculate the t-statistics for each of the coefficients of the independent variables. At 5% significance level, determine whether the book-to-market ratio, the debt-to-equity

ratio and the return on equity are each useful in explaining stock returns. (6 marks)