Question 1 A theory specifies that a firm\'s stock return increases with its gro

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Question 1 A theory specifies that a firm's stock return increases with its growth opportunity (GO) and profitability (PRO). Therefore, you set up the population regression model as You use Ordinary Least Squares estimation based on 100 firm observations to test this theory, a regression equation is written as Stock Return = 0.01 + 0.32GO + 0.67 PRO + 0.26 (GO XPRO) (0.8) (0.59) (0.37) (0.13) The figures in parentheses below show the standard errors of the estimated coefficients 1.1) Suppose that the theory suggests that there is a relation between a firm's stock return and its growth opportunity, but does not predict the direction of this relation. Set up a hypothesis test and compute the t-statistic and p-value for your test for this hypothesis. What would you conclude using a significance level of 5%? [15%] 1.2) Construct a 95% confidence interval for A, the regression slope coefficient and use the 95% conference interval to justify whether you should or should not reject the null hypothesis in Question (1.1) [10%] 1.3) Compute the economic impact of a firm's growth opportunity on its stock returns when the growth opportunity increases by one unit and when the profitability is 10. Also discuss why the regression includes the interaction variable of GO×PRO [15%] 1.4) Suppose that you create a dummy variable of HPRO, in which HPRO equals to one if a firm's profitability is larger than 0.5 and HPRO equals to zero if the firm's profitability is lower than 0.5. A HPRO value of 1 indicates a firm with high profitability and HPRO value of 0 indicates a firm with low profitability. You replace PRO with this dummy variable HPRO in the regression and re-estimate the regression. The result is shown as follows StockReturn = 0.01 + 0.97 GO + 5.6HPRO + 1.28 (GO x HPRO) (0.8) (11.9)(0.59) (0.5)

Explanation / Answer

Question 1-1

H0 :  1 = 0

Ha  : 1   0

Test statistic

t = ^1/ se(b1) = 0.32/0.59 = 0.5424

= t/ sqrt [n- 2 + t2 ] = 0.5424/ sqrt [100 -2 + 0.54242] = 0.5424/ 9.9143 = 0.0547

Here for dF = 98 and alpha = 0.05

tcritical = 1.9624

so t < tcritical so we dont reject the nul hypothesis and can say that the raltion is not significant.

1.2 95% confidence interval for 1 =  ^ 1 +- tcritical se0 = 0.32 +- 1.9624 * 0.59 = (-0.838, 1.478)

The 95% confidence interval consists the value of zero so we shall reject the null hypothesis.

1.3 stock return =  0.01 + 0.32 GO + 0.67 PRO + 0.26 * ( GO x PRO)

stock return (GO, PRO = 10) = 0.01 + 0.32 GO + 0.67 PRO + 0.26 * ( GO x PRO)

= 0.01 + 0.32 GO + 0.67 * 10 + 0.26 * (10 * GO)

stock return (GO + 1, PRO = 10) = 0.01 + 0.32 (GO + 1) + 0.67 * 10 + 0.26 * [ 10 * (GO +1)]

so difference occur in stock return = 0.32 + 0.26 * 10 = 2.92

The regression includes the regression (GO x PRO) it meas that if growth has increased alongwith profitability it will be an important factor in stock price increase.

(4)

Here the regression equation of

stock return =  0.01 + 0.97 GO + 5.6 HPRO + 1.28 * ( GO x HPRO)

Here estimated stock returns for high profitability firm means HPRO = 1

stock return =  0.01 + 0.97 GO + 5.6 HPRO + 1.28 * ( GO x HPRO) = 0.01 + 0.97 GO + 5.6 * 1 + 1.28 * (GO x 1) = 0.01 + 0.97 GO + 5.6 + 1.28 GO = 5.61 + 2.25 GO

estimated stock returns for low profitability firm means HPRO = 0

stock return =  0.01 + 0.97 GO + 5.6 HPRO + 1.28 * ( GO x HPRO) = 0.01 + 0.97 GO + 5.6 * 1 + 1.28 * (GO x 1) = 0.01 + 0.97 GO + 0 + 0 = 0.01 + 0.97 GO

Here for GO = 10

the stock return for high profitability firm on stock return =  5.61 + 2.25 GO

so at GO = 10

additional effect of being high profitability on stock return = (5.61 + 2.25 GO) - (0.01 + 0.97 GO)

=5.60 + 1.28 * GO

= 5.60 + 1.28 * 10 = 18.4

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