Using cross-Sectional data for a sample of 34 U.S firms for 2013, the Following model Was: Finance Assignment, NUS, Singapore

Sample Questions

Question 1

Using cross-sectional data for a sample of 34 U.S. firms for 2013, the following model was

estimated by ordinary least squares

Debt_to_TA_i = b₁ + b₂Growth_i + b₃EBITDA_EV_i +b₄ROC_i + e_i,

where

Debt_to_TA     is the ratio of the market value of debt to the market value of total assets

Growth            is the estimated growth rate of revenues for the next two years

 EBITDA_EV   is the ratio of EBITDA (Earnings Before Interest, Depreciation, and Amortisation) to Enterprise Value

 ROC                is the before-tax return on capital

and e_i is an error term that satisfies Gauss-Markov conditions. The regression results are given below:

The R-square of the regression is 0.28. Using these results, answer the questions below.

a. Test the following (separate) null hypotheses, at significance level a =05, explaining carefully in each case the null and alternative hypotheses, and showing the test statistic, degrees of freedom, and the critical value of the test statistic.

Hypothesis 1: A firm’s Debt to Total Assets ratio is unrelated to its expected growth rate of revenues.

Hypothesis 2: The true value of the constant is 0.20.

b. Test the null hypothesis that the coefficients on growth, EBITDA_EV and are jointly equal to zero at significance level a = 0.05.

c. Calculate the expected Debt to Total Assets ratio of a firm with the following characteristics:

Growth = 0.10, EBITDA_EV =0.06and ROC=0.20

d. Now suppose that the researcher suspects that the effect of EBITDA_EV on a firm’s debt ratio is non-linear and to see if this is the case she estimates the following augmented model with the same set of data:

Debt_to_TA_i = b₁ +b₂Growth_i +b₃EBITDA_EV_i +b₄ROC_i+b₅(EBITDA_EV)²_i +e_i

and obtains the following results:

The R-square of the regression is 0.287.

Using the two regression results given above determine whether there is any statistical evidence that the relationship between the Debt to Total Assets ratio and the EBITDA to Enterprise Value ratio is indeed non-linear.

Question 2

Suppose that a researcher wants to test the effect of having a venture capitalist on the board of directors on profitability for high technology firms. To that end, she collects data on the following variables for a random sample of 33 US high technology firms for the same year:

ROC                Return on total capital

R&D_to_Rev   Research and development spending over total revenue

VC   Dummy variable that equals 1 if there is a venture capitalist on the firm’s board and 0 otherwise.

a. Suppose that she starts by estimating the following model

ROC_i = b₁ + b₂R&D_to_Rev_i + b₃VC_i + e_i

and obtains the following results:

Comment on the signs, magnitudes, and statistical significance of the coefficient estimates in the output above. Is the regression as a whole significant?

b. Calculate the expected ROC for a firm that has a venture capitalist on its board and has an R&D to revenues ratio of 0.15 using the results above.

c. Suppose that the researcher next tries the following specification:

ROC_i = b₁ + b₂R&D_to_Rev_i + b₃VC_i + b₄(VC_i *R&D_to_Rev_i) + e_i

First, interpret the coefficient b₄  in the model. What is the effect that this coefficient is trying to capture? Then, by looking at the regression results, state whether there is any statistical evidence for the inclusion of this new variable,  VC_i *R&D_to_Rev_i, in the model.

d. Graph the two regression outputs given above with ROC on the y-axis and R&D_to_Rev on the x-axis. Make sure that your graphs are as informative as possible.

e. Comment on the number of variables on the right-hand’s sides of the models above. Could the researcher do a better job of predicting the profitability of high tech firms by including additional variables on the right-hand side?

Question 3

In an analysis of whether the relationship between GE’s stock returns and the S&P 500 index returns had a structural shift after the 2008 financial crisis (which affected GE stock rather severely), the following model was estimated:

GE_RET_t = b₀+ b₁ * SP_RET_t + b₂ * CRISIS_t + b₃ * (SP_RET_t*CRISIS_t)  + u_t

where

GE_RET_t        is the continuously compounded monthly return for GE.

SP_RET_t         is the continuously compounded monthly return for the S&P 500 index

the crisis is a dummy variable that equals 1 for observations after 12/2007, and 0 for all other observations.

The following estimates were reported using a sample of 264 monthly returns from 1/1994 – 1/2016:

(a)        Predict GE’s return for a pre-crisis month where the SP_RET equals -0.02.

(b)  Explain the rationale for including the SP_RET_t*CRISIS_t variable in the model.

(c) Describe (in words only, no calculations are necessary) how you would test the hypothesis that there was no structural break in the relationship between GE’s stock returns and the S&P 500 index returns using the model and data given above.

Question 4

Consider the regression model below:

INF_t = b₀+ b₁*INF_t-1 + b₂*DELTAGDP_t-1 + u_t

where

INF_t is the quarterly inflation rate.

DELTAGDP_t is the quarterly GDP growth rate.

The following estimates were reported using a sample of 40 quarters:

a. Comment on the Durbin-Watson test statistic in the table. Does there appear to be evidence regarding autocorrelation in the error terms? (you do not need to report statistical significance.) If yes, does the statistic point towards positive or negative autocorrelation?

b. Briefly explain the consequences of autocorrelated error terms for the parameter estimators in the model above. Specifically, discuss if there will be bias due to autocorrelation in the error terms

c. Now suppose that inflation is also a function of money supply growth (MSG), which is not included in the model above. Money supply growth, in turn, has the following behavior in time:

MSgt = b₀+ b₁*MSgt_-1 + e_t

where  0<b₁< 1 and is an error term that satisfies the Gauss-Markov conditions. Briefly explain how the omission of MSG from the right-hand side of the model above would lead to autocorrelated errors in that model.