Examination Paper 2020/21
MSIN0105: Financial Econometrics
TIME ALLOWANCE: 24 hours
There is ONE (1) section to the examination paper, which consists of four (4) compulsory
questions. The allocations of the marks are indicated in the brackets. Each of the four
questions has multiple subquestions.
MSIN0105 1 TURN OVER
Answer all questions. The value of each ques-
tion is provided in square brackets.
Q1. [20]. Judge if each statement given below is correct or incorrect, providing your reason-
ing. In these statements, (yi, xi) , i = 1, . . . , n, are iid observations of a dependent variable
yi and a vector of regressors xi = (1, x1i, . . . , xKi)
′.
1. Consider a linear model yi = x
′
iβ+ i with E (xii) = 0. This specification implies that
the conditional expectation of yi given xi is x
′
iβ.
2. The ordinary least square estimator for a linear probability model yi = x
′
iβ+i with yi ∈
{0, 1} is inconsistent due to heteroskedasticity of the errors, i.e., V ar(i|xi) depends
on xi.
3. In weighted least square estimation for linear regression model with heteroskedasticity,
an observation whose error variance is larger receives a higher weight in the estimation.
4. Consider a linear regression model with a regressor vector xi that includes an intercept
and two dummy (binary) variables d1i ∈ {0, 1} and d2i ∈ {0, 1}, where all the units
in the data have either one of d1i or d2i equal to 1. That is d1i + d2i = 1 holds for
all i. In this case, we cannot estimate the coefficients of d1i and d2i by OLS due to
multicollinearity.
MSIN0105 LSA 2 TURN OVER
CONTINUED
Q2. [25].
As a consultant working for a commercial bank, you would like to develop an econometric
model that assists bank’s decision for approving loan applications. Suppose you have access
to a database of the past borrowers containing binary Yi ∈ {0, 1} that indicates if borrower
i defaults (Yi = 1) or not (Yi = 0), together with the borrower’s characteristics including
the value of collateral Vi and the interest rate Ri of i’s borrowing. Including an intercept,
we denote other observable characteristics of borrower i by vector Xi. Denote the set of
regressors by Zi = (Vi, Ri, X
′
i)
′.
Consider a probit model
Pr(Yi = 1|Zi) = Φ(βV Vi + βRRi +X ′iβX), (1)
where Φ(·) is the cumulative distribution function of the standard normal random variable.
(a) [5]. Explain how you estimate the coefficient parameters in the probit model.
(b) [5]. Derive the marginal effect of the probability of default with respect to interest
rate Ri, i.e.,
∂
∂Ri
Pr (Yi = 1|Zi). Does the sign of this marginal effect depend on the
conditioning variables, Zi = (Vi, Ri, X
′
i)
′? Explain
(c) [5]. To examine a trade-off between the interest rate and the amount of collateral for
the borrower’s default probability, consider the marginal rate of substitution (MRS)
of the interest rate relative to the value of collateral. Here, MRS is defined by the
quantity measuring how much the interest rate has to adjust in response to a unit
increase of the value of collateral to keep the probability of default constant, i.e.,
MRS = −∂ Pr(Yi=1|Zi)/∂Ri
∂ Pr(Yi=1|Zi)/∂Vi Does the marginal rate of substitution depend on the bor-
rower’s observable characteristics Zi? Discuss.
(d) [5]. You want to develop a prediction rule for who will default on the basis of appli-
cant’s characteristics Xi, collateral to be requested Vi and offered interest rate Ri. A
prediction rule is a function δ (Z) ∈ {0, 1}, i.e., δ(·) = 1 predicts default and δ(·) = 0
predicts repayment. The criterion used to evaluate the performance of prediction rule
δ(X) is the probability of correct predictions,
Pr(δ(Z) = Y ) = E [Y δ(Z) + (1− Y )(1− δ(Z))] .
MSIN0105 LSA 3 TURN OVER
CONTINUED
Show that the prediction rule that maximizes the probability of correct prediction is
given by
δ∗(Z) =
1, if Pr(Y = 1|Z) ≥ 1/2,0, if Pr(Y = 1|Z) < 1/2.
(e) [5]. Would you recommend the prediction rule δ∗(·) obtained in part (d) to the bank
as a way to automate loan approval decisions? Explain your answer.
MSIN0105 LSA 4 TURN OVER
CONTINUED
Q3. [20]. Suppose we are interested in empirically assessing how firm’s debt from the
financial sector affects its competitiveness in a product market. We consider the following
linear structural model
yi = x1iβx + w
′
iβw + ui
where yi denotes the change in the within-industry sales share of firm i after financing the
debt of amount x1i, wi is a vector of observable characteristics (including an intercept) of
firm i that may directly affect firm’s sales, and ui is unobserved heterogeneity. Assume that
the sample consists of iid observations of (yi, x
′
1i, w
′
i), i = 1, . . . , n.
(a) [5]. In the current example, we should view x1i as an endogenous variable. Explain
why.
(b) [5]. Assuming x1i is an endogenous variable, explain why the OLS estimator for βx
fails to consistently estimate the causal effect of x1i on yi. Explain your answer.
(c) [5]. Suppose we can measure the resale value of firm i’s tangible assets when the
debt was financed. To obtain the two-stage least square (2SLS) estimator, consider
using this measure as an instrumental variable. Argue if the exclusion and the rank
conditions are credible or not with this choice of instrument?
(d) [5]. Can we assess validity of the exclusion and rank conditions based on the data?
Explain your answer.
MSIN0105 LSA 5 TURN OVER
CONTINUED
Q4. [35] After finishing your program you are offered a job at your favouriteinvestm
ent bank. Your first client is a firm that is planning on pursuing a merger and yourfirst tas
k is to do analysis on the value of mergers.
Part I: The value of mergers to target firms
The first question your client asked you is how much does an acquirer firm typically
bid for a target firm in excess of the pre-merger price? In other words, if prior to the
merger announcement the target firm’s stock price is £100 per share, what is the average
percent change in post-announcement share price. To answer this question you decide to
produce a graph of the evolution of the stock price of target firms in merger deals around
the announcement date and present figure 1 below to your client.
Figure 1: Evolution of stock returns to target firms around M&A announcement days.
Source: WRDS.
(a) [5]. What is the name of this type of analysis?
(b) [5]. Using this plot, what would you answer to your client?
(c) [5]. Your client, who also attended UCL, knows that to interpret the estimated impact
of mergers on the stock return of target firms one needs to pay attention to statistical
significance. Please comment on the statistical significance of the estimated effect.
MSIN0105 LSA 6 TURN OVER
CONTINUED
Part II: The value of mergers for acquiring firms
Your client also wants to know what is the impact of the merger on its own stock price.
Therefore, the next task your client gives you is to estimate the impact of the planned merger
on its own stock price. This time you analyze the change in stock prices of the acquiring,
target, and combined firms around merger announcement dates (from 1 day before to one
day after, and from 20 days before to the closing of the deal) and produce the following
table.
Figure 2: Evolution of stock returns to target and acquirer firms around M&A announcement
days broken down by decade (1973-1998). Source: Andrade, Mitchell, and Stafford, 2001
(d) [5]. What is the name of this type of analysis?
(e) [5]. Using the information on this table, how would you answer your client? Please
comment on both the economic and statistical significance of the effects.
Part III: Final issues and potential solutions
(f) [5]. You realize that so far you have studied the evolution of the raw returns of target
and acquirer firms, that is, returns that are not adjusted for the overall movement of
the market. However, your client insists that the evolution of market adjusted returns
would be more informative. Why do you think that might be? Is your client correct?
MSIN0105 LSA 7 TURN OVER
CONTINUED
(g) [5]. Your client asks you whether there are any additional changes you could make
to try to improve the accuracy of your estimates of the expected acquirer and target
announcement returns for the specific merger your client wants to pursue. Please
explain one potential econometric change and why it could improve on the analysis so
far.
MSIN0105 LSA 8 END OF PAPER