Midterm Questions
Note: As required for the online exams, the numbers in the numerical questions and the ordering
of the answers in the multiple-answer questions are randomized in the actual exams.
The total points of this exam is 38 points. Please attempt all questions.
1 Multiple-answer questions (10pt)
The following 5 questions are worth 2 points each. There may be multiple correct answers to each
question, please select all correct answers to receive full points.
1. Suppose we have been analyzing a stock return series, and we identified a time series model
that can predict future volatility very well using past returns.
Select the statement(s) that must be true.
(a) The stock return series is a martingale difference sequence.
(b) The stock return series is not a martingale difference sequence.
(c) The stock return series is a mutually independent sequence.
(d) The stock return series is not a mutually independent sequence.
Answer: (d).
2. Let P0, P1, P2, P3 be the stock prices in four periods. Suppose there are no dividend payments.
For t = 0, 1, 2 and k ≥ 2 being a positive integer, let
Rt
L
+1 be the single-period log return from t to t + 1, and Rt
L
→t+k
be the multi-period log
return from t to t + k;
Rt
A
+1 be the single-period arithmetic net return from t to t + 1, and Rt
A
→t+k
be the multi_x005f period arithmetic net return from t to t + k.
Select the correct statement(s).
(a) R0
A
→3 =
Q
3
t=1 Rt
A.
(b) R0
A
→3 =
P
3
t=1 Rt
A.
(c) R0
A
→3 = 1 + Q 3
t=1(1 + Rt
A).
(d) R0
L
→3 =
Q
3
t=1 Rt
L.
(e) R0
L
→3 =
P
3
t=1 ln(1 + Rt
A).
(f) R0
L
→3 =
P
3
t=1 Rt
A.
Answer: (c) and (e).
3. Suppose that we run the following regression model of the monthly stock returns (R) on the
dividend yields (D)
Rt+1 = β0 + β1Dt + β2Dt 1 + β3Dt 2 + et+1
and would like to test H0 : β1 = β2 = β3. We want to formulate this null hypothesis in the
general matrix form:
H0 : Rβ = r, where β =
