- CFA Exams
- CFA Level I Exam
- Topic 1. Quantitative Methods
- Learning Module 4. Probability Trees and Conditional Expectations
- Subject 1. Expected Value and Variance
CFA Practice Question
Consider the following events:
S2: Fed increases interest rates in the first quarter of 2012
S3: Fed leaves interest rates unchanged in the first quarter of 2012
X: Earnings per share for a certain stock
P(S1)=0.3, P(S2)=0.35, P(S3)=0.35, E(X|S1)=3.35, E(X|S2)=3.67, E(X|S3)=3.52
B. $3.52
C. $3.57
S1: Fed decreases interest rates in the first quarter of 2012
S2: Fed increases interest rates in the first quarter of 2012
S3: Fed leaves interest rates unchanged in the first quarter of 2012
X: Earnings per share for a certain stock
We have the following information:
P(S1)=0.3, P(S2)=0.35, P(S3)=0.35, E(X|S1)=3.35, E(X|S2)=3.67, E(X|S3)=3.52
What is the unconditional expected value of the EPS?
A. $3.51
B. $3.52
C. $3.57
Correct Answer: B
The unconditional expected value is calculated as follows: E(X) = 3.35 x 0.3 + 3.67 x 0.35 + 3.52 x 0.35 = $3.5215.
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