- 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)=0.65, P(S2)=0.10, P(S3)=0.25, E(X|S1)=1.75, E(X|S2)=1.50, E(X|S3)=1.67
B. $1.69
C. $1.705
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)=0.65, P(S2)=0.10, P(S3)=0.25, E(X|S1)=1.75, E(X|S2)=1.50, E(X|S3)=1.67
What is the unconditional expected value of the EPS?
A. $1.64
B. $1.69
C. $1.705
Correct Answer: C
The unconditional expected value is calculated as follows: E(X) = 1.75(0.65) + 1.50(0.10) + 1.67(0.25) = $1.705.
User Contributed Comments 6
| User | Comment |
|---|---|
| mrushdi | good question |
| harpalani | Guys, I'm clueless on this. I thought the given answer is "conditional" expected value and NOT "unconditional" expected value. Can someone pls.share thoughts on this? |
| joywind | @harpalani, the answer is "unconditional" expected value, a sum of those "conditional" expected values under different conditions |
| idzani | Technically by summing the individual E(x)s you are getting the expected value for all circumstances i.e. unconditional |
| choas69 | good explanation idzani |
| Huricane74 | The easiest and fastest way to do this is on the calculator by entering value for X and Y using the [DATA] and [STAT] function. Set up a table to make sure you are entering the values correctly. Toggle down until you get to the function: ΣXY = |