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发表于 2011-3-1 15:25 | 只看该作者

Reading 8: Probability Concepts-LOS j 习题精选

center, problem, investment, 2011
Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS j: Diagram an investment problem using a tree diagram.

 

 

There is a 60% chance that the economy will be good next year and a 40% chance that it will be bad. If the economy is good, there is a 70% chance that XYZ Incorporated will have EPS of $5.00 and a 30% chance that their earnings will be $3.50. If the economy is bad, there is an 80% chance that XYZ Incorporated will have EPS of $1.50 and a 20% chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)
 $5.95.
B)
 $3.29.
C)
 $2.75.

The expected EPS is calculated by multiplying the probability of the economic environment by the probability of the particular EPS and the EPS in each case. The expected EPS in all four outcomes are then summed to arrive at the expected EPS:

(0.60 × 0.70 × $5.00) + (0.60 × 0.30 × $3.50) + (0.40 × 0.80 × $1.50) + (0.40 × 0.20 × $1.00) = $2.10 + $0.63 + $0.48 + $0.08 = $3.29.

 

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1215

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2#
发表于 2011-3-1 15:26 | 只看该作者

There is an 80% chance that the economy will be good next year and a 20% chance that it will be bad. If the economy is good, there is a 60% chance that XYZ Incorporated will have EPS of $3.00 and a 40% chance that their earnings will be $2.50. If the economy is bad, there is a 70% chance that XYZ Incorporated will have EPS of $1.50 and a 30% chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)
 $2.00.
B)
 $4.16.
C)
 $2.51.

The expected EPS is calculated by multiplying the probability of the economic environment by the probability of the particular EPS and the EPS in each case. The expected EPS in all four outcomes are then summed to arrive at the expected EPS:

(0.80 × 0.60 × $3.00) + (0.80 × 0.40 × $2.50) + (0.20 × 0.70 × $1.50) + (0.20 × 0.30 × $1.00) = $1.44 + $0.80 + $0.21 + $0.06 = $2.51.

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3#
发表于 2011-3-1 15:26 | 只看该作者

There is a 90% chance that the economy will be good next year and a 10% chance that it will be bad. If the economy is good, there is a 60% chance that XYZ Incorporated will have EPS of $4.00 and a 40% chance that their earnings will be $3.00. If the economy is bad, there is an 80% chance that XYZ Incorporated will have EPS of $2.00 and a 20% chance that their earnings will be $1.00. What is the firm’s expected EPS?

A)
 $3.42.
B)
 $5.40.
C)
 $2.50.

The expected EPS is calculated by multiplying the probability of the economic environment by the probability of the particular EPS and the EPS in each case. The expected EPS in all four outcomes are then summed to arrive at the expected EPS:

(0.90 × 0.60 × $4.00) + (0.90 × 0.40 × $3.00) + (0.10 × 0.80 × $2.00) + (0.10 × 0.20 × $1.00) = $2.16 + $1.08 + $0.16 + $0.02 = $3.42.

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4#
发表于 2011-3-1 15:26 | 只看该作者

Tina O’Fahey, CFA, believes a stock’s price in the next quarter depends on two factors: the direction of the overall market and whether the company’s next earnings report is good or poor. The possible outcomes and some probabilities are illustrated in the tree diagram shown below:

Based on this tree diagram, the expected value of the stock if the market decreases is closest to:

A)
 $62.50.
B)
 $57.00.
C)
 $26.00.

The expected value if the overall market decreases is 0.4($60) + (1 – 0.4)($55) = $57.

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