LiquidAssets10

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) $2.75.

C) $3.29.

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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.

LiquidAssets10

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) $2.51.

B) $2.00.

C) $4.16.

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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.

LiquidAssets10

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.

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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.

LiquidAssets10

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) $26.00.

C) $57.00.

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

LiquidAssets10

The covariance:

A) must be between -1 and +1.

B) can be positive or negative.

C) must be positive.

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Cov(a,b) = σaσbρa,b. Since ρa,b can be positive or negative, Cov(a,b) can be positive or negative.

LiquidAssets10

With respect to the units each is measured in, which of the following is the most easily directly applicable measure of dispersion? The:

A) covariance.

B) variance.

C) standard deviation.

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The standard deviation is in the units of the random variable itself and not squared units like the variance. The covariance would be measured in the product of two units of measure.

LiquidAssets10

Given Cov(X,Y) = 1,000,000. What does this indicate about the relationship between X and Y?

A) It is strong and positive.

B) Only that it is positive.

C) It is weak and positive.

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A positive covariance indicates a positive linear relationship but nothing else. The magnitude of the covariance by itself is not informative with respect to the strength of the relationship.

LiquidAssets10

Which of the following statements is least accurate regarding covariance?

A) A covariance of zero rules out any relationship.

B) Covariance can only apply to two variables at a time.

C) Covariance can exceed one.

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A covariance only measures the linear relationship. The covariance can be zero while a non-linear relationship exists. Both remaining statements are true.

LiquidAssets10

The returns on assets C and D are strongly correlated with a correlation coefficient of 0.80. The variance of returns on C is 0.0009, and the variance of returns on D is 0.0036. What is the covariance of returns on C and D?

A) 0.40110.

B) 0.03020.

C) 0.00144.

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r = Cov(C,D) / (σC x σD)
σC = (0.0009)0.5 = 0.03
σD = (0.0036)0.5 = 0.06
0.8(0.03)(0.06) = 0.00144

LiquidAssets10

If given the standard deviations of the returns of two assets and the correlation between the two assets, which of the following would an analyst least likely be able to derive from these?

A) Strength of the linear relationship between the two.

B) Covariance between the returns.

C) Expected returns.

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The correlations and standard deviations cannot give a measure of central tendency, such as the expected value.