LiquidAssets10

The covariance of the returns on investments X and Y is 18.17. The standard deviation of returns on X is 7%, and the standard deviation of returns on Y is 4%. What is the value of the correlation coefficient for returns on investments X and Y?

A) +0.85.

B) +0.65.

C) +0.32.

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The correlation coefficient = Cov (X,Y) / [(Std Dev. X)(Std. Dev. Y)] = 18.17 / 28 = 0.65

LiquidAssets10

The covariance of returns on two investments over a 10-year period is 0.009. If the variance of returns for investment A is 0.020 and the variance of returns for investment B is 0.033, what is the correlation coefficient for the returns?

A) 0.444.

B) 0.350.

C) 0.687.

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The correlation coefficient is: Cov(A,B) / [(Std Dev A)(Std Dev B)] = 0.009 / [(√0.02)(√0.033)] = 0.350.

LiquidAssets10

The correlation coefficient for a series of returns on two investments is equal to 0.80. Their covariance of returns is 0.06974 . Which of the following are possible variances for the returns on the two investments?

A) 0.02 and 0.44.

B) 0.08 and 0.37.

C) 0.04 and 0.19.

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The correlation coefficient is: 0.06974 / [(Std Dev A)(Std Dev B)] = 0.8. (Std Dev A)(Std Dev B) = 0.08718. Since the standard deviation is equal to the square root of the variance, each pair of variances can be converted to standard deviations and multiplied to see if they equal 0.08718. √0.04 = 0.20 and √0.19 = 0.43589. The product of these equals 0.08718.

LiquidAssets10

There is a 30% chance that the economy will be good and a 70% chance that it will be bad. If the economy is good, your returns will be 20% and if the economy is bad, your returns will be 10%. What is your expected return?

A) 17%.

B) 13%.

C) 15%.

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Expected value is the probability weighted average of the possible outcomes of the random variable. The expected return is: ((0.3) × (0.2)) + ((0.7) × (0.1)) = (0.06) + (0.07) = 0.13.

LiquidAssets10

For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.10, Var(RA) = 0.18, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?

A) 0.2114.

B) 0.1500.

C) 0.1102.

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You are not given the covariance in this problem but instead you are given the correlation coefficient and the variances of assets A and B from which you can determine the covariance by Covariance = (correlation of A, B) × Standard Deviation of A) × (Standard Deviation of B).
Since it is an equally weighted portfolio, the solution is:
[( 0.52 ) × 0.18 ] + [(0.52) × 0.36 ] + [ 2 × 0.5 × 0.5 × 0.6 × ( 0.180.5 ) × ( 0.360.5 )]
= 0.045 + 0.09 + 0.0764 = 0.2114

LiquidAssets10

Use the following data to calculate the standard deviation of the return:

• 50% chance of a 12% return
• 30% chance of a 10% return
• 20% chance of a 15% return

A) 1.7%.

B) 3.0%.

C) 2.5%.

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The standard deviation is the positive square root of the variance. The variance is the expected value of the squared deviations around the expected value, weighted by the probability of each observation. The expected value is: (0.5) × (0.12) + (0.3) × (0.1) + (0.2) × (0.15) = 0.12. The variance is: (0.5) × (0.12 − 0.12)2 + (0.3) × (0.1 − 0.12)2 + (0.2) × (0.15 − 0.12)2 = 0.0003. The standard deviation is the square root of 0.0003 = 0.017 or 1.7%.

LiquidAssets10

After repeated experiments, the average of the outcomes should converge to:

A) the variance.

B) one.

C) the expected value.

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This is the definition of the expected value. It is the long-run average of all outcomes.

LiquidAssets10

Given P(X = 2) = 0.3, P(X = 3) = 0.4, P(X = 4) = 0.3. What is the variance of X?

A) 3.0.

B) 0.3.

C) 0.6.

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The variance is the sum of the squared deviations from the expected value weighted by the probability of each outcome.
The expected value is E(X) = 0.3 × 2 + 0.4 × 3 + 0.3 × 4 = 3.
The variance is 0.3 × (2 − 3)2 + 0.4 × (3 − 3)2 + 0.3 × (4 − 3)2 = 0.6.

LiquidAssets10

Compute the standard deviation of a two-stock portfolio if stock A (40% weight) has a variance of 0.0015, stock B (60% weight) has a variance of 0.0021, and the correlation coefficient for the two stocks is –0.35?

A) 1.39%.

B) 0.07%.

C) 2.64%.

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The standard deviation of the portfolio is found by:
[W12σ12 + W22σ2 2+ 2W1W2σ1σ2ρ1,2]0.5
= [(0.40)2(0.0015) + (0.60)2 (0.0021) + (2)(0.40)(0.60)(0.0387)(0.0458)(–0.35)]0.5
= 0.0264, or 2.64%.

LiquidAssets10

For assets A and B we know the following: E(RA) = 0.10, E(RB) = 0.20, Var(RA) = 0.25, Var(RB) = 0.36 and the correlation of the returns is 0.6. What is the expected return of a portfolio that is equally invested in the two assets?

A) 0.1500.

B) 0.3050.

C) 0.2275.

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The expected return of a portfolio composed of n-assets is the weighted average of the expected returns of the assets in the portfolio: ((w1) × (E(R1)) + ((w2) × (E(R2)) = (0.5 × 0.1) + (0.5 × 0.2) = 0.15.