bmaggie

A two-sided but very thick coin is expected to land on its edge twice out of every 100 flips. And the probability of face up (heads) and the probability of face down (tails) are equal. When the coin is flipped, the prize is $1 for heads, $2 for tails, and $50 when the coin lands on its edge. What is the expected value of the prize on a single coin toss?

A) $1.50.

B) $2.47.

C) $17.67.

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Since the probability of the coin landing on its edge is 0.02, the probability of each of the other two events is 0.49. The expected payoff is: (0.02 × $50) + (0.49 × $1) + (0.49 × $2) = $2.47.

bmaggie

The following information is available concerning expected return and standard deviation of Pluto and Neptune Corporations:

	Expected Return	Standard Deviation
Pluto Corporation	11%	0.22
Neptune Corporation	9%	0.13

If the correlation between Pluto and Neptune is 0.25, determine the expected return and standard deviation of a portfolio that consists of 65% Pluto Corporation stock and 35% Neptune Corporation stock.

A) 10.3% expected return and 16.05% standard deviation.

B) 10.3% expected return and 2.58% standard deviation.

C) 10.0% expected return and 16.05% standard deviation.

bmaggie

For assets A and B we know the following: E(R_A) = 0.10, E(R_B) = 0.20, Var(R_A) = 0.25, Var(R_B) = 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) 0.3050.

B) 0.2275.

C) 0.1500.

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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.

bmaggie

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.

bmaggie

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) 2.64%.

C) 0.07%.

bmaggie

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) 2.64%.

C) 0.07%.

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The standard deviation of the portfolio is found by:

[W₁²σ₁² + W₂²σ₂ ²+ 2W₁W₂σ₁σ₂ρ_1,2]^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%.

bmaggie

For assets A and B we know the following: E(R_A) = 0.10, E(R_B) = 0.20, Var(R_A) = 0.25, Var(R_B) = 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) 0.3050.

B) 0.2275.

C) 0.1500.

bmaggie

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

A) the variance.

B) the expected value.

C) one.

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

bmaggie

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.

bmaggie

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

A) the variance.

B) the expected value.

C) one.