Reading 8: Probability Concepts-LOS l习题精选 returns, standard, expected, interpret, 2010

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Session 2: Quantitative Methods: Basic Concepts
Reading 8: Probability Concepts

LOS l: Calculate and interpret the expected value, variance, and standard deviation of a random variable and of returns on a portfolio.

 

 

 

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) 15%.

C) 13%.

zaestau

c

bmaggie

An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:

• σ_R = 34%
• σ_S = 16%
• r_R,S = 0.67
• W_R = 80%
• W_S = 20%

A) 29.4%.

B) 7.8%.

C) 8.7%.

bmaggie

An investor has two stocks, Stock R and Stock S in her portfolio. Given the following information on the two stocks, the portfolio's standard deviation is closest to:

• σ_R = 34%
• σ_S = 16%
• r_R,S = 0.67
• W_R = 80%
• W_S = 20%

A) 29.4%.

B) 7.8%.

C) 8.7%.

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The formula for the standard deviation of a 2-stock portfolio is:

s = [W_A²s_A² + W_B²s_B² + 2W_AW_Bs_As_Br_A,B]^1/2

s = [(0.8² × 0.34²) + (0.2² × 0.16²) + (2 × 0.8 × 0.2 × 0.34 × 0.16 × 0.67)]^1/2 = [0.073984 + 0.001024 + 0.0116634]^1/2 = 0.0866714^1/2 = 0.2944, or approximately 29.4%.

bmaggie

What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?

A) 6.20%.

B) 0.38%.

C) 6.83%.

bmaggie

What is the standard deviation of a portfolio if you invest 30% in stock one (standard deviation of 4.6%) and 70% in stock two (standard deviation of 7.8%) if the correlation coefficient for the two stocks is 0.45?

A) 6.20%.

B) 0.38%.

C) 6.83%.

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The standard deviation of the portfolio is found by:

[W₁² σ₁² + W₂² σ₂² + 2W₁W₂σ₁σ₂r_1,2]^0.5, or [(0.30)²(0.046)² + (0.70)²(0.078)² + (2)(0.30)(0.70)(0.046)(0.078)(0.45)]^0.5 = 0.0620, or 6.20%.

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.

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ERPort	= (WPluto)(ERPluto) + (WNeptune)(ERNeptune)
	= (0.65)(0.11) + (0.35)(0.09) = 10.3%
σp	= [(w1)2(σ1)2 + (w2)2(σ2)2 + 2w1w2σ1σ2 r1,2]1/2
	= [(0.65)2(22)2 + (0.35)2(13)2 + 2(0.65)(0.35)(22)(13)(0.25)]1/2
	= [(0.4225)(484) + (0.1225)(169) + 2(0.65)(0.35)(22)(13)(0.25)]1/2
	= (257.725)1/2 = 16.0538%

bmaggie

Assume two stocks are perfectly negatively correlated. Stock A has a standard deviation of 10.2% and stock B has a standard deviation of 13.9%. What is the standard deviation of the portfolio if 75% is invested in A and 25% in B?

A) 0.00%.

B) 4.18%.

C) 0.17%.

bmaggie

Assume two stocks are perfectly negatively correlated. Stock A has a standard deviation of 10.2% and stock B has a standard deviation of 13.9%. What is the standard deviation of the portfolio if 75% is invested in A and 25% in B?

A) 0.00%.

B) 4.18%.

C) 0.17%.

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The standard deviation of the portfolio is found by:

[W₁² σ₁² + W₂² σ₂² + 2W₁W₂σ₁σ₂r_1,2]^0.5, or [(0.75)²(0.102)² + (0.25)²(0.139)² + (2)(0.75)(0.25)(0.102)(0.139)(–1.0)]^0.5 = 0.0418, or 4.18%.

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.