Reading 50: An Introduction to Portfolio Management LOS e习题 manager, standard, existing, face, 2010

honeycfa

LOS e: List the components of the portfolio standard deviation formula.

A portfolio manager adds a new stock that has the same standard deviation of returns as the existing portfolio but has a correlation coefficient with the existing portfolio that is less than +1. Adding this stock will have what effect on the standard deviation of the revised portfolio's returns? The standard deviation will:

A) decrease.

B) increase.

C) decrease only if the correlation is negative.

---

If the correlation coefficient is less than 1, there are benefits to diversification. Thus, adding the stock will reduce the portfolio's standard deviation.

 

honeycfa

There are benefits to diversification as long as:

A) the correlation coefficient between the assets is less than 1.

B) there is perfect positive correlation between the assets.

C) there must be perfect negative correlation between the assets.

---

There are benefits to diversification as long as the correlation coefficient between the assets is less than 1.

honeycfa

Stock A has a standard deviation of 0.5 and Stock B has a standard deviation of 0.3. Stock A and Stock B are perfectly positively correlated. According to Markowitz portfolio theory how much should be invested in each stock to minimize the portfolio's standard deviation?

A) 100% in Stock B.

B) 30% in Stock A and 70% in Stock B.

C) 50% in Stock A and 50% in Stock B.

---

Since the stocks are perfectly correlated, there is no benefit from diversification. So, invest in the stock with the lowest risk.

honeycfa

Which of the following statements about portfolio theory is least accurate?

A) Assuming that the correlation coefficient is less than one, the risk of the portfolio will always be less than the simple weighted average of individual stock risks.

B) For a two-stock portfolio, the lowest risk occurs when the correlation coefficient is close to negative one.

C) When the return on an asset added to a portfolio has a correlation coefficient of less than one with the other portfolio asset returns but has the same risk, adding the asset will not decrease the overall portfolio standard deviation.

---

When the return on an asset added to a portfolio has a correlation coefficient of less than one with the other portfolio asset returns but has the same risk, adding the asset will decrease the overall portfolio standard deviation. Any time the correlation coefficient is less than one, there are benefits from diversification. The other choices are true.

honeycfa

An investor calculates the following statistics on her two-stock (A and B) portfolio.

• σ_A = 20%
• σ_B = 15%
• r_A,B = 0.32
• W_A = 70%
• W_B = 30%

The portfolio's standard deviation is closest to:

A) 0.1832.

B) 0.0256.

C) 0.1600.

---

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 = [(0.7² × 0.2²) + (0.3² × 0.15²) +( 2 × 0.7 × 0.3 × 0.2 × 0.15 × 0.32)]^1/2 = [0.0196 + 0.002025 + 0.004032]^1/2 = 0.0256570^1/2 = 0.1602, or approximately 16.0%.

honeycfa

 

Kendra Jackson, CFA, is given the following information on two stocks, Rockaway and Bridgeport.

• Covariance between the two stocks = 0.0325
• Standard Deviation of Rockaway’s returns = 0.25
• Standard Deviation of Bridgeport’s returns = 0.13

Assuming that Jackson must construct a portfolio using only these two stocks, which of the following combinations will result in the minimum variance portfolio?

A) 50% in Bridgeport, 50% in Rockaway.

B) 80% in Bridgeport, 20% in Rockaway.

C) 100% in Bridgeport.

---

First, calculate the correlation coefficient to check whether diversification will provide any benefit.

r_{Bridgeport, Rockaway} = cov_{Bridgeport, Rockaway} / [( s_Bridgeport) × (s_Rockaway) ] = 0.0325 / (0.13 × 0.25) = 1.00

Since the stocks are perfectly positively correlated, there are no diversification benefits and we select the stock with the lowest risk (as measured by variance or standard deviation), which is Bridgeport.

honeycfa

Two assets are perfectly positively correlated. If 30% of an investor's funds were put in the asset with a standard deviation of 0.3 and 70% were invested in an asset with a standard deviation of 0.4, what is the standard deviation of the portfolio?

A) 0.151.

B) 0.426.

C) 0.370.

---

σ portfolio = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ₁σ₂r_1,2]^1/2 given r_1,2 = +1

σ = [W₁²σ₁² + W₂²σ₂² + 2W₁W₂σ₁σ₂]^1/2 = (W₁σ₁ + W₂σ₂)²]^1/2

σ = (W₁σ₁ + W₂σ₂) = (0.3)(0.3) + (0.7)(0.4) = 0.09 + 0.28 = 0.37

honeycfa

Which one of the following statements about correlation is FALSE?

A) Potential benefits from diversification arise when correlation is less than +1.

B) If the correlation coefficient were 0, a zero variance portfolio could be constructed.

C) If the correlation coefficient were -1, a zero variance portfolio could be constructed.

---

A correlation coefficient of zero means that there is no relationship between the stock's returns. The other statements are true.

honeycfa

What is the variance of a two-stock portfolio if 15% is invested in stock A (variance of 0.0071) and 85% in stock B (variance of 0.0008) and the correlation coefficient between the stocks is –0.04?

A) 0.0020.

B) 0.0007.

C) 0.0026.

---

The variance of the portfolio is found by:

[W₁² σ₁² + W₂² σ₂² + 2W₁W₂σ₁σ₂r_1,2], or [(0.15)²(0.0071) + (0.85)²(0.0008) + (2)(0.15)(0.85)(0.0843)(0.0283)(–0.04)] = 0.0007.

honeycfa

Which of the following equations is least accurate?

A) Real Risk-Free Rate = [(1 + nominal risk-free rate) / (1 + expected inflation)] ? 1.

B) Required Returnnominal = [(1 + Risk Free Ratereal) × (1 + Expected Inflation) × (1 + Risk Premium)] ? 1.

C) Standard Deviation2-Stock Portfolio = [(w12 × σ12) + (w22 × σ22) + (2 × w1 × w2 σ1σ2 × ρ1,2)].

---

This is the equation for the variance of a 2-stock portfolio. The standard deviation is the square root of the variance. The other equations are correct.