Reading 50: An Introduction to Portfolio Management LOS c习题 currently, investment, individual, face, 2010

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LOS c, (Part 1): Compute and interpret the expected return for an individual investment and a portfolio.

As a fund manager, Bryan Cole, CFA, is responsible for assessing the risk and return parameters of the portfolios he oversees. Cole is currently considering a portfolio consisting of only two stocks. The first stock, Remba Co., has an expected return of 12% and a standard deviation of 16%. The second stock, Labs, Inc., has an expected return of 18% and a standard deviation of 25%. The correlation of returns between the two securities is 0.25.

Cole has the option of including a third stock in the portfolio. The third stock, Wimset, Inc., has an expected return of 8% and a standard deviation of 10%. If Cole constructed an equally weighted portfolio consisting of all three stocks, the portfolio's expected return would be closest to:

A) 13.9%.

B) 12.7%.

C) 15.9%.

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ER_portfolio = S(ER_stock)(W_{% of funds invested in each of the stocks})

ER = w₁ER₁ + w₂ER₂ + w₃ER₃, where ER = Expected Return and w = % invested in each stock.

Here, use 1/3 for each of the weightings. (Note: If you use 0.33, you will calculate a slightly different result.)

ER =( 1/3 × 12) + (1/3 × 18) + (1/3 × 8) = 4 + 6 + 2.7 = 12.7%

 

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An investor owns the following portfolio today.

Stock	Market Value	Expected Annual Return
R	$2,000	17%
S	$3,200	8%
T	$2,800	13%

The investor's expected total rate of return (increase in market value) after three years is closest to:

A) 36.0%.

B) 12.0%.

C) 40.5%.

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To calculate this result, we first need to calculate the portfolio value, then determine the weights for each stock, and then calculate the expected return. Finally, we determine the compounded rate after three years.

Portfolio Value: = sum of market values = 2,000 + 3,200 + 2,800 = 8,000

Portfolio Weights:
W_A = 2,000 / 8,000 = 0.25
W_B = 3,200 / 8,000 = 0.40
W_C = 2,800 / 8,000 = 0.35

Expected Return
ER_portfolio = Σ[(ER_stock)(W_{% of funds invested in each of the stocks})]
ER = w_RER_R + w_SER_S + w_TER_T, where ER = Expected Return and w = % invested in each stock.
ER = (0.25 × 17.0) + (0.40 × 8.0) + (0.35 × 13.0) = 12.0%

Expected Return after three years
= (1 + return)³ = (1.12)³ ? 1 = 1.405 ? 1 = 0.405, or 40.5%.

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An investor owns the following three-stock portfolio today.

Stock	Market Value	Expected Annual Return
K	$4,500	14%
L	$6,300	9%
M	$3,700	12%

The expected portfolio value two years from now is closest to:

A) $17,975.

B) $16,150.

C) $17,870.

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The easiest way to approach this problem is to determine the value of each stock two years in the future and to sum up the total values of each stock.

Stock	Market Value  ×	Expected Annual Return	=   Total
K	$4,500   ×	1.14 × 1.14	=   5,848.20
L	$6,300   ×	1.09 × 1.09	=   7,485.03
M	$3,700   ×	1.12 × 1.12	=   4,641.28
		Total	=   17,974.51

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An investor owns the following three-stock portfolio.

Stock	Market Value	Expected Return
A	$5,000	12%
B	$3,000	8%
C	$4,000	9%

The expected return is closest to:

A) 29.00%.

B) 9.67%.

C) 10.00%.

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To calculate this result, we first need to calculate the portfolio value, then determine the weights for each stock, and then calculate the expected return.

Portfolio Value: = sum of market values = 5,000 + 3,000 + 4,000 = 12,000

Portfolio Weights:

W_A = 5,000 / 12,000 = 0.4167

W_B = 3,000 / 12,000 = 0.2500

W_C = 4,000 / 12,000 = 0.333

Expected Return

ER_portfolio = S(ER_stock)(W_{% of funds invested in each of the stocks})

ER = w_AER_A + w_BER_B + w_CER_C, where ER = Expected Return and w = % invested in each stock.

ER = (0.4167 × 12.0) + (0.2500 × 8.0) + (0.333 × 9.0) = 10.0%

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LOS c, (Part 2): Compute and interpret the variance and standard deviation for an individual investment and standard deviation for a portfolio.

Betsy Minor is considering the diversification benefits of a two stock portfolio. The expected return of stock A is 14 percent with a standard deviation of 18 percent and the expected return of stock B is 18 percent with a standard deviation of 24 percent. Minor intends to invest 40 percent of her money in stock A, and 60 percent in stock B. The correlation coefficient between the two stocks is 0.6. What is the variance and standard deviation of the two stock portfolio?

A) Variance = 0.02206; Standard Deviation = 14.85%.

B) Variance = 0.03836; Standard Deviation = 19.59%.

C) Variance = 0.04666; Standard Deviation = 21.60%.

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(0.40)²(0.18)² + (0.60)²(0.24)² + 2(0.4)(0.6)(0.18)(0.24)(0.6) = 0.03836.

0.03836^0.5 = 0.1959 or 19.59%.

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A larger range of expected returns compared to a smaller range of expected returns would:

A) have greater risk.

B) translate to a greater certainty of expected future returns.

C) be preferred by a risk averse investor.

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A larger range of expected returns means a larger dispersion and thus a higher standard deviation, or risk.

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A security has a 30% chance of producing a 15% return and a 70% chance of producing a -4% return. The variance of the security is closest to:

A) 0.0057.

B) 0.0077.

C) 7.6.

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The variance is the sum of the probability times the difference between the return and the expected return squared. First, find the expected return as: (0.30)(0.15) + (0.70)(–0.04) = 0.017, or 1.7%. Then, the variance is determined as: (0.30)(0.15 – 0.017)² + (0.70)(–0.04 – 0.017)² = 0.0077.