Tài liệu Tài chính doanh nghiệp ( Bài tập)_ Chapter 10 doc

The variance of the portfolio equals: σ2 = WMAC2σMAC2 + WI2σI2 + 2WMACWIσMACσI[CorrelationRMAC, RI] = the variance of the portfolio WMAC = the weight of Macrosoft stock in the portfol

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Chapter 10: Return and Risk: The Capital Asset Pricing Model (CAPM) 10.1 a Expected Return = (0.1)(-0.045) + (.2)(0.044) + (0.5)(0.12) + (0.2)(0.207)

= 0.005187 Standard Deviation (σ) = (0.005187)1/2

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The correlation between the returns on Highbull’s stock and Slowbear’s stock is 0.9770

10.4 Value of Atlas stock in the portfolio = (120 shares)($50 per share)

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Weight of Atlas stock = $6,000 / $9,000

= 2/3 The weight of Atlas stock in the portfolio is 2/3

Weight of Babcock stock = $3,000 / $9,000

= 1/3 The weight of Babcock stock in the portfolio is 1/3

10.5 a The expected return on the portfolio equals:

E(RP) = (WF)[E(RF)] + (WG)[E(RG)]

where E(RP) = the expected return on the portfolio

E(RF) = the expected return on Security F E(RG) = the expected return on Security G

WF = the weight of Security F in the portfolio

WG = the weight of Security G in the portfolio E(RP) = (WF)[E(RF)] + (WG)[E(RG)]

= the variance of the portfolio

WF = the weight of Security F in the portfolio

WG = the weight of Security G in portfolio

σF = the standard deviation of Security F

σG = the standard deviation of Security G

RF = the return on Security F

RG = the return on Security G

σ2

σP = (σ2

)1/2 = (0.033244)1/2

=18.23%

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If the correlation between the returns of Security F and Security G is 0.2, the standard deviation of the portfolio is 18.23%

E(RP) = (WA)[E(RA)] + (WB)[E(RB B B)]

E(RA) = the expected return on Stock A E(RB) = the expected return on Stock B B

WA = the weight of Stock A in the portfolio

WB = the weight of Stock B in the portfolio

= (0.40)(0.15) + (0.60)(0.25)

= 0.21

= 21%

The expected return on a portfolio composed of 40% stock A and 60% stock B is 21%

The variance of the portfolio equals:

σA = the standard deviation of Stock A

σB = the standard deviation of Stock B

RA = the return on Stock A

RB = the return on Stock B B

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= 0.60 The expected return on the portfolio equals:

E(RP) = (WMAC)[E(RMAC)] + (WI)[E(RI)]

E(RMAC) = the expected return on Macrosoft stock E(RI) = the expected return on Intelligence Stock

WMAC = the weight of Macrosoft stock in the portfolio

WI = the weight of Intelligence stock in the portfolio E(RP) = (WMAC)[E(RMAC)] + (WI)[E(RM)]

= (0.40)(0.15) + (0.60)(0.20)

= 0.18

= 18%

The expected return on her portfolio is 18%

The variance of the portfolio equals:

σ2

= (WMAC)2(σMAC)2 + (WI)2(σI)2 + (2)(WMAC)(WI)(σMAC)(σI)[Correlation(RMAC, RI)]

WMAC = the weight of Macrosoft stock in the portfolio

WI = the weight of Intelligence stock in the portfolio

σMAC = the standard deviation of Macrosoft stock

σI = the standard deviation of Intelligence stock

RMAC = the return on Macrosoft stock

RI = the return on Intelligence stock

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The standard deviation of her portfolio is 13.54%

b Janet started with 300 shares of Intelligence stock After selling 200 shares, she has 100 shares

left

Value of Macrosoft stock in the portfolio = (100 shares)($80 per share)

= $8,000 Value of Intelligence stock in the portfolio = (100 shares)($40 per share)

= $4,000 Total Value in the portfolio = $8,000 + $4,000

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The expected return on Stock A is 7%

Correlation(RA,RB) = Covariance(RB A, RB B) / (σA * σB) B

= 0 / (0 * 0.1050)

The correlation between the returns on Stock A and Stock B is 0

c The expected return on the portfolio equals:

WB = the weight of Stock B in the portfolio E(RP) = (WA)[E(RA)] + (WB)[E(RB B B)]

= (1/2)(0.07) + (1/2)(0.115)

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RB = the return Stock B

The standard deviation of the returns on an equally weighted portfolio is 5.25%

WB = the weight of Stock B in the portfolio E(RP) = (WA)[E(RA)] + (WB)[E(RB B B)]

= (0.30)(0.10) + (0.70)(0.20)

= 0.17

= 17%

The expected return on the portfolio is 17%

The variance of a portfolio equals:

W = the weight of Stock A in the portfolio

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RB = the return on Stock B

The standard deviation of the portfolio is 10.61%

b E(RP) = (WA)[E(RA)] + (WB)[E(RB B B)]

The standard deviation of the portfolio is 4.74%

c No, you would not hold 100% of Stock A because the portfolio in part b has a higher expected

return and lower standard deviation than Stock A

You may or may not hold 100% of Stock B, depending on your risk preference If you have a low level of risk-aversion, you may prefer to hold 100% Stock B because of its higher expected return

If you have a high level of risk-aversion, however, you may prefer to hold a portfolio containing both Stock A and Stock B since the portfolio will have a lower standard deviation, and hence, less risk, than holding Stock B alone

10.10 The expected return on the portfolio must be less than or equal to the expected return on the asset with the

highest expected return It cannot be greater than this asset’s expected return because all assets with lower expected returns will pull down the value of the weighted average expected return

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Similarly, the expected return on any portfolio must be greater than or equal to the expected return on the asset with the lowest expected return The portfolio’s expected return cannot be below the lowest expected return among all the assets in the portfolio because assets with higher expected returns will pull up the value of the weighted average expected return

The standard deviation of the returns on Security B is 0%

b Total Value of her portfolio = $2,500 + $3,500

E(RA) = the expected return on Security A E(RB) = the expected return on Security B B

WA = the weight of Security A in the portfolio

WB = the weight of Security B in the portfolio E(RP) = (WA)[E(RA)] + (WB)[E(RB B B)]

= (5/12)(0.102) + (7/12)(0.065)

= 8.04%

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The expected return of her portfolio is 8.04%

WA = the weight of Security A in the portfolio

WB = the weight of Security B in the portfolio

σA = the standard deviation of Security A

σB = the standard deviation of Security B

RA = the return on Security A

RB = the return on Security B

The standard deviation of her portfolio is 2.45%

10.12 The wide fluctuations in the price of oil stocks do not indicate that these stocks are a poor investment If an

oil stock is purchased as part of a well-diversified portfolio, only its contribution to the risk of the entire portfolio matters This contribution is measured by systematic risk or beta Since price fluctuations in oil stocks reflect diversifiable plus non-diversifiable risk, observing the standard deviation of price movements

is not an adequate measure of the appropriateness of adding oil stocks to a portfolio

10.13 a Expected Return1 = (0.10)(0.25) + (0.40)(0.20) + (0.40)(0.15) + (0.10)(0.10)

= 0.1750 The expected return on Security 1 is 17.50%

Variance1 (σ1) = (0.10)(0.25 – 0.175)2 + (0.40)(0.20 – 0.175)2 + (0.40)(0.15 – 0.175)2

+ (0.10)(0.10 – 0.175)2 = 0.001625

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= 0.1750

= 0.1750 The expected return on Security 2 is 17.50%

Variance2 (σ2) = (0.10)(0.25 – 0.175)2 + (0.40)(0.15 – 0.175)2 + (0.40)(0.20 – 0.175)2

+ (0.10)(0.10 – 0.175)2 = 0.001625

Variance3(σ3) = (0.10)(0.10 – 0.175)2 + (0.40)(0.15 – 0.175)2 + (0.40)(0.20 – 0.175)2

+ (0.25)(0.10 – 0.175)2 = 0.001625

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The correlation between the returns on Security 2 and Security 3 is –0.3848

c The expected return on the portfolio equals:

E(RP) = (W1)[E(R1)] + (W2)[E(R2)]

E(R1) = the expected return on Security 1 E(R2) = the expected return on Security 2

W1 = the weight of Security 1 in the portfolio

W2 = the weight of Security 2 in the portfolio E(RP) = (W1)[E(R1)] + (W2)[E(R2)]

= (1/2)(0.175) + (1/2)(0.175)

= 17.50%

The expected return of the portfolio is 17.50%

σ2

= (W1)2(σ1)2 + (W2)2(σ2)2 + (2)(W1)(W2)(σ1)(σ2)[Correlation(R1, R2)]

σ1 = the standard deviation of Security 1

σ2 = the standard deviation of Security 2

R1 = the return on Security 1

R2 = the return on Security 2

σ2

σP = (0.001125)1/2

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= 3.35%

The standard deviation of the returns on the portfolio is 3.35%

d E(RP) = (W1)[E(R1)] + (W3)[E(R3)]

The standard deviation of the returns on the portfolio is 0%

e E(RP) = (W2)[E(R2)] + (W2)[E(R3)]

The standard deviation of the returns on the portfolio is 2.24%

f As long as the correlation between the returns on two securities is below 1, there is a benefit to

diversification A portfolio with negatively correlated stocks can achieve greater risk reduction than a portfolio with positively correlated stocks, holding the expected return on each stock constant Applying proper weights on perfectly negatively correlated stocks can reduce portfolio variance to 0

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= 13.5%

The expected return on the portfolio is 13.5%

10.15 a The expected return on a portfolio equals:

E(RP) = Σ E(Ri) / N where E(RP) = the expected return on the portfolio

E(Ri) = the expected return on Security i

N = the number of securities in the portfolio E(RP) = Σ E(Ri) / N

= [(0.10)(N)] / N

= 0.10

= 10%

The expected return on an equally weighted portfolio containing all N securities is 10%

Ri = the returns on security i

Rj = the return on security j

N = the number of securities in the portfolio

by the following expression:

(0.0064)(N-1) / N + (0.0144)/(N)

b As N approaches infinity, the expression (N-1)/N approaches 1 and the expression (1/N)

approaches 0 It follows that, as N approaches infinity, the variance of the portfolio approaches 0.0064 [= (0.0064)(1) + (0.0144)(0)], which equals the covariance between any two individual securities in the portfolio

c The covariance of the returns on the securities is the most important factor to consider when

placing securities into a well-diversified portfolio

10.16 The statement is false Once the stock is part of a well-diversified portfolio, the important factor is the

contribution of the stock to the variance of the portfolio In a well-diversified portfolio, this contribution is the covariance of the stock with the rest of the portfolio

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10.17 The covariance is a more appropriate measure of a security’s risk in a well-diversified portfolio because the

covariance reflects the effect of the security on the variance of the portfolio Investors are concerned with the variance of their portfolios and not the variance of the individual securities Since covariance measures the impact of an individual security on the variance of the portfolio, covariance is the appropriate measure

of risk

10.18 If we assume that the market has not stayed constant during the past three years, then the lack in movement

of Southern Co.’s stock price only indicates that the stock either has a standard deviation or a beta that is very near to zero The large amount of movement in Texas Instrument’ stock price does not imply that the firm’s beta is high Total volatility (the price fluctuation) is a function of both systematic and unsystematic risk The beta only reflects the systematic risk Observing the standard deviation of price movements does not indicate whether the price changes were due to systematic factors or firm specific factors Thus, if you observe large stock price movements like that of TI, you cannot claim that the beta of the stock is high All you know is that the total risk of TI is high

10.19 Because a well-diversified portfolio has no unsystematic risk, this portfolio should like on the Capital

Market Line (CML) The slope of the CML equals:

SlopeCML = [E(RM) – rf] / σM

where E(RM) = the expected return on the market portfolio

rf = the risk-free rate

σM = the standard deviation of the market portfolio

SlopeCML = [E(RM) – rf] / σM

= (0.12 – 0.05) / 0.10 = 0.70

a The expected return on the portfolio equals:

E(RP) = rf + SlopeCML(σP)

rf = the risk-free rate

σP = the standard deviation of the portfolio E(RP) = rf + SlopeCML(σP)

A portfolio with an expected return of 20% has a standard deviation of 21.43%

10.20 a The slope of the Characteristic Line (CL) of Fuji equals:

Slope = [E(R ) – E(R ) ] / [(R ) – (R ) ]

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where E(RFUJI)BULL = the expected return on Fuji in a bull market

E(RFUJI)BEAR = the expected return on Fuji in a bear market (RM)BULL = the return on the market portfolio in a bull market (RM)BEAR = the return on the market portfolio in a bear market

Characteristic Line of Fuji

0 0.05 0.1 0.15

10.21 Polonius’ portfolio will be the market portfolio He will have no borrowing or lending in his portfolio 10.22 a E(RP) = (1/3)(0.10) + (1/3)(0.14) + (1/3)(0.20)

= 14.67%

The expected return on an equally weighted portfolio is 14.67%

b The beta of a portfolio equals the weighted average of the betas of the individual securities within

the portfolio

βP = (1/3)(0.7) + (1/3)(1.2) + (1/3)(1.8)

The beta of an equally weighted portfolio is 1.23

c If the Capital Asset Pricing Model holds, the three securities should be located on a straight line

(the Security Market Line) For this to be true, the slopes between each of the points must be equal

Tiêu đề	Return and Risk: The Capital Asset Pricing Model (CAPM)
Trường học	University of Economics and Business (UEB) - https://ueb.edu.vn
Chuyên ngành	Finance
Thể loại	Bài tập
Năm xuất bản	2023
Thành phố	Hà Nội

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