PORTFOLIO RISK AND RETURN: PART I

SOLUTIONSC is appropriate. –10.1% is the holding interval return, which is calculated as: (3,050 2 3,450 1 51.55)/3,450, which consists of a dividend

1. yield of 1.49% ^[1][2][3] 51.55 / (3,450) and a capital loss yield of –11.59% 52400/(3,450).
2. B is appropriate. [(1 1 0.14)(1 2 0.10)(1 2 0.02)] 2 1 ^[4] 0.0055 ^[5][6] 0.55 %.

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[1] . B is appropriate. The annualized charge of return for ETF 2 is 12.05% 5 (1.0110^52/5) 2 1 , which is larger than the annualized charge of ETF 1, 11.93% 5 (1.0461^365/146) 2 1, and ETF 3, 11.32% 5 (1.1435^12/15) – 1. Regardless of having the bottom worth for the periodic charge, ETF 2 has the best annualized charge of return due to the reinvestment charge assumption and the compounding of the periodic charge.

[2] . A is appropriate. The asset’s returns will not be used to calculate the portfolio’s variance [only the assets’ weights, standard deviations (or variances) and covariances (or correlations) are used].

[3] . C is appropriate.

σport 5 qwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12σ211w22σ221 2w1w2ρ1;2σ1σ2

[4] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið^0:3Þ²ð^20%Þ²¹ð^0:7Þ²ð^12%Þ^{21 2}ð^0:3Þð^0:7Þð^0:40Þð^20%Þð^12%Þ

[5] ð0:3600% 1 0:7056% 1 0:4032percentÞ^0:55ð1:4688percentÞ^0:55 12:11%:

[6] . A is appropriate.

σport 5 pwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12σ211w22σ221 2w1w2CovðR1R2Þ

[1] . B is appropriate. The annualized charge of return for ETF 2 is 12.05% 5 (1.0110^52/5) 2 1 , which is larger than the annualized charge of ETF 1, 11.93% 5 (1.0461^365/146) 2 1, and ETF 3, 11.32% 5 (1.1435^12/15) – 1. Regardless of having the bottom worth for the periodic charge, ETF 2 has the best annualized charge of return due to the reinvestment charge assumption and the compounding of the periodic charge.

[1] . A is appropriate. The asset’s returns will not be used to calculate the portfolio’s variance [only the assets’ weights, standard deviations (or variances) and covariances (or correlations) are used].

[1] . C is appropriate.

σport 5 qwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12σ211w22σ221 2w1w2ρ1;2σ1σ2

[1] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið^0:3Þ²ð^20%Þ²¹ð^0:7Þ²ð^12%Þ^{21 2}ð^0:3Þð^0:7Þð^0:40Þð^20%Þð^12%Þ

[1] ð0:3600% 1 0:7056% 1 0:4032percentÞ^0:55ð1:4688percentÞ^0:55 12:11%:

[1] . A is appropriate.

σport 5 pwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12σ211w22σ221 2w1w2CovðR1R2Þ

1. A is appropriate. [(1 1 0.22)(1 2 0.25)(1 1 0.11)]^(1/3) 2 1 ^[1] 1.0157^(1/3) 2 1 ^[2][3] 0.0052 5 0.52 %
2. A is appropriate. The geometric imply return compounds the returns as an alternative of the quantity invested.
3. A portfolio commonplace deviation of 14.40% is the weighted common, which is feasible provided that the correlation between the securities is the same as 1.0. If the correlation coefficient is the same as 1.0, then the covariance should equal 0.0240, calculated as: Cov(R₁, R₂) 5 ρ₁₂σ₁σ₂ 5 (1.0)(20%)(12%) 5 2.40% 5 0.0240.
4. B is appropriate. (1 1 0.080)/(1 1 0.0210) 5 5.8 %. 12. A is appropriate. (1 1 0.065)/(1 1 0.0210) 5 4.3 %.
5. A is appropriate. (1 1 0.080)/(1 1 0.0250) 5 5.4 %.
6. B is appropriate. (1 1 0.0650)/(1 1 0.0250) 5 3.9 %.
7. C is appropriate. Brokerage commissions are negotiated with the brokerage agency. A safety’s liquidity impacts the operational effectivity of buying and selling prices. Particularly, liquidity impacts the bid-ask unfold and might impression the inventory value (if the flexibility to promote the inventory is impaired by the uncertainty related to having the ability to promote the inventory).
8. C is appropriate. Historic knowledge over lengthy intervals of time point out that there exists a constructive threat–return relationship, which is a mirrored image of an investor’s threat aversion.
9. A is appropriate. A risk-free asset has a variance of zero and isn’t depending on whether or not the investor is risk-neutral, risk-seeking, or risk-averse. That’s, on condition that the utility perform of an funding is expressed as

ð Þ          1   σ²

U 5E r 2 A

2

the place A is the measure of threat aversion, then the signal of A is irrelevant if the variance is zero (like that of a risk-free asset).

1. C is appropriate. Essentially the most risk-averse investor has the indifference curve with the best slope.

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[1] qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið^0:3Þ²ð^20%Þ²¹ð^0:7Þ²ð^12%Þ^{21 2}ð^0:3Þð^0:7Þð^20:0240Þ

[2] ð0:3600% 1 0:7056% 2 1:008percentÞ^0:55ð0:0576percentÞ^0:55 2:40%:

[3] . C is appropriate. A portfolio commonplace deviation of 14.40% is the weighted common, which is feasible provided that the correlation between the securities is the same as 1.0.

1. A is appropriate. A destructive worth within the given utility perform signifies that the investor is a threat seeker.
2. C is appropriate. Funding 3 has the best charge of return. Threat is irrelevant to a risk-neutral investor, who would have a measure of threat aversion equal to 0. Given the utility perform, the chance impartial investor would acquire the best quantity of utility from funding 3.

Anticipated

Anticipated        Customary  Utility

1. C is appropriate. Funding 4 supplies the best utility worth (0.2700) for a risk-seeking investor, who has a measure of threat aversion equal to –2.

Funding	Anticipated Return	Anticipated Customary Deviation	Utility A 522
1	18%	2%	0.1804
2	19%	8%	0.1964
3	20%	15%	0.2225
4	18%	30%	0.2700

1. B is appropriate. Funding 2 supplies the best utility worth (0.1836) for a risk-averse investor who has a measure of threat aversion equal to 2.

Chapter 5 Portfolio Threat and Return: Half I 109

Funding	Anticipated Return	Anticipated Customary Deviation	Utility A 5 2
1	18%	2%	0.1796
2	19%	8%	0.1836
3	20%	15%	0.1775
4	18%	30%	0.0900

1. A is appropriate. Funding 1 supplies the best utility worth (0.1792) for a risk-averse investor who has a measure of threat aversion equal to 4.

Funding	Anticipated Return	Anticipated Customary Deviation	Utility A 5 4
1	18%	2%	0.1792
2	19%	8%	0.1772
3	20%	15%	0.1550
4	18%	30%	0.0000

1. A is appropriate. The CAL is the mix of the risk-free asset with zero threat and the portfolio of all dangerous belongings that gives for the set of possible investments. Permitting for borrowing on the risk-free charge and investing within the portfolio of all dangerous belongings supplies for attainable portfolios that dominate dangerous belongings under the CAL.
2. B is appropriate. The CAL represents the set of all possible investments. Every investor’s indifference curve determines the optimum mixture of the risk-free asset and the portfolio of all dangerous belongings, which should lie on the CAL.
3. C is appropriate.
4. R_p 5 w₁ 3 R₁ 1 (1 2 w₁) 3 R₂
5. R_p 5 w₁ 3 16% 1 (1 2 w₁) 3 12 %
6. 15% 5 0.75(16%) 1 0.25(12%).
7. A is appropriate.
8. σport 5 qwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12σ211w22σ221 2w1w2ρ1;2σ1σ2
9. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið^0:5Þ²ð^20%Þ²¹ð^0:5Þ²ð^20%Þ^{21 2}ð^0:5Þð^0:5Þð^{2 0:15}Þð^20%Þð^20%Þ
10. 5   ð1:0000percent1 1:0000% 2 0:3000percentÞ^0:55ð1:7000percentÞ^0:55 13:04%:
11. B is appropriate.
12. σport 5 qwffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi12σ211w22σ221 2w1w2ρ1;2σ1σ2
13. qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið^0:5Þ²ð^20%Þ²¹ð^0:5Þ²ð^20%Þ^{21 2}ð^0:5Þð^0:5Þð^0:00Þð^20%Þð^20%Þ
14. 5 ð1:0000% 1 1:0000% 1 0:0000percentÞ^0:55ð2:0000percentÞ^0:55 14:14%:
15. B is appropriate. The contribution of every particular person asset’s variance (or commonplace deviation) to the portfolio’s volatility decreases because the variety of belongings within the equally weighted portfolio will increase. The contribution of the co-movement measures between the belongings will increase (i.e., covariance and correlation) because the variety of belongings within the equally weighted portfolio will increase. The next equation for the variance of an equally weighted portfolio illustrates these factors:
16. σ2p 5σN2 1 NN2 1 COV 5σN2 1 NN2 1 ρσ2 C is appropriate. The co-movement measures between the belongings will increase (i.e., covariance and correlation) because the variety of belongings within the
17. equally weighted portfolio will increase. The contribution of every particular person asset’s variance (or commonplace deviation) to the portfolio’s volatility decreases because the variety of belongings within the equally weighted portfolio will increase. The next equation for the variance of an equally weighted portfolio illustrates these factors:
18. σ2p 5σN2 1 NN2 1 COV 5σN2 1 NN2 1 ρσ2
19. A is appropriate. Increased correlations will produce much less diversification advantages offered that the opposite elements of the portfolio commonplace deviation don’t change (i.e., the weights and commonplace deviations of the person belongings).
20. C is appropriate. Asset 2 and Asset 3 have returns which can be the identical for End result 2, however the actual reverse returns for End result 1 and End result 3; due to this fact, as a result of they transfer in reverse instructions on the identical magnitude, they’re completely negatively correlated.
21. C is appropriate. An equally weighted portfolio of Asset 2 and Asset 3 could have the bottom portfolio commonplace deviation, as a result of for every final result the portfolio has the identical anticipated return (they’re completely negatively correlated).
22. A is appropriate. An equally weighted portfolio of Asset 1 and Asset 2 has the best degree of volatility of the three pairs. All three pairs have the identical anticipated return; nonetheless, the portfolio of Asset 1 and Asset 2 supplies the least quantity of threat discount.
23. C is appropriate. The minimum-variance frontier doesn’t account for the risk-free charge. The minimum-variance frontier is the set of all attainable dangerous belongings with the best anticipated return for a given degree of threat or the bottom quantity of threat for a given degree of return.
24. C is appropriate. The worldwide minimum-variance portfolio is the portfolio on the minimumvariance frontier with the bottom commonplace deviation. Though the portfolio is attainable, when the risk-free asset is taken into account, the worldwide minimum-variance portfolio will not be the optimum dangerous portfolio.
25. B is appropriate. The Markowitz environment friendly frontier has larger charges of return for a given degree of threat. With respect to the minimum-variance portfolio, the Markowitz environment friendly frontier is the set of portfolios above the worldwide minimum-variance portfolio that dominates the portfolios under the worldwide minimum-variance portfolio.
26. A is appropriate. The usage of leverage and the mix of a risk-free asset and the optimum dangerous asset will dominate the environment friendly frontier of dangerous belongings (the Markowitz environment friendly frontier).
27. B is appropriate. The CAL dominates the environment friendly frontier in any respect factors aside from the optimum dangerous portfolio. The flexibility of the investor to buy extra quantities of the optimum dangerous portfolio by borrowing (i.e., shopping for on margin) on the risk-free charge makes larger charges of return for ranges of threat larger than the optimum dangerous asset attainable.
28. C is appropriate. Every particular person investor’s optimum mixture of the risk-free asset and the optimum dangerous asset is set by the investor’s threat desire.