Answers to Recommended Problems I

Chapter 5

5. 

E(r) = 0.3 * (44) + 0.4 * (14) + 0.3 * (-16) = 14

σ² = 0.3 * (44 - 14)² + 0.4 * (14 - 14)² + 0.3 * (-16 - 14)² = 540

σ = 540^0.5 = 23.24

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6. 

HPR = (End price - start price + dividend) / start price

E(r) = 0.33 * (30) + 0.33 * (10) + 0.33 * (-13.75) = 8.75

σ² = 0.33 * (30 - 8.75)² + 0.33 * (10 - 8.75)² + 0.33 * (-13.75 - 8.75)² = 319.79

σ = 319.79^0.5 = 17.88

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7.a.

HPR₂₀₁₀ = (110 - 100 + 4) / 100 = +14%

HPR₂₀₁₁ = (90 - 110 + 4) / 110 = -14.55%

HPR₂₀₁₂ = (95 - 90 + 4) / 90 = +10%

Arithmetic average = r_A = (14 - 14.55 + 10) / 3 = 3.15%

Geometric average = r_G = [(1 + 0.14) * (1 - 0.1455) * (1 + 0.10)]^1/3 - 1 = 2.33%

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18.

Risk premium = E(r_P) - r_f => 10 = E(r_P) - 6 => E(r_P) = 16

E(r_C) = 0.6 * (16) + 0.4 * (6) = 12

σ_C = y σ_P = 0.6 (14) = 8.4

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CFA 1.

Market value at end of 2011 = 100,000 * (1 + 0.05)⁷ = $140,710

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CFA 7.

E(r_X) = 0.2 * (-20) + 0.5 * (18) + 0.3 * (50) = 20

E(r_Y) = 0.2 * (-15) + 0.5 * (20) + 0.3 * (10) = 10

CFA 8.

σ_X² = 0.2 * (-20 - 20)² + 0.5 * (18 - 20)² + 0.3 * (50 - 20)² = 632

σ_X = 632^0.5 = 25

σ_Y² = 0.2 * (-15 - 10)² + 0.5 * (20 - 10)² + 0.3 * (10 - 10)² = 175

σ_X = 175^0.5 = 13

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CFA 9.

E(r_P) = 0.9 * 20 + 0.1 * 10 = 19

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Chapter 6

7. 

a.  The variance should be higher because the extreme values are more likely

b. 

E(r) = 0.10 * (-37) + 0.20 * (-11) + 0.35 * (14) + 0.35 * (30) = 9.5

σ² = 0.10 * (-37 - 9.5)² + 0.20 * (-11 - 9.5)² + 0.35 * (14 - 9.5)² + 0.35 * (30 - 9.5)² = 454.45

σ = 454.45^0.5 = 21.32

c.  Cov = -42.925

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8. 

E(r_P) = W_S * E(r_S) +  W_B * E(r_B)

σ_P²  = (W_S σ_S)² + (W_B σ_B)² + 2 (W_S σ_S) (W_B σ_B) ρ_SB 

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10.

Employing formula 6.10, w_B = 0.353 and w_S = 0.647

E(r_P) = 0.647 * (15) + 0.353 * (9) = 12.9%

σ_P² = 545.00 => σ_P = 23.35

S_O = (12.9 - 5.5) / 23.35 = 0.317

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11.

a.  S= slope of CAL = [E(r_P) - r_f] / σ_P = 0.317

 => (12 - 5.5) / σ_P = 0.317

 => σ_P = 20.5

b.  E(r_C) = W_f * E(r_f) +  W_P * E(r_P) = 12

 => W_f * 5.5 +  (1 - W_f ) * 12.9 = 12

=> 5.5 W_f + 12.9 - 12.9 W_f = 12

=> 0.9 = 7.4 W_f

=> W_f = 0.12 => W_P = 0.88 => W_B = 0.88 * 0.353 = 0.31, W_S = 0.88 * 0.647 = 0.57

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12.

w_B = 0.50 and w_S = 0.50

σ_P² = 443.45 => σ_P = 21.06

The standard deviation is slightly higher with this portfolio.  Having a risk-free asset to invest in allows the target rate of return to be reached with lower risk.

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CFA 1.

E(r) = 0.50 * (15) + 0.40 * (10) + 0.10 * (6)  = 12.1

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Chapter 7

4.  E(r_i) = r_f + β_i [E(r_M) - r_f ]

 E(r_$1) = 4 + 1.5 (6) = 13%

  E(r_$5) = 4 + 1.0 (6) = 10%

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5.

$1 Discount Store is overpriced because the forecasted return is less than the fair return (12% < 13%).

Everything $5 is underpriced because the forecasted return is greater than the fair return (11% > 10%).

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9.

20 = 5 + β_P (15 - 5) => β_P = 1.5

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CFA 2.

a.

E(r_i) = r_f + β_i [E(r_M) - r_f ]

E(r_X) = 5.0 + 0.8 [14.0 - 5.0] = 12.2

Forecasted return = 14.0 => α = 14.0 - 12.2 = +1.8

E(r_Y) = 5.0 + 1.5 [14.0 - 5.0] = 18.5

Forecasted return = 17.0 => α = 17.0 - 18.5 = -1.5

b.  Skip