Answers to Problems

1

ANSWERS TO PROBLEMS

CHAPTER 1

1 HPR = Ending Value / Beginning Value = 70/50 = 1.4

2 HPY = HPR - 1 = (70/50) - 1= 1.4 - 1 = 0.4 = 40%

3 HPR = Ending Value/Beginning Value = 79.39/51 = 1.5567

4 Annual HPR = (HPR)1/n = (1.5567)1/5 = 1.0925

Annual HPY = Annual HPR - 1 = 1.0925 - 1 = 0.0925 = 9.25%

5 Arithmetic Mean =

6 Geometric Mean

7 E(Ri) = (0.25)(- 5) + (0.50)(5) + (0.25)(15) = 5%

8 s = [(0.25)(-5 - 5)2 + (0.50)(5 - 5)2 + (0.25)(15 - 5)2]1/2 = 7.07%

9 CV = Standard Deviation of Returns/Expected Rate of Return

= 7.07/5 = 1.41

The table provided below can be used to obtain answers for 10 to 13.

10 HPY for stock 1 = (280/220) – 1 = .27 = 27%

11 HPY for stock 2 = (595/455) – 1 = .31 = 31%

12 Market weight for stock 1 = 220/675 = .33 = 33%

Market weight for stock 2 = 455/675 = .67 = 67%

13 Portfolio HPY = .33(.27) + .67(.31) = .297 = 29.7%

CHAPTER 3

1 Large company risk premium = 11.2 - 3.8 = 7.4%

2 Small stock risk premium = 12.4 - 11.2 = 1.2%

3 Horizon premium = 5.3 - 3.8 = 1.5%

4 Default premium = 5.8 - 5.3 = 0.5%

CHAPTER 4

1 Letting X= total investment, Jackie's share will represent 50 percent.

Thus .50X= $45,000 and X = $45,000 ÷.50 = $90,000.

At $25 per share, she can purchase ($90,000 ÷ $25) = 3600 shares.

2 Profit = (40 - 25)(3600) = $54,000

3 Margin = (Market Value - Debit Balance) ÷ Market Value, where

Debit Balance = initial loan value = ($90,000 - $45,000) = $45,000

Market Value = Price x Number of Shares = 3600P

Thus 0.30 = (3600P - $45,000) ÷ (3600P)

1080P = 3600P- 45,000 P = $17.86

4 Letting P = price and Q = quantity of shares,

Heidi's share of the investment will = 40% of PQ.

Thus 0.40PQ = $50,000 and PQ = $50,000 /0.40 = $125,000

\ At $50 per share, she can purchase ($125,000 ÷ $50) = 2500 shares.

5 Profit = (80 - 50)(2500) = $75000

6 Margin = (Market Value - Debit Balance) ÷ Market Value, where

Debit Balance = initial loan value = ($125,000 - $50,000) = $75,000

Market Value = Price x Number of Shares = 2500P

Thus 0.25 = (25007P - $75,000) ÷ (2500P)

625P = 2500P - 75,000 P = $40.00

7 Profit = Total Return - Repurchase Cost - Transaction Costs - Interest

Total Return = Beginning Market Value - Dividend

= $3,225 - 75 = $3,150.00

Repurchase cost = $28.375 x 100 = $2,837.50 (without transaction costs)

Transaction Costs = $45 + $55 = $100.00

Interest = .09 x 0.45($3225) = $130.61

\ Profit = $3150 - $2837.50 - $100 - $130.61 = $81.89

8 Rate of Return = Profit ÷ Initial Investment

Initial investment = (.55 x $3225) = $1,773.75

\ Rate of Return = $81.89/$1,773.75 = 4.62%

9 Rate of return = [55-45+0.85-1.10-0.90]/[45+0.90] = 19.28%

10 Rate of return = [35-45+0.85-0.70-0.90]/[45+0.90] =-23.42%

11 Rate of return = [55-45+0.85-1.10-0.90-

(1-.75)(45)(.0625)]/[(0.75)(45)+0.90] = 23.51%

12 Rate of return = [35-45+0.85-0.70-0.90-

(1-.75)(45)(.0625)]/[(0.75)(45)+0.90] = -33.05%

13 0.30 = [(150)(P) – (0.45)(150)(50)]/[(150)(P)] P = $32.14

CHAPTER 5

1 January 13 index = (25 + 40 + 30) ÷ 3 = 31.67

2 January 14 adjusted divisor = (25 + 40 + 6) ÷ X = 31.67 X = 2.2419

3 January 14 index = (25 + 42 + 7) ÷ 2.2419 = 33.01

4 January 15 index = (27 + 42 + 8) ÷ 2.2419 = 34.35

5 January 16 divisor = (13.5 + 42 + 8) ÷ X = 34.35 X = 1.8486

6 January 16 index = (14 + 44 + 10) ÷ 1.8486 = 36.78

7 January 13 index = 100 by definition

8 Base Value = (25)(1000) + (40)(2000)+(30)(1000) = $135,000

January 14 Value = (25)(1000) + (42)(2000) + (7)(5000) = 144,000

Index = (144,000 ÷ 135,000) x 100= 106.67

9 January 15 Value = (27)(1000) + (42)(2000) + (8)(5000) = 151,000

Index = (151,000 ÷ 135,000) x 100= 111.85

10 January 16 Value = (14)(2000) + (44)(2000) + (10)(5000) = 166,000

Index = (166,000 ÷ 135,000) x 100= 122.96

11 The Arithmetic Average is: (10 + 12 + 10 + 11 + 6) ÷ 5 = 9.8%

12 The Geometric Average is: [(1.10)(1.12)(1.10)(1.11)(1.06)]1/5 - 1 = 9.78%

13 The Arithmetic Average is: (8 + 10 - 14 + 20 - 10) ÷ 5 = 2.8%

14 The Geometric Average is: [(1.08)(1.10)(.86)(1.20)(.9)]1/5 - 1 = 1.99%

15 Price weighted series Dec 2000

=(75 + 150 + 25 + 40)/4 = 72.5

16 Post split series = 72.5

= (37.5 + 75 + 25 + 40)/X

The new divisor, X = 2.4483.

17 Price weighted series Dec 2001

= (50 + 65 + 35 + 50)/2.4483 = 81.69

18 Return on series = (81.69 – 72.5)/72.5 = 12.68%

19 Value weighted series Dec 2000 =

20 Value weighted post split = 100. Not affected by splits.

21 Value weighted series Dec 2000 =

22 Since the base value is 100 and the current index value is

120, the percentage return is 20%.

23 The index value Dec 2000 is 100

24 Post split the index value is 100

25 Index Dec 2001 = (1.33 + 0.87 + 1.40 + 1.25)1/4 (100) = 119.25

26 The return on the index is 19.25%

CHAPTER 6

1 Abnormal Returnit = Rit - Rmt

Abnormal Returnct = 9.8 - 13.0 = - 3.2

2 Abnormal Returnit = Rit - Rmt

Abnormal Returnet = 9.5 - 7.0 = 2.5

3 Abnormal Returnit = Rit - (Beta x Rmt)

Abnormal Returnct = 9.8 - (0.7 x 13.0) = 9.8 - 9.10 = 0.7%

4 Abnormal Returnit = Rit - (Beta x Rmt)

Abnormal Returnit = 9.5 - (1.1 x 7.0) = 1.8%

5 Abnormal Returnit = Rit - Rmt

Abnormal Returnct = 10.3 - 12.0 = - 1.7

6 Abnormal Returnit = Rit - Rmt

Abnormal Returnet = 9.4 - 9.0 = 0.4

7 Abnormal Returnit = Rit - (Beta x Rmt)

Abnormal Returnct = 10.3 - (0.6 x 12.0) = 10.3 - 7.20 = 3.1%

8 Abnormal Returnit = Rit - (Beta x Rmt)

Abnormal Returnit = 9.4 - (1.2 x 9.0) = 9.4 - 10.8 = - 1.4%