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%
Time
3/01/94
3/01/95
3/01/96
3/01/97
3/01/98
3/01/99
5
Price of X-Tech
51.00
58.00
66.12
74.05
72.35
79.39
Return (%) HPR
13.7
14
12
-2.3
9.73
1.137
1.14
1.12
0.977
1.0973
1 N
13.7 + 14 + 12 + (-2.3) + 9.73
HPYt =
= 9.43
Arithmetic Mean = N 
5
t 1
%
N
6
Geometric Mean
  ( HPRt )1 / N - 1
t 1
 (1.137)(1. 14)(1.12)( 0.977)(1.0 973)
1/ 5
1
 1.0925
- 1 = 0.0925 = 9.25%
7
E(Ri) = (0.25)(- 5) + (0.50)(5) + (0.25)(15) = 5%
8
 = [(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
2
The table provided below can be used to obtain answers for 10 to 13.
Stock Shares Price(t) MV(t) Price(t+1) MV(t+1) HPR HPY Weight
1
20
11
220
14
280 1.27 0.27 0.29
2
35
13
455
17
595
1.31 0.31 0.71
675
875
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%
Weighted
HPY
0.058
0.048
0.106
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.
3
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
10
11
Rate of return = [55-45+0.85-1.10-0.90]/[45+0.90] = 19.28%
Rate of return = [35-45+0.85-0.70-0.90]/[45+0.90] =-23.42%
Rate of return = [55-45+0.85-1.10-0.90(1-.75)(45)(.0625)]/[(0.75)(45)+0.90] = 23.51%
Rate of return = [35-45+0.85-0.70-0.90(1-.75)(45)(.0625)]/[(0.75)(45)+0.90] = -33.05%
12
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
4
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 =
 750000  750000  500000  1000000 

 x100  100
 750000  750000  500000  1000000 
20
Value weighted post split = 100. Not affected by splits.
21
Value weighted series Dec 2000 =
 1000000  650000  700000  1250000 

 x100  120
 750000  750000  500000  1000000 
5
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%