Second Exam
DistributionHigh: 100
Median: 91
Low: 6
Average So FarHigh: 99.5
Median: 79.5
Problem 1 (Source: Set 1, #12 & 13)
Direct Approach• N = 12• I/YR = 8.15%• P/YR = 1• FV = 1000• PMT = 0• Compute PV• Result: $390.5546
2-Step Approach• N = 12• I/YR = 5%• FV = 1000• PV = 556.8374• Input this as FV• I/YR = 3%• Compute PV• Result: $390.5546
Problem 2 (Source: Set 2, #8 & 9)
• With currency options, a New York call on the Euro is the same as a Frankfurt put on the dollar
• The premia should match when compared at the spot exchange rate– When rendered on the same scale
• Choice C is correct
Problem 3 (Source: Set 1, #1 & 2)
FRA
Tokyo
NYC
€1= ¥145.85
€1 = $1.2500$1 = €0.80
$1= ¥116.68
€1
¥145.85
$1.2500
€1
Equilibrium
Problem 4 (Source: Set 1, #1 & 2)
Tokyo
FRA
Zurich
€1= ¥ 145.44
¥1 = CHF 0. 0083CHF1 = ¥120. 7152
€0.83= CHF1
¥145.44
€1
CHF 1.2048
¥145.44
Equilibrium
Real return after tax
R (1 – t) – i
1+ir =
4.25% (1 –.35) – 3%
1.03r =
r = –0.2306%
• Problem 5 (Source: Set 1, #16-18)
Problem 6 (Source: Set 1, #4&5, 10-18 )
• Real rate– Switzerland: (3.5% – 0%)/1.00 = 3.5%– England: (?% – 4%)/1.04 = 3.5%
• Equilibrium nominal rate in England would be 7.64%
Problem 7 (Source: Set 1, #21-24)
NYtoday
$1,002,056.84
$1,008,045.54
$1,000,000
$1,002,056.84
Profit = 0
2.5%NY
30 days
3.6250%
3.25%NY
90 days
Problem 8 (Source: Set 1, #3)
• In Japan Yen 145.44 grows to Yen 152.7120
• In Germany, €1 grows to €1.04
• Forward rate must equal Yen 152.7120/€1.04 • Answer: €1 = Yen 146.8385 (Yen1 =
€0.0068)
Problem 9 (Source: Set 1, #12 & 13; see #2)
Direct Approach• N = 5• I/YR = 4.0%• P/YR = 1• PV = –1000• PMT = 0• Compute FV• Result: $1216.6529
2-Step Approach• N = 5• I/YR = 7.12%• PV = –1000• Compute FV• Result: $1410.4342• I/YR = 3%• Compute PV• Result: $1216.6529
Problem 10 (Source: Set 1, #21-24)
NYtoday
$1,124,864.00
$1,215,506.25
$1,000,000
$1,124,864.00
Profit = 0
4%NY
3 years
8.0581%
5%NY
4 years
Problem 11 (Source: Set 3, #45 & 46)Generic Interest Rate Arbitrage: Different Coupons
C(Example: 5%)
C–x(Example: 4%)
C+x(Example: 6%)
Requires three equally-spaced coupons
Price should be average of the two “bookends”
Price is $80
Price is $95Price is $87.50
Problem 12 (Source: Set 1, #7)
$1230 CHF 1180.80
$1280 CHF 1203.20
Equilibrium
NYtoday
$1 = CHF 0.96
$1 = CHF 0.9400
CHF 1 = $ 1.0638
ZURtoday
ZURlater
Spot CHF1180.80
Future CHF1203.20
$1280 NYlater
Spot $1230Future $1280
Problem 13 (Source: Set 1, #3)
• In U.S. $1.00 grows to $1.03
• In Japan, ¥ 116.6950 grows to ¥ 122.5298
• Forward exchange rate must equal ¥122.5298/$1.03
• Answer: $1 = ¥ 118.9609 (¥1 = $0.0084)
Problem 14 (Source: Set 2, #8)
Frankfurt
• Find price of a put to sell $100 in exchange for €78 (exchange at the forward rate)
• Answer:= $2.50 * 0.80 = €2.00
New York• $3.00 buys a call to
purchase €78 for $100 (exchange at the forward rate)
$1 = €0.80 spot
Problem 15 (Source: Set 1, #7)
$80 £ 51.20
$87.03 £ 52.22
Equilibrium
NYtoday
$1 = £0.64
$1 = £ 0.6000
£ 1 = $ 1.6667
LONtoday
LONlater
Spot £51.20Future £52.22
$87.03 NYlater
Spot $80Future $87.03
Problem 16 (Source: Set 3, #45)
Coupon Stripping
• Moving from the 5% coupon to the 4% coupon reduces income by $1 per year, and reduces the price by $6
• Moving from the 4% coupon to the 3% coupon reduces income by $1 per year, and reduces the price by $6
• Thus, the price of a 0% coupon bond would be $68 – (3*$6= $50.
Problem 17 (Source: Set 3, #51& 52)
$75.00 €60.00
Profit = 0
NYtoday
$1.00 = € 0.80
$1.00 = € 0.75
FRAtoday
FRAlater
NYlater
Price €80Face €100
Price ?Future $100
$100 €75
€60.00
Problem 18 (Source: Set 1, #7)
€64.00 $80.00
€68.00 $87.1795
Profit =0; U.S. Future = $110.00
$1.00 = €0.80
$1.00 = €0.78
NYtoday
NYlater
Spot $80.00
Future ?
€68.00
RTDtoday
Spot €64.00
Future €68.00
RTDlater
Problem 19 (Source: Set 1, #7)
CNY489.98 $80.00
CNY536.16 $87.1805
Profit = 0; U.S. Future = $110.00
Beijingtoday
$1.00 = CNY6.1247
$1.00 = CNY6.1500
NYtoday
NYlater
Spot $80.00
Future ?
CNY536.16 Beijinglater
Spot CNY489.98
Future CNY536.16
Problem 20 (Source: Set 1, #9)
CHF 963,000 $ 1,000,000
CHF 978,558.04$ 1,069,607.84
Profit = 0
$1 = CHF 0.9630
$1 = CHF 0.9149 CHF 1 = $1.0930
NYtoday
NYlater
Spot 2040Future 2161.60Dividend 1%
CHF 978,558.04
ZURtoday
ZURlater
R = 3.25%
Problem 21 (Source: Set 3, #51& 52)
$75.00 £48.00
Profit = 0
NYtoday
$1.00 = £ 0.64
$1.00 = £ 0.60
LONtoday
LONlater
NYlater
Price £80Face £100
Price ?Future $100
$100 £60
£48.00
Problem 22 (Source: Set 1, #3)
FRAtoday
$1,000,000 €798,000
$1,026,445.99 €810,892.33
Profit = $0
NYtoday
$1 = €0.7980
$1 = €0.7900FRAlater
3.25%
NYlater
5.2934%
$1,026,445.99
Problem 23 (Source: Set 1, #7)
£768,000 $1,200,000
£ 753,300 $1,215,000
Profit = 0
LONtoday
$1.00 = £0.64
$1.00 = £0.6200
£1.00 = $1.6129
NYtoday
NYlater
Spot $1200Future $1215
£ 753,300 LONlater
Spot £768Future £753.30
Problem 24 (Source: Set 1, #3)
INDtoday
$1,000 IDR12,116,000
$1,011.1573 IDR12,357,360.03
Profit = $0
NYtoday
$1 = IDR 12,116
$1 = IDR12,221.01
IDR1 = $0.0000818
INDlater
4%
NYlater
2.25%
$1,011.1573
Problem 25
€ 6,450,000 ¥944,796,000 ¥941,000,000Net ¥3,796,000(or €25,914.80)
€ 6,620,689.66
€ 6,600,000Net € 20,689.66
(or ¥3,000,000)
€1= ¥ 146.48
€1 = ¥ 145.00
¥ 960,000,000
100,000 bbl
ROTtoday
TOKtoday
TOKlater
ROTlater
Oil € 64.50
Oil € 66.00
Oil ¥ 9,410
Oil ¥ 9,600
100,000 bbl
100,000 bbl100,000 bbl