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