Problem Set 1

Parity Relationships & Arbitrage

Problem 1

NY

LON

FRA

$1=£0.60

$1 = € 0.75

£1 = € 1.50

$1,000,000

£ 600,000

€ 900,000

$1,200,000

Profit = $200,000

Problem 2

NY

LON

ZUR

$1=£0.46

$1=CHF 0.92

£1=CHF 1.60

$1,000,000

£ 575,000

CHF 920,000

$1,250,000

Profit = $250,000

Problem 3

FRAtoday

$1,000,000 €769,230.77

$1,027,766.31 €784,554.44

Profit = $22,822.69

NYtoday

$1.30 = € 1

$1.31 = € 1FRAlater

4%

NYlater

1%

$1,004,943.62

What is not balanced?

Problem 4

• Real rate in Switzerland: (6% – 1%) / 1.01 = 4.95%

• Real rate in United States: (2% – 0.5%) / 1.005 = 1.49%

Money will flow to the higher real rate, flowing from the U.S. into Switzerland

Pressures will be on The U.S. nominal rate to riseThe Swiss nominal rate to decline

Problem 5

• Real rate in Japan: (5% – 1%) / 1.01 = 3.96%

• Real rate in UK: (10% – 7%) / 1.07 = 2.80%

Money will flow to the higher real rate, flowing from the UK into Japan

Pressures will be on The UK nominal rate to riseThe Japanese nominal rate to decline

Problem 6

Net for RRNB: extra 1% each year

This is includes a Floating/Floating Swap

RRNBT-Bill + 1%

CitiCorpLIBOR + 1%

Counterparty

T-Bill

LIBOR

BW Homes

T + 2%

HSBC Bank

LIBOR + 1%

$10,000 per year profit!

Problem 7: Gold

$1,215,306.29 1000 oz.

$1,294,937.14 1000 oz.

Profit = $73,622.84

NYtoday

$1.00 = £ 0.6089

$1.00 = £ 0.5886

LONtoday

LONlater

Spot £740Future £762.20

$1,221,314.30 NYlater

1%

What is not balanced?

Problem 7: Silver

$1,212,021.68 60,000 oz.

$1,291,539.25 60,000 oz.

Profit = $73,525.79

NYtoday

$1.00 = £ 0.6089

$1.00 = £ 0.5886

LONtoday

LONlater

Spot £12.30Future £12.67

$1,218,013.45 NYlater

1%

What is not balanced?

Problem 7: Tin

$1,221,875.51 120,000 lbs

$1,301,936.80 120,000 lbs

Profit = $74,020.80

NYtoday

$1.00 = £ 0.6089

$1.00 = £ 0.5886

LONtoday

LONlater

Spot £6.20Future £6.386

$1,227,916.00 NYlater

1%

What is not balanced?

Problem 8

€ 769,230.77 $ 1,000,000

€ 808,736.22$ 1,059,444.44

Profit = € 20,303.67

$1.30 = € 1

$1.31 = € 1

NYtoday

NYlater

Spot 1350Future 1410

Dividend 1.5%

€ 788,432.55

FRAtoday

FRAlater

R = 5%

What is not balanced?

Problem 9

CHF 920,000 $ 1,000,000

CHF 1,012,511.06$ 1,059,444.44

Profit = CHF 69,545.73

$1 = CHF 0.9200

$1 = CHF 0.9557

NYtoday

NYlater

Spot 1350Future 1410

Dividend 1.5%

CHF 942,965.33

ZURtoday

ZURlater

R = 5%

What is not balanced?

Fisher Effect: R = r + i + ri

• Prob 10: r = 3% i = 4% R = 7.12%

• Prob 11: r = 3% i = 5% R = 8.15%

• Prob 12: r = 3% i = 5% R = 8.15% FV = $1000, PV = $456.81

• Prob 13: r = 4% i = 3% R = 7.12% FV = $1000, PV = $933.53

• Prob 14: r = 4% i = 3% R = 7.12%

• Prob 15: r = 4% i = 3% R = 7.12% FV=$1000, PV = $502.68

Illustration of Real Return after tax

Year zero: Invest $100

• R is 9%

• i is 5%

• Marginal tax rate is 28%

One year later:• Collect $109• Pay tax of $2.52

– Tax is 28% of $9 – $106.48 left over

• Reinvest $105– Keeps real principal intact

• Spend $1.48• Expected real profit is

$1.48/1.05 = $1.41

Expected real return after tax is 1.41%

R (1 – t) – i

1 + ir =

Real return after tax

R (1 – t) – i

1+ir =

9% (1 – .28) – 5%

1.05r =

r = 1.41%

• Problem 16

Real return after tax

R (1 – t) – i

1+ir =

4% (1 – .28) – 3%

1.03r =

r = – 0.12%

• Problem 17

Real return after tax

R (1 – t) – i

1+ir =

21.5% (1 – .7) – 15%

1.15r =

r = – 7.43%

• Real World Example: January 1981

Real return after taxR (1 – t) – i

1+ir =

10% (1 – .28) – 9%

1.09For CD, r = r = – 1.65%

• Problem 18

12% (1 – .28) – 9%

1.09For loan, r = r = – 0.33%

Conclusion: Saving is a drag! Borrow the money and buy now

Basis too big, Problem 19

$1,050,000 500,000 bu.

$1,150,000 500,000 bu.

Profit = $46,928.59

Moneytoday

Wheattoday

$2.00 = 1 bushel

$2.30 = 1 bushelWheatlater

Storage $0.10

$1,103,071.41 Moneylater

10%

Return is 18.45%

Basis too small, Problem 20

$1,000,000 500,000 bu.

$1,015,000 500,000 bu.

Profit = $35,544.20

Moneytoday

Wheattoday

$2.00 = 1 bushel

$2.03 = 1 bushelWheatlater

Storage $0.10

$1,050,544.20 Moneylater

10%

Borrow at 3.02%

Bonds as commodities (Problem 21)

NYtoday

$1,024,960.58

$1,051,580.58

$1,000,000

$1,025,592.43

Profit = $631.85

10.00%NY

90 days

10.15%

10.20%NY

180 days

Bonds as commodities (Problem 22)

NYtoday

$1,017,408.41

$1,035,732.50

$1,000,000

$1,017,634.17

Profit = $225.76

7.00%NY

90 days

7.15%

7.12%NY

180 days

Bonds as commodities (Problem 23)

NYtoday

$1,035,630.37

$1,055,088.67

$1,000,000

$1,035,758.04

Profit = $127.67

7.10%NY

180 days

7.5%

7.25%NY

270 days

Bonds as commodities (Problem 24)

NYtoday

$1,017,408.41

$1,055,088.67

$1,000,000

$1,055,739.13

Profit = $650.46

7.00%NY

90 days

7.50%

7.25%NY

270 days

Problem 25

• Suppose the futures price of Plantonium (a mineral which your firm uses heavily) is $55 per unit for delivery in six months. At the same time the spot price is $60. Assuming that the futures market is reasonably efficient, which of the following is the best choice?a. The market expects a significant increase in available

supplies of plantonium between now and the delivery date.

Problem 26

• After the Chernobyl nuclear disaster in Russia, the prices of agricultural commodities were quickly bid much higher in active trading on the U.S. spot and futures markets.b. Automatically, without government intervention, this

put in place incentives to reduce consumption and increase production of basic foodstuffs; in turn leading to an increase in potential future supplies

c. This action was motivated by the desire for profits

d. Both b and c