Post on 27-Dec-2015
transcript
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