SOLUTIONS: IN CLASS ASSIGNMENT # 1: PPP / Fisher Effect
Real rate of return = 3%, Current spot rate for BP = $2.00
Consumer Price Index
USA
UK
Year 2001
100
200
Year 2002
105
216
Inflation Rate
(105-100)/100 = 5%
(216 - 200)/200 =8%
Interest Rate (Approximate)
3+ 5 = 8%
3 + 8 = 11%
Interest Rate (Exact)
(1.03)*(1.05)-1 = 8.15%
(1.03)*(1.08)-1 = 11.24%
1. Find the expected percentage change in spot rate for BP, according to PPP:
(1.0815) / (1.1124) -1 = - 2.78%
2. Find the expected spot rate for BP one year latter, according to PPP:
2.00 (1-0.0278) = $ 1.944
3. If the spot rate for BP one year latter is $1.98, then the:
(i) BP has appreciated in “real”terms and $ has depreciated in “real”terms
Because the actual SR (1.98) > the PPP-SR (1.944)
4. If the spot rate for BP one year latter is $1.93, then the:
(i) BP has depreciated in “real”terms and $ has appreciated in “real”terms
Because the actual SR (1.93) < the PPP- SR (1.944)
5. Use the Fisher method to estimate both the approximate and the exact interest rates in US and UK:
See the last two rows of the table above.
SOLUTIONS: IN CLASS ASSIGNMENT # 2: IFE
Current spot rate for SF (in direct quote) is $0.50 ( SR0 = $0.50)
Country
USA
Switzerland
Interest rate
6%
2%
$10,000,000
SF 20,000,000
Line of credit
Suppose one-year latter, the spot rate for SF (in direct quote) is $0.54 ( SR1 = $0.54)
The percentage change in:
DQ = 0.54/0.50 - 1 = 8%
IQ = (100/108-1)*100 = -7.41%
The uncovered rate from the viewpoint of:
home country, Ruh =(1+0.02)*
(1+0.08)-1 = 10.16%
foreign country, Ruf = (1+0.06)*
(1-0.0741) - 1 = -1.185%
Your investment strategy should be:
borrow in $
invest in SF
Your estimated profit (in $ or SF):
(10.16 - 6)% of 10,000,000 = $416,000
Suppose one-year latter, the spot rate for SF (in direct quote) is $0.51 ( SR1 = $0.51)
The percentage change in:
DQ = 0.51/0.50 -1 = 2%
IQ = (100/102 -1)*100 = -1.96%
The uncovered rate from the viewpoint of
US = (1+0.02)*
(1+0.02)-1 = 4.04%
SW = (1+0.06)*
(1-0.0196) - 1 = 3.92%
Your investment strategy should be:
invest in $
borrow in SF
Your estimated profit (in $ or SF):
(3.92 - 2)% of 20,000,000 = SF 384,313.73
SOLUTIONS TO IN CLASS ASSIGNMENT # 3: COVERED INTEREST ARBITRAGE
Assume that you have a $10,000,000 credit line in the US and a FF 50,000,000 credit line in France.
1-year interest rate in US
14%
9%
7%
12%
1-year interest rate in France
5%
15%
12%
6%
Spot rate for FF
$0.20
$0.20
$0.20
$0.20
I-year forward rate for FF
$0.22
$0.19
$0.19
$0.21
What is the forward premium ?
(US view point)
10%
-5%
-5%
5%
What is the covered rate of return ?
(US view point)
15.5%
9.25%
6.04%
11.30%
What is the forward premium ?
(Foreign country view point)
-9.09%
5.263%
5.263%
-4.76%
What is the covered rate of return ?
(Foreign country view point)
3.63%
14.73%
12.63%
6.667%
Borrow / Invest in
US/FR
US/FR
FR/US
FR/US
How much is the covered interest arbitrage profit
$150,000
$25,000
ff 315,000
ff 335,000
What should the FP be, based on IRP ?
$0.217
$0.1895
$0.1911
$0.2113