Problem 4.2
Forward Premiums and Discounts
Calculate the percentage premium or discount.
Quoted
180-day
Percent premium
Assumptions
Spot rate
Forward rate
or discount
Days forward
180
180
European euro
($/euro) direct rate
0.8000
0.8160
4.0000%
British pound
($/pound) direct rate
1.5620
1.5300
-4.0973%
Japanese yen
(yen/$) (Japanese Jen--> number would become too tiny --> indirect rate)
120.00
118.00
3.3898%
Swiss franc
(SF/$) indirect rate
1.6000
1.6200
-2.4691%
Hong Kong dollar
(HK$/$) indirect rate
8.0000
7.8000
5.1282%
Note that for the first two currency calculations ($/euro and $/pound), the calculation formula is:
% premium = (F-S)/(S) x (360/180)
While the calculation formula for the remaining currencies (all expressed as currency/$) is:
% premium = (S-F)/(F) x (360/180)
Problem 4.4
Spot and forward quotes for the yen
Calculate the forward premiums for the yen in Exhibit 4.5.
a)
Yen (yen/$)
Implied
Calculated
Assumptions
Mid Rates
Days Forward
Forward Premium
Spot
118.32
1 week
118.23
7
-5142.8571%
1 mo
117.82
30
-1200.0000%
2 mo
117.38
60
-600.0000%
3 mo
116.91
90
-400.0000%
4 mo
116.40
120
-300.0000%
5 mo
115.94
150
-240.0000%
6 mo
115.45
180
-200.0000%
9 mo
114.00
270
-133.3333%
1 yr
112.50
360
-100.0000%
2 yr
106.93
720
-50.0000%
3 yr
101.09
1,080
-33.3333%
4 yr
96.82
1,440
-25.0000%
5 yr
92.91
1,800
-20.0000%
Forward premium = (S-F)/(F) x (360/days)
b)
The premium is gradually getting larger as the maturity lengthens to one year. After
one year it seemingly stabilizes at about 5.5% to 5.6%.
Problem 4.6
Traveling: Copenhagen to St. Petersburg
What is the cross-rate? What is left?
Assumptions
Values
Beginning your trip with Danish kroner
10,000.00
Spot rate (Dkr/$)
8.5515
Spot rate (Roubles/$)
30.962
a)
Calculate the cross-rate
Cross-rate (Dkr/rouble)
0.2762
cross-rate = (Dkr/$) / (Rouble/$)
b)
What would be the proceeds in Rubles?
Converting your Danish kroner into Rubles
36,206.51
Proceeds = Danish kroner / (Dkr/rouble)
Problem 4.7
Riskless profit on the franc
Can you make a profit via triangular arbitrage?
Assumptions
Values
Beginning funds in Swiss francs (SF)
10,000,000.00
Mt. Fuji Bank
(yen/$)
120.00
Mt. Rushmore Bank (SF/$)
1.6000
JPY/USD = 80*1,6 = 128 --> better rate than going direct
Matterhorn Bank (yen/SF)
80.00
Always convert back to the same currency we started with, otherwise we dont know if we made or l
Try Number 1: Start with SF to $
Step 1: SF to $
6,250,000.00
Step 2: $ to yen
750,000,000.00
Step 3: yen to SF
9,375,000.00
Profit?
(625,000.00)
A loss.
Try Number 2: Start with SF to yen
Step 1: SF to yen
800,000,000.00
Step 2: yen to $
6,666,666.67
Step 3: $ to SF
10,666,666.67
Profit?
666,666.67
A profit.
Forward rate > spot rate --> premium
Forward rate < spot rate --> discount
calculation flips
A/B x B/C = A/C
USD/CHF x CHF/EUR = USD/EUR
If the USD/EUR is different possibility of
arbitrage
Not make Arbitrage to loose money