FINA 4360
Homework 2: Solutions
2.1 (Chapter 9)
Country
4-year compounded return
U.S.
(1.09)4 – 1 = 41%
Singapore
(1.06)4 – 1 = 26%
=>
p = (1.41/1.26) - 1 = .119 (11.9%)
The 4-year forward rate should contain an 11.9% premium above today's spot rate of .60, which
means the forward rate (Ft,4-yr) is .60 USD/SGD x (1 + .119) = .6714 USD/SGD. The 4-year
forecast is .6714 USD/SGD (SGD is expected to appreciate against USD by 11.9%).
2.2 (Chapter 9)
Interest Rate Differential
0%
1%
2%
E[ef,t] = 3.12%
Forecast of the % Change in JPY (E[ef,t])
.9(0%) + .8(3%) = 2.4%
.9(1 %) + .8(3%) = 3.3%
.9(2%) + .8(3%) = 4.2%
Probability
30%
60%
10%
2.3 (Chapter 10)
i) TE = EUR 9 M x 15 ARS/EUR = ARS 135M
ii)
90-day mean = 0.018 x 3 = .0540
(or 5.40%)
90-day 2 = 0.0035 x 3 = .0105
(  = sqrt(0.0105) = .1024 or 10.24%)
VaR(99%) = ARS 135M (1 + [.0054-2.33x.1024]) = ARS 110.080080
iii) VaR(99%, mean) = ARS 110.080080 - ARS 135M = ARS -24.91992 M
2.4 (Chapter 10)
The net exposure to each currency in U.S. dollars:
Currencv
Net Inflows in Foreign Currency
DKK
DKK 10,000,000
GBP
GBP - 1,000,000
St
0.15 USD/DKK
1.50 USD/GBP
TE
USD 1.5 M
(USD 1.5 M)
a) NTE = USD 0
The DKK and the GBP are highly correlated. Both the DKK and the GBP exposure show
positive net inflows. The exposure is “hedged” => low exposure.
b) Usually with ρ=1, ef,t (USD/GBP)= .10
=> Change in NTE = 10%. But given that
the base NTE = USD 0 => New NTE = 0 & Change in NTE = 0!
c) ef,t (USD/GBP)= .10
=> ef,t (USD/DKK)= -.10 (St=0.135 USD/DKK).
New NTE = DKK 10,000,000 x 0.135 USD/DKK + (GBP - 1,000,000) x 1.650 USD/GBP =
= USD -250,000
2.5 (Chapter 10) The bottom line is that transaction exposure is reduced since Vegas will have
less receivables in Canadian dollars (CAD). It should be noted that economic exposure will not
necessarily be reduced because a weak CAD could cause a lower demand for its exports.
2.6 (Chapter 10)
.50 USD/NZD
Sales
U.S.
New Zealand
Total
800
400
1,200
(Figures are in USD millions)
.55 USD/NZD
.60 USD/NZD
800
440
1,240
800
480
1,280
Cost of Goods Sold
U.S.
New Zealand
Total
500
50
550
500
55
555
500
60
560
Gross Profit
650
685
720
Operating expenses
EBIT
Interest expenses
Earnings after taxes
300
350
100
250
300
385
100
285
300
420
100
320
The table shows that DeKalb Inc. is adversely affected by a weaker NZD value => DeKalb behaves
like an exporter.
2.7 (Chapter 10) A possible regression model for this task is to regress percentage change in its
stock price over quarter t (stockrett) against the percentage change in the USD/SGD exchange
rate (ef) in the three previous quarters, shown as follows.
stockrett =  + 1 ef,t–1 +  2 ef,t–2 + 3 ef,t–3 + ut
where ut is the error term. The sum of the ßs (1+2+3) measures the sensitivity of stock
prices (through stock returns) to changes in the USD/SGD exchange rate (through ef,t).
2.8 (Chapter 11)
Possible St+T
Prob.
Put Premium
Exercise
(X=.49 USD/NZD)
.44 USD/NZD
.40 USD/NZD
.38 USD/NZD
30%
50%
20%
USD .03
USD .03
USD .03
Yes
Yes
Yes
Amount per Total
Amount
unit Received Received for
NZD 250,000
USD .46
USD 115,000
USD .46
USD 115,000
USD .46
USD 115,000
The probability distribution represents a 100% probability of receiving USD 115,000, based
on the forecasts of the future USD/NZD exchange rate. The put option has established a floor
of USD 115,000.
Note: No information on interest rates, cannot estimate opportunity cost!
2.9 (Chapter 11)
1) Forward hedge (sell GBP forward).
Firm will receive GBP 400,000 x (1.50 USD/GBP) = USD 600,000 in 180 days.
2) Money market hedge (borrow GBP at 9%, convert to USD, invest in U.S. at 8%)
Firm will borrow
GBP 400,000/(1+.09x180/360) = GBP 382,775
Firm will convert to USD
GBP 382,780 x 1.48 USD/GBP = USD 566,507 (amount to
deposit)
Firm will receive
USD 566,507*(1+.08*180/360) = USD 589,167
Comparison: Firm will receive USD 600,000 in 180 days using FH, or about 589,167 in 180 days
using MMT. Firm should use the forward hedge because it delivers the highest payout.
2.10 (Chapter 11)
Put option hedge (Exercise price = .52 USD/NZD; premium = USD .03)
Amount per
Total Amount
Possible Spot
Put Option
Exercise
Unit Received
Received For
Rate
Premium
Option? Including premium NZD 4.000.000 Probability
.50
.03
Yes
.49
1,949,200
20%
.51
.03
Yes
.49
1,949,200
50%
.53
.03
No
.50
1,989,200
30%
Opportunity cost = NZD 4000000 x .03 USD/NZD x .09 = USD 10,800
Expected Amount to be received = USD 1,961,200.
Money market hedge (borrow NZD at 8%, convert to USD, invest in USD at 9%)
1. Borrow NZD 3,703,704 (NZD 4,000,000/1.08 = NZD 3,703,704)
2. Convert NZD 3,703,704 to USD 2,000,000 (at .54 USD/NZD)
3. Invest USD 2,000,000 to accumulate USD 2,180,000 at the end of one year (USD 2,000,000 x
1.09 = USD 2,180,000)
Comparison: The money market hedge is always superior to the put option hedge.
2.11 (Chapter 11)
Forecasted DINTt
1%
2%
3%
Forecast of ef,t
1.1(-5%) + .6(1%) = -4.9%
1.1(-5%) + .6(2%) = -4.3%
1.1(-5%) + .6(3%) = -3.7%
Prob
Approximate Forecasted USD/GBP
40%
50%
10%
1.62 x [1 + (-4.9%)] = 1.54
1.62 x [1 + (-4.3%)] = 1.55
1.62 x [1 + (-3.7%)] = 1.56
1) Option hedge (Buy put option with X = 1.61 USD/GBP; premium = USD .04)
Possible St
Prob
Put
Exercise
Amount per Total
Amount
Premium
(X=1.61 USD/GBP)
unit Received Received for
GBP 1,000,000
1.54 USD/GBP
40%
USD .04
Yes
USD 1.57
USD 1,570,000
1.55 USD/GBP
50%
USD .04
Yes
USD 1.57
USD 1,570,000
1.56 USD/GBP
10%
USD .04
Yes
USD 1.57
USD 1,570,000
2) Forward hedge (sell 1-yr GBP forward)
Total Amount Received for GBP 1,000,000
GBP 1,000,000x1.59 USD/GBP = USD 1,590,000
Comparison: In this exercise, the forward hedge is always better than the option hedge.
2.13 (Chapter 11)
A. Transaction Exposure (TE): TWD 50 M x (1/29.78 TWD/USD) = USD 1.67898 M
Note: The monthly mean (TWD/USD) is -.0077 => The monthly mean (USD/TWD) is .0075
T= 5-mo
5-mo mean = .0077*5 = .0385 (3.85%)
5-mo SD = .014495*sqrt(5) = .0324 (3.24%)
(i) VaR(97.5%) = USD 1.67898 M*[1+(.0385-1.96x.0324)] = USD 1.637 M
(ii) The method used to approximate 5-mo mean returns cannot be used for extremes.
Given the information, we need to make assumptions. Let’s assume the worst case 1-mo
scenario (-.038576) also applies in 5-mo. Then,
Worst case scenario = USD 1.67898 M*(1-.038576) = USD 1.614 M
B. Amount to be received = TWD 50M x 1/(30.12 TWD/USD) = USD 1.66003 M
C. Check lectures notes. But, note that MMH is a replication of IRP. Then,
Ft,150=1/(29.78 TWD/USD) x (1+.013x5/12)/(1+.04x5/12)=.03321 USD/TWD
=> Amount to be received = TWD 50M x .3321 USD/TWD = USD 1.6605 M
2.13 (Chapter 12)
Carlton is subject to a higher degree of EE because it does not have an offsetting cost in Mexico.
But both firms are exposed to EE.
2.14 (Chapter 12)
Forecasted Income Statement for St. Paul (in millions)
0.48 USD/NZD
.50 USD/NZD
.54 USD/NZD
Sales
U.S.
NZ
Total
COGS
U.S.
NZ
Total
100M
288M
388M
105M
300M
405M
110M
324M
434M
200
48
248
200
50
250
200
54
254
Gross Profit
140
155
180
Op. Expenses
U.S. Fixed
U.S. Variable
Total
EBIT
Interest Expense
30
77.6
107.6
32.4
20
30
81
111
42.0
20
30
86.6
116.6
63.2
20
EBT
12.4
22.0
43.2
As the NZD appreciates against the USD there is an increase in EBT. If St. Paul is a U.S. firm it
benefits. If you’re a NZ firm, you are adversely affected. St. Paul could reduce its EE without
reducing its German revenues by shifting expenses to New Zealand.