PHA: Hedging Transaction
Exposure for DW Inc.
PROPOSED SOLUTION
Case Background: Hedging
 Forwards
in advance
(part 1)
 Futures
 Options
 Open positions
in hindsight
(part 2)
Part I: DW’s Hedging Problem
 June
 DW
orders parts valued at JPY 200 million
 Delivery in 2 months, payment within 30
days of delivery
 June 5th
 Confirmation
of delivery in October
 Expected delivery is Oct. 17
In Advance Scenario (Part 1)
Nov-17
30 days payment
JPY 200M
• PHLX options
• OTC options
• Forward contract
Projected delivery
Hedge exchange
rate risk with:
Oct-17
June-5
Order confirmation
Uncertainty over exact
Delivery and Payment Date
Time
Part I: Range Estimates of
Transaction Exposure: Data
 Monthly USD/JPY Exchange Rate Data:
1/31/71 – 8/31/02
 367 Observations
 Monthly Exchange Rate Percentage Changes
 Descriptive Statistics
Std. Deviation
0.033389951
Minimum
-0.109192201
Maximum
0.147448569
Part I: Risk Analysis of
Transaction Exposure
 Sensitivity Analysis
Worst Case Scenario
JPY 200M x .008502 USD/JPY x (1 + .147449)=
USD 1,951,122
Best Case Scenario
JPY 200M x .008502 USD/JPY x (1 - .109192) =
USD 1,514,473
Part I: Risk Analysis of
Transaction Exposure
 Confid. Interval Based on Normal Distribution
Upper Bound
200,000,000 JPY x .008502 x (1 + .065464) =
USD 1,811,700
Lower Bound
200,000,000 JPY x .008502 x (1 - .065464) =
USD 1,589,100
Part I: Hedging Strategies
Proposed
Forward Contracts
PHLX Options
Over-the-Counter-Options
Part I: Hedging Instruments :
Data
 Spot Price (USD/JPY) .008502
 Forward Contracts
6-Month Forward Rate: .008668
 CME Futures
 T=Dec; Ft,Dec = .008679
 PHLX Options: Dec Calls
Contract: premium: USD .000481/unit. X= .0086
Contract: premium USD .000391/unit. X= .0088
Contract: premium USD .000313/unit. X= .0090
 OTC (Over-the-Counter) Options
T= Nov 17th: premium: USD .000345/unit
X= Strike Price .0088
Forward/Futures contracts
Forward (OTC) Contracts
1mo .008530
3mo .008585
6mo .008668
CME Futures
Sep .008596
Dec .008679
Nov-17
Oct-17
Sep-5
June-5
Dec-5
sell forward
OTC
t
Dec-15
exercise if in-the-money
Nov-17
Oct-17
June-5
Call option
A:
X=0.0088,
premium = 0.000391
B:
X=0.0090,
premium = 0.000313
sell option if not exercised
PHLX Options
t
exercise option
if in-the-money and
pay back credit
borrow 200M JPY
and pay bill
Call option
X=0.0088,
premium = 0.000345
European style
Nov-17
Nov-20
Oct-17
June-5
OTC Options
t
Part I: Contract Size
 PHLX Call Option Contracts Needed:
JPY 200M/6.25M = 32 Contracts
 OTC Call Options Needed:
1 Contract
 Forward Contracts Needed:
1 Contract
Part I: Strategy Comparison:
Additional Data
Exchange Rate Distribution
 Using Monthly Percent Change Data
 Create a Frequency Histogram
 Probability Distribution Observed:
St+180
USD .008142
USD .008663
USD .009254
Probability
9%
79%
12%
Part I: Exchange Rate
Distribution Histogram
Frequency
Exchange Rate Distribution
180
160
140
120
100
80
60
40
20
0
-0.12 -0.08 -0.04 0.00
0.04
0.08
0.12
Exchange Rate Percent Changes
0.16 More
Part I: Exchange Rate
Distribution Histogram
Exchange Rate Distribution
Frequency
180
160
140
120
100
80
60
40
20
0
-20
Series1
-0.12
-0.08
-0.04
0.00
0.04
0.08
0.12
0.16
More
0
2
31
153
138
35
7
1
0
Exchange Rate Percent Changes
Exchange Rate Distribution
Spot Rate Forecast Calculation
 -.08(2) + -.04(31) = -1.40
-1.40/33 = -4.24%
33/367 = 9%
.008502 * (1-.0424) = .008142 USD/JPY
 .00(153) + .04 (138) = 5.52
5.52/291 = 1.897% 291/367 = 79%
.008502 * 1.01897 = .008663 USD/JPY
 .08(35) + .12(7) + .16(1) = 3.80
3.80/43 = 8.84%
43/367 = 12%
.008502 * 1.0884 = .009254 USD/JPY
Option Carrying Cost Calculation
OTC Call Option (.0088 Strike Price)
Carrying Cost: USD .000345 * .040850 * 180/360 =
USD .00000705/unit
PHLX Call Option (.0086 Strike Price)
Carrying Cost: USD .000481 * .04085 * 180/360 =
USD .00000982/unit
PHLX Call Option (.0090 Strike Price)
Carrying Cost: USD .000272 * .04805 * 180/360 =
.USD .00000555/unit
OTC vs. PHLX Options
Potential
Spot Price
180
(USD/JPY)
Premium
/unit
Carrying
Cost
.0081415
.0086633
.0092536
OTC 88 N
.000345
.000345
.000345
.000007047
.000007047
.000007047
.0081415
.000481
.0086633
.000481
.0092536
.000481
PHLX 86 D
.000009824
.000009824
.000009824
.0081415
.000272
.0086633
.000272
.0092536
.000272
PHLX 90 D
.000005556
.000005556
.000005556
Exercise
Option ?
Total Price
/unit
Prob
NO
NO
YES
.008494
.009015
.009152
Exp=.008985
9%
79%
12%
NO
YES
YES
.008632
.009091
.009091
Exp=.00905
9%
79%
12%
NO
NO
YES
.008419
.008941
.009278
Exp=.008934
9%
79%
12%
Part I: Instrument Comparison
 Forward
Purchase JPY 6 Months
(.008668USD/JPY) * JPY 200M = USD 1,733,600
 OTC Nov Option Strike Price .0088
.008985 USD/JPY * JPY 200M = USD 1,796,955
 PHLX Dec Option Strike Price .0086
.00905 USD/JPY* JPY 200 M = USD 1,809,912
 PHLX Dec Option Strike Price .0090
.008755145. USD/JPY* JPY 200M = USD 1,786,857
Part I: Recommendation
 OTC Nov Option Strike Price .0088
.008985 USD/JPY * JPY 200M = USD 1,796,955
Why?
- Exact Date
- Option flexibility, especially good with uncertain
arrival date.
- Caps expenses at
.009152 USD/unit * JPY 200M = USD 1,830,409
Part II: Comparisons
 November 6
 Japanese
parts arrived Oct. 11
 Payment due in 5 days (Nov 11)
 Exchange rate: .00907 USD/JPY
 The cost to DW, Inc. will vary depending
on the hedging approach undertaken…
Hindsight: Hedging Evaluation
 3-mo forward contract (Rollover on Sep)
 Dec futures
 No Hedge
 OTC Options
 CME Dec Options
1) 3-mo Forwards
Dec-5
Sell Dec 5 forward here,
and change USD for JPY
at St=Nov 6
Nov-11
Oct-11
Sep-5
Aug-5
July-5
June-5
Sep 5: Rollover ,
Buy JPY 200M at FJune 5, Sep 5.
Sell JPY 200M at St=Sep 5
Buy Dec 5 forward
time
1) 3-month forward contracts
 DW would have taken a long position in the forward
contract, to offset their short position
Amount to be paid for parts
JPY 200,000,000
Ft=Jun 5, Sep 5: 0.008530 USD/JPY
Rollover to another 3-mo contract on Sep 5:
Ft=Sep 5, Dec 5: 0.00907 USD/JPY
Sell Forward contract on Nov 6
Ft=Nov 6, Dec 5: 0.009162 USD/JPY
USD paid for parts
1,746,228
1) 3-mo forward
June-5
Oct-11
Nov-11
Dec-5
sell
forward
t
2) Dec Futures
Dec Futures
Long Dec futures at Ft=June 5,,Dec =0.008679 USD/JPY,
On Nov 6, Dec futures Ft=Nov
SNov 6 = .00907
6,,Dec
= 0.009162 USD/JPY
buy Dec future
Dec-15
Nov-6
Nov-11
Oct-11
June-5
sell 39 day future
time
2) December futures contract
 DW would have taken a long position in the
futures contract, to offset their short position:
16 Dec contracts long. (=200M/12.5M)
June 5 - Bought Dec futures @ .008679 USD/JPY
Nov 6 - Sold Dec futures @ .009162 USD/JPY
2) December futures contract
(Continued)
Gain/(Loss) on Futures Contracts
Long on June 5 (Ft, Jun) 0.008679
Sold on Nov 6 (Ft, Nov)
0.009162
=> Gain/Loss on Futures (0.000483)
Contracts
(16)
16
Gain Discounted Back 30 Days: 96,600/(1 + .0409 * 39/360)
USD
(1,735,800)
1,832,400
96,600
96,174
Borrow JPY 200M @ St=Nov 6 = 0.00907 USD/JPY x JPY 200M = 1,814,000
Net cost = (1,814,000-96,174)*(1+.0409*5/360) = USD 1,718,857
USD paid for parts
USD 1,718,857
3) Not hedged
 DW would bought JPY at the prevailing Spot Rate
when the payment was due.
Amount to be paid for parts
Spot rate at Nov. 6 (St=Nov 6)
JPY 200,000,000
0.00907 USD/JPY
Borrow JPY 200M = 0.00907 USD/JPY x JPY 200M =
= USD 1,814,000
Cost of loan = USD 1,814,000 x (1+.0409*5/360)= USD 1,815,030
USD paid for parts
USD 1,815,00
4) OTC options (Situation St > X)
Nov-17
Oct-11
June-5
SNov 6 = .00907
Nov-6
Nov-11
Exercise
Call option
A: X=0.0088,
premium = 0.000345
B: X=0.0090,
premium = 0.000272
t
4) OTC options (Situation St < X)
Oct-11
June-5
don’t exercise option
Nov-17
SNov 6 = .0084
Nov-6
Nov-11
buy on spot market
Call option
A: X=0.0088,
premium = 0.000345
B: X=0.0090,
premium = 0.000272
t
4) OTC JPY Option
 DW would have bought a call option to cover payables
Variables
Amount (JPY)
Strike Price
Premium
Interest Rate (US)
X
200,000,000
0.0088
0.000345
4.085-4.090
X
Premium
i
St=Nov 6
Premium
(USD/JPY
Exercise? Total USD
Cost
USD Paid
JPY 200M
88
0.00907 0.000345
Yes
0.009145 1,829,971
90
0.00907
Yes
0.009276 1,855,165
0.00272
4) OTC Nov JPY Option
 Carrying costs = Pt * interest rate * (maturity/360)
Fox X=.0088
=> 0.000345*.04085*124/360 =
= USD .00000485
Carrying cost is so small, for practical purposes can be
ignored => only USD 970!
 If St > X => Exercise: Both Options: Exercise!
 For X=.0088 => Borrow to buy JPY = USD 1,829,971
Cost of loan = USD 1,829,971 x (1+.0409*5/360)= USD 1,831,010
 For X=.0090 => Borrow to buy JPY = USD 1,855,165
Cost of loan = USD 1,855,165 x (1+.0409*5/360)= USD 1,856,219
5) PHLX Options
exercise option
Call option
A: X=0.0086,
premium = 0.000481
B: X=0.0090,
premium = 0.000313
SNov 6 = .00907
Dec-15
Nov-6
Nov-11
Oct-11
June-5
exercise since
in-the-money
t
5) JPY Dec. Options (PHLX)
 DW would have bought a call option to cover payables
 Same procedure as the OTC Options
Variables
Amount (JPY)
Strike Price
Premium
Interest Rate (US)
X
200,000,000
0.0086
0.000481
4.0850-4.090
X
Premium
iUSD,bid-ask
St=Nov 6
Premium
(USD/JPY
Exercise? Total USD USD Paid for
Cost
JPY 200M
86
0.00907 0.000481
Yes
0.009088 1,817,554
90
0.00907 0.000313
Yes
0.009317 1,863,481
5) JPY Dec. Options (PHLX)
 Carrying costs = P * interest rate * (maturity/360)
Fox X=.0086
=> 0.000481*.04085*124/360 =
= USD .00000677
 If St > X, Do Exercise
 For X=.0086 => Borrow to buy JPY = USD 1,817,554
Cost of loan = USD 1,817,554 x (1+.0409*5/360)= USD 1,818,859
 For X=.0090 => Borrow to buy JPY = USD 1,863,481
Cost of loan = USD 1,863,481 x (1+.0409*5/360)= USD 1,864,539
PHLX Options (Alternative Scenario:
option out-of-the-money)
buy on spot market
Call option
A: X=0.0086,
premium = 0.000481
B: X=0.0090,
premium = 0.000313
SNov 6 = .0084
Premium Call option
SNov 6 = .0084
X = .0086
σ = .20 (annualized)
T = 39/365
rf-USA = .0409; rf-JPY = .0028
premium = USD .00014831
Total received = USD 29,662
try to sell option
Dec-15
Nov-6
Nov-11
Oct-11
June-5
do not exercise since
out-of-the-money
time
Part II: Summary
Scenario
USD paid for parts
 3 month Forward
USD 1,746,228
 Dec futures
USD 1,718,857
 No hedge
USD 1,815,00
 OTC options
X=88 USD 1,829,971
X=90 USD 1,855,165
 PHLX options
X=86 => USD 1,818,859
X=90 => USD 1,863,481