PHA PHA: Hedging Transaction Exposure for DW Inc. PROPOSED SOLUTION
Jan 03, 2016
PHAPHA: Hedging Transaction Exposure for DW Inc.
PROPOSED SOLUTION
Case Background: Hedging
Forwards Futures Options Open positions
in advance
(part 1)
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)Ju
ne
-5
No
v-17
Oct
-17
Ord
er
con
firm
atio
n
Pro
ject
ed
de
liver
y
30
da
ys p
aym
ent
JPY
20
0MTime
Hedge exchangerate risk with:
• PHLX options• OTC options• Forward contract
Uncertainty over exact Delivery and Payment Date
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 Bound200,000,000 JPY x .008502 x (1 + .065464) =
USD 1,811,700Lower Bound200,000,000 JPY x .008502 x (1 - .065464) = USD 1,589,100
Part I: Hedging Strategies Proposed
Forward Contracts PHLX OptionsOver-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 contractsJu
ne
-5
No
v-17
Oct
-17 t
De
c-5
Se
p-5
sell forwardOTC
CME FuturesSep .008596Dec .008679
Forward (OTC) Contracts1mo .0085303mo .0085856mo .008668
PHLX OptionsJu
ne
-5
No
v-17
Oct
-17 t
Call option A: X=0.0088,
premium = 0.000391B: X=0.0090,
premium = 0.000313
De
c-15
exe
rcis
e if
in-t
he-m
on
ey
sell
op
tion
if n
ot e
xerc
ise
d
OTC OptionsJu
ne
-5
No
v-17
Oct
-17 t
Call option X=0.0088, premium = 0.000345European style
No
v-20
bor
row
20
0M J
PY
a
nd p
ay b
ill
exe
rcis
e o
ptio
n
if in
-th
e-m
on
ey a
nd
p
ay b
ack
cre
dit
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 DataExchange Rate Distribution Using Monthly Percent Change Data Create a Frequency Histogram Probability Distribution Observed:
St+180 ProbabilityUSD .008142 9 %USD .008663 79%USD .009254 12%
Part I: Exchange Rate Distribution Histogram
Exchange Rate Distribution
020406080
100120140160180
-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12 0.16 More
Exchange Rate Percent Changes
Fre
qu
en
cy
Part I: Exchange Rate Distribution Histogram
Exchange Rate Distribution
-20
0
20
40
60
80
100
120
140
160
180
Exchange Rate Percent Changes
Fre
qu
ency
Series1 0 2 31 153 138 35 7 1 0
-0.12 -0.08 -0.04 0.00 0.04 0.08 0.12 0.16 More
Exchange Rate DistributionSpot 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
Potential
Spot Price 180
(USD/JPY)
Premium /unit
Carrying Cost
Exercise
Option ?
Total Price
/unit
Prob
.0081415
.0086633
.0092536
OTC 88 N
.000345
.000345
.000345
.000007047
.000007047
.000007047
NO
NO
YES
.008494
.009015
.009152
Exp=.008985
9%
79%
12%
.0081415
.0086633
.0092536
PHLX 86 D
.000481
.000481
.000481
.000009824
.000009824
.000009824
NO
YES
YES
.008632
.009091
.009091
Exp=.00905
9%
79%
12%
.0081415
.0086633
.0092536
PHLX 90 D
.000272
.000272
.000272
.000005556
.000005556
.000005556
NO
NO
YES
.008419
.008941
.009278
Exp=.008934
9%
79%
12%
OTC vs. PHLX Options
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 ForwardsJu
ne
-5
No
v-11
Oct
-11 time
De
c-5
July
-5
Au
g-5
Se
p-5
Sell Dec 5 forward here,and change USD for JPYat St=Nov 6
Sep 5: Rollover ,Buy JPY 200M at FJune 5, Sep 5.Sell JPY 200M at St=Sep 5
Buy Dec 5 forward
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/JPYRollover to another 3-mo contract on Sep 5:
Ft=Sep 5, Dec 5: 0.00907 USD/JPYSell 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
Nov-11
t
Dec-5
Oct-11sell forward
2) Dec FuturesJu
ne
-5
No
v-11
Oct
-11 time
De
c-15
No
v-6
buy Dec future
sell 39 day future
Dec FuturesLong Dec futures at Ft=June 5,,Dec =0.008679 USD/JPY,
On Nov 6, Dec futures Ft=Nov 6,,Dec = 0.009162 USD/JPYSNov 6 = .00907
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 Contracts USD
Long on June 5 (Ft, Jun) 0.008679 (16) (1,735,800)
Sold on Nov 6 (Ft, Nov) 0.009162 16 1,832,400
=> Gain/Loss on Futures (0.000483) 96,600
Gain Discounted Back 30 Days: 96,600/(1 + .0409 * 39/360) 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 JPY 200,000,000
Spot rate at Nov. 6 (St=Nov 6) 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)Ju
ne
-5
No
v-11
Oct
-11 t
No
v-17
No
v-6
Exe
rcis
e
Call option A: X=0.0088,
premium = 0.000345B: X=0.0090,
premium = 0.000272
SNov 6 = .00907
4) OTC options (Situation St < X)Ju
ne
-5
No
v-11
Oct
-11 t
No
v-17
No
v-6
don’t exercise option buy
on
sp
ot m
arke
t Call option A: X=0.0088,
premium = 0.000345B: X=0.0090,
premium = 0.000272
SNov 6 = .0084
4) OTC JPY Option
DW would have bought a call option to cover payables
Variables
Amount (JPY) 200,000,000
Strike Price X 0.0088
Premium Premium 0.000345
Interest Rate (US) i 4.085-4.090
X St=Nov 6
(USD/JPY
Premium Exercise? Total USD Cost
USD Paid JPY 200M
88 0.00907 0.000345 Yes 0.009145 1,829,971
90 0.00907 0.00272 Yes 0.009276 1,855,165
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 1,829,971Cost of loan = USD 1,829,971 x (1+.0409*5/360)= USD 1,831,010
For X=.0090 => Borrow to buy JPY = USD 1,855,165Cost of loan = USD 1,855,165 x (1+.0409*5/360)= USD 1,856,219
5) PHLX Options
Call option A: X=0.0086,
premium = 0.000481B: X=0.0090,
premium = 0.000313
SNov 6 = .00907
exercise since in-the-money
Jun
e-5
No
v-11
Oct
-11 t
De
c-15
No
v-6
exe
rcis
e o
ptio
n
5) JPY Dec. Options (PHLX)
DW would have bought a call option to cover payables Same procedure as the OTC Options
Variables
Amount (JPY) 200,000,000
Strike Price X 0.0086
Premium Premium 0.000481
Interest Rate (US) iUSD,bid-ask 4.0850-4.090
X St=Nov 6
(USD/JPYPremium Exercise? Total USD
CostUSD Paid for 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 1,817,554Cost of loan = USD 1,817,554 x (1+.0409*5/360)= USD 1,818,859
For X=.0090 => Borrow to buy JPY = USD 1,863,481Cost of loan = USD 1,863,481 x (1+.0409*5/360)= USD 1,864,539
PHLX Options (Alternative Scenario: option out-of-the-money)
Call option A: X=0.0086,
premium = 0.000481B: X=0.0090,
premium = 0.000313
SNov 6 = .0084
do not exercise since out-of-the-money
try to sell option
Jun
e-5
No
v-11
Oct
-11 time
De
c-15
No
v-6
buy
on
sp
ot m
arke
t Premium Call optionSNov 6 = .0084X = .0086σ = .20 (annualized)T = 39/365rf-USA = .0409; rf-JPY = .0028premium = USD .00014831Total received = USD 29,662
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 1,818,859X=90 => USD 1,863,481