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