1: Example Financing in the
Sumitomo Copper Scandal
Background
+ Sumitomo rogue copper trader Hamanaka
purchased much of the physical supply of
copper in LME warehouses from 1993-1996
+ Copper prices in 1993 (time of first trades)
- Spot price $1620
- One year futures price $1680
+ Hamanaka sold deep in-the-money put options
and forwards on copper to large US banks
In what way is this transaction like a loan?
!
Copyright Bruce
+ i.e., what are the cash flows on expiration? N. Lehmann 2000-2011!
The Actual Transaction
Sumitomo sells two derivatives to bank
+ Put for 700K metric tons of copper struck at
$2150 expiring in 11/94 for $289.1 million
+ Forward contract for 650,000 metric tons of
copper at a price of $1680 expiring in 11/94
- Actual forward at strikes that made them have
positive value and at different expiration dates
Alleged motive for trade
!
+ Sumitomo had a long position to hedge
+ Bank wanted forward to hedge option position
Copyright Bruce N. Lehmann 2000-2011
!
Cash Flows from Put/Forward
Transaction
Cash Flow on Expiration if:
Position
Initial
Cash Flow
PC 2150
PC > 2150
Short 700,000
puts @ 2150
$289.1
MM
[2150 PC]
x 700,000
0
Short 650,000
forwards @ 1680
0
[PC 1680]
x 650,000
[PC 1680]
x 650,000
Total
$289.1
MM
!
470 x 650K [PC 1680]
[2150PC] x 50K x 650,000
Copyright Bruce N. Lehmann 2000-2011
!
Look for Equivalent Call OptionLoan-Underlying Asset Portfolio
Sumitomo sold portfolio of forward and put
and underlying asset
+ Actually forward contract replicates underlying
Put/call parity means there is an equivalent
portfolio comprised of call and riskless loan
+ Actual portfolio has small forward position due
to slight mismatch between number of puts and
forward contracts sold by Sumitomo
!
How much did Sumitomo receive from
implicit loans and call option sales?
Copyright Bruce N. Lehmann 2000-2011
!
Cash Flow Manipulations: Find
the Implicit Loan Size
Position
Cash Flow on Expiration if:
PC 2150
PC > 2150
[2150PC]x700K
Starting Position [PC1680]x650K [PC1680] x 650K
Add and subtract
470 x 700K
470 x 700K
$329 MM
+ 470 x 700K
+ 470 x 700K
470 x 700K
470 x 700K
[1680PC]x700K [P 2150] 650K
C
[PC1680]x650K
+ x 470 x 50K
Total
!
Copyright Bruce N. Lehmann 2000-2011
!
Cash Flow Manipulations: Adjust
Forward Position Size
Cash Flow on Expiration if:
Position
PC 2150
PC > 2150
470 x 700K
470 x 700K
[1680PC]x700K [PC 2150] x 650K
+ 470 x 50K
Starting Position [PC1680]x650K
Add and subtract
[1680PC]x50K
[1710PC]x50K
+ [1680PC]x50K
0
[PC 2150] x 700K
470 x 700K
470 x 700K
[1680PC]x50K
[1680PC]x50K
Total
!
Copyright Bruce N. Lehmann 2000-2011
!
Equivalent Call/Loan/Forward
Transaction
Cash Flow on Expiration if:
PC 2150
PC > 2150
Position
Initial CF
Sell 700K
calls @ 2150
$???
0
[PC2150]x700K
Buy 50K
fwds @1680
0
[1680PC]x50K
[1680PC]x50K
Borrow
$329 MM
$???
470 x 700K
470 x 700K
Total
$289.1
MM
470 x 650K
[2150PC] x 50K
[PC 1680]
x 650,000
!
Copyright Bruce N. Lehmann 2000-2011
!
Summary of Equivalent Call/
Loan/Forward Transaction
Actual transaction
+ Put for 700K metric tons of copper struck at
$2150 expiring in 11/94 for $289.1 million
+ Forward contract for 650,000 metric tons of
copper at a price of $1680 expiring in 11/94
Equivalent call/loan/forward transaction
+ Sell 700K deep out-of-the-money calls @ 2150
+ Buy 50K forward contracts @1680
+ Borrow $329 MM
!
What is the implicit interest rate?
Copyright Bruce N. Lehmann 2000-2011
!
Why the Banks Funded
Sumitomo with Derivatives
A upper bound on the implicit interest rate
+ The call price is at least zero which implies that
Simple interest rate = 329 MM/289.1 MM 1
= 13.80%
Implied break-even call option value
+ Sumitomo could borrow at LIBOR 0.15% =
3.375% 0.15% = 3.225%
+ ! Implied call value = 329 1.03225 x 289.1
= 30.576525
+ ! Implied call price=30.576525/0.7=43.68075
!
Copyright Bruce N. Lehmann 2000-2011
!
Why the Banks Funded
Sumitomo, Continued
Black-Scholes put and call prices
+ Call = $2.44163!
+ Put = $464.21027!
Implied Black-Scholes values of put and
call positions @ volatility of 13% per year
+ Call value = 2.44163 x 700,000 = 1,709,141
+ Put value = 464.21027 x 700,000 = 324,947,189
At these option values, Hamanaka either:
+ Borrowed at inflated interest rate of 13.21%
!
Copyright Bruce N. Lehmann 2000-2011
!