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Basic derivatives contracts
• Forward contracts; Call options; Put options
Types of positions and payoff / profit diagrams
• Long / Short position
Risk management
• From producer’s and buyer’s perspective
Empirical evidence on hedging
Reasons to hedge or not to hedge
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Today
Expiration date
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A forward contract specifies
• The features and quantity of the asset to be delivered
• The delivery logistics , such as time, date, and place
• The price (forward price) the buyer will pay at the time of delivery
Two parties sign the contract
• Long forward: agree to pay THE price to buy
• Short forward: agree to sell for THE price
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Payoff for a contract is its value at expiration .
Profit for a position in a contract is net value at expiration of all relevant cash flows .
We can use diagrams to show the value of a position at expiration.
Forward: (1) zero cash flow at initiation, (2) pay forward price at expiration, (3) get asset (value
S
T
) at expiration
For forward contract, payoff = profit
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Example: S&R (special and rich) index
Today: Spot price = $1,000
6-month forward price = $1,020
In six months at contract expiration:
Case 1: Spot price = $1,050
• Long position payoff = $1,050 – $1,020 = $30
• Short position payoff = $1,020 – $1,050 = – $30
Case 2: Spot price = $1,000
• Long position payoff = $1,000 – $1,020 = – $20
• Short position payoff = $1,020 – $1,000 = $20
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X-axis: S&R index level 6-month later.
Y-axis: payoff for 6month forward
6-month forward price = $1,020
Long: y = x – 1,020
Short: y = 1,020 – x
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Futures contracts are the same as forwards in principle except for some institutional and pricing differences.
Forward contracts are OTC products.
Futures contracts exist in exchange market.
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Low of the day
High of the day
The open price
Expiration month
Index Futures Settlement price
Daily change
Open interest
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Hang Seng Index Futures Daily market report on
August 22, 2012. Source: www.hkex.com.hk
HSI - Hang Seng Index Futures HK$50 per index point
Contract *Open *Daily *Daily Settle- Chg in *Contract *Contract Volume Open Change in
Month Price High Low ment Setl High Low Interest OI
Price Price
AUG-12 20,000 20,015 19,839 19,858 -277 20,311 18,600 59,973 93,147 +1,900
SEP-12 19,918 19,934 19,760 19,777 -275 21,238 17,750 3,359 12,135 +1,271
DEC-12 19,875 19,875 19,740 19,748 -278 20,915 17,725 195 5,842 +61
MAR-13 19,830 19,830 19,690 19,699 -277 20,124 19,248 73 120 +28
All Contracts Total 63,600 111,244 +3,260
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Outright purchase:
• Invest $1,000 in index and own the index.
Forward:
• Invest zero, sign the contract
• Invest $1,020 at expiration and own the index.
Same outcome: own the index at expiration.
Why investing $1,000 now results in the same outcome as investing $1,020 later? Price indication?
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Forward payoff Bond payoff
Forward + bond = Spot price at expiration – $1,020 + $1,020
= Spot price at expiration
Figure
Summing the value of the long forward plus the bond at each S&R
Index price gives the line labeled
“ Forward + Bond ” .
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Type of settlement
• Cash settlement: less costly and more practical
• Physical delivery: often avoided due to significant costs
Credit risk of the counter party
• Major issue for over-the-counter contracts
• Credit check, collateral, bank letter of credit
• Less severe for exchange-traded contracts
• Exchange guarantees transactions, requires collateral
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A call option ( put option ) gives the owner the right but not the obligation to buy ( to sell ) the underlying asset at a predetermined price during a predetermined time period
The seller of a call option is obligated to sell if asked
The seller of a put option is obligated to buy if asked
Today Expiration date or at buyer’s choosing
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Strike (or exercise) price: predetermined price
• Call: the amount paid by the option buyer for the asset if he/she decides to exercise
• Put: the amount the option buyer receives for selling the asset if he/she decides to exercise
Exercise: the act of paying the strike price to buy
(for call) or selling the asset for the strike price
(for put)
Expiration: the date by which the option must be exercised or become worthless
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Exercise style: specifies when the option can be exercised
• European-style: can be exercised only at expiration date
• American-style: can be exercised at any time before expiration
• Bermudan-style: Can be exercised during specified periods
Focus: European-style options.
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Hang Seng Index options
Hang Seng Index Options Daily market report on top-10 traded options on August 22, 2012.
Source: www.hkex.com.hk
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A 1000-strike call on S&R Index
• Underlying asset: S&R Index with current (spot) price of $1,000
• Strike price: $1,000
• Expiration date: 6 months later
Today:
• call buyer acquires the right to pay $1,000 in six months for the index, but is not obligated to do so
• call seller is obligated to sell the index for $1,000 in six months, if asked to do so
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Six months later at contract expiration:
• If the spot price S
T is higher
Payoff = spot price – 1,000 than $1,000, the call buyer will exercise the option: pay $1,000, get S
T
.
• If the spot price S
T is lower than $1,000, the option buyer will walk away and do nothing. Payoff = 0.
Payoff = Max [0, spot price – strike price]
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Call option preserves the upside potential ( ), while at the same time eliminating the unpleasant
( ) downside (for the buyer)
Why would anyone agree to be on the seller side?
• The option buyer must pay the seller an initial premium of $93.81 (option pricing)
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Payoff = Max [0, spot price at expiration – strike price]
Profit = Payoff – future value of option premium
Suppose effective 6-month risk-free rate is 2%
• If index value in six months = $1,100
• Payoff = max [0, $1,100 – $1,000] = $100
• Profit = $100 – ($93.81 x 1.02) = $4.32
• If index value in six months = $900
• Payoff = max [0, $900 – $1,000] = $0
• Profit = $0 – ($93.81 x 1.02) = – $95.68
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Payoff at expiration Profit at expiration y = max [0, x – 1,000]
– (93.81 x 1.02)
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Call writer: the option seller
• To receive the premium for option sold
• To have the obligation to sell if requested
Seller ’ s payoff and profit is opposite to the buyer
• Payoff = - max [0, spot price at expiration – strike price]
• Profit = Payoff + future value of option premium
The payoff and profit diagram of a written call is the mirror image of a purchased call, symmetric with regard to the X-axis
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Figure
Profit for writer of 6-month
S&R call with strike of $1000 versus profit for short S&R forward.
y = (93.81 x 1.02)
– max [0, x – 1,000]
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Payoff/profit of a purchased (i.e., long) put
• Payoff = max [0, strike price – spot price at expiration]
• Profit = Payoff – future value of option premium
Payoff/profit of a written (i.e., short) put
• Payoff = – max [0, strike price – spot price at expiration]
• Profit = Payoff + future value of option premium
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S&R Index 6-month Put Option
• Strike price = $1,000, Premium = $74.20
, effective
6-month risk-free rate = 2%
If index value in six months = $1,100
• Payoff = max [0, $1,000 – $1,100] = $0
• Profit = $0 – ($74.20 x 1.02) = – $75.68
If index value in six months = $900
• Payoff = max [0, $1,000 – $900] = $100
• Profit = $100 – ($74.20 x 1.02) = $24.32
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Figure
Profit on a purchased S&R index put with strike price of
$1000 versus a short S&R index forward.
y = max [0, 1,000 – x]
– (74.20 x 1.02)
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A call option becomes more profitable when the underlying asset appreciate s in value
A put option becomes more profitable when the underlying asset depreciate s in value
Moneyness
• In-the-money: positive payoff if exercised immediately
• At-the-money: zero payoff if exercised immediately
• Out-of-the money: negative payoff if exercised immediately
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Table Maximum possible profit and loss at maturity for long and short forwards and purchased and written calls and puts.
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Figure
Profit diagrams for the three basic long positions: long forward, purchased call, and written put.
(Long w.r.t. the underlying asset.)
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Figure
Profit diagrams for the three basic short positions: short forward, written call, and purchased put.
(Short w.r.t. the underlying asset.)
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Table Forwards, calls, and puts at a glance: a summary of forward and option positions.
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In general, to hedge against price increase in the future:
• Take derivatives positions with positive payoff when price is high
• Long forward, long call, short put
To hedge against price decrease in the future:
• Take derivatives positions with positive payoff when price is low
• Short forward, short call, long put
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Firms convert inputs into goods and services output input commodity producer buyer
A firm is profitable if the cost of what it produces exceeds the cost of its inputs
A firm that actively uses derivatives and other techniques to alter its risk and protect its profitability is engaging in risk management
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Half of nonfinancial firms report using derivatives
Among firms that do use derivatives, less than
25% of perceived risk is hedged, with firms more likely to hedge short-term risk
Firms with more investment opportunities are more likely to hedge
Firms that use derivatives have a higher market value and more leverage
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A producer selling a risky commodity has an inherent long position in this commodity
When the price of the commodity  , the firm’s profit  (assuming other costs are fixed)
A buyer that faces price risk on an input has an inherent short position in this commodity
When the price of the input  , the firm’s profit 
(assuming other costs are fixed)
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A short forward contract allows a producer to lock in a price for his output
Example: the firm enters into a short forward contract, agreeing to sell gold at a price of
$420/oz. in 1 year.
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Buying a put option allows a producer to have higher profits at high output prices, while providing a floor on the price
Example: the mining firm purchases a 420strike put at the premium of $8.77/oz
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A written call reduces losses through a premium, but limits possible profits by providing a cap on the price
Example: the mining firm sells a 420-strike call and receives an
$8.77 premium
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Insurance is not free !…in fact, it is expensive
How to reduce the cost of insurance (at the same time, reducing the benefit of insurance)?
In the case of hedging against a price decline by purchasing a put option , one can
• using a put with a lower strike price instead  lower the price
• in addition, sell a call  reduce the total price
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Call and put premiums for gold options with one year until expiration.
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Figure Comparison of profit for
Golddiggers using three different put strikes.
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Figure Comparison of Golddiggers hedged with 420strike put versus hedged with 420-strike put and written 440-strike call (420–440 collar).
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A long forward contract allows a buyer to lock in a price for his input
Example: a firm, which uses gold as an input, purchases a forward contract, agreeing to buy gold at a price of $420/oz.
in 1 year
(revenue after other cost adjusted: $460/oz)
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Buying a call option allows a buyer to have higher profits at low input prices, while being protected against high prices
Example: a firm, which uses gold as an input, purchases a 420-strike call at the premium of
$8.77/oz
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Hedging changes the distribution, not the value, of cash flows.
Golddiggers’ example: the hedging strategies shift dollars from more profitable states (when gold prices are high) to less profitable states
(when gold prices are low).
Hedging can be optimal for a firm when an extra dollar of income received in times of high profits is worth less than an extra dollar of income received in times of low profits.
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How hedge adds value
• Consider a firm with cost per unit of $10
• The selling price is either $11.20 or $9, with 50% probability
• Thus, the firm has either a $1.20 profit or $1 loss
• The expected profit per unit = ____ $0.10
__________
• If the tax rate on profit is 40%, after-tax profit is either $0.72 or – $1
• After-tax expected profit = ______ -$0.14
__________
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If the firm sells forward at strike $10.10
• The profit is fixed at $0.10 with certainty
• After-tax profit per unit is $0.06
B
Slope = 1-tax rate
After-tax profit
Slope = 1
$0.06
C
D
-$0.14
Selling price
A
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Concave profits can arise from
Taxes: differential taxation treatment on gains or losses, capital or ordinary incomes, across countries
Bankruptcy and distress costs: avoid huge loss
Costly external financing: smooth cash reserves in the firm
Preservation of debt capacity: reduce riskiness of cash flows
Managerial risk aversion: reduce firm risk
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Reasons why firms may elect not to hedge
• Transaction costs of dealing in derivatives (such as, commissions and the bid-ask spread)
• The requirement for costly expertise
• The need to monitor and control the hedging process
• Complications from tax and accounting considerations
• Potential collateral requirements
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One of the risks faced by a company that trades derivatives: an employee who has a mandate to hedge or to look for arbitrage opportunities may become a speculator.
Barings Bank Case (more detail in Appendix):
• One of the most infamous tales of financial demise
• The 200-year-old British bank was wiped out in
1995 by the activities of one trader, Nick Leeson , in Singapore
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One of the most infamous tales of financial demise
The 200-year-old British bank was wiped out in
1995 by the activities of one trader, Nick Leeson , in Singapore
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In 1993, Nick Leeson was appointed general manager of the bank's Barings Futures subsidiary in
Singapore.
The mandate is to look for arbitrage opportunities between the Nikkei 225 futures price on the
Singapore exchange and the Osaka exchange.
Over time, Leeson moved from being an arbitrageur to being a speculator : bets on the future direction of the Nikkei 225 using futures and options.
When incurring losses, he began to take bigger speculative positions.
By the time Leeson’s activities were uncovered, the total loss was close to one billion dollars.
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One trading strategy Leeson used: written straddle – selling put and call options on the
Nikkei 225 Index.
A written straddle is a bet on the volatility being low. Hence it will produce positive earnings when markets are stable but can result in large losses if markets are volatile .
When an earthquake in Japan caused a steep drop in the Nikkei 225 equity index, Leeson's unauthorized trading positions suffered huge losses and his operation unraveled.
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Leeson managed both the trading and back office function as the general manager. Thus he was able to conceal his unauthorized trading activities for over a year.
The senior managers at Barings came primarily from a merchant banking background and knew very little about trading .
In March 1995, Dutch banking group ING bought Barings for one British pound , assumed its debts, took over operations and renamed it ING Barings.
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Leeson pleaded guilty to fraud and was sentenced to six and a half years in prison. (He was released from prison in July 1999 for good behavior.)
During his detention, he was diagnosed as suffering from colon cancer which he survived.
When in prison, Leeson wrote a book “Rogue Trader”, which was made into a movie.
Nick Leeson now is CEO of Galway United Football
Club (Ireland)
In June of 2005, Leeson released a new book “Back
from the Brink: Coping with Stress”.
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