MFIN6003 Derivative Securities
Lecture Note Two
Faculty of Business and Economics
University of Hong Kong
Dr. Huiyan Qiu
2-1
Outline
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
2-2
Forward Contracts
Forward contract: a binding agreement
(obligation) to buy/sell an underlying asset in
the future, at a price set today
Today
Expiration
date
2-3
Forward Contracts
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
2-4
Payoff and Profit
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
ST) at expiration
For forward contract, payoff = profit
2-5
Payoff on a Forward Contract
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
2-6
Payoff Diagram for Forwards
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
2-7
Futures Contracts
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.
2-8
Low of the day
High of the day
The open price
Reading Price Quotes
Index Futures
Settlement price
Daily change
Open interest
Expiration month
2-9
Hang Seng Index Futures
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 SettleMonth
Price
High
Low
ment
Price
AUG-12
SEP-12
DEC-12
MAR-13
20,000
19,918
19,875
19,830
20,015
19,934
19,875
19,830
19,839
19,760
19,740
19,690
19,858
19,777
19,748
19,699
Chg in *Contract *Contract
Setl
High
Low
Price
-277
-275
-278
-277
20,311
21,238
20,915
20,124
18,600
17,750
17,725
19,248
All Contracts Total
Volume
59,973
3,359
195
73
Open Change in
Interest
OI
93,147
12,135
5,842
120
+1,900
+1,271
+61
+28
63,600 111,244
+3,260
2-10
Forward vs. Outright Purchase
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?
2-11
Forward vs. Outright Purchase
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”.
2-12
Additional Considerations
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
2-13
Call Option and Put Option
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
2-14
Terminology
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
2-15
Exercise Style
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.
2-16
Reading Price Quotes
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
2-17
Call Option on S&R Index
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
2-18
Payoff for the Buyer
Six months later at contract expiration:
• If the spot price ST is higher than $1,000, the call
buyer will exercise the option: pay $1,000, get ST.
Payoff = spot price – 1,000
• If the spot price ST is lower than $1,000, the option
buyer will walk away and do nothing. Payoff = 0.
Payoff = Max [0, spot price – strike price]
2-19
Call Option on S&R Index
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)
2-20
Payoff and Profit for the Buyer
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
2-21
Diagrams for Purchased Call
Payoff at expiration
Profit at expiration
y = max [0, x – 1,000]
– (93.81 x 1.02)
2-22
Payoff/Profit of a Written Call
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
2-23
Profit Diagram for a Written Call
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]
2-24
Put Options
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
2-25
Put Option Examples
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
2-26
Profit Diagram for a Long Put Position
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)
2-27
A Few Items to Note
A call option becomes more profitable when the
underlying asset appreciates in value
A put option becomes more profitable when the
underlying asset depreciates in value
Moneyness of option:
• 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
2-28
Summary on Forward & Option
Table Maximum possible profit and loss at maturity
for long and short forwards and purchased and
written calls and puts.
2-29
Summary on Forward & Option
Figure
Profit diagrams
for the three basic
long positions:
long forward,
purchased call,
and written put.
(Long w.r.t. the
underlying asset.)
2-30
Summary on Forward & Option
Figure
Profit diagrams
for the three
basic short
positions: short
forward, written
call, and
purchased put.
(Short w.r.t. the
underlying
asset.)
2-31
Summary on Forward & Option
Table Forwards, calls, and puts at a glance: a
summary of forward and option positions.
2-32
Basic Risk Management
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
2-33
Basic Risk Management
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
2-34
Empirical Evidence on Hedging
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
2-35
The Producer and the Buyer
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)
2-36
Producer: Hedging With Forwards
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.
2-37
Producer: Hedging With a Put Option
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
2-38
Producer: Insuring by Selling a Call
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
2-39
Adjusting the Amount of Insurance
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
2-40
Gold Options
Call and put premiums for gold options with one
year until expiration.
2-41
Figure Comparison of profit for
Golddiggers using three different put strikes.
2-42
Figure Comparison of Golddiggers hedged with 420strike put versus hedged with 420-strike put and
written 440-strike call (420–440 collar).
2-43
Buyer: Hedging With Forwards
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)
2-44
Buyer: Hedging With a Call Option
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
2-45
Why Do Firms Manage Risk?
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.
2-46
An Example
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__________
2-47
An Example (cont’d)
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
After-tax profit
Slope = 1-tax rate
$0.06 C
Slope = 1
D
-$0.14
Selling price
A
2-48
Why Do Firms Manage Risk?
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
2-49
Reasons Not to Hedge
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
2-50
What can Go Wrong?
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
2-51
End of the Notes!
2-52
Appendix:
Barings Bank Case
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
2-53
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.
2-54
Barings Bank Case
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.
2-55
Barings Bank Case
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.
2-56
Leeson Afterwards
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”.
2-57