FNCE4030 Investments and Portfolio Management -...
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
FNCE4030 – Investments and
Portfolio Management
Introduction on Derivatives
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
What is a Derivative?
• A derivative is an instrument whose value
depends on, or is derived from, the value of
another asset.
• Examples:
– Futures
– Forwards
– Swaps
– Options
– Exotics
– …
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Why Derivatives Are Important
• Key role in transferring risks in the economy
• Underlying assets include stocks, currencies,
interest rates, commodities, debt instruments,
electricity, insurance payouts, weather, etc.
• Many financial transactions have embedded
derivatives
• The real options approach to assessing
capital investment decisions has become
widely accepted
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
How Derivatives Are Traded
• On exchanges such as the Chicago Board
Options Exchange
• In the over-the-counter (OTC) market where
traders working for banks, fund managers
and corporate treasurers contact each other
directly
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Size of OTC & Exchange-Traded Markets
Source: Bank for International Settlements. Chart shows total principal amounts for
OTC market and value of underlying assets for exchange market
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Growth of OTC Market by Product
0
100
200
300
400
500
600
700
Jun.98 Jun.99 Jun.00 Jun.01 Jun.02 Jun.03 Jun.04 Jun.05 Jun.06 Jun.07 Jun.08 Jun.09 Jun.10 Jun.11 Jun.12
Commodity
Equity-linked
Credit default swaps
Interest rate
FX
$ trilli
ons
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
How Derivatives are Used
• To hedge risks – e.g. you are a producer of oil or a consumer of
soy beans, or are paid in a different currency
• To speculate (take a view on the future
direction of the market)
• To lock in an arbitrage profit
• To change the nature of a liability
• To change the nature of an investment
without incurring the costs of selling one
portfolio and buying another
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Forwards
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Forward Price
• DEFINITION: the delivery price that
would be applicable to the contract if
negotiated today
(i.e. the delivery price that would make
the contract worth exactly zero today)
• The forward price may (and will likely)
be different for contracts of different
maturities
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Some Terminology (more to come)
• The party that has agreed to buy has a long
position
• The party that has agreed to sell has a short
position
• Selling a derivative is sometimes referred to
writing a derivative (forwards, options, etc.)
• The contract delivery date is sometimes
referred to expiration date, or maturity date
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Forward Example
• On Jan 10, 2013 the treasurer of a
corporation enters into a long forward
contract to buy £1 million in six months at an
exchange rate of 1.6115
• This contract obligates the corporation to pay
$1,611,500 for £1 million on the maturity date
(July 10, 2013)
• What are the possible outcomes?
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Profit from a Long Forward
• K = delivery price = forward price at time
contract is entered into
Profit
Price of Underlying at
Maturity, ST K
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Profit from a Short Forward
• K = delivery price = forward price at time
contract is entered into
Profit
Price of Underlying at
Maturity, ST K
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Futures Contracts
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Futures Contracts
• Agreement to buy or sell an asset for a
certain price at a certain time
• Similar to forward contract, but there are
• Differences:
– A forward contract is traded OTC, a futures
contract is traded on an exchange
– A futures contract requires daily settlement of the
value of the contract, a forward contract has a
cash flow only a maturity
• WARNING– This is what the book says but it is not
strictly true. More on this later.
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Exchanges Trading Futures
• CME Group (formerly Chicago Mercantile
Exchange and Chicago Board of Trade)
• NYSE Euronext
• BM&F (Sao Paulo, Brazil)
• TIFFE (Tokyo)
• and many more (see list at end of Hull book)
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Examples of Futures Contracts
• You think gold will appreciate during the year:
Buy 100 oz. of gold @ 1662 $/oz in Dec.
• You will receive GBP in March but want USD:
Sell £62,500 @ 1.661 US$/£ in March
• You are an oil producer and want to hedge:
Sell 1,000 bbl. of oil @ 92 $/bbl in April
• You are a soybean buyer looking to lock your
input costs:
Buy 1mm bushels of soybean in 6m
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Futures/Forwards vs. Options
• A futures/forward
contract gives the
holder the
obligation to buy
or sell at a certain
price
• An option contract
gives the holder
the right to buy or
sell at a certain
price
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Who Trades Derivatives?
• Hedgers use derivatives to mitigate the risk
they are already exposed to, coming from
their business or assets/liabilities
• Speculators use derivatives to express a
view – often with leverage – on a financial
sector/asset
• Arbitrageurs use derivatives to lock in a
specific payout for a risk-free profit
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Hedging Examples (pages 10-12)
• A US company will pay £10 million for imports
from Britain in 3 months and decides to
hedge using a long position in a forward
contract
• An investor owns 1,000 Microsoft shares
currently worth $26.88 per share. A two-
month put with a strike price of $27.00 costs
$1. The investor decides to hedge by buying
10 contracts
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Speculation Example
• You have $2,000 to invest
• You believe that a stock price will increase
over the next 2 months
• The current stock price is $20
• The price of a 2-month call option with a
strike of 22.50 is $1
• What are the alternative strategies?
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Arbitrage Example
• A stock price is quoted both in London and in
New York. The prices are:
– £100 in London
– $155 in New York
• The current exchange rate is 1.6100
• (ask your self what are the units of that figure)
• Is there an arbitrage opportunity?
• If so what is it?
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Dangers
• Traders can switch from being hedgers to
speculators or from being arbitrageurs to
speculators
• It is important to set up controls to ensure that
trades are using derivatives in for their
intended purpose
• SocGen is an example of what can go wrong (see Hull, Business Snapshot 1.3 on page 17)
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Hedge Funds (see Business Snapshot 1.2, page 11)
• Mutual Funds must
– disclose investment policies,
– makes shares redeemable at any time
– limit use of leverage
– take no short positions.
• Hedge Funds
– Are not subject to the same rules as mutual funds
– Cannot offer their securities publicly
– Use complex trading strategies are big users of
derivatives for hedging, speculation and arbitrage
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Swaps
C le an up s lid e sC le an up s lid e s
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Nature of Swaps
• A swap is an agreement to exchange
cash flows at specified future times
according to certain specified rules – Typically swaps have two legs as there are two
parties…swapping cash flows
Counterparty
A
Counterparty
B
Cash flow
Cash flow
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Vanilla Interest Rate Swap
• An agreement to swap fixed rate cash flows
for floating cash flows over a specified period
of time
– Tenor
• determines how often payments are made
• In the US
– floating payments are generally every 3 months
– Fixed payments are made every 6 months
– Floating cash flows reference a “trusted”
benchmark rate – e.g. LIBOR
• Generally the reference rate is fixed at the beginning of
a period and paid at the end
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
E.g. “Plain Vanilla” Int. Rate Swap
• An agreement by Microsoft to
– receive 6-month LIBOR
– pay a fixed rate of 5% per annum every 6 months
– Start date: 5 March 2012,
– Maturity: 5 March 2015
– Notional: $100m
• Next slide illustrates* cash flows that could
occur
* illustrative trade, day count conventions are not
considered, payment frequency not typical
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
A Possible Outcome for Cash Flows
Date LIBOR Floating Cash
Flow
Fixed Cash
Flow
Net Cash
Flow
Mar 5, 2012 4.20%
Sep 5, 2012 4.80% +2.10 −2.50 −0.40
Mar 5, 2013 5.30% +2.40 −2.50 −0.10
Sep 5, 2013 5.50% +2.65 −2.50 + 0.15
Mar 5, 2014 5.60% +2.75 −2.50 +0.25
Sep 5, 2014 5.90% +2.80 −2.50 +0.30
Mar 5, 2015 +2.95 −2.50 +0.45
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Typical Uses of an Int. Rate Swap
• Converting a liability from
– fixed rate to floating rate
– floating rate to fixed rate
• Converting an investment from
– fixed rate to floating rate
– floating rate to fixed rate
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Swap Fixed for Floating
• You enter an interest rate swap
– Notional: 100m
– Maturity: 5 March 2015
– Semi-annual payments
– Pay Fixed: 5%
– Receive Floating: 6 Month USD LIBOR
5 March
2013
5 Sep
2013
5 March
2014
5 Sep
2014
5 March
2015
2.5% 2.5% 2.5% 2.5% 2.5%
6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR 6M LIBOR
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Other types of swaps
• Credit Default Swaps (CDS)
• Currency Swaps
• Commodity Swaps
• Mortgage Swaps
• Equity Swaps (on price or dividends)
• Variance Swaps
• etc.
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Options
C le an up s lid e sC le an up s lid e s
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Basic Option Terminology
An option gives the holder the
right but not the obligation to
buy(sell) the underlying asset
at some time or times in the
future.
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Underlying Assets
• Stocks
• Currencies
• Stock Indices (not indexes)
• Futures
• Commodities (individual and index)
• Interest Rates (swaptions)
• Credit products (credit default swaptions)
• etc.
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Option Types
• A Call option is
an option to buy
a certain asset by
a certain date for
a certain price
(the strike price)
• A Put option is an
option to sell
a certain asset by
a certain date for
a certain price
(the strike price)
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Options Style
• An American
option can be
exercised at
any time
during its life
• A European
option can be
exercised only
at maturity
A Bermudan option can be
exercised only at fixed times
before maturity (e.g. monthly)
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Option Contracts Specs
• Expiration date
• Strike price (or Exercise price)
• European or American (option style)
• Call or Put (option class or type)
• Delivery details
– Cash or Physical delivery
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Mechanics of Options
Markets
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University of Colorado at Boulder – Leeds School of Business – FNCE4030
Payoff Diagrams
• A common technique for understanding
options is to draw a payoff diagram
• This will usually show the value of the option
at expiry
• Note – you will see payoff diagrams that
deduct the the premium paid from the payoff
– Many diagrams in the Hull book do this
– Generally this is frowned upon in the industry,
because you are adding values at different times
– The following slides will chart just payoffs
![Page 41: FNCE4030 Investments and Portfolio Management - …leeds-courses.colorado.edu/FNCE4030/MISC/slides/FNCE4030...University of Colorado at Boulder – Leeds School of Business – FNCE4030](https://reader034.fdocuments.us/reader034/viewer/2022042411/5f29d8738dd74b0c451ab231/html5/thumbnails/41.jpg)
University of Colorado at Boulder – Leeds School of Business – FNCE4030
Long Call Option
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10
Payo
ff
Terminal Asset Price
Payoff for a European Call option with a strike of $5
𝑃𝑎𝑦𝑜𝑓𝑓 = 𝑀𝑎𝑥[0, 𝑆𝑇 − 𝐾]
![Page 42: FNCE4030 Investments and Portfolio Management - …leeds-courses.colorado.edu/FNCE4030/MISC/slides/FNCE4030...University of Colorado at Boulder – Leeds School of Business – FNCE4030](https://reader034.fdocuments.us/reader034/viewer/2022042411/5f29d8738dd74b0c451ab231/html5/thumbnails/42.jpg)
University of Colorado at Boulder – Leeds School of Business – FNCE4030
Short Call Option
-6
-5
-4
-3
-2
-1
0
0 1 2 3 4 5 6 7 8 9 10
Payo
ff
Terminal Asset Price
Payoff for a European Call option with a strike of $5
𝑃𝑎𝑦𝑜𝑓𝑓 = −𝑀𝑎𝑥[0, 𝑆𝑇 − 𝐾]
![Page 43: FNCE4030 Investments and Portfolio Management - …leeds-courses.colorado.edu/FNCE4030/MISC/slides/FNCE4030...University of Colorado at Boulder – Leeds School of Business – FNCE4030](https://reader034.fdocuments.us/reader034/viewer/2022042411/5f29d8738dd74b0c451ab231/html5/thumbnails/43.jpg)
University of Colorado at Boulder – Leeds School of Business – FNCE4030
Long Put Option
0
1
2
3
4
5
6
0 1 2 3 4 5 6 7 8 9 10
Payo
ff
Terminal Asset Price
Payoff for a European Put option with a strike of $5
𝑃𝑎𝑦𝑜𝑓𝑓 = 𝑀𝑎𝑥[0, 𝐾 − 𝑆𝑇]
![Page 44: FNCE4030 Investments and Portfolio Management - …leeds-courses.colorado.edu/FNCE4030/MISC/slides/FNCE4030...University of Colorado at Boulder – Leeds School of Business – FNCE4030](https://reader034.fdocuments.us/reader034/viewer/2022042411/5f29d8738dd74b0c451ab231/html5/thumbnails/44.jpg)
University of Colorado at Boulder – Leeds School of Business – FNCE4030
Short Put Option
-6
-5
-4
-3
-2
-1
0
0 1 2 3 4 5 6 7 8 9 10
Payo
ff
Terminal Asset Price
Payoff for a European Put option with a strike of $5
𝑃𝑎𝑦𝑜𝑓𝑓 = −𝑀𝑎𝑥[0, 𝐾 − 𝑆𝑇]