27/08/2023
FIN 413
Risk Management
Keith Godfrey
2023
Week 1
FIN 413 Risk Management
This course studies the characteristics of derivative
contracts including:
• Forwards
• Futures
• Options
• Swaps
• Credit derivatives.
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The aims are:
• To know the characteristics of derivatives and their
markets;
• To understand the theoretical approaches for
determine their values;
• To be able to design and evaluate strategies for
using derivatives to reduce financial risks.
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Risk Management - Week 1
Recap (e.g. from FIN 301):
• What is a derivative? Forwards. Futures. Options.
• Hedgers, Speculators, Arbitrage.
Futures:
• Markets. Underlying assets.
• Trading: Opening and Closing. Quotes. Order Types.
• Contract Specifications: Delivery. Cash Settlement.
• Margin Accounts and Marking to Market.
• Price Convergence to Spot.
• Energy futures markets.
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What is a derivative?
• A financial instrument whose value is derived from
(related to) the value of some other underlying
asset (or possibly more than one)
• Examples:
• A contract to supply a tonne of coffee in three months
• A futures position in gold for delivery in June
• An option to buy 1000 barrels of oil at $40 by September
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“Derivatives are
financial weapons
of mass destruction”
“Blaming derivatives for
financial losses is akin
to blaming cars for
drunk driving fatalities”
- Warren Buffett
- Christopher Culp
Investor, Omaha
Adjunct Professor, Chicago
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Common derivative types
Forwards/futures: Commitment to buy or sell an
asset in the future or to settle the
cash value.
Options:
Holder has the right (but not
obligation) to buy or sell an asset
in the future.
Swap:
Commitment to swap asset cash
flows or pay the net differences at
a series of future dates.
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What is a forward contract?
A forward contract is a contract between two parties
to trade (buy and sell) something at a later date at a
price agreed upon today.
Buyer : Long position
Seller : Short position
A forward contract is made over-the-counter (OTC)
or nowadays over the phone or internet.
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What is a futures contract?
A futures contract is a similar to a forward but
conducted through a futures exchange.
Differences from forwards:
• The trading is anonymous.
• The exchange specifies the contract terms.
• Traders decide price competitively.
• Daily marking to market reduces risk of default.
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Forwards versus Futures
Forwards (OTC)
Over the counter (OTC)
private contract
Futures (Exchange Traded)
Contract specification:
- what to trade,
- where to trade,
- when to trade
Customized / Negotiated
(can define anything you want
because it is over the counter)
Standardized
(but may have range of quality,
delivery locations, and dates)
Price
Settled at termination
Settled daily
(marked to market)
Security
None, or collateral agreed
Margin account required
Counterparty risk
Borne by counterparties
Borne by clearing house
Liquidity risk
No easy exit. Make a new
contract to offset the old one.
Easy to offset the position to
close out the obligation.
Most typical closure
Delivery
(i.e. genuine participants)
Offset (closed out) prior to
delivery (i.e. speculators)
Method of trading
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Traded via an exchange
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What is an option?
Call Option: The right (but not obligation) to buy a preagreed quantity of the underlying asset for
a pre-agreed price (exercise or strike price)
by a pre-agreed date (expiration date).
Put Option: The right (but not obligation) to sell a preagreed quantity of the underlying asset for
a pre-agreed price (exercise or strike price)
by a pre-agreed date (expiration date).
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Options vs Futures/Forwards
Options
Futures/Forwards
Price for a given maturity
Choice of strike price
Single futures price
Cost of entry
Premium based on strike
Zero
Commitment
Right to choose whether to
exercise (buy/sell) or not
Obligation to deliver/receive
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Risk Management
• We separate business risks from financial risks.
Consider a farmer growing wheat.
Business risks: weather, equipment, …
Financial risks: price of wheat, price of fuel, …
• Risk management with derivatives is concerned
with managing the financial risks.
• How do we pay for transferring financial risks?
What are the roles of hedgers and speculators?
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Hedgers
These people or organizations have a real interest in
the underlying asset or commodity.
Examples:
• Farmers growing wheat
• Airlines buying jet fuel
They want to reduce their financial risk.
They are willing to pay for risk reduction.
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Speculators
These people or organizations do not have a real
interest in the underlying asset but they are willing to
take a position that they expect will gain from
anticipated price movements.
They take on risk.
They expect to make money on average from
carrying the risk.
They help markets with “price discovery”.
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Arbitrageurs
These people or organizations aim to buy and sell
two or more related financial instruments or
commodities at the same time to exploit mispricing
and make a risk-free profit.
Their actions cause pressure on the market prices,
moving the prices closer together again, until there is
no longer an arbitrage opportunity.
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Is speculation gambling?
Futures exchanges only set up contracts where there
is a genuine need for hedging.
i.e. there must be some hedgers in the market.
A market only for speculators would be a zero sum
game (or negative sum game with trading costs).
i.e. like pure gambling at a casino.
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Can speculators dominate?
There can be more speculators in the market than
hedgers. It is okay for hedgers to be the minority.
It is also okay for speculators to be betting in both
directions. This helps with price discovery.
The speculators are still taking calculated risks.
This is good for the market (not pure gambling).
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Compensation for transferring risk
with futures and forwards
How does a grain farmer hedge his/her crop and how
does a speculator earn money from this?
When all the farms are having a bumper crop, the
farmer is worried prices will drop due to excess supply.
• Farmer could enter a short futures/forward position
• Speculator agrees on a futures price which is lower
than he/she expects the market will be in the future
• Farmer gets certainty
• Speculator expects profit on average
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Compensation for transferring risk
with options
How does a grain farmer hedge his/her crop and how
does a speculator earn money from this?
When all the farms are having a bumper crop, the
farmer is worried prices will drop due to excess supply.
• Farmer could purchase a put option on grain
• Speculator sells the option for a price that he/she
expects will exceed his/her average losses (from the
years that the farmers exercise their options)
• Farmer gets certainty
• Speculator expects profit on average
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Futures Markets - Underlyings
• Energy products (crude oil, heating oil, natural gas, ...)
• Metals (aluminium, nickel, zinc, copper, gold, ...)
• Agricultural commodities
(wheat, corn, cattle, pork, soy, butter, cocoa, coffee, ...)
• Currencies (euro, pound, yen, Australian dollar...)
• Interest rate derivatives
(short term interest rates, bonds, swaps, ...)
• Stocks (MSFT, GOOG, BHP, ...)
• Indices (S&P 500, DJIA, Nasdaq, ASX 200, ...)
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Futures
Industry Association
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https://fia.org/sites/default/files/uploaded/2017-Volume-Highlights-Infographic_FINAL.jpg
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Futures
Industry Association
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https://fia.org/sites/default/files/uploaded/2017-Volume-Highlights-Infographic_FINAL.jpg
at 4 Jan 2019
Note that the nearest contract is the most actively traded.
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at 4 Jan 2019
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The words “price” and “value”
• The futures “price” of oil might be $50 per barrel.
• The “value” of a futures contract on crude oil might
be $2000 because the oil price has changed by $2
per barrel since the previous settlement and the
contract is for 1000 barrels.
• The “contract price” might be $50,000 if you are
delivering or receiving the 1000 barrels at the $50.
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The forward curve
We can plot the forward/futures prices for a
commodity for successive months into the future.
This is called a forward curve.
Horizontal axis: maturity or delivery date
Vertical axis:
futures price for that date
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CL WTI Crude Oil Futures – Jan 2019
CL Crude Oil Futures at 7 Jan 2019
54.5
53.5
52.5
51.5
50.5
49.5
48.5
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Feb-28
Aug-27
Nov-27
Feb-27
May-27
Aug-26
Nov-26
Feb-26
May-26
Aug-25
Nov-25
Feb-25
May-25
Aug-24
Nov-24
Feb-24
May-24
Aug-23
Nov-23
Feb-23
May-23
Aug-22
Nov-22
Feb-22
May-22
Aug-21
Nov-21
Feb-21
May-21
Aug-20
Nov-20
Feb-20
May-20
Aug-19
Nov-19
Feb-19
May-19
47.5
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CL WTI Crude Oil Futures – Sept 2019
CL Crude Oil Futures at 22 Sept 2019
60
58
56
54
52
50
48
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Aug-27
Nov-27
Feb-27
2023
May-27
Aug-26
Nov-26
Feb-26
May-26
Aug-25
Nov-25
Feb-25
May-25
Aug-24
Nov-24
Feb-24
May-24
Aug-23
Nov-23
Feb-23
May-23
Aug-22
Nov-22
Feb-22
May-22
Aug-21
Nov-21
Feb-21
May-21
Aug-20
Nov-20
Feb-20
May-20
Nov-19
46
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WTI futures curve on 20 April 2020
WTI crude oil for May closed at -$37 per barrel.
• Some futures contracts can achieve negative prices due to
the way their deliveries are structured.
• On the same day, Brent crude oil closed at +$26.
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GC Gold Futures
GC Gold Futures at 7 Jan 2019
1500
1450
1400
1350
1300
1250
1200
Jul-24
Sep-24
Nov-24
May-24
Jan-24
Mar-24
Nov-23
Jul-23
Sep-23
Jan-23
May-23
Nov-22
Mar-23
Jul-22
Sep-22
May-22
Jan-22
Mar-22
Nov-21
Jul-21
Sep-21
May-21
Jan-21
Mar-21
Nov-20
Jul-20
Sep-20
May-20
Jan-20
Mar-20
Jul-19
Sep-19
Nov-19
May-19
Jan-19
Mar-19
1150
Why such a straight line? Gold has holding costs which affect hedging.
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Normal and inverted markets
Futures prices usually increase with maturity.
i.e. the futures price for oil for Dec 2024 is likely to
be higher than for Jan 2023, all else being equal.
This is called a “normal” market.
If the futures price is declining with maturity then it
is an “inverted” market.
Sometimes it can be part normal and part inverted.
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Seasonal effects
Sometimes there are repeated patterns of normal
and inverted futures pricing of an asset due to
seasonal effects.
Examples where this occurs include:
• RBOB gasoline futures (more demand in summer)
• Heating oil futures (more demand in winter)
• Electricity futures (more base load in summer)
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RBOB Gasoline Futures
RBOB = Reformulated Gasoline Blendstock for Oxygen Blending
Feb-19
1.3478
Feb-20
1.4129
Feb-21
1.4796
Feb-22
1.4736
Mar-19
1.3618
Mar-20
1.4318
Mar-21
1.5065
Mar-22
1.4961
Apr-19
1.5529
Apr-20
1.6261
Apr-21
1.7032
Apr-22
1.693
May-19
1.5682
May-20
1.641
May-21
1.7231
May-22
1.7117
Jun-19
1.5763
Jun-20
1.6428
Jun-21
1.7266
Jun-22
1.7047
Jul-19
1.5742
Jul-20
1.6428
Jul-21
1.7059
Jul-22
1.6963
Aug-19
1.5637
Aug-20
1.6316
Aug-21
1.6783
Aug-22
1.6776
Sep-19
1.5455
Sep-20
1.6203
Sep-21
1.6498
Sep-22
1.6396
Oct-19
1.4336
Oct-20
1.4972
Oct-21
1.5199
Oct-22
1.5097
Nov-19
1.4155
Nov-20
1.473
Nov-21
1.4869
Nov-22
1.4767
Dec-19
1.4058
Dec-20
1.4527
Dec-21
1.4635
Dec-22
1.4533
Jan-20
1.405
Jan-21
1.4587
Jan-22
1.4617
Jan-23
1.4515
Futures prices at 7 Jan 2019
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RBOB Gasoline Futures
1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1
Oct-22
Dec-22
Jun-22
Aug-22
Apr-22
Feb-22
Oct-21
Dec-21
Jun-21
Aug-21
Apr-21
Feb-21
Oct-20
Dec-20
Jun-20
Aug-20
Apr-20
Feb-20
Oct-19
Dec-19
Jun-19
Aug-19
Apr-19
Feb-19
1
Futures prices at 7 Jan 2019
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Trading Terminology
• Opening a position (entry)
• Limit orders
• Market orders
• Open interest.
• Trading volume.
• Closing a position (exit)
• Physical delivery
• Cash settlement
• Offset (close out by the opposite trade to the original)
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Opening a position
Suppose at some
time you see for
Feb 2019 CL futures:
What is the bid-ask
spread?
What happens if you
enter long?
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Bid-Ask Spread
At that instant, the crude oil futures for Feb 2019 are
trading at
$49.01 - $49.02
This means the highest bid is $49.01 per barrel and
the lowest ask is $49.02.
If you want to go long right now you can enter at
$49.02, or you can enter short at $49.01.
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What do you pay?
Suppose you enter long now at $49.02.
How much do you pay?
Nothing! Why? Because both sides think the $49.02
is a fair price and neither expects to win or lose.
You are not actually buying the oil yet. You will do
that in Feb 2019 (unless you close out before).
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Limit Orders and Market Orders
Limit orders specify the price limit beyond which you
are not willing to transact. These orders do not
execute immediately (unless your limit is already
beyond the best bid or ask).
Limit orders become the bids and asks that are
observable in the market depth.
Market orders execute immediately at the best bids
and asks in the order book.
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Examples
Suppose crude oil futures for February are trading at
$49.01 - $49.02
If you submit a limit order to “buy 2 contracts at $48.50”
(i.e. a limit buy order below best bid) then your order will
sit in the order book depth until the market moves lower
enough to execute (if at all).
If you submit a market order to “buy 2 contracts” then
you will get 2 contracts at $49.02 assuming there are
sellers for at least 2 contracts at $49.02.
(In the screenshot there were 19 contracts available.)
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Trading Volume and Open Interest
Trading Volume = number of contracts traded today
Open Interest
Risk Management – Keith Godfrey
= number of contracts outstanding
(i.e. the number of long positions,
or equivalently the number of short
positions – remember that each
contract has two parties)
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How Open Interest Changes
Suppose nobody has traded the GCH9 (gold futures on CME for
March 20x9 e.g. 2019). The open interest is zero.
If you enter long one GCH9 contract (and someone enters short
as your counterparty) the open interest of GCH9 becomes 1.
If you exit your position by offsetting (you short one GCH9) and
someone else enters long (effectively takes over your position)
then the open interest would remain 1.
If those two parties then each offset their positions (so the
short party buys one GCH9 and the long party sells one GCH9),
then the open interest would decrease by one (back to zero).
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Closing a position
• Most futures positions are closed out by offset
(entering the opposite position to the original)
instead of being held through until delivery.
• To offset you must enter in the opposite direction
and the same contract (the same underlying and
delivery month etc. otherwise it opens a separate
position in a different contract.)
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Delivery
If you hold a position through to delivery, then you
have to be able to receive (and pay for) the asset or
to supply (and receive payment for) the asset.
The short party (the one that is selling the asset)
decides when to deliver within the delivery period.
The short party gives notice of intention to deliver.
The exchange will then choose a long party to accept
delivery on the same date.
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Critical dates
First notice day
The first date that the short party
can give notice of intention to
deliver.
Last notice day
The last such permitted date.
Last trading day
The last date that the contract can
be traded, usually a few days before
the last notice day.
A long position might not receive notice in the first few
days and might still be able to close out (offset) before
receiving notice – but if speculating the only safe time to
close out is before the first notice day.
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Cash Settlement
Some futures are settled only in cash.
Example: the ES (E-mini S&P 500 futures)
Why? Otherwise you would have to deliver a basket
of shares in the S&P 500 companies.
Some assets offer futures contracts of both types.
e.g. CME Crude oil CL is physical delivery
CME Crude oil WS is financially settled
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Contract specifications
The Exchange specifies, for any futures contract:
• The underlying asset (including quality spec)
• The quantity of asset (in one contract)
• The settlement method (physical delivery or cash settled)
• The delivery month and arrangements
• Price quotation style, movement limits, position limits, …
The price is determined by market forces
i.e. supply and demand.
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https://www.cmegroup.com/trading/metals/precious/gold_contract_specifications.html
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Contract size
The GC spec says:
• Contract size 100 troy ounces
• Price quotation US dollars and cents per troy ounce
• Minimum price fluctuation $0.10
If the futures price of gold is $1200 per troy ounce then one
contract (which is for 100 ounces) would be for $120,000.
The minimum price move is $0.10 per troy ounce. For one
contract (100 ounces) means a change of $10 in the $120,000.
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Contract price = contract size  futures price
$120,000 = 100 ounces × $1,200 per ounce
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Note the GC contract is physically deliverable.
https://www.cmegroup.com/trading/metals/precious/gold_contract_specifications.html
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Margin
Buying “on margin” is the act of borrowing money to
buy securities.
The margin is like your “equity” – it is the difference
between the value of the securities you hold and the
loan from your broker.
(like your equity in a home mortgage)
With futures, your margin account ensures that you
can meet your commitment at the delivery date.
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Margin example
Suppose you enter long crude oil at $50.
You are committing to buy 1000 barrels in the future.
You are committing to pay $50,000.
If the futures price drops to $45 you will need to come up
with $5000 more than you had anticipated. You must
have this in your margin account otherwise your broker
will close out your position.
Another way to think about it - you committed to spend
$50,000 but the market price is only $45,000 now so you
are losing $5,000 on this contract.
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Marking to market
Futures contracts are “marked to market” every day
(or “settled” daily).
If you entered long crude oil at $50 and the price settles at
$45 at the end of the day, $5000 will be removed from
your margin account (1000 barrels).
You no longer have that equity, but now the price going
forward is $45 not $50, and your commitment is $45,000
instead of $50,000.
If you don’t have enough funds, your broker will send you
a “margin call” to deposit more funds.
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Margin terminology
Initial margin
The amount of money that
must be deposited initially to
be able to open a position.
Maintenance margin The amount of money that
must be maintained at all
times to be able to maintain
an open position.
Margin call The requirement to top up to the initial
margin, typically within 24 hours, if the
maintenance margin is breached.
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The margin requirements are higher for the nearer contracts because of their higher volatility.
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Worked example
For CME CL crude oil:
• The maintenance margin for the nearest contract is $4275,
• The initial margin is 110% of this level, i.e. $4702.50,
• The contract size is 1000 barrels.
Suppose you enter long 2 contracts at $50.00.
• How much margin must you deposit?
• If you deposit the minimum that you have to, what price
would trigger a margin call?
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Transaction Sequence
Suppose you enter long 1 crude oil contract at $50.
This means you expect to pay $50,000 for 1000 barrels.
Suppose by the delivery date the futures price has
increased to $70. This means you will have received
$20,000 into your margin account.
You will pay $70 per barrel, so $70,000 for 1000 barrels.
You will spend $50,000 of your own money (as you had
planned) plus the $20,000 that you received.
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Futures Price Convergence
Futures price = price decided now for delivery at
a date in the future
Spot price
= price for immediate delivery
The spot price is the futures price for no time
remaining until delivery.
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Futures price converges to spot
Spot and forward/futures prices
price
April
futures
price
Entry
Payoff
(here in this example a
loss for long side and
a profit for short side)
Spot
price
0
T
time
February
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March
April
Keith Godfrey 2009
Delivery
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Why do at least some contracts for each asset have
physical delivery?
Physical delivery helps to ensure that there is a
convergence in pricing between the physical market
and the futures market at the futures’ expiry.
Any price difference at the delivery date would be an
opportunity for arbitrage between the futures and
the physical asset.
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Basis
price
Basis
April
futures
price f0(T)
We say the basis is “$5 under April”
Basis
(negative)
Spot
price
S0
fT
ST
0
T
time
February
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Normal and Inverted Markets
If the futures price is above the spot price
(negative basis) then the futures market is normal.
If the futures price is below the spot price
(positive basis) then the futures market is inverted.
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Inverted market
(positive basis)
price
Temporary
supply shortage
Price
convergence
April futures price
Spot price
S0
Normal market
(negative basis)
0
February
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March
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April
time
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Contango and Normal Backwardation
If the futures price is decreasing over time towards
the expected future spot price (i.e. the futures price
was too high) then then the market is in contango.
If the futures price is increasing over time towards
the expected future spot price (i.e. the futures price
was too low) then the market is in backwardation
(also called normal backwardation).
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Inverted market
(positive basis)
price
Temporary
supply shortage
Normal Backwardation
(futures under expected spot)
Expected April price
Speculators
bought low
Price
convergence
April futures price
S0
Spot price
Normal market
(negative basis)
0
February
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March
April
2023
time
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Energy Futures Markets
• Crude Oil
CME/ICE, WTI/Brent
• Natural Gas
Henry Hub
• Refined Products
RBOB gasoline, HO heating oil
• Crack Spread
RBOB versus CL
• Electricity
Base load, peak load
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1-4 CC
Cracking
Thermal cracking
Steam cracking
Catalytic cracking (gasoline)
Hydrocracking (add H2)
5-10 CC
10-16 CC
14-20 CC
20-70 CC
20-50 CC
>70 CC
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Examples on eClass to discuss
1. CME Crude Oil (CME CL)
- Contract Specs
- Quotes
- Margins
2. Henry Hub Natural Gas (CME NG) - Contract Specs
- Quotes
- Margins
3. RBOB Gasoline (CME RB)
- Contract Specs
- Quotes
4. RBOB Crack Spread (CME ARE)
- Contract Specs
- Quotes
5. Dutch Power Peak Load (ICE)
- Contract Specs
- Prices
Risk Management – Keith Godfrey
2023
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35