ECN107 FOUNDATIONS OF FINANCE
Lecture 5: Derivatives*
Dr Manolis Noikokyris
* The lecture notes use material from the main textbook and other resources listed on the module’s Qmplus page
→ Feedback on your understanding
Question 1
Suppose that a company’s stock is selling for £100 today. It is
expected that at the end of the year it will pay a dividend of £5 per
share and then be sold for £110. Calculate the expected rate of return
for the shareholders.
A. 10%
B. 15%
C. 5%
D. 20%
Answer: B
£5 + £110 − £100
= 15%
£100
Question Go to www.menti.com and use code 2727 1516
1
A reason is: Log returns are additive over time, making
them more suitable for calculations involving multiple
periods. Simple returns, on the other hand, are not
additive.
→ A question
TSLA
Feb 15, 2024
200.45
Feb 16, 2024
199.95
Feb 20, 2024
193.76
Feb 21, 2024
194.77
Feb 22, 2024
197.41
199.95
×100
200.45
193.76
ln
×100
199.95
194.77
ln
×100
193.76
197.41
ln
×100
194.77
ln
-0.250
-3.145
0.520
1.346
Sum -1.528
ln
Tesla Inc Stock price
Source Yahoo finance
Simple
Returns
Log(Returns)
197.41
×100 = −1.528
200.45
(199.95 − 200.45)
×100
200.45
(193.76 − 199.95)
×100
199.95
(194.77 − 193.76)
×100
193.76
(197.41 − 194.77)
×100
194.77
-0.249
-3.096
0.521
1.355
Sum -1.469
(197.41 − 200.45)
×100 = −1.517
200.45
2
→ Feedback on your understanding
Question 3
Wilfred plc has a price-earnings ratio (P/E) of 6 and a stock price of
£30. Calculate the earnings per share (EPS) of the company. Use one
decimal point in your answer; that is, if the answer is 10.8021 the right
answer will be 10.8.
A. £5 per share
B. £0.2 per share
C. £10 per share
D. £6 per share
Answer: A
𝑃
𝑃 30
= 6 ⇒ 𝐸𝑃𝑆 = =
= £5
𝐸𝑃𝑆
6
6
Question Go to www.menti.com and use code 7264 8396
3
In this Lecture…
By the end of this session students will be able to:
• Understand the core principles of risk management
• Understand the use of insurance as a method to reduce risk
• Understand hedging using financial options
• Understand hedging using forward contracts
• Understand the basics of the futures market
4
SECTION A
Understand the core principles of risk management
Any questions?
5
Hedged
On risk management…
Risk Management:
o Financial transactions
undertaken only to reduce
risk and not add value in
perfect and efficient markets.
✎ Hedging reduces the
variability of expected cash
flows around the mean of
the distribution. This
reduction of distribution
variance is a reduction of
risk.
Firm’s cash flows
Unhedged
Expected NPV
6
On risk management…
• Hedging is a risk management strategy to mitigate potential losses arising
from adverse unexpected price movements in financial markets, such as in
currency exchange rates, interest rates, or commodity prices.
The Company has established a variety
of programs including the use of
derivative
instruments
and
other
financial instruments to manage the
exposure to financial market risks as to
minimize volatility of financial results
DuPont de Nemours, Inc. 10-K Form
2023
‘Derivative financial instruments are
used within the Company for hedging
purposes.
The
Company
holds
derivative financial instruments to hedge
its foreign currency and interest rate risk
exposures.’
BMW Annual Report 2022
7
On risk management…
To Hedge or not?
➜Hedging is a zero-sum game:
Hedging does not eliminate risk, but simply passes the risk to another party. In
competitive and efficient markets where all parties have the same information, they
negotiate the terms of the hedging and reach a fair agreement (zero-NPV).
➜Investors’ do-it-yourself alternative:
Corporations do not need to manage financial risks and incur the cost of hedging;
investors can diversify their portfolios on their own.
This holds if individuals and firms have the same investment opportunities, information,
transaction costs and tax rates (i.e., perfect capital markets).
8
On risk management…
• Hedging reduces the variability of expected cash flows around
the mean of the distribution. This reduction of distribution
variance is a reduction of risk.
“Rolls-Royce should absolutely manage risk and should
continue to stick to their hedging policy,” says Mr
Cunningham. “The best thing you can do is smooth out
any sharp fluctuations in the currencies in which you
operate. By smoothing out that risk, even if it costs you
a bit of money, it will help reduce your cost of capital.”
[FT https://on.ft.com/3G8D1uM ]
9
On risk management…
o Lower variability of expected cash flows makes financial planning
simpler, reduces the risk of financial distress, and the risk of missing
out on valuable investment opportunities, and helps keep track of and
motivate managers better.
o Hedging can increase the value of the firm in highly geared firms (as it
eliminates the risk of bankruptcy). Stulz, R. (1996).
o Similarly, evidence by Graham and Rodgers (2002) suggests that hedging
allows firms to reduce costs of financial distress ➜ to increase their debt
capacity.
10
On risk management…
o Brown (2001) examines factors affecting why and how a real company
manages its “foreign exchange exposure through the use of internal firm
documents, discussions with managers, and data on 3,110 foreignexchange derivative transactions.”
o Motivations for firm’s risk management programme:
➜‘Earnings smoothing’: minimizing the impact of changes in foreign
exchange rates on cashflow and reported earnings and presenting linear
earnings’ growth.
➜Competitiveness: allow the firm to undertake competitive pricing in the
output market without significantly reducing margins. Especially when the
firm’s primary target is to maintain margins.
➜Facilitation of internal contracting: internal planning and evaluation.
11
On risk management…
o A Framework for Risk Management by Kenneth A. Froot, David S.
Scharfstein, and Jeremy C. Stein in Harvard Business Review, 1994
→The role of risk management is to ensure that a company has the cash
available to make value-enhancing investments.
→Multinational companies must recognize that foreign-exchange risk
affects not only cash flows but also investment opportunities.
12
On risk management…
o Hedging allows investors assess managers’ performance as it clears the
noise in cash flows and earnings that is not due to managers’ actions
[DeMarzo and Duffie (1995)]
o But hedging might also increase temptation to managers for speculation
with shareholders; especially when the firm gets closer to financial
distress.
➜An interesting rumored story: FedEx’s founder desperate to save the company in its
early years flew to Las Vegas to play blackjack with the last of the company money.
He won so the company is still here. But what if he had lost?
13
SECTION B
Understand the use of insurance as a method to reduce risk
Any questions?
14
Insurance
o Insurance is a contractual arrangement where an individual or entity pays
a premium to an insurer in exchange for financial protection against
specified risks, such as damage, loss, illness, or death.
o In the event of a covered occurrence, the insurer compensates the
policyholder according to the terms of the policy. Risk is transferred to the
insurance company.
15
Insurance
o Insurance companies have developed expertise which allows them to
estimate probabilities of loss and hence can price risk more effectively.
o An insurance company can pool risks by holding a diversified portfolio of
policies. The claims on an individual policy can be uncertain but claims on
a portfolio of policies is more stable.
16
→ Insurance
How are premium prices determined?
• Administrative costs:
An insurance company incurs a variety of admin costs in
arranging the insurance policies and its operations. Examples
include staff salaries, rent for office space, utilities, technology
and software expenses, marketing and advertising costs, legal
fees, regulatory compliance expenses, customer service
resources, and overhead expenses related to maintaining
physical and digital infrastructure. All these costs are reflected in
the premiums charged.
17
→ Insurance
How are premium prices determined?
• Adverse selection:
Unless an insurance company can distinguish between good and
bad risks, the latter who have a a higher risk of making claims are
more likely to purchase insurance. Insurers increase premiums to
compensate or require owners to share any losses.
→If individuals with a history of accidents or traffic violations are more
likely to purchase insurance, the insurer will face a higher probability
of claims from these high-risk drivers. To offset this increased risk,
the insurer may raise premiums for all policyholders, including those
with clean driving records. As a result, individuals with low risk may
end up paying higher premiums due to adverse selection driving up
overall costs for the insurer.
18
→ Insurance
How are premium prices determined?
• Moral Hazard:
Once the risk has been insured, the owner may be tempted to take fewer
precautions against damage.
→Consider an individual with comprehensive coverage for their vehicle
(insurance company will cover the cost of repairs for any damages,
regardless of fault). This individual might become less cautious when
driving or parking because they know that their insurance will cover the
costs of any damage. As a result, they may engage in riskier behavior,
such as speeding or parking in high-risk areas increasing the likelihood of
insurer's payout frequency and, consequently, their overall costs. To
compensate for this increased risk, the insurer may raise premiums for all
policyholders, including those who are careful drivers, thus passing on the
cost of moral hazard to all insured individuals through higher premiums.
19
→ Insurance
How are premium prices determined?
o When the costs of administration, adverse selection and moral hazard are high,
insurance premiums are high and thus a costly way to protect against risk.
o Insuring against jump risks or systematic risks can be very costly to insurance
companies.
→Systematic risks, also known as market risks or undiversifiable risks, are inherent to the entire
market or a particular segment of the market. These risks affect all assets within the market
and are typically driven by macroeconomic factors such as interest rate changes, inflation,
geopolitical events, or systemic financial crises.
→Jump risk refers to the risk associated with sudden and significant price movements or
"jumps" in the value of an asset or security. They occur dur to occur due to various factors
such as unexpected news events, changes in market sentiment, or sudden shifts in
supply and demand dynamics.
o Along risk pooling, the industry uses risk sharing, which distributes a fixed
amount of risk among many investors.
o As more and more policies are pooled together, they are shared by ever-more
investors, thus preventing any individual’s total risk from growing with the number
of policies.
20
SECTION C
Understand hedging using financial options
Any questions?
21
Financial options
oFirms may use financial options to set a limit on the losses that they
can suffer from an adverse change in the price of an asset (real and
financial).
oA financial option is a contract that gives the holder the right, but not
the obligation, to buy or sell a specified asset at a predetermined
price within a specified timeframe.
oThere are two main types of options: call options, which give the
holder the right to buy the underlying asset, and put options, which
give the holder the right to sell the underlying asset.
oOption buyers pay a premium for the right to buy (in the case of call
options) or sell (in the case of put options) the underlying asset at a
specified price within a certain timeframe.
→The premium is the price that the option buyer pays to the option seller for
granting them this right.
22
Assume that Mexican government
(oil exporter) wants to secure its
revenues from selling oil.
o Arranges an annual hedge
against potential fall in oil prices.
→Buying a put option on 250
million barrels of crude oil at a
price of $55 dollars per barrel.
→If exercised revenues will be:
$55×250m = $13.75 billions
Revenues $ billions
Financial options
Example 27-3 from main textbook
Inspired by current business practice (see FT article
here: https://on.ft.com/48lLglg)
$13.75
$55 per barrel
23
Financial options
$16.25
Revenues $ billions
If Mexican government was
unhedged:
o If oil price was $65 per barrel the
total revenues would have been:
$65×250m = $16.25 billions
$13.75
$55
$65
24
If Mexican government was
unhedged:
o If oil price was $45 per barrel the
total revenues would have been:
$45×250m = $11.25 billions
Revenues $ billions
Financial options
$13.75
$11.25
$45
$55
25
If Mexican government was hedged
using a financial option:
o If oil price was $45 per barrel the
total revenues would not have been:
$45×250m = $11.25 billions
The government would exercise the
option locking in minimum price of
$55:
$55×250m = $13.75 billions
o The company would have paid the
premium which was estimated to be
around $1 billion. So, revenues
would be reduced by that amount.
Revenues $ billions
Financial options
$13.75
$45
$55
26
If Mexican government was hedged
using a financial option:
o If oil price was $65 per barrel the
total revenues would have been:
$65×250m = $16.25 billions
o The government would not exercise
the option (allow it to lapse) and
realise the upward potential from this
happy surprise.
o The company would have paid the
premium which was estimated to be
around $1 billion. So, revenues
would be reduced by that amount.
$16.25
Revenues $ billions
Financial options
Hedging using financial options do not completely
eliminate the chance of happy surprises.
$13.75
$55
$65
27
Financial options
o An American style option is an option that can be exercised on any date
before its expiry.
o A European style option is an option that can be exercised only at expiry.
o Options provide flexibility: they allow a company to protect itself against
adverse market movements while at the same time it retains the ability to
profit from favourable options.
28
SECTION D
Understand hedging using forward contracts
Any questions?
29
Forward contracts
o A forward contract is a customized agreement between two parties to buy
or sell an asset at a predetermined price on a specified future date.
→Unlike financial options it involves no initial payment and is binding,
obligating both parties to fulfil the terms of the contract at maturity.
o The forward price is the agreed-upon price in a forward contract at which
the underlying asset will be bought or sold in the future. It is determined at
the outset and remains fixed until the contract's expiration, regardless of
changes in the market price of the underlying asset.
o The spot price is the price for immediate delivery.
30
Forward contracts
o The counterparty which has agreed to buy the underlying at maturity has a
long position in the contract and the counterparty which is selling has the
short position.
o Forward contracts are tailor-made to meet the requirements of the parties.
Flexibility on the amounts and delivery dates.
o Forwards are not traded on an organized exchange but are ‘over-thecounter instruments’: private agreements outside the regulation of an
exchange.
31
FORWARD HEDGE
Long position
Short position
Arctic Fuels
company
agrees to buy
1m gallons of
oil in 3
months at
$2.40 per
gallon
Northern
Refineries
company will
sell 1m
gallons of oil
in 3 months at
$2.40 per
gallon
3-month forward
price is $2.40 per
gallon
Heating oil
In 3 months:
→ Arctic Fuels pays $2,400,000 to receive 1m
gallons of heating oil from Northern
Refineries. Cost of purchase is locked at the
outset.
→ Northern Refineries will receive $2,400,000
from the sale of 1m gallons of heating oil to
Arctic Fuels. Sale proceeds are locked at
the outset.
32
Regarding the cost of the forward hedge…
o While the cost of purchase/sale proceeds is locked at the outset, the cost of
hedging can only be determined ex-post as it depends on the future spot price
prevailing on the settlement date of the forward contract (which is unknown on
the day we agree to the forward contract). Counterparties in a forward agreement
are exposed to counterparty risk of default (i.e. the risk that the other party will
not deliver on the agreement).
o We need to compare the cost of purchase/sales with and without hedging.
→The real cost of hedging is an opportunity cost.
o If at maturity spot price of heating oil was $2.50 per gallon the purchase would
have cost $2.5 million:
→instead of $2.4m that Artic Fuels had paid, so the buyer would have been better off by
$100,000 and the seller (Northern Refineries) worse off by the exact same amount. The
risk grows in proportion to the extent to which the spot price diverges from the forward
price as the incentive to back out increases.
33
SECTION E
Understand the basics of the futures market
Any questions?
34
Futures contracts
o A futures contract is a standardised agreement between two parties to
buy or sell a specified asset (such as commodities, currencies, or financial
instruments) at a predetermined price on a specified future date. Unlike
forward contracts, futures contracts are traded on regulated exchanges.
o The price of a futures contract is fixed today, but payments are made in the
future. To ensure that both parties can meet their financial obligations as
the contract's value fluctuates, you are required to put up a margin.
→margin refers to the initial deposit of funds or securities required by
both buyers and sellers to initiate a futures position
o Futures contracts are marked-to-market: each day, any profits or losses
on the contract are calculated and you pay the exchange’s clearing house
any losses and receive any profits.
35
Futures contracts
o The buyer and the seller of a futures contract do not transact with each
other directly. The clearing house (a financial intermediary) becomes the
formal counterparty to every transaction. This reduces the risk of noncompliance with the contract.
o With futures you are committed and are unable to back away, like you do
in options.
o Taking a futures position means that you can lose multiples of the amount
you used to take a futures position.
36
→ Futures contracts
An example*
o Wheat will be harvested in six months. Farmer A needs to lock in a price
for his wheat, and a counterparty (say, Bakery A) agrees to purchase the
wheat from the farmer six months at a price of £60 per tonne.
o The agreement is not directly between the two counterparties but with an
exchange – a clearing house-.
o Bakery A hopes that wheat price is higher than £60, so that they can make
profit.
→e.g., if price of wheat in 6 months is £65 Bakery A makes a profit £5
per tonne by selling wheat purchased at £60 for £65 at the prevailing
sport price.
*Example from Arnold, G., 2019. Corporate Financial Management, 6th Ed., Pearson Education.
37
→Futures contracts
An example
o The clearing house takes on a large amount of credit risk. To minimise that
it operates a margining system by which the futures buyer or seller must
provide in cash an initial margin.
→Initial margin is not a ‘down payment’ for the underlying, but it stays with the clearing
house. It is refunded when the futures position is closed.
o The clearing house operates a system of daily marking to market. At the
end of the trading day the counterparty’s profits/losses as a result of that
day’s price changes are calculated, and each member’s margin account
change accordingly.
o The following morning the losing counterparty receives a margin call to
inject more cash to cover the loss if the money in the account has fallen
below a threshold level, called the maintenance margin.
38
→ Futures contracts
An example
o Farmer A has only a promise from Bakery A that they will pay £60 per
tonne six months from today. If price drops, Farmer A fears that Bakery A
will walk away from the deal.
→To reassure Farmer A, Bakery A is asked to put money in a margin
account (assume they agree a maintenance margin of £6 per tonne).
o So, if Bakery A walks away:
→Farmer A collects the money from the margin account and sells the wheat
in the spot market. So, if price in six months' time is £54 per tonne, Farmer
A collects £6 from margin account plus £54 from selling at spot (total: £60).
39
→ Futures contracts
An example
But if the price is below £54?
o Farmer A faces risk, so the clearing house requires Bakery A to top up the margin
account daily so that there is always the buffer (i.e., the maintenance margin)
o So, if the day after the futures contract is agreed the price of wheat is £57, then to
bring the margin account up to the £6 buffer, Bakery A will be required to top-up
the margin account with another £3 (£57 is the spot price, the futures price
agreed is £60 + £3 left from initial margin + £3 top-up to the margin).
o If the next day the price falls to £50 Bakery A will be receive a margin call to put
another £7 per tonne.
o By putting top-ups as the price moves against Farmer A, it is ensured that there is
at least £6 per tonne as a buffer.
40
Futures contracts
An illustration
o Imagine a buyer and a seller of a future with an underlying value of £50,000 are
each required to provide an initial margin of 10% (£5,000).
o The buyer will make profits if the price rises while the seller will make profits if the
price falls.
o It is assumed that counterparties must keep all the initial margin throughout the
duration of futures contract as a buffer (i.e., maintenance margin is £5,000).
o The daily changes to counterparties’ margin accounts are known as variation
margin.
41
Futures contracts
An illustration
Contract
expires on
Friday
Monday
Tuesday
Wednesday
Thursday
Friday
£50,000
£49,000
£44,000
£50,000
£55,000
Underlying Asset Price
Change:
(£55,000 − £50,000)
= 10%
£50,000
Buyer’s % Return
£5,000
= 100%
£5,000
Day of the week
Value of Future
(daily closing price)
Buyer's position
Initial margin
£5,000
Variation margin
0
Accumulated profit (loss)
-£1,000
-£5,000
£6,000
£5,000
-£1,000
-£6,000
0
£5,000
Seller's position
Initial position
£5,000
Variation margin
0
Accumulated profit (loss)
£1,000
£5,000
-£6,000
-£5,000
£1,000
£6,000
0
-£5,000
Seller’s % Return
−£5,000
= −100%
£5,000
42
Focus on Financial Futures Contracts
Suppose you think that French stock market will outperform other European
markets over following 6 months.
o Strategy A: commit your funds today to buy French stocks, pay spot price,
and wait.
o Strategy B: ‘buy forward’ by buying futures contracts on CAC index of
French stocks
→Buy 15 six-month futures contracts at index level 4,500. Each contract has
a value of €10 times the value of the index, so take a long position of
€675,000.
→If CAC index goes up (down), the exchange puts the profits in your margin
account (reduces your margin account).
43
Focus on Financial Futures Contracts
o Suppose CAC ends up at 5,000 after six months. Your profit is:
15× 5,000 − 4,500 ×€10 = €75,000
→You could have earned the same profit with Strategy A, but the difference is that you would
need to have committed all funds from the beginning and lost any interest that you would have
earned on the purchase price of €675,000. But with strategy B, you missed any dividend
payments.
o So, the relationship between spot price today 𝑆! and futures prices of a
financial futures contract lasting 𝑡 periods 𝐹" is:
F# = S! ×(1 + r$ − y)#
where 𝑟% is the risk-free rate that you would have earned if you bought the futures
rather than buying stocks for immediate delivery, and 𝑦 is the dividend yield.
44
Focus on Commodities Futures Contracts
o The delayed payment by entering a futures contract allows you to earn
interest on the money that you would have committed if you did buy for
immediate delivery.
o Commodities require storage costs. When buying forward you save these
costs.
o Futures contracts give no convenience yield, which is the value of being
able to quickly access the asset for consumption or production purposes.
→For example, convenience yield of oil is expected to increase if there are supply
disruptions or geopolitical factors, and hence there are increasing benefits associated
with holding physical oil.
45
Focus on Commodities Futures Contracts
oSo, the relationship between spot price today 𝑆! and futures prices
of a commodities futures contract lasting 𝑡 periods 𝐹" is:
F# = S! ×(1 + r$ + storage costs − convenience yield)#
Net convenience yields are typically positive, and futures are below
spot prices (backwardation).
But in case of high storage costs and ample supply of physical
commodity, futures price can be above spot and market is said to be in
contango.
See a definition of contango by the Financial Times: https://on.ft.com/3aI9CYv
46
Futures prices and spot prices
o Price discovery in the stock market refers to the process by which the
market determines the fair value of a security, such as a stock, based on
the collective actions of buyers and sellers.
o Can futures prices reveal traders’ forecasts of spot prices?
47