Risk management
Introduction
Live session 1
Risk management Process
1. Identify relevant risk factors
2. Understand the joint distribution of those risk factors
3. Estimate the impact of probable adverse moments in those risk factors on the strategic plan
4. Decide whether to hedge or not (or how much to hedge)
5. Choose the appropriate financial instrument
The normal distribution
The normal distribution is symmetric and entirely determined by mean and variance
o Provides reasonable approximation for the distribution of the returns of many assets (exchange
rates, commodities, stocks, and so on)
The pth percentile of a distribution is a number Φ (p) such that there is a probability of p percent that the
random variable y is below Φ (p) and (100 – p) that it is above
o The percentiles of the standard normal distribution N(0,1) are known:
Exchange rate example
Take example of US$ - Euro exchange rate (# of US$ per 1 Euro)
o Best prediction for tomorrow’s rate is its current rate (‘random walk hypothesis’)
o Annualized long-term volatility: 11%
o Suppose exchange rate returns follow normal distribution with mean = 0 and volatility = 11%
Page 1 of 96
,Some questions
What is the probability of a return below 0%?
o 50%
How to interpret a negative return?
o A negative return is an appreciation of the dollar, which is good news for
European firms that make sales in the US
US firms that buy input goods in Europe
What is the probability of a return below -10%?
o Normdist(-10%,0,11%,TRUE)=18.2%=Normsdist((-10%-0)/11%)
What is the probability of a return between -10% and +10%?
o 1 – 2 x 18.2% = 0.636
What is the lowest return for which you can say with 99% confidence that it will not be exceeded?
o Norminv(0.01,0,11%)=-25.6%=Normsinv(0.01)*11%=-2.33*11%
What is the answer to this question if…
The average return is 1%?
o The whole distribution moves 1% to the right: -24.6%
The volatility increases to 20%?
o The distribution widens? -2.33*20% = -46.6%
What is the answer to this question if the returns are not normally, but t-
distributed (with 10 degrees of freedom)
o The t-distrubtion has fatter tails than the normal:
o T.INV(0.01,10)*11% = -30.4%
What is the average return in the worst 1% of cases?
o Not straightforward, but in Excel we can draw returns from this distribution and approximate the
answer: 28%
Motivation: derivatives
This course will teach you how derivatives can be used to hedge various types of exposures
1. Hedging with forward, futures and swaps
Payoffs are linear in value of underlying!
Most commonly used for short-term (recurring) exposures
2. Hedging with options
Payoffs are non-linear in value of underlying
Options are particularly useful in case the exposure is uncertain
Studying option pricing models is useful in many other contexts (besides risk
management), such as in “real options”
Intuition (I)
A firm will extract 100 million pounds of copper over the next year.
o With derivatives, the firm can fix a selling price for future production
o Obligation (short futures) or right (put option) to sell copper at a pre-agreed price at a pre-agreed
time in the future.
The current price of copper is 3$ per pound.
o What will be the total revenue one year from now without hedging?
o What will be the total revenue if the company takes a short futures position that gives the firm the
obligation to sell 100 million pounds of copper at a price of 3$ per pound?
o What will be the total revenue if the company owns a put option that gives the firm the right (not
an obligation!) to sell 100 million pounds of copper at a price of 3$ per pound?
This course is about understanding these (and other) alternative hedging strategies, calculating what
these hedging strategies cost, assessing their relative attractiveness, and so on
o The option strategy must be more expensive than the futures strategy. Why?
Page 2 of 96
,Hedging needs to be done with care!
The infamous Metallgesellschaft (MGS) hedging debacle
MGS had long-term forward commitments to deliver oil (and other energies) at fixed price X to customers
Is MGS afraid of the oil prices to rise above or fall below X?
o Rise above: MGS receives X, but could have received the higher market price if it didn’t have the
long term commitment
To hedge, MGS took long positions in oil futures, which obligated MGS to buy oil at a fixed price Y ≈ X
o When the oil prices rises, MGS loses on long-term commitment, but makes a gain on the futures
position
When energy prices plummeted in 1993, MGS lost around 1.3 billion $ and almost entered bankruptcy
o How??
How did this happen?
Plummeting oil prices became a problem for at least two reasons:
1. MGS seemed to have underestimated “liquidity risk”
o While the gains on the long-term forward commitments (short) would only be realized in the long-
term
o The losses on the futures positions (long) were settled daily, st MGS suddenly had to cover huge
margin calls
Major difference between forwards and futures: forwards are traded OTC and settled at maturity, futures
are traded on exchanges and settled daily
2. MGS seemed to have underestimated “basic risk” , which arises when the hedge is not perfect
o The futures contracts used to hedge were short-dated, because this market was more liquid, so
that the horizon of the hedge did not properly match their long-term forward commitments
o Every time a short-dated futures expired, they rolled over into a new short-term contract with
futures price slightly above the spot price of the previous expiration, which generates negative
returns
Oil market had switched form backwardation to contango
Hoorcollege 1
What is risk?
o A possible future event which, if it occurs, will lead to an undesirable outcome
o Thus, risk is the possibility of suffering loss
o Although the event may not occur, it is the uncertainty that individuals, investors and corporations
do not like
When driving a car, you may have an accident
What is risk management?
o Any set of actions taken by individuals, investors, or corporations to alter the risk arising from
their primary line(s) of business
You can limit the probability of an accident by adapting driving style, driving sober,
avoiding bad weather conditions…
Hedging
A hedge is a financial position – often a derivative – used to reduce the impact of a risk one is exposed
to…”
Hedging means putting on a hedge
Car insurance is an example of a hedge
o Receive financial compensation if an accident occurs
o Basis risk: the hedge is imperfect (and we will see this often the case): the insurance may not fully
cover the financial (as well as physical and emotional) damage of the accident
Is risk always bad?
Some risks are worth taking because the possible benefit exceeds the possible costs (ex ante)
o You risk taking a plane to go to your favourite holiday destination
As noted byy the economic Milton Friedman in 1975: “There is no such thing as a free lunch”
You should avoid risk you do not know about
o Exchange rates represent a risk factor for Coca-cola, because it sells worldwide. However, coca-
cola’s core strength is marketing, not speculating on future exchange rates by moving sales
across countries
Page 3 of 96
, Page 4 of 96
Introduction
Live session 1
Risk management Process
1. Identify relevant risk factors
2. Understand the joint distribution of those risk factors
3. Estimate the impact of probable adverse moments in those risk factors on the strategic plan
4. Decide whether to hedge or not (or how much to hedge)
5. Choose the appropriate financial instrument
The normal distribution
The normal distribution is symmetric and entirely determined by mean and variance
o Provides reasonable approximation for the distribution of the returns of many assets (exchange
rates, commodities, stocks, and so on)
The pth percentile of a distribution is a number Φ (p) such that there is a probability of p percent that the
random variable y is below Φ (p) and (100 – p) that it is above
o The percentiles of the standard normal distribution N(0,1) are known:
Exchange rate example
Take example of US$ - Euro exchange rate (# of US$ per 1 Euro)
o Best prediction for tomorrow’s rate is its current rate (‘random walk hypothesis’)
o Annualized long-term volatility: 11%
o Suppose exchange rate returns follow normal distribution with mean = 0 and volatility = 11%
Page 1 of 96
,Some questions
What is the probability of a return below 0%?
o 50%
How to interpret a negative return?
o A negative return is an appreciation of the dollar, which is good news for
European firms that make sales in the US
US firms that buy input goods in Europe
What is the probability of a return below -10%?
o Normdist(-10%,0,11%,TRUE)=18.2%=Normsdist((-10%-0)/11%)
What is the probability of a return between -10% and +10%?
o 1 – 2 x 18.2% = 0.636
What is the lowest return for which you can say with 99% confidence that it will not be exceeded?
o Norminv(0.01,0,11%)=-25.6%=Normsinv(0.01)*11%=-2.33*11%
What is the answer to this question if…
The average return is 1%?
o The whole distribution moves 1% to the right: -24.6%
The volatility increases to 20%?
o The distribution widens? -2.33*20% = -46.6%
What is the answer to this question if the returns are not normally, but t-
distributed (with 10 degrees of freedom)
o The t-distrubtion has fatter tails than the normal:
o T.INV(0.01,10)*11% = -30.4%
What is the average return in the worst 1% of cases?
o Not straightforward, but in Excel we can draw returns from this distribution and approximate the
answer: 28%
Motivation: derivatives
This course will teach you how derivatives can be used to hedge various types of exposures
1. Hedging with forward, futures and swaps
Payoffs are linear in value of underlying!
Most commonly used for short-term (recurring) exposures
2. Hedging with options
Payoffs are non-linear in value of underlying
Options are particularly useful in case the exposure is uncertain
Studying option pricing models is useful in many other contexts (besides risk
management), such as in “real options”
Intuition (I)
A firm will extract 100 million pounds of copper over the next year.
o With derivatives, the firm can fix a selling price for future production
o Obligation (short futures) or right (put option) to sell copper at a pre-agreed price at a pre-agreed
time in the future.
The current price of copper is 3$ per pound.
o What will be the total revenue one year from now without hedging?
o What will be the total revenue if the company takes a short futures position that gives the firm the
obligation to sell 100 million pounds of copper at a price of 3$ per pound?
o What will be the total revenue if the company owns a put option that gives the firm the right (not
an obligation!) to sell 100 million pounds of copper at a price of 3$ per pound?
This course is about understanding these (and other) alternative hedging strategies, calculating what
these hedging strategies cost, assessing their relative attractiveness, and so on
o The option strategy must be more expensive than the futures strategy. Why?
Page 2 of 96
,Hedging needs to be done with care!
The infamous Metallgesellschaft (MGS) hedging debacle
MGS had long-term forward commitments to deliver oil (and other energies) at fixed price X to customers
Is MGS afraid of the oil prices to rise above or fall below X?
o Rise above: MGS receives X, but could have received the higher market price if it didn’t have the
long term commitment
To hedge, MGS took long positions in oil futures, which obligated MGS to buy oil at a fixed price Y ≈ X
o When the oil prices rises, MGS loses on long-term commitment, but makes a gain on the futures
position
When energy prices plummeted in 1993, MGS lost around 1.3 billion $ and almost entered bankruptcy
o How??
How did this happen?
Plummeting oil prices became a problem for at least two reasons:
1. MGS seemed to have underestimated “liquidity risk”
o While the gains on the long-term forward commitments (short) would only be realized in the long-
term
o The losses on the futures positions (long) were settled daily, st MGS suddenly had to cover huge
margin calls
Major difference between forwards and futures: forwards are traded OTC and settled at maturity, futures
are traded on exchanges and settled daily
2. MGS seemed to have underestimated “basic risk” , which arises when the hedge is not perfect
o The futures contracts used to hedge were short-dated, because this market was more liquid, so
that the horizon of the hedge did not properly match their long-term forward commitments
o Every time a short-dated futures expired, they rolled over into a new short-term contract with
futures price slightly above the spot price of the previous expiration, which generates negative
returns
Oil market had switched form backwardation to contango
Hoorcollege 1
What is risk?
o A possible future event which, if it occurs, will lead to an undesirable outcome
o Thus, risk is the possibility of suffering loss
o Although the event may not occur, it is the uncertainty that individuals, investors and corporations
do not like
When driving a car, you may have an accident
What is risk management?
o Any set of actions taken by individuals, investors, or corporations to alter the risk arising from
their primary line(s) of business
You can limit the probability of an accident by adapting driving style, driving sober,
avoiding bad weather conditions…
Hedging
A hedge is a financial position – often a derivative – used to reduce the impact of a risk one is exposed
to…”
Hedging means putting on a hedge
Car insurance is an example of a hedge
o Receive financial compensation if an accident occurs
o Basis risk: the hedge is imperfect (and we will see this often the case): the insurance may not fully
cover the financial (as well as physical and emotional) damage of the accident
Is risk always bad?
Some risks are worth taking because the possible benefit exceeds the possible costs (ex ante)
o You risk taking a plane to go to your favourite holiday destination
As noted byy the economic Milton Friedman in 1975: “There is no such thing as a free lunch”
You should avoid risk you do not know about
o Exchange rates represent a risk factor for Coca-cola, because it sells worldwide. However, coca-
cola’s core strength is marketing, not speculating on future exchange rates by moving sales
across countries
Page 3 of 96
, Page 4 of 96
