This summary includes all lectures (lecture 1 up until lecture 5) of the course Risk management.
I also included tutorial 1 and 2 in this summary.
I explain how things work in excel too.
Topics include:
- Introduction to risk management
- To hedge or not to hedge
- VaR and CFaR
- Forwards and fu...
Risk = a possible future event, if it occurs, will lead to an undesirable outcome. The
importance lies in the possibility that it can occur. It does not mean that this undesirable
outcome will occur always. This uncertainty is the one that investors do not like.
Risk management is defined as any set of actions taken by individuals, investors, or
corporations to do something about this risk that arises from their primary line(s) of business.
Basically, you try to manage the risks to avoid them/ lower the chances of the risks
occurring.
Risks are managed by using hedging instruments.
Hedging = a financial position, often a derivative, used to reduce the impact of a risk one is
exposed to (“putting on a hedge”).
Derivative = payoff is dependent on some other value.
Financial position = certain payoff is guaranteed whenever something bad indeed happens.
An example might be a car insurance (which pays you a certain amount when you have a
car accident to cover the car reparation costs).
When the hedge is imperfect, that is, the financial position does not fully cover the losses,
this is called basis risk. Full costs are almost never covered (there might be
emotional/physical damage as well).
Is risk always bad?
There might be some risks worth taking, because the possible benefit exceeds the possible
costs (ex ante, that is before you incur this risk). This idea is captured in the famous phrase
of Milton Friedman: “there is no such thing as a free lunch”. Basically, he was trying to say
that you need to take some risk to have a chance of a high payoff.
take the risks where the possible benefits > possible costs (ex ante).
However, risks that you do not know about should be avoided. “Cobbler, stick to your last”.
Risk management process
1) Identify relevant risk factors
2) Understand the joint distribution of those risk factors
3) Estimate the impact of probable adverse movements 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
1) Risk factor identification
Some risks might be:
- Interest rates: they are procyclical, such that the interest rates go up in good
economic times. They are important for investment projects, since they determine the
PV of projects ( used as discount factor).
- Exchange rate
- Business conditions at home market and/or foreign competitors’ markets.
- Etc.…
Some correlations between variables might increase risk, while others might reduce risk.
For example, when demand is high for some product in the US, they need to borrow more.
Since the demand is high in an economic boom, the interest rate is high too (procyclical) and
therefore, borrowing is expensive. This decreases risk, since the payoff is a bit lower in good
economic times (because borrowing costs increase), but when there are bad economic
,times, the payoff will be a bit higher than expected, since it is relatively cheap to borrow
money.
this is an example of what joint distribution of risk factors might do.
However, if good times are made even better and bad times even worse because of the
relation between 2 variables, this increases risk!
The correlation between risk factors is therefore really important.
2) Understand the joint distribution of those risk factors
When a portfolio asset is not perfectly positively correlated, there are diversification benefits
to be gained. Perfectly negative correlation reduces risk the most ( variance is minimized).
Historical distribution of some risk factors:
- Dollar/euro exchange rate
o Appreciation of the euro means that people have to pay more dollars to buy
the same €, or they get less €’s than before with 1 dollar. The dollar is
basically worth less, because you have to pay more dollars than before to
obtain the same €. Over the year, the exchange rate can vary a lot.
o If you are a US firm with sales in Europe, you are worried about a
depreciation of the € (appreciation of the dollar), since then you have to pay
more €’s for the same dollar and the value of your sales decreases in dollar
terms.
o Value of the sales are dependent on the exchange rate.
o Therefore, we want to know the distribution of the exchange rate.
o Exchange rate volatility is large and coincides with political events. When
there is nervousness, this puts down the value of the currency. People do not
trust it anymore.
- Stock price
o This is a valuation of a certain company
- Crude oil price
o There was an oil crash in 2020. This is not so good for airlines. The demand
for oil decreased a lot, because there was no demand due to the corona
virus.
- US interest rates
o Determine the PV of the future cash flows.
o Important risk factor for firm valuation.
To measure risk of investing in the stock market: volatility index. When VIX is small, the risk
is small. It represents changes, but it does not say anything about in which direction the risk
goes. VIX is a good representation in stock markets, but also in other asset classes (for
example exchange rates, interest rates, etc.).
in most cases it is extremely difficult to predict future values of risk factors.
We can, however, use the historical data to construct a probability density function (PDF).
This function describes things that can happen with accompanying probabilities.
Example: dollar/euro exchange rate
- Rule of thumb: the best prediction for tomorrow’s rate is its current rate random
walk hypothesis.
- Normal distribution: outcomes around the mean are more likely.
- PDF: gives you for any outcome, the probability.
o Construct a standardized normal variable, using the formula: (x – mean)/sd.
o With this z-score, we can use the Z-table to know in which percentile this z-
score lies.
, o The table is constructed for probabilities on the left of the z-score:
o Table:
o First column = first numbers, second column is additional decimals. The blue
lines indicate that 0.8944 is the probability of z < 1.25. In %, this means that
89.44% is smaller than 1.25.
o To calculate values < - number, use the property that the whole area under
the graph is equal to 1. Look up the positive z-value and then do 1 – the value
found in the table that complements this positive z-value.
- CDF: gives you the probability of a certain return below a certain %. For example, the
probability of a return below 18%? It approaches 1, since we know that all possible
outcomes lie below a certain %.
- When the distribution is flatter, the outcomes in the tails are more likely, such that the
chance of extreme outcomes occurring is increasing.
3) Estimate the impact of adverse movements in those risk factors on the strategic plan
We have various tools for this:
- Value-at-Risk
- Cash-Flow at Risk
4) Decide whether to hedge or not and how?
lecture 5.
How to reduce risk exposure?
- Diversify product line: especially when prices of the products are not perfectly
correlated.
- Manage expenditure: increase variable costs relative to fixed costs.
- Reduce leverage, such that firm has fewer obligations: coupons are fixed, but
dividends are more flexible.
- Use derivatives: often very cheap and flexible.
What is a derivative?
A derivative is a financial instrument with promised payoffs derived from the value of one or
several contractually specific underlyings.
Underlyings = risks to which economic agents are exposed.
Liquid derivatives = underlyings to which many agents are exposed (stock prices, exchange
rates, interest rates, commodity prices). Liquid meaning cheaper and easier to access.
Underlyings can be anything.
2 flavors of derivatives:
, - Plain vanilla
o Forwards and futures: represent an obligation to buy/sell some
underlying at a fixed price at some time in the future (at maturity).
o Swaps represent a portfolio of forwards and futures.
o Options: represent the right to buy/sell some underlying at a fixed price
at some time in the future.
- Exotic derivatives
o This is more complex
o There is a complex determination of payoff (depending not on value of
underlying at maturity, but average, minimum or maximum) or non-standard
underlying (weather, elections).
Where are derivatives traded?
- Exchange: cheap, but standardized contracts. Transaction costs are low since there
are many traders (seeking time is low).
- Over-the-counter (OTC): two parties agree on trade without meeting through an
organized exchange. These are customized contracts, and therefore more
expensive.
- The majority of derivatives is in OTC, because it is difficult to find a standardized
contract that exactly fits the factors of risk a company is facing.
There was a strong growth in derivatives usage since the beginning of 1970s because of:
- Oil crisis in 1970: made it clear to firms that they would have wanted to hedge on oil
prices.
- More volatility on exchange rates (termination of Bretton-Woods system) + interest
rates (currencies were linked to gold, but they wanted more self-power).
- Growth in trade and portfolios because of access to derivatives.
- Exchanges specialized in trading standardized derivative products.
- Model of derivatives.
Derivatives can be dangerous
If derivatives are not well understood, trading in derivatives can lead to large losses that may
endanger the financial health of corporations and other derivative traders (the counterparty).
For example, Baring Bank went bankrupt, because of one guy in Singapore office that
constructed a big position in derivatives on Japanese currency. He did this behind the back
of other managers. In 1995 he created such large positions, that when there was an
earthquake in Japan, it pushed the price of the Japanese currency down (because investors
did not want to invest in the currency anymore). Company banks lost money.
In the media, derivatives are often considered as highly dangerous and on which one always
makes losses.
The message from this course is that they are not so dangerous, unless they are well
understood. If they are used properly, they can help to reduce/eliminate the risk a company
is facing.
In other words, corporations that do not hedge using derivatives are exposed to immense
risks, as are corporations that hedge without understanding these derivatives.
LIVE SESSION WEEK 1:
A normal distribution is symmetric and entirely determined by mean and variance (standard
deviation). It provides a reasonable approximation (not per se the best!) for the distribution of
the returns of many assets.
Percentile: indicating the value below which a given percentage of observations in a group of
observations falls. A 50th percentile is the same as a "median”. A 95th percentile says that
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