Summary Financial Risk Management
Unit 1
Introduction is skipped.
Risk taking it by itself is not a bad thing, only one has to be beware of the risk, understand it and
measure it:
- Risk needs to be recognized, identified
- Once recognized, the risk has to be qualified
- And - as far as possible - it must be measured with numbers, financial or non-financial; the risk
has to be quantified.
Risk qualification
There are four different types of financial risk that companies have to manage:
Market risk -> the possible values of an asset or liability at some point in the future (and the
probabilities of these values occurring). We will elaborate on interest rate risk (the risk of falling
income flows from falling rates and rising costs from rising rates), price or value risk (caused by
changes in market interest rates that result in price or value changes of financial instruments and
their derivatives) and further discuss stock market and foreign exchange rate risk.
Liquidity risk -> over what period of time and at what price can a position be closed.
Counterparty risk or credit risk -> the probability of default of the counterparty to a deal and, in the
event of default, th elikely recovery rate.
Operational risk -> losses through fraud, malfeasance or operational error. Entrepreneurial risk is
of a complete other order and will not be discussed here.
Financial leverage and risk
The asset side of a company’s balance sheet shows the capital that creates an income flow. The
liabilty side shows the financial structure by which the asset side is financed and the degree of
financial leverage.
The composition of the liability-side is called the financial (or capital) structure of a company: how
much debt of one type or other and how much owner’s equity is used for financing the assets. The
more debt compared to owners’ equity, the higher the financial leverage or financial gearing of the
company.
As long as the return on the total investment in assets (=balance sheet total), in short return on
assets or ROA exceeds the cost of borrowing, higher leverage leads to a higher return on equity
(ROE).
ROA = net income / total assets
total assets -> average from current and previous year
ROE = net income / total equity
total equity -> average from current and previous year
FL (financial leverage) = ROE/ROA
Watch out: take also a look at the operating income when calculatin the ROA.
**take a look at the exercises in the slides**
Risk of traditional banking
,Summary Financial Risk Management
When a bank’s balance sheet consists out of short term funding (15,000) to finance long term
loans (15,000) there is a naturally mismatch between the funding and the lending.
The mismatch is the source of income of traditional banking: in a normal yield curve environment
the bank earns the interest rate spread between funding cheaper at short term rates and lending at
higher long term rates.
For examples look at 1.4 of unit 1.
This form of interest rate risk can be determined by:
Simulation -> given interest rate sensitive positions and expected liquidity flows, a computer
prgram calculates the effect of interest rate changes.
Gap analysis -> netting asset and liabilities within th esame maturity-intervals, producing the net
exposure in these maturity-intervals.
Duration analysis -> calculate the duration of all items on the balance sheet, giving the overall
duration. Duration is the weighted remaining time to maturity of a cash flow, a good approximation
of the basis point value of financial instruments.
Liquidity risk management: read once at page 18 of unit 1.
Operational risk -> is the field of administrative organization and controlling.
Unit 2
Market risk -> refers to the risk that the fluctuations of market prices will have a negative impact on
cash flows and market value of a company.
Market risk in the banking industry -> the potential loss in on and off-balance sheet positions that
arise from adverse movements in the market prices.
Market risk -> the sensitivity of the financial instrument’s value to the movements of the underlying
value-determinants.
Types of market risk:
- Equity risk -> refers to the risk that unanticipated movements in the value of stock prices will
adversely impact the value of the portfolio or the company’s positions.
- Commodity risk -> the risk that arises from the adverse movements in commodity prices that will
negatively influence the company’s positions.
- Currency risk -> refers to the potential loss due to an unexpected exchange rate movements.
- Interest rate risk -> the exposure of a company financial condition ot an unfavourable changes in
the market interest rate that will negatively impact the revenues, cash flows and the market value
of the firm.
Value at risk definition
The VaR (Value at Risk) is a model that tries to give us an indication about how much we could
lose if there is an adverse movements in market risk factors such as equity prices, exchange rates
etc.
The VaR will not only tell us that there is X percent probability that we will lose at most Y amount of
money, but also whether this estimated loss will take place in the next trading day, week, month or
year.
,Summary Financial Risk Management
The VaR can be defined as the maximum amount of money the company can lose on an
investment over a given time period and with a pre-set prbability.
Example that includes the confidence level and significance level:
Value at risk quantification
Historical value at risk
This approach requires following many steps in order to arrive to the Historical VaR.
1. Rate of return calculation -> there are different methods to calculate the rate or return but the
most used models are the arithmetic average and logarithmic average. The arithmic average
formula can be expressed as follows:
Sometimes the arithmetic rate of return does not make sense. And to avoid such quirk,
professionals tend to use logarithmic returns.
2. Portfolio re-valuation -> once the rate of return of an asset or a portfolio are culculated, we can
start revaluing our portfolio to generate the daily profits and losses (P/Ls). The P/Ls are always
expressed in absolute values such as dollars and euros. Therefore, we need to multiply the rate
of return by the inital investment (amount of money you have invested in this stock).
3. Sorting the portfolio profit and loss values -> once we get the P/Ls dataset, we need to sort it
from the smallest to the largest values because the VaR emphasis is on the left tail of the
distribution where highest losses reside. The smallest value will be the largest losses occured in
the P/Ls dataset while the largest values will be the largest profits.
,Summary Financial Risk Management
4. Probability allocation -> we need to consider whether these P/Ls may occur either with the same
or different likelihood in the near future. Some argue that all past observations or values have
equal chances to re-produce themselves in the near future. Thus, the chance of having a loss
equivalent to the one that took five years ago is similar to the chance of having a loss that just
happened in th elast recent five days. This is called average probability method.
The opponents of this approach claim that recent observations (P/Ls) are more significant than the
ancient ones. Since there observations are close to the near future, there is more chance for the
near-future observations to look like the recent-past observations. Therefore, we need to assign
more weights or probabilities to the most recent observations and vice versa. This can easily be
achieved by assigning a gradually ascending weights to the unchronological sorted P/Ls. This
approach is named the exponential probability method.
(Average probabililty method is used)
To calculate the probability of each observation in our dataset, we need to divide 1 by the total
number of observations.
5. Cumulative probability -> measures the odds of more than two observations happening given
that each observation needs to be independent of the others. This means that you cannot have
two observations that occur simultaneously. In case of the average probability method, then
each observation is the P/Ls dataset will have equal weights regardless of whether the
observation is an acient or recent one within the portfolio time horizon.
After assigning equal weights to each observation we need to present the resulting data in a
cumulative percentile form, so that we can identify value at risk at many high confidence levels
(probabilities). We do that by assigning the lowest probability to the largest profit observation.
6. Value at Risk identification -> Identify the VaR in the Sorted P/Ls data set. To be able to locate
the VaR we need to determine first the confidence level we are interested in. After that, one can go
to the cumulative weights dataset and ook for the required probability. Then one can read the
corresponding value ot that probability in the sorted P/Ss dataset and take it away from the
average P/L of the portfolio.
VaR time-conversion
To know how accurate the VaR model is, we need to back test the results produced by the VaR
model. In other words, we need to compare the VaRs with the actual losses at the end of the time
horizon.
, Summary Financial Risk Management
If a portfolio has a daily value at risk of 1 million EUR at a 95% confidence level (in other words:
the portfolio has 5% probability of having losses that exceed value at risk by the end of a trading
day). If for every day in the very near future the actual loss exceeds the VaR, then we can say the
VaR model may not be accurate.
That is to say, we need to look at how many times the actual losses exceeded the VaR. If the
frequency of such breaches are high, then one can conclude that the VaR model is inaccurate.
For a portfolio, we expect the actual losses to breach the VaR on 5 out of 100 days (5%).
Example:
Expected shortfall
Value at risk model gives an indication about the expected loss of a portfolio or an asset under
normal economic conditions. For some investors the VaR is not enough because they want to
know that would be the worst case scenario if the market moves against expectations. The
expected shortfall can be defined as the expected loss over pre-specified time horizon, conditional
on the loss being greater than the VaR (expected shortfall is just the average of losses that exceed
a given value at risk).
Unit 3
Introduction
Unlike stocks and bonds which are backed by the firm’s assets, derivatives derive their value from
the change in the value of the inderlying assets. For instance, the value of a stock option depends
