BACHELOR THESIS

RISK MEASURES AND THEIR ROLE IN RISK

MANAGEMENT:

VALUE AT RISK & CASH FLOW AT RISK

Name : Dirk Jan Loeters

ANR : 272918

Study programme : Pre-Master Finance

Type : Literature research

Supervisor : Y. Zhou

Subject : Risk Measures and their role in Risk Management:

Value at Risk & Cash flow at Risk

Date of submission : 05-18-2012

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Abstract

Most firm managers have heard of Value at Risk (VaR) and Cash Flow at Risk (CFaR). But

some small firm managers may not know how to calculate those measures of risk while

measuring firms risk is becoming more important in current economic markets. This can lead

to situations where companies face more risk than managers expect them to do.

In this paper I try to explain both measures of firm risk more clearly and aim for a manager‟s

better understanding of calculating and interpreting both measures. To get to the results for

this paper I used other publications about the subjects. I have read those publications and

filtered the useful information and combined that information into this paper. Furthermore I

wrote some conclusions about the methods of calculation.

With this paper, I hope to achieve that small firm managers get a better idea of both the VaR

and the CFaR and how those measures can be calculated. So that in the future companies can

calculate and thus handle their risk better than they do now.

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Table of contents.

Chapter. Title. Page.

1. Introduction 4 2. Literature survey 6 2.1 When does one need to measure firm market risk? 6 2.2 What is VaR? 7 2.3 How is the Value at Risk calculated? 9 2.3.1 Historical simulation 9 2.3.2 Delta-Normal Approach 11 2.3.3 Monte Carlo Simulation 14 2.3.4 Which method is most practical in use? 15 2.4 What is Cash Flow at Risk (CFaR)? 16 2.5 How is Cash Flow at Risk calculated? 16 2.5.1 Bottom-Up method 16 2.5.2 Top-down method 17 2.5.3 Which of the methods is most practical in use? 19 2.6 Why or why not is the top-down method usable for calculating the

VaR? 19

3. Example of calculating VaR and CFaR 20 3.1 Calculating the Value at Risk using historical simulation method 20 3.2 Calculating the Cash Flow at Risk using the top-down method 22 4. Conclusions 24 References

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1. Introduction

Due to globalization the „financial world‟ is becoming smaller. Therefore proper risk

management is becoming more important to companies. The exchange rate exposure, the

interest rate exposure but also the risk exposure taken by firms when they enter derivative-

contracts, are a few examples of risk exposure firms face every day.

For risk managers there are many ways of measuring a firm‟s risk. One of the most used

measures of risk within risk management is the VaR (Value at Risk). This is a way of

measuring the risk exposure of market risk for firms. VaR is typically used by financial

institutes. Risk managers and investors use the VaR to measure the risk of firms or stock

portfolios. In that way they are able to choose a portfolio that has an acceptable risk rate and

still has a respectable rate of return. Which level of return and risk is acceptable differs for all

companies and investors.

Searching for that acceptable risk rate is really important for investors and managers of firms

since it enables them to reduce the risk of losing money and simultaneously creating firm

value because by reducing the risk, the managers make sure the continuity of the company is

guaranteed. If the company‟s continuity is guaranteed, investors might buy more shares of

that company. The role of risk measurement within risk management is that a company or an

investor can measure how much money is at stake.

Despite earlier research about the VaR, a misunderstood concept for firm managers especially

in relatively „small‟ firms is risk management. What if the CEO of the company wants to

know how much risk his company is facing? In that case you, as risk manager, can say „the

VaR of our company is $1.000.000‟ but there is a chance that your boss does not know what

VaR means.

In this paper I want to describe what VaR means, the mechanism of how it is calculated and

try to explain the measure easier so that it can be used and understood more easily by firm

managers. I also want to compare the VaR measure with other measures of market risk, such

as the CFaR (Cash Flow at Risk) and want to describe which measure is the most practical to

use in which situation. To answer that question I want to use the following research questions;

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- How does one use the Value at Risk and Cash Flow at Risk theories and are they the

„best‟ ways to measure firm risk?

o When does one need / want to measure risk?

o What is the Value at Risk (VaR)?

o How is the Value at Risk calculated?

o What is the Cash flow at Risk (CFaR)?

o How is the Cash flow at Risk calculated?

o Which of the models is most practical in which situation?

The Value at Risk and Cash Flows at risk can be calculated using the „Historical simulation

method‟, the „Delta-Normal approach‟ and the „Monte Carlo simulation method‟. The Cash

Flow at Risk has the additional „Top-Down method‟. I think the historical simulation method

is most practical method of calculating the VaR for relatively small companies because it is

the easiest manner of calculating the VaR. In order to calculate the Cash Flow at Risk, I think

the top-down method is most practical. Because using that method the risk manager does not

have to create a formula with all the factors that influence their cash flows. But to say if those

methods are „best‟ ways to measure the firm‟s risk is hard if not impossible to say. It depends

on the preferences and knowledge of the manager that needs to calculate them. But it is

certain that both are two reliable, complete and relatively easy ways of measuring firm‟s

Value and Cash Flow at Risk.

This paper consists of 4 chapters. Chapter 1 consists of a short introduction. In chapter 2 I

give a literature survey and will answer most of my research questions. In chapter 3 I

calculate the VaR and CFaR to measure risk mostly using real and sometimes using

hypothetical data. I would like to discuss the positive and negative sides of both measures

since I would like to investigate which one of the theories is the most practical to use in

different situations. Finally I want to conclude, in chapter 4, which methods of calculating the

VaR and the CFaR are most practical to use.

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2. Literature survey

2.1 When does one need to measure firm market risk?

Companies sometimes want to calculate how much risk they bear with their business. Two

ways of measuring firm risk are the VaR (Value at Risk) and the CFaR (Cash Flow at Risk).

Companies calculate the Value at Risk to guarantee the continuity of their company which

can lead to more investors buying assets of that company which can lead to an increase in

firm value.

To give an example, the Value at Risk with a 5 percent confidence level and a time horizon of

1 month is €5,000,000. In that case the company also needs €5,000,000 „stashed away‟ to

prevent any financial trouble. The confidence level and time horizon are explained later in this

paper.

Some firms, for example banks, investment banks, pension funds or other financial

institutions, continuously calculate the risk they bear. Other firms, for example non financial

institutions, calculate it less often, for example once per month. They do this less often

because of the smaller and often less volatile portfolio they have. If firm managers think the

risk is too high, they can take steps to reduce that risk within acceptable proportions. In order

to do so, they can use, for example, financial derivatives or other risk reducing steps to reduce

firm risk such as moving costs and profits to countries with the same currency. After they

took those risk reducing steps, they want to measure their risk again to check whether their

risk is actually reduced.

For example, imagine that you work for a relatively small public utility housing enterprise.

The independent accountant that handles the yearly audit of your financial statements advises

you to enter some financial derivates to reduce the interest risk the enterprise is facing. He

tells you that the VaR the enterprise faces is €2.500.000 and that the CFaR is €1.500.000. It

sounds like your company is in real financial distress. You will calculate the VaR and CFaR

yourself and come to the conclusion the accountant is right. So you enter the derivatives and

you calculate your risk again to check whether the firm risk has decreased.

Reasons of knowing a firm‟s CFaR are: “1. Capital Structure Policy, 2. Risk management

Policy” (Jeremy C. Stein et al. (2000)).

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The first reason, Capital structure policy, means that with measuring a company‟s CFaR one

can determine if a company has too much or too little debt. If the volatility of cash flows is

relatively low, the CFaR is also relatively low and the company faces little risk. They might

be able to increase their debt position to benefit more from the tax advantages and have more

cash to invest. But if the volatility of cash flows is relatively high, in that case the CFaR is

also relatively high and the company faces more risk. If they are able, it might be interesting

to reduce their debt position to guarantee the continuity of the company. The second reason,

Risk management policy, is named because a company‟s management wants to know if their

risk management strategies worked out as intended. The management wants to know how

much money their strategies have cost them and how much money they have yielded. Do the

benefits of risk management exceed the cost of those strategies?

In my opinion a third reason to calculate the Cash Flow at Risk is, such as the Value at Risk,

to guarantee the company‟s continuity. If the company keeps producing positive cash flows at

all times, they can invest that money into new projects, continue to grow and thereby

guarantee their continuity and keep their lead due to competitive advantage.

Some companies never calculate their risk bearings, this may be because the managers think

they do not need to calculate it or it may be because sometimes small firm managers (with

emphases on managers of small firms) do not know what VaR and CFaR mean and how they

are being calculated. In this chapter I am going to describe what those measures mean and

how they can be calculated.

It is important that it is known how both are being calculated because it might be very

important to know how much risk the company is facing, if a derivative does reduce the firm

risk and if so, with what amount the risk is reduced.

2.2 What is VaR?

VaR (Value at Risk) is first mentioned in the late 1980‟s to measure portfolio risk of large

financial institutes such as investment banks. In 1994, JP Morgan gave value at risk a market

standard which helped the VaR grow enormously. Now it is used worldwide by financial

firms, investors and the use is starting to grow by non financial companies.

Value at Risk is a measure to help investors, managers etc. interpret the maximum of losses

their investments bring along. VaR gives the manager a number in Euros or Dollars or other

currencies. That amount is the maximum loss a company or investor can face resulting out of

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a normal distributed market. And because VaR only consists of one number it is easy to use in

meetings hold by the board of directors, when the meaning of VaR is known by all that are

involved in those meetings.

According to Darrel Duffie and Jun Pan (1997) “Measure the extent of exposure by trade,

profit center, and in various aggregates” is one of the objectives in managing market risk. The

Value at Risk is a way of measuring that exposure by trade. To use VaR, a time horizon (t)

and a confidence level (p) need to be chosen. The Value at Risk (VaR) can be interpreted as

such; the VaR is the loss a company can face over the chosen time horizon (t) with the

probability 1 – p, were p is the chosen confidence level.

For example, a public utility housing enterprise has entered some financial derivatives to

reduce their firm interest risk. The CEO of the enterprise wants to know the firm risk. The

CFO calculates the VaR and will, for example, use a time horizon of one week and a

confidence level of 95%. Then when the CFO tells the CEO “our VaR is $1.000.000” it

means that the loss of the enterprise will exceed $1.000.000 in one week with a probability of

5%.

When calculating the VaR the user is free to choose whatever time horizon or confidence

level he wants. Obviously when the time horizon is longer, the VaR will be higher. And when

the confidence level is higher, for example 99%, the VaR will also be higher. This is all based

on a normally distributed market. Typically used confidence levels are 1, 2.5 and 5 percent

and most used time horizons are 1, 2, 10 days (workdays) and 1 month (Thomas J. Linsmeier

and Neil D. Pearson 2000). The time horizon depends on the type of company the VaR is

measured for. Due to the higher trading volume of financial firms, financial firms need to

measure risk more often, sometimes even more than once per day, and with a higher

confidence level compared to non financial firms.

In order to calculate the Value at Risk, the risk manager or investor need to identify the return

rates of the individual stocks in the portfolio, the prices of those individual stocks and with

those data one can calculate the value of the portfolio. In some cases the manager or investor

needs to add more variables such as the exchange rate between two currencies. Which

variables are needed depends on by which variables the market value of the portfolio is

affected (Thomas J. Linsmeier and Neil D. Pearson (2000)).

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For example, company A has signed a contract to deliver 1 million Dollars in 2 months (61

days). In exchange for those 1 million Dollars company A will receive 1.2 million Euros. In

that case the variables that influence the market value of that contract are: the spot exchange

rate (Dollars/Euro) of the contract (S), the 2 month interest rate of the Dollar (rD) and the 2

month interest rate of the Euro (rE).

The formula for the mark to market value of the contract in the example will be:

where S in this formula denotes the expected spot exchange rate of, in this case, the two

currencies, rE denotes the expected interest rate of the Euro and rD denotes the expected

interest rate of the Dollar. In chapter 4 I will present some calculations based on real data1.

2.3 How is the Value at Risk calculated?

There are three common methods of calculating VaR, the „historical simulation‟, the „delta-

normal approach‟ and the „Monte Carlo simulation‟ (Thomas J. Linsmeier and Neil D.

Pearson (2000)).

2.3.1 Historical simulation.

In order to calculate VaR according to the „historical simulation‟, it is required to make some

assumptions about the distribution of the market factors involved in the calculation.

In this approach it is necessary to use historical data about the exchange rates of the in the

portfolio used currencies and the interest rates of the used currencies. In that way it is possible

to calculate the expected mark-to-market value of the portfolio based on historical data. And

with those mark-to-market values one can calculate the expected profits and losses on the

portfolio value. One can make a distribution of those profits and losses (similar to the figure

on the next page) and with the confidence level, agreed on forehand, it is possible to read the

VaR in the distribution.

1 The data that is used in order to calculate this, is found using DataStream.

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The distribution below shows the frequency of all the profits and losses in market value of the

portfolio. In this example, the 5 percent biggest losses is the VaR and this is pointed out with

the green arrow.

Distribution of profits and losses, necessary for calculating the VaR.

To determine the VaR by using the historical simulation approach, it is necessary to perform

five steps.

Step 1. Identify the factors that influence the market value of the portfolio. Such as the

formula in „equation 1‟.

Step 2. Search for historical values of the factors that influence the market value. The

more records, the more reliable the outcome will be. The values will be used to calculate the

market values named in step 1 and 3.

Step 3. Calculate the expected profit and losses in comparison of today‟s portfolio for

each record found in step 2. With using the values found in step 2 one can calculate the daily

market value of the portfolio. Once the hypothetical daily market values are subtracted from

the actual value of the portfolio the daily losses and profits are calculated.

Step 4. Sort the expected losses en profits in order to make the distribution that looks like

the distribution shown in figure 1.

Step 5. Use the sorted outcomes to make the distribution and see what loss is exceeded

with (for example) 5 percent certainty. The value that belongs to that 5 percent is the actual

value that is at risk (VaR). That loss can be interpreted as follows, „we can say that the loss

our company will have to bear with a probability of (for example) 5% (5 out of a 100 times) is

at least $x,xxx,xxx‟.

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Since a portfolio does not only hold one type of derivate but (often) the portfolio is more

diversified, some of the steps are slightly different. As mentioned earlier, step 1 needs to be

extended because the market value of the portfolio depends on much more market factors

when there are more different derivatives involved. The daily losses and profits based on

historical data have to be summed up before they are ordered from highest to lowest (Thomas

J. Linsmeier and Neil D. Pearson (2000)).

Why or why not the historical simulation method?

Why is the historical simulation method to calculate the VaR used that often? An answer to

that question can be the following; the VaR is relatively simple to calculate using this method,

it is possible to use portfolios that include options. It is also rather easy to implement if there

are past values of the relevant market factors available. Furthermore the results are relatively

easy to understand by other managers of the firm. But, if financial history is not normally

distributed or available, this approach could produce misleading information which could lead

to erroneous decisions by firm management concerning the company. Also I think this

method requires more effort to calculate if the portfolio is dependent on more market factors.

Because all those factors have to be determined before one can calculate the VaR using this

method.

2.3.2 Delta-Normal Approach.

In the Delta-normal approach the assumption is made that the market factors used in a

portfolio are multivariate normally distributed. By using that assumption, it is possible to

determine the distribution of the mark-to-market profits and losses. As all the profits and

losses are obtained, it is possible to determine what loss will equal or exceeded at, for

example, 5 percent of the time. Once that value is determined the VaR with probability 5% is

known. (Thomas J. Linsmeier and Neil D. Pearson (2000)).

In this approach the VaR is calculated by using the formula shown in Equation 2: 2

2 Thomas J. Linsmeier and Neil D. Pearson (2000)

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To make it less difficult I assume that, in this example, the expected change in portfolio value

is zero. Moreover this assumption is often made when there is a relatively short holding

period or a short time horizon and means that the portfolio will not be changed during the

time horizon. If the portfolio value changes, perhaps because of adding „new‟ shares to the

portfolio, the calculation needs to be redone.

If the standard deviation in this example is €45,000 the VaR in this example is as follows:

Since the expected change in portfolio value is very often assumed to be zero, the most

important variable in this formula is the standard deviation. This variable depends on the

standard deviations in all individual stocks and/or derivatives in the portfolio. It is also

important to know how they correlate. Because of the fact that a portfolio often exists of many

individual stocks and/or other derivatives, it is almost impossible to know all the individual

standard deviations and the correlations of them. Therefore a replicating portfolio is made.

That portfolio, a rather small portfolio, exists of stocks/bonds and a risk free loan, that

replicating portfolio needs to have the same risk level and rate of return as the original

portfolio. With that replicating portfolio the VaR is then calculated.

There are several steps to take when determining the VaR using the Delta-normal Approach.

Step 1. It is important to identify all relevant market factors and their standardized

positions. Then those positions have to be compared to a forward contract. In order to

calculate the standardized positions, it is necessary to know the relevant market factors.

In the following example I use the same situation as described before. First I have to know the

exposure to US$ interest rate. It can be calculated using the formula shown in Equation 4.

Then I need to know the value of the Euro part of the agreement in US$. This is calculated

using the following formula.

The fact that Y2 is equal to Y3 is because they both represent the value of the Euro part in

US$.

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Step 2. During this step one needs to make the assumption that the percentage changes

in the market factors mentioned in step 1 are normally distributed. I then estimate the values

of that distribution. The standard deviations and correlations needed for calculating the VaR

will need to be listed. They can be requested for example by investment banks or institutions

such as Reuters.

Step 3. This step is used to determine the standard deviations and correlations of the

standardized positions calculated in step 1. If a standardized position changes with 2 percent

when the attendant market factor changes with 1 percent, the standard deviation of the

standardized position is twice as big as the standard deviation of the underlying market factor.

Step 4. Once the standard deviations and the correlations of the standardized positions

are known, one can calculate the real portfolio variance and standard deviation. And with

those variables it is possible to calculate the VaR of the portfolio. The variance of the mark-

to-market portfolio can be calculated using the following formula3:

Assume that portfolio = €20,000. Then the VaR has to be calculated as follows4:

Why or why not Delta-Normal approach method?

First of all, the Delta-Normal approach is rather easy to implement for portfolios restricted to

currencies if there is any capable software available and if the information that you need is

available such as volatility of all the shares within the portfolio. If that software or the

information it is not available it is not that easy to implement. It also becomes more difficult

to implement if the portfolio gets bigger and contains more different financial products.

Moreover this approach is rather difficult to explain to other firm managers. And like the

historical simulation method this approach could produce misleading information if financial

past is not normal. Furthermore it is not always possible to create a suitable replicating

portfolio which has the same level of risk and level of return the original portfolio has.

5 + 6 Thomas J. Linsmeier and Neil D. Pearson (2000)

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2.3.3 Monte Carlo Simulation5.

This method has a lot of resemblance with the historical simulation method. The difference is

that with the historical simulation method, expectations are based on historical data. With this

method, the Monte Carlo Simulation, the expectations are based on statistical distributions

that give an approximation of the possible changes in portfolio value. With help of a

computer, many random changes in the market factors are made. Due to that the mark-to-

market value of the portfolio changes constantly. These hypothetical changes will produce

many hypothetical profits and losses on the portfolio. By using those/these profits and losses

the VaR can be calculated in the same way as the historical simulation method.

Also the Monte Carlo Simulation has a few steps which lead to the Value at Risk.

Step 1. The first thing to do is to search for the market factors that are relevant for your

portfolio. Obtain, with those factors, a formula by which the mark-to-market value can be

calculated. This step is the same as step 1 of the historical simulation method.

Step 2. In this step one needs to choose a distribution for the variation in market

factors that influence the mark-to-market values. The risk manager is free to choose whatever

distribution he likes but usually the normal distribution is used.

Step 3. The next step is to use a random number generator which generates a lot of

(more than 1,000 or even more than 10,000) hypothetical values of market factors. With these

changes and the formula obtained in step 1, all the mark-to-market values can be calculated.

Step 4 and step 5 are equal to step 4 and 5 in the historical simulation method.

Why or why not the Monte Carlo Simulation method?

First of all, because of the fact that a computer generates the random numbers, with this

method it is relatively easy to add more variables when the portfolio gets more diversified and

complicated. That is one of the most obvious differences with the historical simulation

method. Furthermore this method is still usable when financial past is not normal. But due to

the computer system it is not always easy to implement and it can be expensive for smaller

companies.

5 Thomas J. Linsmeier and Neil D. Pearson (2000)

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2.3.4 Which method is most practical in use? Historical simulation Delta-Normal approach Monte Carlo simulation

Many different and

complicated financial

derivatives.

XX X XXX

Easy to explain? XXX X XX

No historical

information present?

- XX XXX

Easy to implement? XXX X XX

Advantages and disadvantages of VaR approaches.

The more X‟s there are in a box, the more suitable that approach is.

To say which of the three models is best, is not possible. As is shown in Table 1, it depends

on the type of portfolio you have. Does your portfolio consist of many different and

complicated financial products, such as many different options, then the historical or Monte

Carlo Simulation is probably the best way to calculate the VaR. If it is most important to

make your calculations clear to other firm managers, the historical simulation method is the

best. If no historical information is present, then the Delta-Normal or Monte Carlo simulation

methods seem to be the most practical to use. The choice the risk manager has to take when

choosing the methodology depends on what he thinks is most important for the company he

works for. I personally think the historical simulation method is most practical for smaller

companies who do not have to calculate the VaR that often. Because the information needed

to calculate the VaR is available in most cases. Furthermore the calculations are rather easy if

that information is indeed available, for an example of the calculation see chapter 3 of this

paper. For companies that have to calculate the VaR more than once per day, I think the

Monte Carlo simulation method is most practical to use because the computer system quickly

generates the changes in market value of the portfolio. An overall disadvantage of the VaR

measure is that it is assumed that the normal distribution provides a realistic view of the

portfolio return distribution. In reality the tails of the distribution are often „fat‟ what means

that the 5 percent gives a distorted picture of the reality. A possible solution to that problem is

to use the Expected Shortfall method. Instead of the minimal loss the company faces with a,

for example, 5 percent possibility, the average loss with that confidence level is used.

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2.4 What is the Cash Flow at Risk (CFaR)?

An alternative for the Value at Risk is the Cash Flow at Risk. Cash Flow at Risk (CFaR) is

used by firms to measure the risk of not receiving the expected cash flows or receiving less

than expected. A distribution of operating cash flows over a time horizon in the future is

made. The distributions can be used to obtain information about the worst case scenario‟s a

company can have regarding their cash flows. The outcome of the Cash Flow at Risk can be

interpreted as: “with what value will my cash flows decrease with a certain confidence level

(in percentages) over a certain time horizon?”

The calculation methods of the Cash Flow at Risk are almost the same as the Value at Risk.

The main difference is that Cash Flow at Risk uses the expected cash flows instead of using

market values of the portfolio. It is used by many different companies but especially by non-

financial firms. Financial firms use the VaR more often because they typically have many

portfolios with financial derivatives, stocks or other financial products. Nonfinancial firms

often don‟t have those portfolios, their continuity typically depends more on cash flows.

That‟s the reason why non financial firms more often use CFaR as risk measure.

2.5 How is the Cash Flow at Risk calculated?

There are two main methods of calculating the Cash Flow at Risk. First there is the Bottom-

Up method and secondly there is the Top-Down method. (Jeremy C. Stein et al. (2000)).

2.5.1 Bottom-Up method.

The Cash Flow at Risk can be calculated on the exact same way as the Value at Risk except

the Cash Flow at Risk is based on cash flows instead of market values. Typically the CFaR is

being calculated using the Monte Carlo simulation (Thomas J. Linsmeier and Neil D. Pearson

(2000)). The Monte Carlo simulation is used because of the many different variables that

influence the cash flows. But there are some important differences between using the Monte

Carlo simulation for the VaR and the CFaR. First of all, the focus is not on changes in market

value anymore. Now the focus of the calculation is on Cash flows. Hypothetical market

factors need to be combined with all different types of cash flows. With those combined

hypothetical market factors, one can create a hypothetical distribution similar to the VaR.

When using this method, all future cash flows have to be included in the distribution. This is

necessary because one does not only want to calculate the CFaR of cash flows that are

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affected by the financial derivatives a company has, but also the cash flows that derive from

„normal‟ operating.

Because operating cash flows depend on many different market factors, it is hard to determine

what market factors are necessary to calculate the CFaR. The market factors are more

diversified in comparison to the VaR calculation. Another factor that makes the calculation

more difficult is that the time horizon of the CFaR usually is significantly longer than the time

horizon used in calculating the VaR. Furthermore mostly the incentive of calculating the

CFaR is not to measure and control the risk a company faces, but to use it as a variable in

making decisions regarding new investments the firm wants to make.

During the bottom-up method, it is necessary to conduct research on all market factors that

influence the future cash flows of the company. When those factors are known, one needs to

search for data regarding those factors. If the data is found, the calculation of the Cash Flow at

Risk is similar to the calculation of the Monte Carlo simulation.

2.5.2 Top-down method.

Because of the fact that the factors that are needed for the bottom-up method are sometimes

very difficult to determine, Jeremy C. Stein et al. (2000) developed a top-down approach to

measure Cash Flows at Risk.

As an example I will use the television section of the Philips concern. They manufacture and

sell televisions and accessories. It is easy to understand that the cash flow of the TV section of

Philips depends on a large number of variables. All those variables bring along different risks

in cash flows.

When one is using the bottom-up approach as mentioned before, it is very difficult to

determine all those variables (in the VaR approach those variables are called market factors).

If one managed to determine all relevant cash flow factors and risks, he needs to try to

quantify those risks. When using the same approach as the bottom-up approach, some risks

can easily be omitted or some risks will be wrongly interpreted by firm managers. Because of

that wrong estimates of Cash Flows at Risk can be made.

Given those conditions, it is more logical to, for example, to directly look at Philips historical

cash flows and use that data to determine the new Cash Flow at Risk. In that case it is not

necessary to examine all different variables that influence the cash flows anymore because all

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those variables are already used when calculating historical cash flows. Because of that, one

does not have to create a new detailed model of the cash flows and all the variables that affect

that cash flow. That being said, it seems very favourable to determine the Cash Flow at Risk

using historical data of Philips cash flows. But in most cases it is only possible to use

quarterly cash flows, which leads to a very small set of observations. By using this small set

of observations this will not lead to a significant forecast of new cash flows or a predictable

Cash Flow at Risk. A possible solution to that problem is to use a group of companies that are

comparable to Philips. If a group of, for example, 20 companies is made, the number of

observations will grow significantly. In “A Comparables Approach to Measuring Cashflow-

at-Risk for Non-Financial Firms, (2000)” Jeremy C. Stein et al. calls this method a „top-down,

comparables-based approach to C-FaR measurement‟.

The top-down method goes as follows: first the risk manager has to search for companies that

are comparable with, in this example, Philips. Those companies have to be compared with

Philips on four dimensions: 1. market capitalization, which means that the total value of

tradable shares of the company needs to be almost equal, 2. Profitability, 3. Industry riskiness,

the riskiness of the total industry needs to be almost equal, 4. Stock-price volatility, the

changes in stock-price (in percentages) needs to be almost equal.

Because the conclusions of the Cash Flow at Risk are directly based on historical changes in

cash flows, this method automatically produces an average Cash Flow at Risk.

A major disadvantage of using this method is when your company is atypical and does not

match other companies in the group, you might draw the wrong conclusion about the Cash

Flow at Risk. In other words, if one creates a group of 20 companies he thinks are similar to

Philips in order to calculate Philips‟s Cash Flow at Risk, and Philips‟s marketing division is

significantly better than the others, this is not included in the calculation. Another

disadvantage of the fact that historical information is used is that it is not possible to forecast

the change in Cash Flow at Risk when a company is changing their strategy. In those cases I

think the bottom up method, especially the Monte Carlo simulation, is the better methodology

to use.

When the manager finds all data (based on the four dimensions mentioned earlier) that is

necessary for the calculation, he has to make a distribution of all cash flows of all companies.

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The data that is most commonly used cash flows for the calculation are the EBITDA

(Earnings Before Interest, Taxes, Depreciation and Amortization) or the EBIT (Earnings

Before Interest and Taxes).

2.5.3 Which of the methods is most practical in use?

Advantages and disadvantages of CFaR approaches.

The more X‟s there are in a box, the more suitable that approach is.

CFaR can be calculated in the same way as the VaR, the advantages and disadvantages of

those calculations are the same (see the table above). But there is a fourth way of calculating

the Cash Flows at Risk. That fourth measure is called the „top down method‟. It is hard to say

which way of calculating the CFaR is best. If the company that is subject of the calculation is

a typical company and there is the opportunity of assembling data of „peer‟ companies, than

the top down method seems to be most practical in use. Because when using the Top-down

method, the manager that calculates the CFaR does not have to determine all the factors that

influence the cash flows. The manager only has to find the necessary information from „peer‟

companies. But if the company that is subject of the calculation is an atypical company, it is

hard and if not impossible to assemble data of „peer‟ companies. In that case, the Monte Carlo

simulation seems to be best.

2.6 Why or why not is the top-down method usable to calculate the VaR?

At first you might think „why not use the top-down method when calculating the VaR?‟ I

think the answer to that question is hard to give. It depends on what the manager of the firm

wants. If an overall impression of the firm‟s portfolio risk is sufficient, than I think the top-

down method can be of use. But the Value at Risk is often used to measure risk of a portfolio

that consists of more than one financial product. In such a case the manager might want to

know which of the products bears most of the risk. If that is what the manager wants to know,

Historical

simulation

Delta-Normal

approach

Monte Carlo

simulation

Top-down method

Typical or atypical

organization?

Atypical Atypical Atypical Typical

Easy to explain? XXX X XX XX

No historical

information present?

- XX XXX -

Easy to implement? XXX X XX XX

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I think the top-down method is not of use because it only provides an overall look at the

portfolio. In most cases, when the managers want to know which product bears most risk, I

think one of the bottom-up methods is better to use to calculate the VaR. Because the first

thing the manager needs to do when using one of those measures is to derive all market

factors that influence the portfolio value. When that is known the manager can also derive

what factor bears the highest risk and thus what financial product bears the highest risk.

Furthermore I think it is not necessary to use the top-down method in order to calculate the

VaR. In many cases, especially for small firms who often have small portfolios, most of the

information to make a distribution of profits and losses on portfolio value are rather easy to

find.

3. Example of calculating VaR and CFaR

To give an example of how to calculate the VaR and CFaR I have chosen to calculate the VaR

by using the historical simulation method. The reason why I chose that method is that it is

quite similar to the Monte Carlo simulation method. So with explaining one method it

becomes clear how to use two methods. Furthermore those are the two methods I think are

most uncomplicated to understand by managers of small firms who need to work with them.

In order to calculate the CFaR I chose to use the top-down method since the other methods are

calculated on the exact same way as for the VaR.

3.1 Calculating the Value at Risk using historical simulation method

Assume a forward contract of selling 10mln Euro (short position) for 11mln Dollar (long

position) in 3 months.

In the table below an example is given of how to calculate a hypothetical mark-to-market

value and with that value the profit or loss on a forward contract. I need to calculate these

profit and losses for all hypothetical data to calculate the 5% biggest losses to determine the

VaR.

Calculation of mark to market profit/loss on a forward contract..

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The table on the previous page shows the actual values of interest rate of the US Dollar, the

Euro and the actual value of the exchange rate on 3 different dates, the data is found using

DataStream.

The USD interest rate is found by using an USdollar 3 month treasury bill and the Euro

interest rate is found by using the EURIBOR interest rate. The first thing that is necessary to

do is finding the actual values of those nine variables. With those variables the historical

percentage change can be calculated using this formula:

Why do I use 14th of November? That‟s because it is 100 working days before 30th of March.

In that case I can compute 100 observations to base my distribution on.

To get the hypothetical future values of those variables I used this formula:

(9)

With those variables, I can calculate the hypothetical future market value of the portfolio and

with that future market value I can compute the hypothetical profit or loss on the portfolio.

The table on the next page shows all profits and losses after they are sorted from biggest loss

to biggest profit. As can be seen, the 5 percent biggest losses exceed 188,000.00 Euro, so the

VaR this company faces with this portfolio is €188,886.19.

In this example the mark to market value today and the hypothetical mark to market value in

the future have to be calculated using the formula:

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Sorted profits and losses.

The data used to calculate the VaR is found using DataStream.

3.2 Calculating the Cash Flow at Risk using the top-down method

In order to calculate the Cash Flow at Risk, I chose to use the top-down method using

hypothetical data. It is possible to calculate the CFaR using the same approach as the VaR

only use cash flows instead of market values but if using one of those approaches it is

necessary to distinguish all factors that influence the cash flows. If your company is similar to

other companies in that industry, it is possible to use the top-down method.

Assume that the CEO of Philips wants to know the Cash Flow at Risk of the company‟s TV

division and that that sector is typical within the industry. The manager of that Division is

then going to search for other companies that are like Philips‟s TV division and do answer to

the four dimensions that need to be fulfilled (the four dimensions are described earlier in this

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paper). If the manager assembled the list of companies, he needs to determine all quarterly

cash flows of those companies. The more observations the more accurate the calculation will

be. The cash flows need to be adjusted to the size of the companies. A way of adjusting to size

can be to find EBITDA per share and multiply that by the total number of common shares

outstanding. All observations need to be listed from smallest cash flow to biggest cash flow.

In that way, a list is created similar to the list in the table below. The 5 percent smallest cash

flows together form the Cash Flow at Risk within the next quarter.

Cash Flows of different companies necessary for the Top-down method.

In this case it can be seen that the CFaR this company faces is €42,800.71. That means that

with a probability of 5% this company can lose €42,800.71 of its cash flow over the next

quarter.

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4. Conclusions Value at Risk measures the risk of a company losing money on their portfolio of assets and

derivatives. It makes use of market values of all the assets, derivatives and other financial

products that the company holds in its portfolio.

The Cash Flow at Risk measures the risk of a company not to earn as much money as

expected. This measure makes use of cash flows instead of market values, therefore this

measure is called „Cash Flow at Risk‟.

The Value at Risk and Cash Flows at Risk can be calculated using the „Historical simulation

method‟, the „Delta-Normal approach‟ and the „Monte Carlo simulation method‟. The Cash

Flow at Risk has the additional „Top-Down method‟. I think the historical simulation method

is the most practical method of calculating the VaR for relatively small companies because it

is the easiest way of calculating the VaR. Another usable and relatively easy way of

calculating the VaR is the Monte Carlo simulation method. This method resembles the

historical simulation method but makes use of a variable generator to create the required

distribution. Therefore I think this method is more practical of use when the VaR has to be

calculated more often and if the portfolio consists of more different variables.

In order to calculate the Cash Flow at Risk, I think the top-down method is most practical.

Because using that method the risk manager does not have to create a formula with all the

factors that influence their cash flows. If historical information is not available, I think the

Monte Carlo simulation method is best to calculate the cash flows because hypothetical

changes in all different factors that influence the cash flows are quickly generated using the

computer controlled variable generator.

To say if those methods are „best‟ ways to measure the firm‟s risk is hard to say, if not

impossible. It depends on the preferences and knowledge of the manager that needs to

calculate them and even more on the situation the company is facing. But it is certain that all

are reliable, complete and relatively easy ways of measuring firm‟s Value and Cash Flow at

Risk.

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References

- Andrén, Niclas, Håkan Jankensgård and Lars Oxelheim (2010), Exposure-Based Cash-Flow-at-Risk for Value-Creating Risk Management under Macroeconomic Uncertainty, Journal of Applied Corporate Finance 17, 76-86.

- Artzner, Philippe, Freddy Delbaen, Jean-Marc Eber and David Heath (1999), Coherent measures of risk, Mathematical Finance 9, 203-228.

- Beaver, William, Paul Kettler and Myron Scholes (1970), The association between market determined and accounting determined risk measures, The Accounting Review 45, 654-682.

- Delbaen, Freddy (2000), Coherent Risk Measures on General Probability Spaces.

- Duffie, Darrel, and Jun Pan (1997), An overview of Value at Risk, The Journal of Derivatives 4, 7-49.

- Frittelli, Marco, and Emanuela Rosazza Gianin (2002), Putting order in risk measures, Journal of Banking & Finance 26, 1473-1486.

- Linsmeier, Thomas J, Neal D. Pearson (2000), Value at Risk, Financial Analysts Journal 56, 47-67.

- Stein, Jeremy C, Stephen E. Usher, Daniel LaGattuta and Jeff Youngen (2000), A Comparables Approach to Measuring Cashflow-at-Risk for Non-Financial Firms Journal of Applied Corporate Finance 13, 100-109.