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2012 Cambridge Business & Economics Conference ISBN : 9780974211428

A Simulation Model To Forecast Future Cash-Flows – A Financial Risk

Management Tool

Ralf Bernsau

Karlsruhe Institute of Technology (KIT)

Institute of Applied Informatics and Formal Description Methods (AIFB)

Karlsruhe, Germany

+49 176 32189761

[email protected]

Andreas Vogel



Karlsruhe, Germany

+49 721 60845393

[email protected]

Detlef Seese



Karlsruhe, Germany

+49 721 60846037

[email protected]

June 27-28, 2012Cambridge, UK 1

mailto:[email protected]




A Simulation Model To Forecast Future Cash-Flows – A Financial Risk Management Tool

ABSTRACT

This article describes a simulation model which enables the user to forecast the possible

trend of the companies’ Cash-Flow based on historical data, individual estimations,

multivariate regression and the Value-at-Risk concept. The simulation model is able to

simulate Cash-Flows for different individual scenarios and serves due to that as a financial

risk management tool. One interesting feature is that the model uses not just time series of the

relevant market parameters, the multivariate regression includes an additional extern

parameter. This parameter describes the influence of the environment on the future price

trends of the relevant market parameters. The implementation of the extern parameter follows

a random walk. Therefore, the model is not just focusing on a small number of main market

parameters, it also captures the development around these main parameters in one single

factor.

INTRODUCTION

The competition conditions for the manufacturing industry have changed considerably in

recent years. Due to the increasing globalization and the simultaneous fluctuations in

international financial markets, companies face new challenges. As a result of the stronger

integration of the economy and the consequent increase in volatility of commodity prices,

equities, interest and exchange rates, the financial risks of companies have increased.

Especially the recent past confirms that extreme market fluctuations occur at shorter time

intervals and as a consequence the financial position and stability of banks, industrial and



commercial companies and even of nations is constantly challenged. The financial risk

management is therefore an operational function which importance is increasing more and

more. The success or failure of companies in a challenging environment is essential for their

existence and global competitiveness.

Established on these facts, a lot of companies and academics, such as the National

Economic Research Association (NERA) with the cooperation of the Harvard professor

Jeremy Stein (2000) or the RiskMetrics Group by Alvin J. Lee (1999), developed several

Financial Risk Management Tools to simulate future price trends of stocks, commodities,

interest and exchange rates and so forth. However, the opinions and approaches of these

academics and professionals differ. That’s why Jan Duch (2006) subdivides the different

approaches in two groups. One group is called the Top-Down approach and the other group is

called the Bottom-Up approach.

According to Jan Duch (2006) the aim of the Bottom-Up approach is to make a statement

about the probability that a certain future Cash-Flow adopts a specific value due to the

influencing factors. Attributed to the required knowledge of the business-related effect

relationships, the approaches are called internal models. Additionally, the approach is closely

based on the Value-at-Risk concept. Therefore, it is necessary to implement these models to

start with searching and identifying market-price-based risk factors, which have a significant

impact on the Cash-Flow. Ongoing, the identified financial risks are analyzed by using the

exposure maps according to their importance for the outcome. After that the identified risks

are brought into a functional relationship to simulate the future Cash-Flows. Finally, the

calculation of the Cash-Flow-at-Risk is realized with a user-specific confidence level. On one

hand, Chris Turner (1996) emphasized that the Bottom-Up approach is simple in the way of

the intuitive interpretation of the result. It returns a value, which is exceeded with a given

probability. In addition, it is possible to specify the risk of the probability of deviation from an



expected value or a quasi-reliable Cash-Flow. On the other hand, Turner states that the

Bottom-Up models can be very complex. The calculation depends very much on the interplay

of the various influencing factors. It is necessary to compute correlations between the

individual parameters, which means that a big data base of time series has to be available.

Furthermore, according to Turner (1996) you have to take in consideration how well the

identified risk factors explain the Cash-Flow. A couple of various different methods are

available to forecast future market prices. One method, which is analyzed by J. Kim, A. Malz

and J. Mina (1999), is based on implied volatilities for short time periods by using

deterministic forward prices. Moreover, according to Lee (1999) a simulation with a random

walk can be implemented, based on historical moments of the distribution of the influencing

factors. Finally, Lee (1999) of the RiskMetrics Group presented an estimation of the Cash-

Flow development by using econometric methods with a so-called Vector Error Correction

Model (VECM).

The perspective of the Bottom-Up approach is not undisputed, because of the many

interdependencies in terms of complexity. Stein (2000) emphasized that the danger might be

large, to observe measurable risks, but easily to ignore other non-financial risks. Unlike the

Bottom-Up approaches, the Top-Down approaches don’t consider separate individual risk

factors. The first Top-Down approaches are the regression models and introduced by Bartram

(1999). The regression models put the Cash-Flow in direct focus. Thus a study of individual

or even entire risk exposures is also possible for non-company employees. The basis is the use

of exclusively public capital market data. Therefore, based on Bartram the regression models

are also called external regression models. The estimation of the volatility of the Cash-Flows

is based on historical deviations. Through this procedure all risks, not only financial, also

operational influences are taken into account, mentioned Stein (2000). Internal Cash-Flow

data is either not available or it is in insufficient amount. Therefore, to explain the variation,



the models resort to regression analysis for example, with the stock returns or various capital

market data. Another Top-Down model is the benchmark model, which estimates on

historical Cash-Flow distributions and even to some extents from Cash-Flow distribution of

competing companies, the variations. This benchmark model was developed by U.S.

companies. The goal of this approach is to picture a company-wide aggregate risk, without

using individual market parameters as the previous models. Simply put, it compares historical

Cash-Flows from other companies in the same sectors with the company looked at, and then

draws conclusions about possible future Cash-Flow trends. Therefore, no detailed knowledge

is required about internal relationships in order to make a statement about the risk exposure of

the company. The consulting firm National Economic Research Associates (NERA) from

New York developed in 2000 such a model called C-FAR, where C-FAR stands for Cash-

Flow-at-Risk. Like the two previous simulation models this model is also based on historical

Cash-Flow time series. Although Stein (2000) highlighted in his paper, that the general

problem is, that there are not enough empirical Cash-Flows existing, especially due to

changes in corporate structure or company size.

The model, which will be explained in this article, belongs to the Bottom-Up approach.

The aim of that developed and implemented model is to anticipate future market movements

and to measure the hazard on company’s financial strength and stability. The model is able to

consider many single factors, which directly or indirectly influence the company’s wealth and

economic strength. As a model stays always a model and can never predict the future with

absolute certainty, nevertheless it is fundamental for global and international as well as

national active companies to manage their risks. The model gives a good indication on

possible future situations and simulates different economical scenarios. The company using

the modeli will be able to deal with their risk and to get a better overview about coherences,



market factors and the consequences of their movements to evaluate the simulated world

against reality.

The model uses regression analysis and historical time series. However, none of the

outlined models are able to describe the development of the environment and include the

trend in the prediction of future prices.

The article starts with explanations and descriptions of our simulation model and will

continue with providing analyses and the evaluation of the model. The summary will

conclude the described explanations and analyses of our simulation model.

THE MODEL

Portfolio optimization is primarily understood as the ability to simulate and evaluate a

combination of several products. For economic reasons, it is realistic that a company produces

and sells several products. Every company is able in our model to produce multiple products

with different features. On one hand, the company has to determine for each product in its

portfolio, the income elasticity and price elasticityii. On the other hand, a product-based

allocation of sales, the expected value and standard deviation of the sales need to be indicated.

Furthermore, each product is assigned a price, which is ideally above the production costs in

order to realize a profit margin. Finally, each product must be assigned a breakdown in

percentage proportion of the raw materials required. Through that, different products can be

simulated with different features.

Through the implementation of the individual products, the total sales of a company

results from the sum of the sales of the individual products. The single turnovers arise from

the sales of the products in Germany. The price of each product develops analogous to the



Consumer Price Index (CPI) and automatically adjusts to the corresponding demand. Thus,

the formula to show the price trend is:

Product Price x ,t=Product Pricex ,t−1∗CPI t

CPI t−1

(1)

with x : Product

The turnover itself is derived from the sales of the previous period multiplied by the

domestically economic development, the gross domestic product (GDP), is due to the income

elasticity of demand. In addition, the turnover is influenced by the pricing of the product and

weighted by the price elasticity. Alike the model considers diverse volatilities in sales, which

can occur due to production, demand or external reasons. Fluctuations in production may

arise for example, through line stoppage, staff absences or raw material supplies. This

fluctuation is realized through the generation of a normally distributed random variable using

the polar method of George Marsagliaiii. Thus, the calculation of product-specific sales results

from the formula:

Salesx ,t=Salesx ,t−1∗[1+( GDPt

GDP t−1−1)∗ϵ x, e]∗[1+( CPI t

CPI t−1−1)∗ϵ x, p]∗[1+RandomVariable (μ ,σ )]

(2)

with x : Productϵ x, e : Income elasticity of t he product xϵ x, p: Price elasticity of t h e p roduct xμ : Expected value of t he salesσ : Standard deviation of t h e sales

The company also incurred product-specific costs, which are explained in terms of

material costs. As already mentioned, each commodity is traded in US-Dollar. Furthermore,

we make the assumption that the storage is refilled with raw materials at the beginning of



each quarter to keep the storage constant. It will be bought just as much material as is required

in order to realize the simulated sales. Thus, the product-specific material costs result from the

sum of the portions of each commodity multiplied by its price and then adjusted for the EURUSD

- exchange rate.

Material Costs per Unit x ,t=∑i=1

n

Fractioni∗Pricei , t(USDTons

)

Exc hange Rate t(EURUSD

)

(3)

with x : Producti : Market Parameter (Commodities)

The three above derived formulas are taken together and described as a so-called

exposure map. This exposure map is individually constructible for each product of a

company. For consideration of the overall risk, the risk potential of the various influencing

factors or market parameters on the Cash-Flows needs to be identified. To use the Cash-Flow-

at-Risk it is necessary to determine the sensitivity to changes in the considered market

parameters and for these circumstances the exposure map is used. According to Duch (2006)

the exposure map is an economic mapping, which derives its focus on changes for the

company's profit, due to changes in the revenue . Thus, the Cash-Flow for a product results by

using the formula:

CF x ,t=( Product Price x ,t−Material Costsx ,t )∗Salesx ,t (4)

with x : Product

Through the consideration of multiple products it is necessary, to calculate the total

turnover of the company in a quarter, to add up the individual product-specific Cash-Flows.



OCF t=∑x=1

x

CF x ,t

(5)

with CF x ,t : Cas h−Flow for Product x

The five mentioned formulas are the base to calculate the Cash-Flows of a company. As

outlined in the preparation of the exposure maps, we identified four key market parametersiv,

which are essential to simulate the future Cash-Flows of an industrial enterprise. There is the

gross domestic product (GDP) of the Federal Republic of Germany, the consumer price index

(CPI), the long-term interest rate EURIBOR and the EURUSD - exchange rate.

The gross domestic product (GDP) reflects directly the added value of the observed

economy in the corresponding quarter. However, the problem with this measure is the

frequency of data collection. Therefore to achieve a high statistical reliability, it is necessary

to use a relatively long observation period of the past. Nevertheless, the quarterly GDP

represents the key indicator for the quantification of the economy. In addition, we use

seasonally and calendar adjusted values of the GDP, which the Federal Statistical Office of

Germanyv makes available to avoid distortions of the actual economic development by

seasonal influencesvi . By stating to the quarterly values in determining the economy, all other

parameters need to be stated to quarterly values as well. This raises the fundamental question,

whether we rely on average values of the quarters, or on a daily rate during the quarter.

According to Siebert (2010) a calculation of quarterly averages distorts the actual volatility of

the price developments, that’s why we use the closing price of the last trading day of each

quarter.

The next key indicator is the exchange rate. Based on the quarterly data supply of the

GDP, the exchange rate will also be evaluated at the end of every quarter. The euro reference



rates of the European Central Bank (ECB) deliver the needed data of the EURUSD - exchange

rate. These euro reference rates are determined and published each business day through the

participation of the European Central Bank and the National Central Banks and reflect the

market price of the euro against major international currencies, stated Siebert (2010). The data

series for the euro reference rates are accessible on the website of the German National Bankvii

.

It is also for the interest rate necessary to find a reference price, which reflects the general

interest rate trends. Here arises the problem that, unlike the exchange rate many differing

interest rates, for which banks lend money, are available. An appropriate index for the interest

rate development is the Euro Interbank Offered Rate (EURIBOR). The EURIBOR is a

reference rate, calculated by the ECB for time deposits in the interbank marketviii . This rate

refers, in contrast to existing competition interest rates, such as the London Interbank Offered

Rate (LIBOR), exclusively on the Euroix . Since the EURIBOR is calculated at different

maturities and serves as a reference rate for floating rate notes and swaps, its use provides the

representation for our interest rate. To map the corresponding long-term interest rates we

chose the EURIBOR with the longest duration, twelve months. The historic EURIBOR time

series are available on the website of the German National Bank. Like the GDP we use for the

interest rate the quarterly value of the daily closing price of the last trading day of each

quarter.

As part of this market model we made the assumption that changes in commodity prices

develop in line with prices in the economy. Against this background, the consumer price

index (CPI), which is determined monthly by the Federal Statistical Office of Germany, is an

accurate measure of consumer prices based on the Laspeyres price indexx. The CPI is used as

a benchmark in wage negotiations and is constituted as the central indicator for the



assessment of monetary developments in Germany. Furthermore, the changes in the consumer

price index or its internationally adapted form, called the harmonized consumer price index,

are a measure of inflation in Germany. As we saw with the GDP, is it also necessary for the

CPI to use seasonally and calendar adjusted values to avoid distortions of the actual

development. Therefore, like Siebert (2010) we also used the value of the CPI of the last

month of each quarter during the considered time period.

Once the metrics are defined to quantify the key market parameters, the influences among

the parameters need to be estimated. This turns out to be difficult, because on the theoretically

profound basis you can find out, which factors affect another factor. The problem is that you

cannot make precise statements about the strength and delay of the influence. Like the

conventional risk models, the forecasts of the market parameters are calculated from returns.

According to that, the influence of a parameter on another parameter is not based on the

absolute value but on the return. The relevant relations of the derived market parameters were

determined by using the theoretical principles. In addition, we used the t-statistics and the

analysis of the correlations based on time series, for supporting the given theoretical relations.

The correlation of two time series measures the significance of the direct influence of the

return of a market parameter in t-1 on the return of a market parameter in t. The t-statistics

measures the goodness of the gradient of the correlation and therefore rejects or supports the

observed theoretical principles and estimated correlations of the market parameters. The news

service Bloomberg provides the needed time series of the various market parameters. Beyond

that, we used time series from the first quarter of 1990 to the second quarter of 2011, to

provide a solid base of data to estimate influences and correlations between the market

parameters. For example, we assessed a direct influence of the exchange rate on the long-term

interest rate. The theory implies that expectations about the future exchange rate have a direct

impact on net foreign investments. These net foreign investments arise from the difference



between investments of residents abroad and of domestic investments of foreigners. In

absence of arbitrage the expectation of a re-valuation of the domestic currency leads to a

higher demand for domestic bonds. Through that context, the domestic interest rate falls and

the price of bonds rises. On the other hand, it is an expectation of a devaluation of domestic

currency. As a result, the investment in foreign money is attractive. This leads to an outflow

of capital to foreign countries. The reason for this observation is, that foreigners are now

investing in their own country and nationals in the foreign country, based on the higher

expected returns in the foreign country. Therefore, the net foreign investments decrease and

the demand of domestic bonds regresses, whereby the interest rate raisesxi. As a result of this a

connection between the development of the exchange rate and the development of the interest

rate is supposed. Additionally, the estimated correlation of the time series of the exchange rate

and the interest rate is supported by the t-statistics and therefore the estimated direct influence

cannot be statistically rejected.

We determined direct influences between the four key indicators and moreover a

relationship to the individual raw materials. The direct influences between all the relevant

market parameters are shown in table 1. The letter X implies a direct influence. The raw

materials we used to simulate different products in our fictive simulation are aluminium

(Alu.), copper, nickel and zinc. The times series of the four mentioned raw materials are also

provided by Bloomberg and are based on the time period of 1990 to 2011.

Once we evaluated all the relevant effect relationships between the relevant market

parameters, we define now a regression analysis, which will be implemented and applied at a

later point to give these relationships a real number in the context of a coefficient. The

primary scope of the regression analysis is the investigation of causal relationships, or the so-

called cause-and-effect relationships. In the simplest case, such a relationship can be

expressed between two variables, the dependent variable Y and the independent variables X.



The variables X and Y always correspond to the respective returns of a market parameter,

which can be determined in the simulation model. The multivariate regression approach has

the following formxii :

Y j=a0+a1∗x1+a2∗x2+…+ai∗x i+ek (6)

with j : Dependent market parameterY j : Estimation of t h e dependent variablesY−market parametera0: Constant Variablea i : Regressioncoefficient of t he Market Parameters ix i : Independent variable−Returnof t h emarket parameterek : Deviation of t he estimated value of t h eobservation value

It consists of the sum of the individual influencing market parameters, together with

respective regression coefficients. Due to the fact, that between the regression line and the

observed values deviations exist, it can be assumed, that there is no straight line on which all

the observed (x, y) – combinations belong to. The consulted market parameters are not

sufficient to describe the entire process of a specific market parameter. The influencing

variables which are not covered of the empirical Y- values are reflected in very low deviations

from the regression line. These deviations can be represented by a vector e, whose values ek is

known as residuals. Thus, Y is additively from its systematic components, the identified

influencing factors and the residual ek. The regression coefficients a i have an important

substantive meaning, they indicate the marginal effect of the change of an independent

variable on the dependent variable Y. The quantity of the regression coefficients should not be

regarded as a measure of the importance of that variable. The calculation of the regression

coefficients a i is based on the minimization of the sum of squared residuals.

Once all regression coefficients are calculated, it is now necessary to determine the

environmental influence. In the multivariate regression model, it is not possible to integrate

directly the environment, because there are no empirical variables and returns of the



development of the environment. The special feature of this simulation model is exactly the

basis of our approach, we determine the environmental factors as well as its impact. Based on

that, we imply the unexplained portion in the regression function as an influence with a

regression coefficient and a variable. To realize this approach, we use the multiple

determination R2. The multiple coefficient of determination is a global quality measure, which

indicates how well the dependent variable is explained by the regression model. The basis are

the calculated residuals. In order to assess these residuals, we need a benchmark. This

benchmark is calculated as the difference between the observations yk and the mean y.

Furthermore, it requires the scattering decomposition based on the total sum of squared

deviationsxiii. Thus, follows the calculation of the multiple coefficient of determination the

equation:

R2=∑k=1

K

( yk− y ) ²

∑k=1

K

( yk− y ) ²=Declared Spread

Total Spread

(7)

with R2 : Coefficient of Determinationyk : Values of t he dependent variablesyk : Determined estimated value of Y for xk

y : MeanK : Number of observations(k=1,2 ,.. , K )

The multiple coefficient of determination is a normalized value and represents values in

the interval [0,1]. The greater the proportion of the explained variation to total variation is, the

greater is the value of R2. The coefficient of determination can be determined as the square of

the correlation. However, in the multivariate case the estimated variables must be formed by

linear combinations of several independent variables. Therefore, R refers to a multiple

correlation coefficients. By considering the environment with the multivariate regression

model, we assume a bivariate context. According to this, the relationship can be expressed as:



ρextern , j=√1−R2

(8)

with R2 : multiple Coefficient of Determinationρextern , j : Correlation between t he environment

¿market parameter j

The formula approximates the correlation of the environment with the respective

multivariate regression model of each market parameter. The determined correlations are now

the basis for the derivation of the influences and regression coefficients for the environment.

However, one should bear in mind, that this is an approximation to the actual value.

To determine the influence coefficients aextern , j, we have to adjust the calculated

correlation with the standard deviation of the environment and the relevant market parameter.

Thus, the formula for calculating the influence of an exogenous variable on a market

parameter isxiv.

aextern , j=ρextern , j∗σ j

σ extern

(9)

with σ j : Standard deviation t hereturn of t he parameter jσ extern: Standard deviation t h ereturn of t h eenviromentρextern , j : Correlation of t heenviroment wit h parameter j

Because the environment returns are constructed as random numbers, the choice of the

standard deviation is arbitrary. In this context, the standard deviation of the environment

returns is set at one percent and the influence coefficients aextern , j are calculated according to

equation 9. Regarding the expectation values of the normally distributed environment returns,

the historical arithmetic average values of the corresponding market parameters shall be

considered, to reflect the historical trend of the market. For example, the chosen economic

indicator GDP, generally shows an empirical rising trend, which justifies the use of this trend.

For the final determination of the expectation value μ of the environment return we used the



previously determined influence coefficients. According to Siebert (2010) the expectation

value of the environment return has to be chosen in that way, that it explains the given

expected development of a market parameter, which cannot be completely described by the

considered influencing factors. As soon as we simulate different scenarios, we assume an

expected trend of a market parameter, and due to that the environment return will be adjusted

to that trend. If we don’t consider an individual trend for a specific market parameter, we

determine the expectation value of the environment return through the historical market

average of the corresponding parameter and the historical averages of the influencing factors.

Return j ,t=aextern , j∗μextern j ,t−1+∑i=1

8

ai∗Returni ,t−1

(10)

mit aextern: Influence of t h eenvironment on ja i : Influence of t h emarket parameter on i on jReturn j ,t : empirical averagereturn of parameter j∈tReturni ,−1 t : empirical averagereturn of parameter i∈t−1

Due to formula 10, the expectation value of the corresponding environment return can be

determined through the calculated influence coefficients and the historical average values.

Thus, the environment returns are given as normally distributed random numbers with the

standard deviation of one percent and with the expected value μextern , j−1. The normal

distributed random values are realized through the polar method of George Marsagliaxv.

Hence, all the basics to calculate the development of the various market parameters are

now given. The implementation results from the sum of the newly estimated regression

coefficients of each market parameter plus the influence of the environment. According to

this, the formula to simulate future returns of each market parameter is given by the weighted

sum of the yield of individual influencing factors and the rate of change of the environment,

which is simulated by generating a random number.



Return j ,t=aextern , j∗Returnextern j ,t−1+∑i=1

8

ai∗Returni ,t−1

(11)

mit aextern: Influence of t h eenvironment on ja i : Influence of t hemarket parameter on i on jReturni , t−1 : Returnof t hemarket parametersi∈t−1Returnextern j ,t−1: Returnof t h eenvironment for i∈t−1

On the basis of this multivariate regression analysis, the future price developments of the

individual market parameters are simulated and ongoing the Cash Flows are calculated with

the presented exposure map. Once the simulation model simulated a user-defined time period,

the model returns the Cash-Flow-at-Risk to an expected value of zero or a specified

benchmark.

The model itself has a very flexible character to simulate the regarded world. It’s

individual and company specific and can be expanded and supplemented by other relevant

factors. One suggestion of the model and its application are shown and illustrated in the

following chapter.

EVALUATION

To evaluate our simulation model, it is necessary to back test it. This is done through

stress testing, to estimate how a simulated portfolio of a company responds to extreme

economic conditions.. To do so, we have to follow two steps. First, we develop plausible

scenarios with market fluctuations. Then the evaluation of the portfolio with respect to a

given scenario follows. In this paper, the simulated portfolio includes a maximum of three

different products, which are composed from the given resources of the simulation model.

The three products are presented in the exposure map (table 2) and consist of four different



raw materials. The raw materials are aluminum, copper, nickel and zinc, which allow to

produce various metal products. These raw materials should constitute the basis of this

analysis. The pricing of a product is based on the partial prices of the raw materials and does

not include any additional fixed costs. The market fluctuations for the stress testing are

generated of the standard deviations and the corresponding expectation values of the market

parameters. Moreover, due to possible variations in sales on the corporate basis, the sales of a

product are controlled by its expected value and volatility. Fluctuations can occur in this

context by machine breakdowns, lacks of production means or technical know-how. In

addition, the company can not sell the goods in foreign countries; otherwise we have to

consider additional exchange rate risks.

The simulation period in all simulated scenarios is 16 quarters or four years. The choice

of the four years is due to the fact, that we consider a short-term cycle in the sense of Kitchin

(1923). The fluctuations in this Kitchin-cycle are caused by the storage and production of

companies, which leads to a reasonable observation period. However, also exogenous effects

can occur, such as wars, natural disasters or financial instability in the world's economies.

The validity of a simulation is thereby strengthened and interpreted as soon as it is

repeated several times. Only by this way it is possible to obtain a distribution of Cash-Flows,

which can be analyzed with the confidence level. To strengthen and to increase the

significance of a scenario we chose as part of the stress tests a number of 5000 simulation

runs. To calculate the Cash-Flow-at-Risk to a expected value of zero, we determined for all

scenarios a confidence level of 95 %. This means that with a probability of 95 % the future

Cash-Flows exceed the calculated Cash-Flow-at-Risk.

Once all required parameters are specified, the implementation of the various scenarios

follows. Subsequently the generated Cash-Flow distributions are analyzed by using

theoretical fundamentals and charts.



Standard and 20 % Volatility: In the first two scenarios, we consider the portfolios

with three different products. The layout of the products can be found in table 2. The first

scenario Standard uses the obtained average returns, correlations and regression coefficients

of the historical time series, to simulate future prices. In the second scenario Vola_20%, all

implied volatilities of all market parameters are increased by 20 %. This test is intended to

help analyzing how the model behaves with strong market fluctuations of all market

parameters.

The results of the simulations are shown in Figure 1. The Cash-Flow-at-Risk of scenario

Standard is less than the Cash-Flow-at-Risk for the scenario Vola_20%.

Furthermore, by increasing the volatility of each market parameter, the volatility of the

Cash-Flow distribution is higher. This observation fulfills the expectation. The variation in the

volatility of a market parameter describes the direct influence of the environment on the

current market parameter. With an increased volatility, the influence of the environment is

greater (Equation 9). The development of the environment is not predictable, because based

on the Polar-method the future development is generated by a random walk. Therefore, the

results show a possible plausible development at a higher volatility of the market parameters.

The small deviation between the Cash-Flow-at-Risk results probably stems from the fact that

the general development of the simulation model suggests a growing economy and thus an

increase in sales. Based on the assumption that the historical time series imply a positive

development of the economy and consumption, the distribution of the Standard scenario also

seems to be plausible. The products and in particular the prices of the products are conceived

in that way that in any case, the prices cover the variable costs and so have a positive Cash-

Flow.

Challenging economic conditions: So far we simulated a scenario based on historical

time series and one scenario with an increased volatility of 20 %. However, the observation of



extreme market volatility is of particular interest in the evaluation of the simulation model.

Therefore, we simulated in the following section, three scenarios that will test the simulation

model at extreme negative developments. The first scenario BIPnull reflects a prolonged

recession with no growth in the economy. The second scenario is MetalsUp which simulates

the impact on the Cash-Flow by using two times the expected price increase of the raw

materials. This scenario for example could arise by an increasing demand of metals from

developing countries.

The third scenario MetalsUp_SalesDown exacerbates the previous scenario by falling

sales of all three products by 20 % caused by internal conditions. Here machine breakdowns

or material defects may be responsible for a falling rate of production. The distributions of the

simulated scenarios are shown in Figure 2. The Cash-Flow-at-Risk results of each scenario

show, that with rising prices of raw materials, the highest probability for a negative outcome

is achieved. However, the lowest mean of the Cash-Flows is achieved by the scenario with

rising metal prices and dropping sales. Therefore, the average of the lowest Cash-Flow is

generated by the third scenario. Moreover, the volatility of the third scenario is significantly

lower and the concentration of the results to a particular sample space is higher. This

concentration results from the simultaneous decrease in the rate of production and the rising

prices. On the one hand, the sales decrease and on the other hand, the costs increase

significantly. The results of the three scenarios seem also to be plausible.

The simulated Cash-Flows with the increased prices for raw materials and the stagnant

economy are significantly lower than the previous scenarios. On the one hand, the production

of products gets more expensive, and thus reduces the profit margin significantly. On the

other hand, through a stagnant economy the sales are hampering and the revenue is

collapsing.



Booms and economically beneficial scenarios: After we examined negative

developments, which can occur, we are now analyzing economically beneficial scenarios.

There are two different scenarios constructed. These scenarios are based on the exact opposite

trends as the previously considered scenarios. The first scenario implies a recovering

economy as it occurred in the years 2009 and 2010 in Germany. The Federal Statistical Office

of Germany recorded in the 3rd Quarter of 2009 a growth of the gross domestic product of

2.3 %.

Therefore, in the first scenario we assume a growth in gross domestic product of 2.5 %,

which should contribute to increasing sales. The second scenario implies falling metal prices,

which should lead to lower production costs. The prices of raw materials develop exactly

opposite to the average empirical development of the last decades. The distributions of

simulated Cash-Flows are shown in Figure 3. As you can see in the two charts, an economic

upturn has a greater positive influence on the market and the production volume and therefore

on the Cash-Flow development, as falling prices. Falling prices increase the profit margin but

not the sales and thus the revenue.

Comparison of considered business cycles: Finally, we are now comparing the different

results from three different types of scenarios. The goal is to contrast the different

distributions of Cash-Flows. Figure 4 shows the simulated Cash-Flows of the scenarios

Standard, BIPnull and BIPup. In the diagram you can see clearly the differences between the

two extreme scenarios and the standard scenario. The shifts in the Cash-Flow distributions

show that the simulation model is able to generate possible future Cash-Flow developments,

based on the changed market parameters. Figure 5 shows the shift of the Cash-Flows with

falling and rising commodity prices compared to the simulation with the average empirical

development based on historical time series. However, it can be recognized that the shifts of

the distributions to the left and right on the X-axis are lower as in the previous scenarios. This



means that the impact of falling and rising commodity prices has a smaller impact on the

future Cash-Flow development in comparison to cyclical market fluctuations.

Figure 6 illustrates the Cash-Flow-at-Risk results of each scenario. The diagram shows

that the results are similar for the same respective circumstances. With an increasing

economic activity and falling prices of raw materials, a significantly higher Cash-Flow-at-

Risk can be determined, in comparison to the standard development and in particular to rising

commodity prices and the sluggish economy.

Furthermore, the difference between an increase in volatility and the simulation with the

average historical development is evident. The Cash-Flow-at-Risk is lower, equally the mean

of the scenario Vola_20%. However, the chart 1 shows that the distributions are very similar.

In scenario Vola_20% you would expect to see the consequences of the higher deviations with

a more significant effect in results in comparison with the Standard scenario. This is not

observable, because the model implicitly takes coherences between market factors into

consideration and that leads to the resulting distribution. The Cash-Flow-at-Risk result for the

scenario MetalsUp is almost zero, that’s why it cannot be seen in the diagram 6. The result is

mapped between the result of the scenarios BIPnull and MetalsUp_SalesDown.

In Table 3 are all the results of the Cash-Flow-at-Risk calculations of each scenario

presented. Like mentioned before, the simulated Cash-Flows aren’t including any fixed costs

the company faces through the production of the products. Through that assumption, the

Cash-Flow-at-Risk results in the following table seem big and aren’t negative or zero for the

scenarios you would expect that. However, the Cash-Flow-at-Risk results of the different

scenarios differ significantly and show that the simulation model works as it was expected.

In summary, we conclude that the simulation model explains the relationships of the

various market parameters well. The generated simulations show that the expected results

occur, and thus the robustness and stability of the model is proved. Even in extreme market



fluctuations, the simulation model provides reasonable results and does not reject the

calculated correlations.

CONCLUSION

The simulation model is based on System Dynamics, bivariate and multivariate

regression analysis and also on the principle of random walk and the Cash-Flow-at-Risk

approach. This macroeconomic market model is able to simulate and aggregate in the context

of a corporate exposure map and the inclusion of business-relevant market factors, future

Cash-Flows.

The simulation model is capable of simulating different scenarios with different

configurations of the various market parameters. The scenario analysis shows that the model

has the required quality and robustness to deliver plausible results even in extreme market

situations. Moreover, an adaptation of the implementation on other companies is feasible with

relatively little effort, based on the circumstance of the individual configuration. The fact that

the model uses the multivariate regression analysis to measure the direct influence of

individual market parameters on other factors increases the validity and reflects the theoretical

and the empirical correlations in more detail.

The consideration of an exogenous variable which is defined as the environment and the

evaluation of an influence of that variable on the development of the considered market

parameters is in contrast to a lot of other models. However, not only the implication of an

exogenous variable, also the consideration of historical returns to predict the future

development, differs from various models. The use of empirical data is efficient and often the

only possibility for quantifying theoretical relationships. However, the projection of empirical

relationships for the future can lead to incorrect results. Historical data deliver just snapshots



of possible developments, which will not recur in the same constellation in the future. That’s

why it is possible that through structural breaks in the context of the market dynamic these

empirical correlations lose their validity. The problem in this context is the low frequency of

data to describe stable relationships.

Starting points for future studies would be in the observation of the nonlinearity of the

regression coefficients. Bartram (1999) describes the non-linearity as the complexity of the

exposure and the difficulty of a correct evaluation of financial risks through the capital

markets. That could lead to small changes in exchange rates, which are superimposed of other

price relevant information. This means that financial market participants consider only large

exchange rate fluctuations in the business valuation or Cash-Flow calculation. In addition, the

use of historical data to forecast future prices is in the literature discussed with controversy.

Above that, the model shows a flexible character with the possibility of implementing further

enhancements. That could be considering default risk within supply or storage costs due to

fluctuation in demand.



TABLES

t-1\t GDP CPIEUR/USD Interest Alu. Copper Nickel Zinc

GDP X X X X X X XCPI X X X X X X XEUR/USD X X X X X X XInterest X X X X X X XAlu. X XCopper X XNickel X XZinc X X

Table 1: Matrix of the influencing coefficients

Product 1 Product 2 Product 3Income elasticity 1 0.5 1.2Price elasticity -1 -1 -1.5Price 1000 1100 40Sales 3000 3000 15000Sales μ 0 0 0Sales σ 0 0 0Aluminium 0.2 0.3 0.01Copper 0.02 0.02 0.001Nickel 0.005 0.001 0Zinc 0.005 0 0Table 2: Stresstesting Exposure Map

CFaR Mean of the CF‘s Standard deviationStandard 30,372,894.69 56,600,668.43 14,475,630.82Vola_20% 23,184,192.12 56,283,574.33 17,779,785.99BIPnull 2,417,715.73 35,492,772.54 18,699,541.03MetalsUp 15,330.14 35,717,172.65 19,902,825.30MetalsUp_SalesDown 5,068,065.91 17,718,321.23 7,124,585.93BIPup 87,656,579.66 100,611,857.40 7,234,513.07MetalsDown 63,029,150.07 79,346,077.07 9,010,692.07Table 3: Results of the scenarios



FIGURES

Figure 1: Standard development and volatility increases by 20%

Figure 2: Sluggish economy, rising commodity prices and sales decline



Figure 3: Improving economy and falling commodity prices

Figure 4: Comparison of standard development with a stagnating and attractive economy



Figure 5: Comparison of standard development with falling and rising commodity prices

Figure 6: Cash-Flow-at-Risk distribution of scenarios



REFERENCES

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Duch, J. (2006). Risikoberichterstattung mit Cash-Flow at Risk-Modellen. Frankfurt am Main: Lang

Junius, K., & Kater, U., & Meier, C. P., & Müller, H. (2002). Handbuch Europäische Zentralbank : Beobachtung, Analyse, Prognose. Bad Soden/Ts.: Uhlenbruch

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Seese, D., & Schlottmann, F., & Vogel, A. (2011). Market modelling for anticipating risk in a context of macroeconomic stresstest. Proceedings of International Business Research Conference. Dubai

Siebert, L. (2010). Modellierung eines makroökonomischen Modells: Bachelor Thesis, Karlsruhe Institut für Technologie (KIT), Karlsruhe, Germany

Spremann, K., & Gantenbein, P. (2007). Zinsen, Anleihen, Kredite (4th ed.). München: Oldenbourg

Stein, J., & Usher, S. E., & LaGatutta, D., & Youngen, J. (2001). A Comparables Approach To Measuring Cash-Flow-at-Risk for Non-Financial Firms. Journal of Applied Corporate Finance, 13(4)



Thome, H. (2005). Zeitreihenanalyse: eine Einführung für Sozialwissenschaftler und Historiker. München: Oldenbourg Wissenschaftsverlag

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i The developed model is an enhancement. For further details see also Seese, Siebert, Vogel (2011) or Seese, Schlottmann, Vogel (2011) ii Income and price elasticity need to be estimated by internal research processes. They are individual and depend on the company’s products. iii See Veith (2006)iv Those parameters turned out to be the most relevant market drivers of the company having a closer look at for sample reasonsv See http://www.destatis.devi See Rothengatter, Schaffner (2008):vii See http://www.bundesbank.deviii See Junius, Kater, Meier, Müller (2002)ixSee Spremann, Gantenbein (2007)x See http://www.destatis.de/jetspeed/portal/cms/Sites/destatis/Internet/DE/Presse/abisz/VPI,templateId=renderPrint.psmlxi See Lang (2005)xii See Backhaus, Erichson, Plinke, Weiber (2008)xiii See Backhaus, Erichson, Plinke, Weiber (2008)xiv See Thome (2005)xv See Veith (2006)

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