2012Cambridge Business & Economics ConferenceISBN : 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
Andreas Vogel
Karlsruhe Institute of Technology (KIT)
Institute of Applied Informatics and Formal Description Methods (AIFB)
Karlsruhe, Germany
+49 721 60845393
DetlefSeese
Karlsruhe Institute of Technology (KIT)
Institute of Applied Informatics and Formal Description Methods (AIFB)
Karlsruhe, Germany
+49 721 60846037
June 27-28, 2012
Cambridge, UK1
2012Cambridge Business & Economics ConferenceISBN : 9780974211428
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
Thecompetition conditionsfor the manufacturingindustryhave changed considerablyin recentyears. Due tothe increasingglobalizationandthe simultaneousfluctuationsin internationalfinancial markets,companiesfacenewchallenges. As a resultof the strongerintegration of the economyandtheconsequent increase involatilityofcommodity prices, equities, interest and exchange rates, thefinancial risksof companieshaveincreased.Especially the recent past confirms that extrememarketfluctuationsoccurat shortertimeintervalsandas a consequencethe financial positionandstabilityofbanks, industrial and commercial companiesand even of nationsisconstantly challenged. Thefinancial riskmanagement is thereforean operationalfunction which importance isincreasingmore and more.The success orfailure of companiesin a challengingenvironmentis essentialfortheir existence andglobal competitiveness.
Established on these facts, a lot of companiesand 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 theBottom-Upapproachistomake a statement aboutthe probability that acertainfuture Cash-Flow adoptsa specific valuedue to theinfluencingfactors. Attributed tothe requiredknowledge of thebusiness-relatedeffect relationships, the approaches are calledinternalmodels. Additionally, the approach is closelybased ontheValue-at-Risk concept. Therefore,it is necessary to implement these models to startwith searching and identifying market-price-based riskfactors, which have asignificant impactonthe Cash-Flow.Ongoing, the identifiedfinancialrisks are analyzed byusingthe exposuremapsaccording to theirimportancefortheoutcome.After thatthe identifiedrisks arebrought into afunctional relationshipto simulatethefuture Cash-Flows.Finally, thecalculationofthe Cash-Flow-at-Riskis realized witha user-specific confidence level.On one hand, Chris Turner (1996) emphasized that the Bottom-Upapproach is simple in the way of the intuitiveinterpretationof the result.It returns avalue, whichis exceeded with agiven probability.In addition,it is possible to specify the risk of the probabilityof deviationfrom an expected valueora quasi-reliable Cash-Flow.On the otherhand, Turner states that theBottom-Upmodels can beverycomplex.The calculationdepends very much on theinterplayof the variousinfluencing factors. It is necessary to compute correlationsbetween theindividual 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 wellthe identifiedriskfactorsexplaintheCash-Flow.A coupleof variousdifferentmethods are available to forecastfuture marketprices. One method, which is analyzed by J. Kim, A. Malz and J. Mina (1999),is basedon impliedvolatilities forshort timeperiods by using deterministicforward prices.Moreover,according to Lee(1999) a simulation with a random walk can be implemented, based on historicalmoments of the distributionofthe influencingfactors.Finally, Lee (1999) of the RiskMetrics Grouppresentedan estimation of theCash-Flow development byusing econometricmethodswitha so-calledVector ErrorCorrectionModel (VECM).
Theperspectiveof theBottom-Upapproachis not undisputed, becauseof the manyinterdependenciesin terms of complexity.Stein (2000) emphasized that the danger might belarge, toobservemeasurablerisks, but easily to ignoreother non-financialrisks.Unlike the Bottom-Upapproaches, the Top-Down approachesdon’t considerseparateindividual riskfactors.The firstTop-Downapproachesare theregressionmodels and introduced by Bartram (1999).The regression models puttheCash-Flow in direct focus. Thusa study of individualorevenentireriskexposures isalso possible fornon-company employees. The basis isthe useofexclusivelypubliccapitalmarket data.Therefore,based on Bartram theregressionmodelsare also calledexternalregressionmodels. The estimationof the volatilityof theCash-Flowsisbased on historicaldeviations. Throughthisprocedure allrisks, not only financial, alsooperationalinfluences aretaken into account, mentioned Stein(2000). InternalCash-Flowdatais eithernot availableor it isininsufficientamount.Therefore,to explainthe variation,the models resort toregressionanalysis for example, withthestock returnsorvarious capitalmarketdata. Another Top-Down model is thebenchmarkmodel, whichestimatesonhistoricalCash-Flowdistributions and evento some extents from Cash-Flow distribution ofcompeting companies, the variations. This benchmarkmodel wasdeveloped byU.S. companies. The goal of thisapproach is to picture acompany-wide aggregaterisk, without using individualmarket parameters asthe previous models.Simply put, itcompareshistoricalCash-Flowsfrom other companies inthesamesectors with the company looked at, and thendrawsconclusionsabout possible futureCash-Flowtrends. Therefore, nodetailedknowledge is requiredabout internalrelationshipsin order tomake a statement aboutthe riskexposureof the company.The consulting firmNational Economic ResearchAssociates(NERA) from New York developed in 2000such amodelcalled C-FAR, where C-FAR stands forCash-Flow-at-Risk. Like thetwoprevious simulationmodelsthis model is also basedon historicalCash-Flowtime series.Although Stein (2000) highlighted in his paper, that the general problem is, that there arenotenoughempiricalCash-Flowsexisting, especially due to changes in corporatestructure orcompany 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 model[i]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 usesregression 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 elasticity[ii].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 implementationof the individual products, the total sales of a companyresults from thesum of the salesof the individual products.The singleturnoversarisefrom the sales of the products in Germany.The priceof each productdevelopsanalogousto the Consumer PriceIndex(CPI) and automatically adjusts tothecorrespondingdemand.Thus, theformula toshow the price trend is:
/ (1)with
The turnover itselfis derived from thesales of theprevious periodmultiplied bythe domestically economicdevelopment, the gross domestic product (GDP), isdueto theincomeelasticityof demand.In addition,the turnover isinfluencedbythe pricingof the product andweighted by thepriceelasticity.Alike the model considers diverse volatilities in sales, which can occur due to production, demand or external reasons. Fluctuations in production mayarise for example, throughline stoppage, staff absencesorraw material supplies. This fluctuationis realized throughthe generationof a normally distributedrandom variableusing thepolarmethodof GeorgeMarsaglia[iii].Thus, thecalculationofproduct-specific salesresultsfrom the formula:
/ (2)with
The companyalsoincurredproduct-specificcosts, which are explained in terms ofmaterialcosts. As alreadymentioned,eachcommodity istradedin US-Dollar. Furthermore,we make theassumptionthat the storage is refilled withraw materials at the beginningof each quarterto keepthestorageconstant.Itwill beboughtjust asmuch materialasisrequiredin order to realizethe simulatedsales.Thus, theproduct-specific materialcostsresult from thesumof the portionsof each commoditymultiplied byitsprice and thenadjusted for the -exchange rate.
/ (3)with
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-Riskit is necessary to determinethe sensitivity to changes in the considered market parameters and for these circumstances the exposure map is used. According toDuch (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:
/ (4)with
Through the considerationof multiple products it is necessary,tocalculatethetotalturnover of the companyin a quarter,toadd up the individualproduct-specific Cash-Flows.
/ (5)with
The five mentioned formulas are the base to calculate the Cash-Flows of a company.As outlinedin the preparationof the exposuremaps, we identifiedfour keymarket parameters[iv],whichare essentialto simulate thefuture Cash-Flowsof an industrial enterprise.Thereis thegrossdomestic product(GDP) of the FederalRepublic ofGermany, theconsumerprice index(CPI), the long-term interest rateEURIBOR andthe -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 Germany[v] makes available to avoid distortions of the actual economic development by seasonal influences[vi].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 werelyon 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 usethe 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 -exchange rate.These euro reference rates are determined and published each business day through the participation of the European Central Bank and theNational 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 Bank[vii] .
It is also for theinterest rate necessaryto find areference price, which reflects thegeneralinterest rate trends.Herearisesthe problem that, unlike the exchange rate manydifferinginterestrates, for which bankslendmoney, are available. An appropriate indexforthe interestratedevelopment is theEuro InterbankOffered Rate(EURIBOR). TheEURIBORis a reference rate,calculatedby the ECBfor time depositsin the interbank market[viii] . This raterefers, in contrast to existingcompetitioninterest rates, such as theLondonInterbankOffered Rate(LIBOR), exclusively on the Euro[ix] . Since theEURIBOR is calculatedat differentmaturities andserves as areference ratefor floatingrate notesand swaps, its useprovides the representationfor ourinterest rate.To mapthecorrespondinglong-term interest rateswe chosethe EURIBORwith the longestduration, twelve months. ThehistoricEURIBORtime series are available onthe website of the German National Bank. Like the GDP we use for the interest rate the quarterlyvalueof the dailyclosing price of the lasttrading dayof each quarter.
As partof thismarket model we made theassumptionthatchanges incommodity pricesdevelop in line with pricesin the economy.Against thisbackground,theconsumerprice index(CPI), which is determinedmonthly by theFederal StatisticalOffice of Germany,isan accuratemeasureofconsumerpricesbased on theLaspeyres priceindex[x].The CPIis usedas a benchmarkin wagenegotiationsand is constituted as the centralindicatorfor the assessmentof monetarydevelopments in Germany.Furthermore, thechanges in the consumerpriceindex orits internationallyadaptedform,called the harmonizedconsumerpriceindex, are ameasureof inflation inGermany. As we saw with the GDP,is it also necessary for the CPIto use seasonally and calendaradjusted values toavoiddistortions of theactualdevelopment.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 parameteris 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 goodnessof the gradient of thecorrelation and therefore rejects or supports the observed theoretical principles and estimated correlations of the market parameters.Thenews serviceBloomberg provides the needed time seriesof the various marketparameters.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 theoryimplies 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-valuationof the domestic currency leads to a higher demand for domestic bonds. Through thatcontext, 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 owncountry 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 raises[xi].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 pointto give these relationships a real number in the context of a coefficient. The primaryscope of theregressionanalysis is theinvestigationofcausalrelationships, or the so-calledcause-and-effect relationships. In the simplestcase,such a relationship canbe expressedbetween twovariables, the dependent variableY andthe independentvariablesX. The variablesXandYalways correspond to therespectivereturns of amarketparameter, whichcan be determinedin the simulation model. Themultivariateregressionapproach has the followingform[xii]: