2.1 Definition Of Risk:

It is obvious that there have been many definitions of risk over years. The literature on risk is comprehensive. Origin of the word risk can be traced back to Latin, through the French “risque” and the Italian “risco”. Risk concept is firstly seen in ancient Italian maritime trade. It was defined as the combination of chance or uncertainty to mean the loss of ships and cargo on the seas. Merchants used a term risk because of uncertainty they faced. (Jorion, 2001)

In a broader manner Hargreaves and Mikes (2001) defined risk as “Uncertain future events that could expose the firms to the chance of loss. Here, loss is a relative concept. It needs a reference level to be defined. The reference level is the list of the objectives stated in the business plan of the firms. Consequently, risk can be defined as uncertain events that could influence the achievement of the firms’ strategic, operational and financial objectives.” Jorion (2001) further used risk as the volatility of unexpected outcomes, generally the value of assets or liabilities of interest.

It is very certain that risk components have considerable effect on the management of the firms, which should be examined carefully. Firms should manage risk because it offers both profits and losses. This management is entitled such as risk management or enterprise wide risk management. Briefly it is defined as a “process by which various risk exposures are identified, measured, and controlled.” (Jorion, 2001) Non-financial firms seek to benefit from their risk exposure while avoiding its catastrophic outcomes. There are many financial derivatives in financial markets to hedge the risks of the firms. These instruments help firms to manage their risks by using the tradeoff between risk taking and its rewards. Risk management has been one of the interesting topics for both academicians and practitioners. Although risk management is popular, there have been long debates about whether it can contribute to shareholder value or not. Debates are due to the complexity of risk concept and its management. It is complex because non-financial firms have difficulties to determine what type of risk to study. They haven’t decided what type of risk play considerable role in the survival of them. 

Firms having high risk exposure, rely more on the cash flow than the others. Financial distress is main reason for this proposal. Facing high risk signals the financial weakness of the firms. Once they are financially weak today it is very probable that they are weak in the future. These firms need more external funds to survive. They need these funds to sustain their obligations. But it is not very easy for these firms to find the needed funds because of having financing premium. Firms should carry the burden of higher costs of external funding than before. These firms are also in the risk of loosing chances of profitable investments. As a consequence, these firms are more cash-flow dependent. (Sterken et al. 2002)

All of the interpretations stated above underline the difficulty and the importance of risk and its management. Risk measurement and evaluation is hard work because risk is a qualitative element. How can non-financial firms estimate their over all risk? How can they evaluate their risk exposure? There is no problem if these firms’ incomes are more than their expenditures. But what if their expenditures are more than their incomes? They will soon go bankruptcy because of their inability to manage their risk.

Non-financial firms are in need of a quantitative tool to forecast their operating cash flows. Cash flow-at-risk, an analytic model was designed to help non-financial firms for that purpose. The model was developed from the roots of another analytic model Value-at-risk. In order to understand the usefulness of C-FaR, VaR model should be examined before hand.   

2.2 Value At Risk (VaR):

“VaR is defined as a measure of the maximum potential change in value of a portfolio of financial instruments with a given probability over a pre-set horizon. VaR answers how much can the firm lose with x% probability over a given time horizon.” (J.P Morgan/Reuters, 1996)  Actors taking part in financial markets face risks such as counterparty default and market risk. Financial analysts use VaR as a measure to quantify market risk, which is the potential loss related with market behavior. VaR output, which is a single, summary statistical measure, stems from normal market movements. Greater losses than VaR expected have only small probabilities. The concept of VaR was emerged because of the significant efforts to measure market risk by academicians, practitioners and regulatory bodies. A statistical approach, VaR, and scenario analysis approach, revaluation of a portfolio under different values of market rates and prices, were two important outputs of these efforts.  But what was the reason behind the increased interest about market risk measurement? The answer lies in the root of early studies about VaR and considerable changes that financial markets have experienced over years.

Leavens (1945) can be regarded as the pioneer of early VaR studies by his simple quantitative example. Although there were some scientists who covered the virtues of the diversification, Leavens, published his studies in a paper in 1945, which was the first, and the most comprehensive study about the benefits of diversification. Although he did not unequivocally present VaR model, he presented the spread between probable losses and gains for non-technical audience with the portfolio theory in his mind. (Leavens, 1945)  Markowitz (1952) and later Roy (1952) followed Leavens by publishing the same VaR measures independently. The technology was not competent to prove the practical use of their findings in 1950s but their proposed measures were to support the portfolio optimization. They both presented the covariance between risk components for hedging and diversification effects. Markowitz (1959) further published a book about his optimization scheme for computations.

William Sharpe (1963) used a better VaR measure in his Ph.D. thesis. Although the measure is different from Markowitz’s diagonal covariance matrix, it helped Sharpe to propose capital asset pricing model (CAPM). There were innovations in 1970s and 1980s in the financial markets as well as in every field of human life. The effect of these innovations was the rising of leverage. As this was the case, firms had a tendency to find new ways to manage risk. This in turn leads new measures of risk.

Garbade(1986) proposed VaR measures to model every bond upon its price sensitivity due to changes in yield. His model assumed that portfolio market values are normally distributed. The standard deviation of portfolio value can be found by the covariance matrix for yields at various maturities. His work drew little attention because Garbade was working for a private firm and his work was distributed only to clients.  He further progressed his work in 1987.

Group of 30, a non-profit organization asked JP Morgan to lead a study of derivatives in 1992. Dennis Weatherstone, chairman of JP Morgan, formed a committee for that purpose. The committee’s final product was 68-page report published in July 1993. The report was published under the name of “ Derivatives: Practices and Principles” This document is significant because of being the first to use the word “value-at-risk” In October 1994 Guldiman from JP Morgan proposed a new system called RiskMetrics. It was a free computer system, which provides risk measures for 400 financial instruments across 14 countries. These risk measures are forecasts of risk and correlations revised daily. The company pursued a noticeable public relation campaign to attract potential customers. (Holton, 2002)

In 1996 JP Morgan agreed with Reuters to cooperate on Risk Metrics. VaR notion was progressed and republished in a technical document in 1996. By the introduction of new RiskMetrics, managers can scale the data for their individual trading profiles. RiskMetrics provides covariance matrices to run VaR calculations. It also supplies the data for historical simulation and stress testing.

Financial markets were facing drastic changes by the rapid improvement in technology while the studies were going on about VaR between 1970s and 1990s. The management techniques were reshaping as the data processing was developing. New environment in financial markets was different because increased liquidity and pricing availability could ease the implementation of frequent assessment of positions, the mark-to-market concept. Firms became more interested in managing their daily earnings from a mark-to-market perspective. They were also interested in estimating the potential effect of changes in market conditions on their positions because of the slow but gradual increases in the volatility of earnings. Estimations in risk/return profile drew attention as well. Financial firms integrated their risk measurement process into their overall philosophy. They also formed and used market risk monitoring systems, which can provide timely information about positions and potential losses. All in all, these changes were about either performance or securitization. (J.P Morgan/Reuters, 1996)

Practitioners welcome the simplicity of VaR process because the basics of the VaR are very straightforward. It is also appealing because it offers market risk in a single number given the probability. (Manganelli, Engle, 2001)  The management can use this number in boardroom, reporting to regulators and in firm’s annul reports for risk reporting, risk in internal capital allocation and performance measurement.

Beyond its benefits, managers do not solely trust VaR for their risk management. That is, VaR is an important tool in risk management but not unique. It is mostly used as a starting point because VaR is not sufficient in measuring event or market crash risk. Therefore managers sometimes go into detail and make more complicated analysis such as simulations and stress test. Greek letters such as delta, gamma and vega are in use as assistant tools as well. (Linsmeier, Pearson, 1996) In fact, it was designed by its creators to be used in derivative markets but it is now widely used by financial firms to measure their financial risks.

As for the full VaR models’ computation, there are three common approaches: Historical simulation, Monte Carlo simulation and parametric or variance-covariance approach.  Historical approach is easy to use and demands few assumptions. It is mostly functional under a full valuation model. The profit and losses distribution of a portfolio is built upon current portfolio and subjecting it to actual changes during each of the last K periods, mostly days for financial firms. The computation of the theoretical profits and losses by actual historical changes in rates and prices is the distinctive feature of historical simulation. When the theoretical mark-to-market profit or loss for each of the last K periods have been calculated, the distribution of profits and losses and the value at risk, can then be found out.

The Monte Carlo simulation is not very different from historical simulation approach. The basic difference is about doing the simulation. Different from historical simulation approach, Monte Carlo simulation approach uses statistical distribution and artificial random generator to generate many theoretical changes in market factors. Then, these random numbers are used to build many portfolio profits and losses on the current portfolio and the distribution. Final step is to find value-at-risk from this simulated distribution. At the end, one can deduce that this method can facilitate in generating more paths of market returns than historical simulation. 

Analytic method, used as an analogous for variance and covariance approach, is constructed upon market factors’ having multivariate normal distribution. It becomes possible with this assumption to find the distribution of mark-to-market portfolio profits and losses, expectantly normal. Basic mathematical calculations should be applied to find the loss by the help of normal distribution properties. Risk mapping, mapping actual instruments into a set of simpler and standardized positions, is the heart of this method. (Linsmeier, Pearson, 1996)

Implied volatilities and user-defined scenarios are two ways of calculations for the partial VaR models. Implied volatility is the market’s forecast of possible volatility in the future. It is mostly pull out from a particular option-pricing model to make comparison to history to distill risk analysis. Besides, user-defined rate and price movements are used as a complementary in case of historical patterns do not repeat themselves.  

This section summarized the basics of VaR but remained one critical question, selecting appropriate measurement method. Each method shows differences in capturing the risks of options, easiness in implementation, explanation, and reliability of results. The selection process is all apt to managers because cost and benefit trade-offs are different for each manager, his position in the market, the number and types of instruments traded and available technology. 

2.3 Cash Flow At Risk (C-FaR):

C-FaR is defined as an analytic method of measuring with high degree of probability the risk of cash flow shocks for non-financial firms by its producers. This model helps firms by being a measure to evaluate the changes in their values. The model is proposed as a form of VaR for finding the overall risk against a firm’s cash flow. (Financial engineering news, 2001) C-FaR model tries to figure out the probability having inadequate cash to fund firms’ strategic investments. It is also defined as the “probability distribution of a firm’s operating cash flows over some time horizon in the future, usually the coming quarter or year, based on the information today.”  These forward-looking probability distributions as in the VaR model are used to reach some statistics such as worst-case scenarios outcomes. These outcomes can be used by the management of the firms to measure the probability of rare negative events. It is evident that these negative events can produce a significant drop in the firms’ earnings. Furthermore, the model covers every source of potential risks, which firms can be exposed.

Since the more volatile a firms’ cash flow, the less debt it can safely carry in finance, the attention should be on the cash flow volatility of non-financial firms. There are also three basic reasons to explain the importance of cash flow volatility. They are:

 Capital Structure Policy

 Evaluating hedging instruments and insurance strategies

 Forecasting the earnings of the firms

The firms want to know their C-FaR for the purpose of their capital structure policy. Capital structure policy means the debt-equity choice of the firms. These firms try to exploit the benefits of debt against the potential costs such as financial distress. C-FaR helps firms to evaluate their probability of financial distress by interpreting the cash flow volatility. And C-FaR helps them to consider new investments and make strategic decisions.

Risk management and shareholder value correlation was discussed in the first chapter. In order to quantify the potential benefits of the risk management, non-financial firms need to have a holistic picture of their cash flow distributions. Firms can evaluate existing hedging instruments and insurance strategies by the help of this model.

Both institutional and individual investors are watching the earnings of the firms. This in turn, forces firms’ managements to achieve their planned goals. And investors can use C-FaR model to compare the expected earnings of the firms they are interested. The management of the firms’ can use it for the same purpose as well.

After the VaR model became popular, there were some expectations from risk consultants about VaR’s application in non-financial firms. VaR is very applicable for financial firms but they are very different from the non-financial firms. Quantification of risk components and adding them up is easy for very liquid assets. Moreover, the data for liquid assets can be wide and easily reachable. This is not the same in non-financial firms, which have mostly illiquid assets. Potential problems would be solved if the overall thinking of VaR model were redesigned for non-financial firms.

Both academicians and practitioners worked together to progress new solutions as it is seen in the VaR case. Some consulting firms motivated academicians to apply VaR model to non-financial firms. These major firms are cited as RiskMetrics Group, which initiated the VaR model, Risk Capital Management Partners, and National Economic Research Associates (NERA). These companies compete with each other to produce the new product to non-financial firms. RiskMetrics was the winner of course. The company published a technical document in April 1999 by Alvin Y. Lee. The company proposed a new software package, CorporateMetrics, in this technical document. It is defined as a “conceptual framework for measuring market risk in the corporate environment.” (Lee, 1999) The model quantifies the impact of market risks on earnings and cash flow. It shows the connection between changes in market rates and their effect on financial outcomes. There are basically five benefits for non-financial firms to use this model.  These are increased transparency of risks, communicational benefits, hedging decisions, capital allocation and performance evaluation, and control. While these are the events for RiskMetrics other companies work hard to introduce their products.                     

In the mid 1999 National Economic Research Associates (NERA) vice president Stephen Usher formed a distinguished group of people. Nera is an international economic consulting firm who operates all over the world. Jeremy C. Stein from Harvard University economics department and two senior consultants Daniel LaGattuta and Jeff Youngen from NERA were the group members under the management of Stephen Usher. (Rich, 2001)  Louis Guth senior advisor in Nera, Ken Froot and Paul Hinton supported the study. Omar Choudry and Amy Shiner were the research assistances of the team. (Stein, Usher, LaGattuta, Youngen, 2001)

The group was aiming to progress the VaR model application, especially to non-financial firms. The study group facilitates the new approach proposed by Hayt & Song’s (1995) study. Hayt & Song proposed a new bottom approach in their study. It associates the VaR. Contrary to Hayt & Song the study grouped used the top-down approach for C-FaR application. 

Nera published the outcomes of the study in August 2000 by a working paper called “Comparables approach measuring cash flow at risk (C-FaR) for non-financial firms”. It was introduced as a computer-simulated method. The detailed findings were published in 2001 in the Journal of Applied Corporate Finance with the same title.

The thesis intends to concentrate on the Nera’s C-FaR model and its application for practical purposes. Nera consultants aimed to obtain data on as many non-financial firms as possible. Then they used the quarterly income statement and the balance sheets of the firms. Four or five years’ quarterly data was seen enough for the application of the model. Earnings before interest and taxes, depreciation, and amortization (EBITDA) or earnings before interest and taxes (EBIT) was used as a basic measure for the operating cash flow. Firms’ EBITDA values were divided by the total assets of the firms, in order to compare them with each other. This scale, EBITDA/TA, was regarded similar to market-to-book, price to earnings or price-to-cash flow scale by the Nera committee. Then consultants smoothed the data by discarding the large scales, outliers. The outliers usually belonged to small firms. This smoothing was done for the elimination of having very large scales. Also scales having more than 50% changes in their assets were cleared. Consultants thought that this move was for elimination of drastic changes in the firms’ assets. They also stated that change volume could be adjusted from 20%-to-%50 for practical purposes in the future studies.

Firms’ EBITDA/TA values would be used to forecast the expected cash flow. C-FaR model advocators needed a model to do this job and they used simple auto regression. EBITDA/TA scale in quarter t was regressed against four lags of itself. That is, EBITDA/TA in t-1, t-2, t-3 and t-4. t was the dependent variable and the other scales were the independent variables. The aim was not to make precise estimation but focusing on the entire probability distribution of shocks to cash flow, namely the tails of the distribution. The committee needed a benchmark for cash flows in the absence of shocks so that the forecast errors were used as deviations of cash flows from their expected values.

The data was collected only from recent six years for 3500 firms. Six-year data for these firms constituted 84000 forecast errors (6*4*3500=84000) for the U.S. As for a particular firm, six-year data meant 24 (6*4=24) forecast errors, which was not enough to make a judgment about cash flow volatility. On the other hand, pool of 84000 forecast errors contained different information about wide range of firms to the researchers. If firms and their errors were grouped according to similar characteristics then there would be small pools of forecast errors available for making inferences. Grouping meant dividing forecast errors into subsamples, which contain identical firms. Subsamples did contain neither 84000 errors nor 24 errors. They contained sufficient data to comment on firms’ cash flow volatility. Four characteristics were designated to divide forecast errors into subsamples. These were market capitalization, profitability, industry risk and stock price volatility of the firms. Firms, which were in the same subsample, were expected to have similar cash flow volatility history as well. Similar firms were called peers, which have similar characteristics and background. That is why C-FaR is called as comparables based technique. Grouping was done through dividing the forecast errors into subsamples. The forecast errors were divided into three subsamples for firms’ market capitalization initially. Firms were compiled according to their market cap size. Top one-third of the firms and their forecast errors were regrouped in “market-cap bucket 1”, middle one third of them in “market-cap bucket 2” and the bottom one-third them in “market-cap bucket 3”. Each market-cap bucket was then divided into three subsamples according to second characteristic, namely profitability. After this process, there were nine forecast error buckets. The dividing process went on in this manner. Finally, there were 81 subsamples containing approximately more than 1000 forecast errors each. The researchers assumption was that forecast errors form an identical group of firms, peers. Each final subsample was regarded as “bin”.

 In order to find any firms’ C-FaR, one should look at which bin it belongs to. The fifth percentile of the empirical distribution of the bin was regarded as the five-percent tail for a particular firm. Tail values of the bins were regarded as C-FaRvalues of the firms. And firm’s expected EBITDA would decrease as amount of tail intercept multiplied by the total assets in a five-percent worst-case. Briefly, the exact change in EBITDA is tail value times total assets. The outcome of the analysis was the final figure showing the change in operating cash flow of the firm in a five percent worst-case scenario. The probability was chosen as a five percent but can take other values as well. (Stein et al. 2001)

2.4 The Comparison Of Value-At-Risk With Cash Flow-At-Risk:

VaR model is called as a bottom-up method. That is, quantification of each risk component of the portfolio and adding them up. C-FaR method is referred as a “top-down” method on the other hand. Financial firms work mostly with liquid assets. Lets say a particular financial firm has a portfolio of three liquid assets. The VaR model’s bottom-up approach means finding risk exposure of its assets first and adding them up. The VaR model cannot be applied with the same approach to non-financial firms. If the bottom-up approach is used in non-financial firms, some significant risk elements are neglected. Therefore, it is very obvious to have misleading result if the bottom-up approach is used. In the top-down approach, the model looks at the assets overall risk exposure. The overall risk exposure can be found through the variations in firms’ operating cash flows.

Financial firms have high liquid assets. Their assets are easy to value but it is not the same for non-financial firms. Non-financial firms have assets, which are not easy to value because the assets cover both tangible and intangible components. Tangible assets are physical components such as property, plant and equipment. Intangible assets are brand, patent, and labor and supply agreements. It is very hard to value the assets of the non-financial firms because of this mixed structure.

VaR model also depends on normality assumptions. Contrary to VaR, C-FaR distributions appear to fatter-tailed than normal distributions, as well as somewhat right-skewed. VaR model demands more data than C-FaR. VaR model demands risk components’ historical data in a large scale. This is not applicable in the C-FaR model because quarterly figures cannot be traced back more than five years. Although the data are available, the experts do not recommend it. Non-financial firms are rapidly changing and it is not healthy to go beyond this time frame.