The role of value-at-risk in purchasing: an application to the foodservice industry.
Risk management is the process of identifying, measuring, and controlling relevant risks that impact the business unit. While risk management has a variety of meanings to a purchasing organization (Smeltzer and Siferd 1998), one of the key areas revolves around the volatility of market-based pricing (Lo 1999; Thuong and Ho 1987). As supply chain management evolves over the next 10 years, Garter et al. (2000) suggest that underlying commodity risk will become more transparent with an increased reliance on formula pricing approaches. Furthermore, the management of commodity-based risk is likely to be concentrated among specialized firms. This trend begs for a simple metric of measuring risk that is easily understood at the corporate level. Value-at-Risk (VaR) is just such a tool. Value-at-Risk measures the downside risk of a portfolio at a particular confidence level over a given time horizon. For example, a VaR estimate of $1 million with a 95 percent level of confidence suggests that potential portfolio losse s will exceed $1 million with a 5 percent probability over a given time horizon (e.g., one day). In essence, VaR attempts to measure extreme events in the lower tail of a retum distribution of a portfolio--events likely to cause financial distress to a firm if they occur (Figure 1). Since VaR focuses solely on downside risk (bad outcomes) and is usually expressed in dollars, it is considered to be an intuitive and transparent risk measure for top-level management. This is especially true in comparison to traditional risk measures, such as standard deviation, that take into consideration both positive and negative outcomes. These traits of VaR have aided in its growing popularity. The popularity of Value-at-Risk as a risk measurement tool has generated considerable interest among risk management practitioners and academics alike. The academic literature regarding VaR, however, has largely focused on estimation procedures. This line of literature, while important, neglects to address the realistic needs of corp orate risk managers and other decision makers for such a comprehensive risk measure. This article discusses VaR from an implementation perspective. In particular, what are the business demand and potential applications for VaR estimates? For instance, what information is required by the various decision makers within a corporatewide risk management system in general and the purchasing function in particular? Therefore, the overall objective of this article is to provide a tutorial on VaR and specifically illustrate, through examples and discussion, how VaR can be used to measure and manage risks throughout the supply chain.
After introducing Value-at-Risk and briefly reviewing the related literature, VaR is examined in the context of a corporate purchasing department of a commodity end user. Specifically, the system examined is that of a publicly held foodservice company that has exposure to market risk in underlying agricultural commodities. However, this example and related issues easily extend to any purchasing business that is exposed to commodity price risk (e.g., metals and energy). The informational demands placed on VaR by various functional units within the firm are presented and alternative uses for the VaR methodology are suggested. From this exercise, practitioners can make an informed assessment of VaR's potential as a tool or metric for risk management within the purchasing department, and more generally, the overall firm. Furthermore, this research can help researchers target their efforts to address issues involving VaR's applicability in these business settings.
VALUE-AT-RISK: A PRIMER
Evolution of Value-at-Risk
Much of the interest in Value-at-Risk stems from its use in risk disclosure and risk reporting, especially with respect to derivatives positions. In the wake of several well-publicized derivatives disasters (e.g., Barrings Bank; Proctor and Gamble), regulatory agencies, in particular the BASLE Committee on banking regulation, the U.S. Federal Reserve Board, and the Securities and Exchange Commission (SEC), were in need of a transparent and easily interpreted risk measure that could aggregate the risks of many types of derivatives and nonderivative assets alike into a single number (Jorion 1997). These agencies advocated Value-at-Risk as a tool for this use. In response, in 1994, JP Morgan published its internal risk measurement system on the World Wide Web, RiskMetrics[TM], which described its method for calculating and using VaR. As a result, VaR continued to gain popularity among financial firms and large trading banks that dealt heavily with derivatives and other highly market-sensitive assets such as cash commodity positions (e.g., grains, meats, and petroleum products). In 1997, the use of VaR received a major push when the SEC established rules for the quantitative and qualitative reporting of risks associated with derivatives and other highly market-sensitive assets by reporting firms. Value-at-Risk was one of the methods recommended and approved for this purpose (Linsmeier and Pearson 1997). In addition, banking regulatory bodies, namely the Federal Reserve and the Bank for International Settlements (BIS), often set capital adequacy limits based on VaR. Today, VaR is being adopted by many nonfinancial firms as the foundation for their corporate risk management systems. Particularly, VaR is used for internal risk reporting and setting risk limits among diverse business units within a corporate risk management framework. Its popularity in these applications is similar to its popularity in regulatory uses--its ease of understanding and transparency due to its focus on downside risk as well as its ability to aggregate risk across asset classes.
Along these lines, VaR can be used as a way to communicate the downside risk associated with purchases, or future purchases, of products that possess considerable market price variability (e.g., agricultural commodities) among decision makers within and outside of the purchasing department. For example, suppose a purchasing agent at a food processing firm needs to make a large purchase of wheat (e.g., 25,000 bushels) sometime in the future. What happens if the price of wheat skyrockets before the purchasing agent can lock in a price? Could this price fluctuation cause the overall planned purchasing costs of the firm to be exceeded? Could this price increase in wheat inputs eventually cause the firm to miss its earnings estimates? Purchasing agents, purchasing managers, and other decision makers within the corporation could benefit from a concise measure that could summarize the risk of this wheat purchase relative to the overall planned costs for the input. Furthermore, VaR can be used to aggregate the risks across various input purchases. For instance, if a food processing company buys wheat, soybean oil, beef, and coffee beans, the VaR of this portfolio of market-sensitive food inputs can be calculated and examined relative to planned purchasing costs, or the overall profit objectives of the company as a whole. In essence, VaR not only can be used as a valuable piece of information within the purchasing department but can also relay downside risk information to key decision makers throughout the firm. However, before examining a specific case of how VaR can be used in a comprehensive corporate risk management system, a brief examination and evaluation of VaR estimation techniques is necessary.
Estimation of Value-at-Risk
In essence, Value-at-Risk relies on forecasts of the volatility of portfolio revenue or returns over a given holding period, with special attention paid to the lower tall of the distribution. Value-at-Risk estimation procedures are typically divided into two general methods: parametric and simulation. Parametric procedures rely on point estimates of portfolio volatility that are scaled to a desired confidence level under the assumption of normality. Therefore, VaR can be defined as:
VaR = [W.sub.o][[sigma].sub.p][alpha]
where [W.sub.o] is the initial portfolio value, [[sigma].sub.p] is the estimated portfolio standard deviation, and [alpha] is a scaling parameter corresponding to the desired confidence level
The formula above is often referred to as the variance-covariance method in the Value-at-Risk literature (Jorion 1997). The most common confidence levels used in financial applications are the 90 percent ([alpha]=1.28), 95 percent ([alpha]=1.65), and 99 percent ([alpha]=2.33) levels, respectively. Ultimately, the confidence level used needs to be commensurate with the needs of the user and the risks being measured.
To illustrate the calculation of VaR using the variance-covariance method, suppose that the expected one-day portfolio volatility forecast for a portfolio of market-sensitive assets is 4 percent and the current value of this portfolio is $1 million. Therefore, at the 95 percent level of confidence, the Value-at-Risk over this holding period (one day) would be $66,000 ($1,000,000 x 0.04 x 1.65). This is a loss one would expect only 5 percent of the time under normal market conditions. A variety of methods have been proposed for the appropriate estimator of the portfolio's volatility; however, they all rely to some extent on historical volatility levels (see Duffle and Pan 1997; Hendricks 1996; Hopper 1996; Jotion 1997; Boudoukh, Richardson, and Whitelaw 1997).
Simulation procedures, including historical and Monte Carlo simulation, attempt to model the entire return distribution and thus do not rely on parametric estimates of volatility. That is, they do not necessarily assume that returns follow a normal distribution. Once the return distribution of the portfolio is simulated, the VaR measure is taken as the percentile associated with the desired confidence level (Linsmeier and Pearson 1996, 1997; Jorion 1997; Duffie and Pan 1997). Historical simulation exposes the current portfolio to historical returns of the various assets in the portfolio over a given historical time period such as three years (Linsmeier and Pearson 1996, 1997; Butler and Schachter 1997; Mahoney 1995). Hence, new portfolios are simulated from these past historical returns given the current portfolio weights. The VaR is then taken from the appropriate percentile associated with the desired confidence level. Bootstrap historical simulation is also commonly used where the historical asset returns are sampled several hundreds or thousands of times, with replacement, in simulating the return distribution (Duffie and Pan 1997; Jorion 1997). Monte Carlo procedures are similar to historical simulation; however, they generate pseudo-random values of the various assets in the portfolio based on a predetermined data generating process (Linsmeier and Pearson 1996, 1997; Jotion 1997). Since simulation procedures do not rely on the assumption of normality, many consider them a more flexible and potentially accurate approach to estimating VaR.
Considerable research effort has been expended to determine the statistical attributes for these various methodologies of computing Value-at-Risk measures. This research has yielded numerous insights into the performance of these competing methodologies. For instance, it is generally accepted that parametric methods are relatively easy to implement, especially for portfolios that contain little or no options positions. Furthermore, it is easy to perform scenario analysis, commonly referred to as "stress-testing" using parametric methods, where the risk manager examines the effect of VaR under different values of key parameters of the estimate. For instance in the preceding example, a risk manager might be interested to see how the VaR estimate would change if the portfolio standard deviation went up to 5 percent instead of 4 percent. The major drawback to parametric methods, however, is their reliance on the properties of the normal distribution, the same assumption that in many ways helps make it relatively easy to estimate using basic statistics. Specifically, the distributions of asset returns tend to be characteristically fat-tailed (e.g., more observations fall into the tails of the distribution than prescribed by the properties of the normal distribution), which may lead to misleading VaR estimates. In fact, advocates of simulation procedures claim that since simulation procedures do not explicitly rely on normality of price returns, they more accurately account for fat-tails. However, simulation procedures, especially Monte Carlo simulation, tend to be more difficult to estimate and explain to upper-level management, and they are not easily adapted to stress-testing. Despite the pros and cons of all the competing methodologies for estimating VaR, it has been found that both parametric and simulation procedures adequately capture portfolio losses at modest confidence levels (e.g., 90 percent and 95 percent) despite the common acceptance that asset return distributions are often fat-tailed (Hendricks 1996; M ahoney 1995; Jackson, Maude, and Perraudin 1997; Manfredo and Leuthold 2001). Debate continues as to the most robust and accurate procedure for estimating VaR over a wide range of potential portfolios, confidence levels, and time horizons. (1)
As the popularity of Value-at-Risk has grown, numerous commercial software packages have been developed and marketed. Many of these software packages allow for the estimation of VaR using both parametric as well as simulation methods, and have a wide range of various features. However, VaR calculations, especially parametric methods, can be made or programmed using standard spreadsheet software such as MS Excel, risk analysis spreadsheet ad-in software (e.g., @RISK), or various statistical packages. Given the variety of software and programming options available, a firm's purchasing managers, risk managers, IT departments, and other key decision makers need to match their software/programming needs to the size of the business, the sophistication of the portfolio, as well as the informational demands for a risk measure like VaR. (2)
Given its intuitive appeal, transparency, and ability to aggregate risks over a variety of asset classes, Value-at-Risk can play a key role in a corporation's overall risk management system. Therefore, it is important that researchers and practitioners understand the various business demands for VaR estimates. VaR is a widely applicable concept, and each firm can have its own uses for this metric. Summarizing these is not an easy task. Although VaR is frequently thought of as simply a means of measuring market exposure, it can actually provide a much more robust tool for managing corporate risk. To illustrate, the authors draw upon an example of a commodity end user and price risk emanating from the supply chain.
THE CASE OF A COMMODITY END USER
Take the case of a publicly held foodservice firm that has exposure to commodity price risk. Figure 2 presents a general view of the informational flows among functional units within the firm. It is the role of the risk manager to provide timely and accurate risk information in a usable format. The following discussion examines the potential informational needs of the key players. Special emphasis is placed on the use of VaR as a flexible metric within the supply chain and the firm. (3) For illustrative purposes, throughout this discussion the variance-covariance method is used for estimating VaR.
Value-at-Risk: An Example for a Foodservice Firm
Assume that a foodservice firm's essential inputs include soybean oil (frying shortening), wheat (hamburger buns), boneless beef (hamburger patty), and raw coffee beans (coffee). The purchasing manager (Figure 2- A) has arranged for particular items to be priced on a cost-plus formula from the nearby futures price for each raw commodity, where the nearby futures contract is the futures contract month closest to expiration. (4) The nearby futures contract is normally used in formula pricing since it is typically the most liquid futures contract traded, and most closely reflects the underlying cash price at that particular time. For example, if the nearby futures price for wheat is $3.50 per bushel on the day of purchase, and the purchasing manager has agreed to pay $0.05 above nearby futures price, then the cost of the wheat would be $3.55 per bushel. Of course, if the nearby futures contract on the day of purchase were $4.00 per bushel, then the total cost paid for wheat would be $4.05 per bushel under this formula. So, the price paid for the final product, in this case buns, would be the price of wheat plus the agreed upon margin plus overage to mill flour and ultimately manufacture the buns. Likewise, the cash price paid by the purchasing manager for each commodity-driven input (shortening, buns, beef patties, and coffee) is directly tied to the nearby futures price. Unless the cash price is fixed, either through a supplier contract or an internal hedging program, it fluctuates directly with the price of the underlying futures contract. Therefore, for this example, the firm's raw commodity price risk is defined using nearby Kansas City wheat futures, soybean oil futures, coffee futures, and boneless beef futures.
Take the situation where it is the beginning of the firm's fiscal third quarter and input pricing is complete for the quarter; however, fourth-quarter pricing is open. The business or operating unit (Figure 2 - B) has planned food costs for the fourth quarter at $3.004 million on a raw commodity basis, which is flat versus the current market (Table III). However, the business executives are worried about their market exposure. A substantial increase in food costs will cause them to miss their planned numbers and potentially their earning estimates. The business unit asks purchasing for a risk assessment (Figure 2).
Tables I, II, and III summarize the necessary information for a risk assessment using the variance-covariance approach to estimating VaR Summary statistics (mean and standard deviation) of weekly nearby futures returns for Kansas City wheat, soybean oil, and coffee beans are presented in Table I. The futures returns represent the relevant risk because the final products are priced on a cost-plus basis, where the futures price represents the base price (see above example). Since the boneless beef futures contract is relatively new, with a short history, cash prices are used as a proxy for nearby futures. Returns for nearby Kansas City wheat futures, soybean oil futures, coffee futures, and boneless beef cash prices are calculated as Friday-to-Friday log relative price changes (ln([p.sub.t]/[p.sub.t]-1)). The data span from April 1986 through June 1998 (635 weekly observations). It is clear that coffee is the most volatile commodity followed by boneless beef, soybean oil, and wheat (Table I). Table II presents the correlations between the various prices. The standard deviations in Table I, correlations in Table II, and portfolio weights in Table III are all used in forecasting portfolio standard deviation, which is a critical input into the VaR calculation when using the variance-covariance method. In addition, purchasing risk managers must always be cognizant of three other key issues that go into calculating a VaR number: the benchmark, the time horizon, and the confidence interval. Sometimes these are predetermined by company policy, but at other times it is at their discretion to use those that are most appropriate to communicate the relevant point.
In this case, the benchmark is the planned food cost ($3.004 million) which reflects the current market. The time horizon is 91 days or one quarter hence since the current quarter is covered and the firm is looking ahead to the next quarter. Although not explicitly requested, a confidence interval of 90 percent is utilized. In this case, the firm does not have pricing for its fourth fiscal quarter; so, the risk is that the markets composing its total food costs collectively advance -- resulting in the "bad outcome" of lower margins. As shown in Table IV, the VaR for a 91-day horizon at the 90 percent confidence level is $0.335 million. So, there is a 1-in-10 chance that total food costs at the start of the fourth quarter will exceed $3.339 million ($3.004 million + $0.335 million).
The purchasing department communicates this risk assessment to the business unit. The business unit can then decide if this risk versus its budget is worth assuming for the opportunity that prices may decline. In this case, the business executives decide that they have to "make their numbers," and they ask the purchasing department to "lock-in" current prices.
In this example, the purchasing department has its own futures accounts for hedging price risk. To protect against rising raw material prices, it purchases the appropriate quantity of futures contracts for each commodity. In doing so, it has protected the business from rising prices (see Leenders and Fearon 1997). Take wheat, for example. If wheat is currently priced at $3.50 per bushel, and 75,000 bushels of wheat are necessary over a three-month period, then the total value of the wheat position is currently $262,500 (Table III). Assuming that the current futures price is also equal to $3.50 per bushel (zero basis), the purchasing manager buys 15 futures contracts, appropriate to cover 75,000 bushels of wheat (5,000 bushels per futures contract). If the price of wheat jumps to $3.60 per bushel at the end of the quarter resulting in the total wheat position now costing $270,000, the purchasing manager buys the actual cash wheat for $3.60 per bushel and simultaneously sells the 15 futures contracts at $3.60 p er bushel. The gain received from the buying and selling of the futures contract (buy at $3.50; sell at $3.60) provides a profit of $0.10 per bushel or $7,500, thus offsetting the increase in price on the cash side of the transaction. Ultimately, the purchasing manager has locked in a price of $3.50 per bushel ($262,500) for wheat. (5) However, he or she has also created new demands within the firm for VaR estimates.
For instance, the treasury department (Figure 2- E) is responsible for settling daily cash balances in the futures margin account. Futures and options positions are marked-to-market daily. Risk is measured versus the market, i.e., cash flows due to adverse market price movements. Furthermore, the confidence interval needs to be very high (e.g., 99 percent or greater) because regulators retain the right to liquidate positions if cash is not presented upon request. Also, an unexpectedly large cash requirement may force the firm to draw upon sub-optimal financing, which increases operating cost.
The VaR at the 99 percent confidence level for one day is $63.7 thousand (Table IV). So, Treasury must be prepared to wire at least $63.7 thousand about once every 100 days. If this particular hedge position is held until the start of the fourth fiscal quarter (91 days hence), then almost assuredly, treasury at some point will be faced with a cash outlay of this magnitude. Note, however, it is equally likely to have a cash inflow of the same amount. This is precisely the point: VaR informs treasury of the potential fluctuations in cash requirements.
The accounting department needs (Figure 2-D) VaR numbers on derivative positions to meet SEC reporting requirements. For these, the time horizon may be 28 days and the confidence interval 95 percent. The benchmark is the market because regulators are concerned about losses that could push the firm into insolvency. Under these guidelines, the VaR can again be pulled from Table IV, and it is $238.3 thousand dollars.
When using Value-at-Risk, the informational demands placed on the risk measure by various decision makers within a firm are different. While the above example emphasizes the use of VaR in measuring the risks of a portfolio of market prices, and subsequently how the risks of unhedged and hedged positions can be disclosed to various parties, there are other potential uses for VaR that may be useful to purchasing managers, and thus also place unique informational demands on the risk measure. Another application of VaR that is particularly relevant for purchasing managers is the evaluation of market risk in supply contracts that contain price escalator or deesclator clauses. That is, VaR analysis can be used to estimate the likelihood that price escalation clauses in long-term supply contracts are triggered and to assess the dollar risk they pose to the firm. These escalator/deescalator clauses are common in contract prices that are closely linked to fuel and packaging costs in particular. For instance, many dist ribution contracts include price adjustments based on the Department of Energy's posted on-highway diesel fuel price. In this case, risk is represented by changes in this price and can be modeled using the Value-at-Risk framework.
Also of importance to purchasing managers and others throughout the firm is the ability of Value-at-Risk to be used as a performance metric. As a performance metric, VaR is often utilized to scale returns to a risk-adjusted basis and to identify specific operational areas that are exposed to inordinate downside risk. That is, operating units (or traders) with their own profit and loss statements can be evaluated on a risk-adjusted basis with a VaR measurement. For instance, a company may have a retail sales unit and an importing unit, both of which have volatile earnings. The downside risk for each business unit can be measured in a Value-at-Risk framework and used to normalize their respective returns. Clearly, if two operating units are providing equal returns, it is important that executives know if one (or both) of the units is placing the corporation in a situation where there is a high probability of a substantial loss. This use of VaR can serve as a means of spotting operational risks, risks that stem from lack of control and human error in derivatives trading (e.g., fraud or unauthorized trading), within the firm (Falkenstein 1997).
In summary purchasing managers, buyers, individual traders, executives, and others within the firm may want or need risk assessments for their own products, purchasing responsibilities, and communication needs. Therefore, the time horizons, confidence intervals, and benchmarks are likely to be different across the supply chain and throughout the firm. For instance, a trader may want to know the one-day risk versus the market at the 99 percent confidence interval. On the other end of the spectrum, executives may need to know their quarterly (91-day) VaR at the 90 percent level to make sure that the firm's total risk position has not exceeded the maximum level set by the board of directors. Given this, all users of VaR need to be aware of what they want the risk measure to accomplish for their unique situation, and ultimately of the informational demands placed on this risk measure.
DISCUSSION AND CONCLUSIONS
Clearly, VaR is a very flexible tool. The uses of VaR analysis in managing price-based risk in the supply chain are numerous. VaR is reasonably easy to calculate and communicates downside risk in simple terms (dollars) to upper management. In essence, because it summarizes the downside risk of a potentially complex portfolio into a single number, it is easy to interpret. Yet, it is a statistically sound and rigorous concept. It is not surprising then that it is being quickly adopted within financial firms and corporations that rely heavily on the treasury function. Its potential for monitoring risk stemming from the purchasing function and other components of the supply chain is equally compelling. However, despite the statistical rigor that can enter a VaR calculation, at heart, it is still just a management and communication tool. Thus, it is not a panacea for sound risk management practices. As such, it must be tailored (benchmark, time horizon, and confidence interval) to each specific situation. The most appropriate information regarding risk must be conveyed to a potentially nontechnical management team. Thus, 4it is critically important to remember the typical management goal of VaR in the overall system--no surprises. The communicated VaR must adequately measure and explain the appropriate risks for the given audience. The uses and methods of calculating VaR can be as varied as the audience itself.
Given this, purchasing managers, risk managers, and other users of VaR within the firm must also be cognizant of VaR's drawbacks. Most of these drawbacks deal directly with the properties of the different estimation techniques previously discussed (e.g., violations of the normality assumption with parametric methods; reliance on historical data; distributional assumptions with Monte Carlo methods)--all of which could yield VaR estimates that are either too conservative, or worse, underestimate bad outcomes. To circumvent these potential problems, risk managers should stress-test the VaR estimate under extreme conditions (Jorion 1997). For example, what would happen to the value of the portfolio examined in Table III if the prices of some or all of the commodities move by extreme amounts not suggested by the historical standard deviation estimates? Would the VaR estimate adequately anticipate such an extreme event? Risk managers should stress-test their VaR estimates by using alternative values of the critical parameters (individual standard deviations and correlations) used in calculating portfolio standard deviation, and subsequently VaR. This stress-testing essentially allows risk managers and other users of the estimate to establish a range of VaR estimates. Surprises can also be avoided by "scaling up" the VaR estimate. For instance, the 1995 BASLE Committee proposal on banking regulation suggested that banks multiply their VaR estimates by a predetermined factor (e.g., 2) to provide an additional cushion against adverse market movements not suggested by historical market data (Jorion 1997).
Ultimately, it is the role of the risk manager to adequately measure and control risk within the system. The risk manager must make sure that each concerned party gets the appropriate information to perform their function while effectively monitoring the overall risk exposure of the firm. At the same time, the risk manager must be certain that the measurement techniques being utilized are as accurate and robust as possible given implementation costs and constraints.
In this tutorial, Value-at-Risk was examined from a corporate risk management perspective. In addition to introducing VaR and related estimation procedures, this research isolated the informational demands placed on VaR in the context of a hypothetical but realistic corporate risk management system for a commodity end user (Figure 2). The example focused on food-related market risks, but it is widely applicable to any end user with market-based risk (e.g., energy or metals). As purchasing and supply chain management become an increasingly concentrated source of market risk, it is important that purchasing executives adopt a way to measure that risk and communicate it accurately within the firm. VaR provides a tool for meeting the ever-increasing informational demands of upper management and shareholders.
Table 1 SUMMARY STATISTICS FOR WEEKLY FUTURES RETURNS, 1986-1998 K.C. Boneless Soybean Coffee Wheat Beef Oil Beans Mean 0.11% -0.01% -0.08% -0.14% Standard Deviation 2.79% 3.42% 2.98% 5.29% ([[sigma].sub.i] Returns are the log relative price change, [DELTA][p.sub.t]= ln([P.sub.t]/[P.sub.t-1]) for the nearby futures contract (635 observations). The variances are stastically different at the 1% level for each market pair except soybean oil and wheat (p-value = 0.1085). Table II CORRELATIONS BETWEEN WEEKLY FUTURES RETURNS, 1986-1998 K.C. Boneless Soybean Coffee Wheat Beef Oil Beans K.C. Wheat 1.0000 Boneless Beef 0.0228 1.0000 Soybean Oil 0.2391 -0.0005 1.0000 Coffee Beans 0.0795 0.0456 0.0385 1.0000 The above are simple correlation coefficients ([rho].sub.ij]) between log relative price changes, [DELTA][p.sub.t]=ln([P.sub.t]/[P.sub.t-1]). The standard error of the estimate is [(1/n-3).sup.0.5]). So, with n=635, the standard error is 0.0526 and a correlation greater than 0.1226 is statistically different from zero at the 1% level (two-tailed test). Therefore, soybean oil and wheat demonstrate a correlation that is statistically different from zero (1% level). Table III PORTFOLIO CHARACTERISTICS AND EXAMPLE OF VALUE-AT-RISK Monthly Months Current Position Portfolio Usage Coverage Price ($) Value ($) Weight K.C. Wheat (bu.) 25,000 3 3.50 262,500 0.0874 Boneless Beef (cwt.) 5,000 3 125.00 1,875,000 0.6242 Soybean Oil (cwt.) 4,800 3 25.00 360,000 0.1199 Coffee Beans (cwt.) 1,125 3 150.00 506,250 0.1685 Total 3,003,750 1.0000 7-Day Portfolio St. Deviation 0.02412 7-Day VaR at the 99% confidence level $119,170 Table IV VALUE-AT-RISK OVER ALTERNATIVE HORIZONS AND CONFIDENCE INTERVALS Confidence Interval Time Horizon 90% 95% 99% 1-Day $35,094 45,042 63,704 7-Day 92,849 119,170 168,545 28-Day 185,698 238,341 337,090 91-Day 334,772 429,675 607,697 Note: The values are calculated using the equation in the test. The base time horizon is 7 days with a standard deviation of 2.412%. The standard deviation is then scaled by the square root of time. For instance, the 28-day standard deviation is 2.412%x2 (the square root of 28/7).
(1.) An exhaustive examination of the properties and performance of parametric and simulation procedures is beyond the scope of this article. See Manfredo and Leuthold (1999) for a review of studies that compare the performance of these methodologies. Also see the "All About Value-at-Risk" Web site (www.GloriaMundi.org), which serves as a clearinghouse for VaR research, including both published work as well as working papers with much of the emphasis toward the development and examination of alternative estimation procedures for VaR.
(2.) For a list of various commercial VaR software packages, see the "All About Value-at-Risk" Web site (www.GloriaMundi.org) The authors do not endorse nor provide review of any of these products.
(3.) While this case is fictitious and made relatively simplistic for expository purposes, it is conceptually very similar to actual corporate risk management systems used by foodservice firms with which the authors are familiar.
(4.) Kansas City Board of Trade wheat futures have the following delivery months: December, March, May, July, and September. For example, If today's date were June 1, the July contract would be the nearby contract.
(5.) This is a very simple example used solely to illustrate the basic mechanics of hedging Input price risk and assumes a zero basis and no basis risk. A thorough discussion of hedging using futures and options is beyond the scope of this tutorial. See Leenders and Fearon (1997), Leuthold, Junkus, and Cordier (1989), and Thuong and Ho (1987) for specific examples of using hedging to control price risk.
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Dwight R. Sanders is an assistant professor of agribusiness economics at Southern Illinois University in Carbondale, Illinois.
Mark R. Manfredo is an assistant pro fessor in the Morrison School of Agribusiness and Resource Management at Arizona State University in Tempe, Arizona.
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|Author:||Sanders, Dwight R.; Manfredo, Mark R.|
|Publication:||Journal of Supply Chain Management|
|Date:||Mar 22, 2002|
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