More About @RISK 5.0
» The @RISK Library
» The Compound Function
» @RISK for Six Sigma (web)
» RISKOptimizer 5.0

@RISK 5.0 Example Models
» Asset Price Random Walks
   and Option Values
» Discounted Cash Flow
» Insurance Claims with
   RiskCompound
» Product Mix with
   RISKOptimizer
» Six Sigma DOE
» Value at Risk (VAR)

“@RISK 5.0 is intuitive, flexible and technically excellent. It is a quantum leap in all aspects of functionality and user experience.”
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Chase Cooper Ltd

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Larry Hoberg
Raytheon

“The look and feel of @RISK 5.0 is a step up. Much more intuitive. This package seems really well put together.”
Albert Perrella
Institute for Defense Analyses

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All @RISK 5.0 purchases made by February 29, 2008 will be shipped with a FREE copy of Financial Models Using Simulation and Optimization by Wayne Winston and all accompanying example models. First published in 1998, this book has been updated for @RISK 5.0 in a new 3rd edition and has become the reference for business and financial modeling under uncertainty. Packed with over 100 real-life example spreadsheets, it comes with step-by-step instructions on a wide range of topics in finance and business. This offer ends February 29.

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More About @RISK 5.0

The @RISK Library
@RISK 5.0 Professional and Industrial versions include the @RISK Library, a separate database application for sharing @RISK input probability distributions and comparing results from different simulations. The @RISK Library uses SQL Server to store @RISK data. Different users in an organization can access a shared @RISK Library in order to access:

• Common input probability distributions which have been pre-defined for use in an organization’s risk models
• Simulation results from different users in an organization

Probability distribution functions in the @RISK Library may be accessed from the Define Distribution window like any other distribution.

The @RISK Library will make standardization and consistency of analysis much easier than ever before. With the @RISK Library, workgroup efficiency will be greatly improved.

The Compound Function
The new RiskCompound function, especially applicable to the insurance industry, is used for “frequency – severity” modeling and takes two distributions to create a single new input distribution. This function takes two arguments. Each argument can be an @RISK function, or can be a cell reference to another formula. In a given iteration, the value of the first argument specifies the number of samples which will be drawn from the distribution entered in the second argument. Those samples from the second distribution are then summed to give the value returned by the RiskCompound function.

For example, the function:

RiskCompound(RiskPoisson(5),RiskLognorm(10000,10000))

would be used in the insurance industry where the frequency or number of claims is described by RiskPoisson(5) and the severity of each claim is given by RiskLognorm(10000,10000). Here the sample value returned by RiskCompound is the total claim amount for the iteration, as given by a number claims sampled from RiskPoisson(5), each with an amount sampled from RiskLognorm(10000,10000).

RiskCompound can eliminate hundreds or thousands of distribution functions from existing @RISK models by encapsulating them in a single function. The result is models that are much simpler to use, and run much faster.

RiskCompound supports cell references with formulas for more complex modeling, such as accounting for the timing of claims paid.

Included with the Industrial version of @RISK 5.0 and the DecisionTools Suite, RISKOptimizer 5.0 has been re-engineered from the ground up in a stunning new version. A streamlined interface, full support for cell ranges, enhanced monitoring of optimization progress, a faster engine and more make RISKOptimizer PC World’s “most practical power tool around.”

RISKOptimizer combines the Monte Carlo simulation technology of @RISK with genetic algorithm optimization technology to allow the optimization of Excel spreadsheet models that contain uncertain values. Take any optimization problem and replace uncertain values with @RISK probability distribution functions that represent a range of possible values. For each trial solution RISKOptimizer tries during optimization, it runs a Monte Carlo simulation, finding the combination of adjustable cells that provides the best simulation results.

» More on RISKOptimizer 5.0

@RISK 5.0 Example Models

Asset Price Random Walks and Options Valuation
Models of the prices of assets (stocks, property, commodities) very often assume a random walk over time, in which the periodic price changes are random, and in the simplest models are independent of each other. The future price level of the asset may result in some contract or payoff becoming valuable, such as in the case of financial market options. In these cases, the value of the contract (contingent payment or option) is calculated as the average discounted value of the future payoff. In the special case of European options on a traded underlying asset, the value calculated from the simulation may be compared with mathematical formulas that analytically provide the valuation, such as the Black-Scholes equation. This particular model compares the average simulated payoff for European Call and Put options with the Black-Scholes valuation.

For the case of the correlated random walks of multiple assets with a constant correlation coefficient, these can be set up using the Correlated Time Series feature of @RISK.

» Download example model: AssetPrices.Options.BS.Multi.xls

Discounted Cash Flow (DCF)
Discounted cash flow (DCF) calculations are a frequent example of the use of @RISK. In the example model, the sources of risk are the revenue growth rate and the variable costs as a percentage of sales. After taking into account the assumed investment, and applying a discount factor, the DCF is derived. Following the simulation, the average (mean) of the DCF is known as the net present value (NPV). The decision as to whether to proceed or not with this project will depend on the risk perspective or tolerance of the decision-maker. This example has also been extended to calculate the distribution of bonus payments on the assumption that a bonus is paid whenever the net DCF is larger than a fixed amount. It also uses the @RISK Statistics functions RiskMean, RiskTarget, and RiskTargetD to work out the average net DCF, the probability that the net DCF is negative and the probability that a bonus is paid.

» Download example model: CashFlow.xls

Insurance Claims with RiskCompound
@RISK’s RiskCompound function uses two distributions to create a single new input distribution, streamlining insurance models that must account for frequency and severity of claims. This model illustrates how the RiskCompound function is created, and shows properties such as mean, standard deviation, and a target value of the resulting RiskCompound function.

» Download example model: RiskCompound.xls

Product Mix with RISKOptimizer
A manufacturing plant is trying to find the optimal quantities of each of four products to manufacture to maximize the mean of total revenues. The demand for each product is uncertain, and represented with probability distribution functions. The quantity of each product produced must meet constraints related to the resources available for manufacturing each product. Here, all constraints are specified in one step, using RISKOptimizer's ability to define constraint limits as ranges. RISKOptimizer will vary the amount of each product produced, subject to the constraints of resources, to maximize revenues.

» Download example model: ProductMix.xls

Six Sigma DOE
Suppose you are analyzing a metallic burst cup manufactured by welding a disk onto a ring. The product functions as a seal and a safety device, so it must hold pressure in normal use, and it must separate if the internal pressure exceeds the safety limit. The output is the weld strength, which is affected by process and design factors such as disk thickness, weld time, and more. The model accounts for the variation for each factor, and forecasts the product performance in relation to the engineering specifications.

Modeling a response based on multiple factors can often be accomplished by generating a statistically significant function through experimental design or multiple regression analysis. In this example, @RISK simulates the variation using Normal distributions for each factor.

The output is Weld Strength (N) and contains a RiskSixSigma property function that includes the Lower Specification Limit (LSL), Upper Specification Limit (USL), and Target value specified. After you run the simulation, Six Sigma statistics are generated using @RISK Six Sigma functions for Cpk-Upper, Cpk-Lower, Cpk, and PPM Defects (or DPM). Standard @RISK statistics functions (like RiskMean) were also used.

» Download example model: SixSigmaDOE.xls

Value at Risk (VAR)
The concept of value at risk (VAR) has been used to help describe a portfolio's uncertainty. Simply stated, the value at risk of a portfolio at a future point in time is usually considered to be the fifth percentile of the loss in the portfolio's value at that point in time. In other words, there is considered to be only one chance in 20 that the portfolio's loss will exceed the VAR. This model shows how @RISK can be used to measure VAR. The example also demonstrates how buying puts can greatly reduce the risk in a stock. The two outputs represent the range of the percentage gain if we do not buy a put vs. the percentage gain if we do buy a put. The results illustrate there is a greater chance of a big loss if we do not buy the put, although the average return is slightly higher if we do not buy the put.

» Download example model: VAR.xls

More Example Models online:

» Finance
» Insurance
» Six Sigma