If I have sold the stock short, a decline in price is a desirable outcome for me. Many, but not all, risks involve choices. By taking some action, we may deliberately expose ourselves to risk — normally because we expect a gain that more than compensates us for bearing the risk. If you and I come to a bridge across a canyon that we want to cross, and we notice signs of weakness in its structure, there is uncertainty about whether the bridge can hold our weight, independent of our actions.
If I choose to walk across the bridge to reach the other side, and you choose to stay where you are, I will bear the risk that the bridge will not hold my weight, but you will not. If the stakes are high enough, we can and should deal with risk explicitly, with the aid of a quantitative model.
In fact, much research shows that we have cognitive biases, such as over-weighting the most recent adverse event and projecting current good or bad outcomes too far into the future, that work against our desire to make the best decisions. Quantitative risk analysis can help us escape these biases and make better decisions. It helps to recognize up front that when uncertainty is a large factor, the best decision does not always lead to the best outcome.
Risk analysis can help us analyze, document, and communicate to senior decision-makers and stakeholders the extent of uncertainty, the limits of our knowledge, and the reasons for taking a course of action. Simulation software, properly used, is a relatively easy way to overcome the drawbacks of conventional what-if analysis. Instead of a few what-if scenarios done by hand, the software runs thousands or tens of thousands of what-if scenarios, and collects and summarizes the results using statistics and charts.
Instead of arbitrarily choosing input values by hand, the software makes sure that all the combinations of input parameters are tested, and values for each parameter cover the full range. For example, if we have just 10 suppliers, and the quantities of parts they supply have just 10 different values, there are or 10 billion possible scenarios. What can we do? The Monte Carlo method was invented by scientists working on the atomic bomb in the s.
It was named for the city in Monaco famed for its casinos and games of chance. They were trying to model the behavior of a complex process neutron diffusion. Since that time, Monte Carlo methods have been applied to an incredibly diverse range of problems in science, engineering, and finance — and business applications in virtually every industry. A full year of maintenance is included when you purchase your software. Shortly before your maintenance plan expires, renewal notices are sent via e-mail.
If you choose not to renew your maintenance plan, none of the above benefits will be available to you. Lapsed maintenance plans may only be renewed at higher prices and with reinstatement fees. Michael Watson. Palisade Brochure. Industry Example Models. Monte Carlo Simulation By sampling different possible inputs, RISK calculates thousands of possible future outcomes, and the chances they will occur.
More About Monte Carlo Simulation. Sensitivity Analysis RISK identifies and ranks the most important factors driving your risks, so you can plan strategies—and resources—accordingly. Learn About Sensitivity Analysis.
Graphs and Reports RISK offers a wide variety of customizable, exportable graphing and reporting options that let you communicate risk to all stakeholders. Extensive Modeling Features With a broad library of probability distributions, data fitting tools, and correlation modeling, RISK lets you represent any scenario in any industry with the highest level of accuracy. Every probability distribution can be represented by a cumulative distribution function, as shown below:.
By definition, a random value from a probability distribution is equally likely to be at any cumulative probability. Reversing that logic, we can generate a random number for the variable by sampling from a Uniform distribution between 0 and 1, and then use the cumulative curve to translate this into a sample value for the variable. In the illustration above, a random value of 0. This idea is key to Monte Carlo simulation.
In effect, for every random variable of a Monte Carlo simulation model, samples are taken from Uniform 0,1 distributions, so each generated scenario is just as likely to occur as any other. However, due to the shape of each cumulative curve, more values will be generated where the cumulative curve is at its steepest, as shown below:.
It is because these generated scenarios are all just as likely as each other that we can simply make a histogram distribution or cumulative distribution from the generated output results, and the resultant distributions can be interpreted as approximations to the true theoretical distributions of the output variables. The more samples sometimes called iterations that are run in a simulation, the smoother the resultant distributions become and the more precisely they match the true theoretical result.
In order to produce a high quality Monte Carlo simulation, one must have a method of generating Uniform 0,1 random numbers. Vose Software simulation products uses the Mersenne Twister. The algorithm uses the generated value as an input to produce the next value.
The random number generating algorithm starts with a seed value , and all subsequent random numbers that are generated will rely on this initial seed value. ModelRisk and Tamara both offer the possibility of specifying the seed value for a simulation, an integer from 1 to 2,,, It is good practice always to use a seed value and to use the same numbers habitually like 1, or your date of birth as you will remember them in case you want to reproduce the same results exactly.
Providing the model is not changed, and for ModelRisk that includes the position of the distributions in a spreadsheet model and therefore the order in which they are sampled, the same simulation results can be exactly repeated. EPA designed its human health risk assessment guidance e. EPA is aware that true risks are probably less than its estimates, but has chosen a regulatory policy of giving the benefit of uncertainty surrounding the risk assessment to the exposed public.
These protective risk estimates sometimes create difficulty for Agency decision-makers and the public. Site-specific Regional risk assessments usually present risk as a single number, or single-point estimate, accompanied by a qualitative discussion of uncertainty.
The public tends to focus on the single-point estimate and to overlook the uncertainty, which may span several orders of magnitude. EPA risk managers, though aware of the uncertainty, must still justify their decision to either accept or reduce the single-point risk.
If the risk is close to the maximum acceptable level, it is likely that different assumptions would have produced a different risk number, leading to a different decision. In this way, single-point risk assessment methods place the risk assessor in an inappropriate risk management role.
Recent EPA guidance on risk characterization EPA, discusses this problem in depth, and recommends the use of multiple risk descriptors in addition to protective single-point risk estimates. Inclusion of these additional risk descriptors provides the public with more complete information on the likelihood of various risk levels, and risk managers with multiple risk-based cleanup goals from which to choose.
This guidance mentions Monte Carlo simulation as an effective source of multiple risk descriptors. Monte Carlo simulation is a statistical technique by which a quantity is calculated repeatedly, using randomly selected "what-if" scenarios for each calculation.
Though the simulation process is internally complex, commercial computer software performs the calculations as a single operation, presenting results in simple graphs and tables.
0コメント