There are very few performance comparisons available when considering the acquisition of an Excel-based Monte Carlo solution. It is with this in mind and a bit of intellectual curiosity that we decided to evaluate Oracle Crystal Ball, Palisade @Risk, Vose ModelRisk and Frontline Risk Solver in terms of speed, accuracy and precision. We ran over 20 individual tests and 64 million trials to prepare comprehensive comparison of the top Monte-Carlo Tools.
Modeling in Excel or with any other tool for that matter is defined as the visual and/or mathematical representation of a set of relationships. Correlation is about defining the strength of a relationship. Between a model and correlation analysis, we are able to come much closer in replicating the true behavior and potential outcomes of the problem / question we are analyzing. Correlation is the bread and butter of any serious analyst seeking to analyze risk or gain insight into the future.
Given that correlation has such a big impact on the answers and analysis we are conducting, it therefore makes a lot of sense to cover how to apply correlation in the various simulation tools. Correlation is also a key tenement of time series forecasting…but that is another story.
In this article, we are going to build a simple correlated returns model using our usual suspects (Oracle Crystal Ball, Palisade @RISK , Vose ModelRisk and RiskSolver). The objective of the correlated returns model is to take into account the relationship (correlation) of how the selected asset classes move together. Does asset B go up or down when asset A goes up – and by how much? At the end of the day, correlating variables ensures your model will behave correctly and within the realm of the possible.
Copulas and Rank Order Correlation are two ways to model and/or explain the dependence between 2 or more variables. Historically used in biology and epidemiology, copulas have gained acceptance and prominence in the financial services sector.
In this article we are going to untangle what correlation and copulas are and how they relate to each other. In order to prepare a summary overview, I had to read painfully dry material… but the results is a practical guide to understanding copulas and when you should consider them. I lay no claim to being a stats expert or mathematician… just a risk analysis professional. So my approach to this will be pragmatic. Tools used for the article and demo models are Oracle Crystal Ball 11.1.2.1. and ModelRisk Industrial 4.0
One of the cool things about professional Monte-Carlo Simulation tools is that they offer the ability to fit data. Fitting enables a modeler to condensate large data sets into representative distributions by estimating the parameters and shape of the data as well as suggest which distributions (using these estimated parameters) replicates the data set best.
Fitting data is a delicate and very math intensive process, especially when you get into larger data sets. As usual, the presence of automation has made us drop our guard on the seriousness of the process and the implications of a poorly executed fitting process/decision. The other consequence of automating distribution fitting is that the importance of sound judgment when validating and selecting fit recommendations (using the Goodness-of-fit statistics) is forsaken for blind trust in the results of a fitting tool. Now that I have given you the caveat emptor regarding fitting, we are going to see how each tools offers the support for modelers to make the right decisions. For this reason, we have created a series of videos showing comparing how each tool is used to fit historical data to a model / spreadsheet. Our focus will be on :
The goal of this comparison is to see how each tool handles this critical modeling feature. We have not concerned ourselves with the relative precision of fitting engines because that would lead us down a rabbit hole very quickly – particularly when you want to be empirically fair.
Over the last 3 months, we have seen 3 of the 4 major players in the Excel Monte-Carlo Simulation arena introduce new releases. We hear a lot of talk about which tool is best and the truth is there is no perfect answer – it’s a personal thing dictated by user skill, preference and need.
For this reason, we have created a series of videos showing comparing how each tool is used to apply Monte-Carlo simulation to a model / spreadsheet. Our focus will be on :
To keep the playing field level, we have used a simple additive model, which is simply defining a series of distributions (i.e. costs, budget items…), summing them up and analyzing the resulting sensitivity analysis. We have kept things simple, so we are not correlating any of the variables nor using any fancy math.
As you will see, there are definite differences AND similarities regarding how these packages tackle building a model. We are going to focus on those relating to inserting and copying input distributions as well as defining and analyzing model outputs. The objective is to compare the ease, usability and efficiency of each tool and give people the opportunity to choose for themselves which tool reflects their needs and preferences better.