RRRIIISSSKKK SSSIIIMMMUUULLLAAATTTOOORRR UUUssseeerrr MMMaaannnuuuaaalll JJJooohhhnnnaaattthhhaaannn MMMuuunnn,,, PPPhhh...DDD...,,, MMMBBBAAA,,, MMMSSS,,, BBBSSS,,, CCCRRRMMM,,, FFFRRRMMM,,, CCCFFFCCC,,, MMMIIIFFFCCC RRReeeaaalll OOOppptttiiiooonnnsss VVVaaallluuuaaatttiiiooonnn,,, IIInnnccc... REAL OPTIONS VALUATION, INC. This manual, and the software described in it, are furnished under license and may only be used or copied in accordance with the terms of the end user license agreement. Information in this document is provided for informational purposes only, is subject to change without notice, and does not represent a commitment as to merchantability or fitness for a particular purpose by Real Options Valuation, Inc. No part of this manual may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, for any purpose without the express written permission of Real Options Valuation, Inc. Materials based on copyrighted publications by Dr. Johnathan Mun, Ph.D., MBA, MS, BS, CRM, CFC, FRM, MIFC, Founder and CEO, Real Options Valuation, Inc., and creator of the software. Written, designed, and published in the United States of America. Microsoft® is a registered trademark of Microsoft Corporation in the U.S. and other countries. Other product names mentioned herein may be trademarks and/or registered trademarks of the respective holders. © Copyright 2005-2012 Dr. Johnathan Mun. All rights reserved. Real Options Valuation, Inc. 4101F Dublin Blvd., Ste. 425 Dublin, California 94568 U.S.A. Phone 925.271.4438 • Fax 925.369.0450 [email protected] www.risksimulator.com www.realoptionsvaluation.com Table of Contents 1. INTRODUCTION TO RISK SIMULATOR .................................. 1 1.1 Welcome to Risk Simulator ............................................................................................................. 1 1.2 Installation Requirements and Procedures ........................................................................................ 2 1.3 Licensing .......................................................................................................................................... 2 1.4 What’s New in Version 2012 ........................................................................................................ 5 1.4.1 General Capabilities .......................................................................................................................... 5 1.4.2 Simulation Module ............................................................................................................................ 6 1.4.3 Forecasting Module ........................................................................................................................... 7 1.4.4 Optimization Module ....................................................................................................................... 7 1.4.5 Analytical Tools Module .................................................................................................................. 8 1.4.6 Statistics and BizStats Module ........................................................................................................ 9 2. MONTE CARLO RISK SIMULATION ........................................ 11 2.1 What Is Monte Carlo Simulation? .............................................................................................. 11 2.2 Getting Started with Risk Simulator ............................................................................................ 12 2.2.1 A High-Level Overview of the Software ................................................................................... 12 2.2.2 Running a Monte Carlo Simulation ............................................................................................ 13 2.2.3 Forecast Chart Tabs ........................................................................................................................ 21 2.3.4 Using Forecast Charts and Confidence Intervals .................................................................... 23 2.3 Correlations and Precision Control ............................................................................................... 26 2.3.1 The Basics of Correlations ............................................................................................................ 26 2.3.2 Applying Correlations in Risk Simulator .................................................................................... 27 2.3.3 The Effects of Correlations in Monte Carlo Simulation ........................................................ 27 2.3.4 Precision and Error Control ......................................................................................................... 29 2.3.5 Understanding the Forecast Statistics ......................................................................................... 31 2.3.6 Understanding Probability Distributions for Monte Carlo Simulation .............................. 35 2.4 Discrete Distributions ................................................................................................................... 38 2.5 Continuous Distributions.............................................................................................................. 45 3. FORECASTING .............................................................................. 64 3.1 Different Types of Forecasting Techniques ..................................................................................... 65 3.2 Running the Forecasting Tool in Risk Simulator ......................................................................... 68 3.3 Time-Series Analysis .................................................................................................................... 69 3.4 Multivariate Regression................................................................................................................. 72 3.5 Stochastic Forecasting .................................................................................................................... 76 3.6 Nonlinear Extrapolation ............................................................................................................. 78 3.7 Box-Jenkins ARIMA Advanced Time-Series ............................................................................ 80 3.8 AUTO-ARIMA (Box-Jenkins ARIMA Advanced Time-Series) .......................................... 85 3.9 Basic Econometrics ....................................................................................................................... 86 3.10 J-S Curve Forecasts .................................................................................................................... 89 3.11 GARCH Volatility Forecasts .................................................................................................. 90 3.12 Markov Chains .......................................................................................................................... 93 3.13 Limited Dependent Variables: Logit, Probit, Tobit (Maximum Likelihood Estimation) ........ 94 3.14 Spline (Cubic Spline Interpolation and Extrapolation) .............................................................. 97 4. OPTIMIZATION ............................................................................ 99 4.1 Optimization Methodologies ......................................................................................................... 99 4.2 Optimization with Continuous Decision Variables .................................................................... 101 4.3 Optimization with Discrete Integer Variables ............................................................................ 106 4.4 Efficient Frontier and Advanced Optimization Settings ............................................................. 109 4.5 Stochastic Optimization .............................................................................................................. 111 5. RISK SIMULATOR ANALYTICAL TOOLS ............................... 116 5.1 Tornado and Sensitivity Tools in Simulation .............................................................................. 116 5.2 Sensitivity Analysis ..................................................................................................................... 123 5.3 Distributional Fitting: Single Variable and Multiple Variables ................................................ 127 5.4 Bootstrap Simulation .................................................................................................................. 131 5.5 Hypothesis Testing ...................................................................................................................... 133 5.6 Data Extraction and Saving Simulation Results ....................................................................... 135 5.7 Create Report.............................................................................................................................. 136 5.8 Regression and Forecasting Diagnostic Tool ................................................................................ 137 5.9 Statistical Analysis Tool ............................................................................................................. 144 5.10 Distributional Analysis Tool.................................................................................................... 147 5.11 Scenario Analysis Tool ............................................................................................................