About the Exam

1. About the Exam • No cheat sheet • Bring a calculator • You may NOT use the calculator on your phone or iPad or computer or other media device • Short essay answers • Math problems to be solved • Materials presented in Lab will also be include in the exam • The Exam may include material from this lecture

2. Materials for Lecture 13 • Chapter 2 pages 6-12, Chapter 6, Chapter 16 Section 3.1 and 4 • Read Richardson & Mapp article • Lecture 13 Business.xlsx • Lecture 13 Probability of Revenue.xlsx • Lecture 13 Flow Chart.xlsx • Lecture 13 Farm Simulator.xlsx • Lecture 13 Uniform.xlsx

3. Definitions for Simulation • The word Monte Carlo is used several ways • Monte Carlo is a country where gambling is widespread and is romanticized in movies • Monte Carlo is a hotel in Las Vegas, NV • In the area of simulation Monte Carlo is used two ways: • Monte Carlo is a method for generating random variables that randomly draws values from the distribution A better method is to use Latin hypercube to simulate random variables. It uses a systematic approach to be more complete.

4. Definitions for Simulation • Monte Carlo simulation means the model has one or more random variables that are simulated to estimate the distribution for a KOV. • Monte Carlo simulation is the SAME as stochastic simulation • Stochastic means Random

5. Forecasting and Risk Analysis for Business • Forecasts always have risk that is unexplained by the model. Can’t include every source of risk in forecasts • Forecast models we learned to use are: • Trend, seasonal, cyclical, exponential smoothing, OLS structural, and Time Series • None of these methods yield perfect forecasts as the residuals are not Zero • To add risk to our forecasts we will use Monte Carlo (stochastic) Simulation – then use forecasts in business models • Simulation will allow you to put confidence intervals on your business model without using Calculus and higher level Statistics

6. · Determ forecast Probabilistic Forecasting (PF) - PF are inter-temporal forecasts of a random variable with stochastic components · Prob forecast Yt = a + b Xt + (randomly drawn e from residuals) - PF involves simulating an econometrically estimated forecast equation with the appropriate risk - Purpose is to evaluate the risk in a forecast - Readings: Chapter 15 - Lecture 16 Probabilistic Forecasting.XLSX - Lecture 16 Probabilistic Time Series.XLSX Lecture 16

7. Types of Business Decisions that Benefit From Simulation • Expand or Contract a business • Vertically integrate to control the supply chain • Sell off a less profitable line • Inventory Management: Buy Inputs and Sell Products • Manage purchase and sale prices • Contract price, hedge price, options market, etc. • Schedule purchases and sales for inventory purposes • Enterprise changes • Add a new enterprise (e.g., add cow herd or stockers; add a fast food counter to a grocery store) • Many more applications

8. What are the Considerations? • What will be the change in annual income? • Will income increase with a high probability? • Does it increase the risk on income? • What will be the impact on annual ending cash reserves? • What is the chance of a cash flow deficit? • What will be the impact on ending net worth? • What is the chance we lose real net worth? • Business in place to increase net worth!!! • What will be the effect on stock pries and how will the stock holders react? • Fire me or give me a bonus?

9. Risk is a Major Consideration • In business there is always risk, questions are: • What are the sources of risk? • Can we manage the risk? • Is the benefit of the business change worth the risk? • Sources of risk for agribusiness • Production risk – crop yields, daily rate of gain and death loss for livestock, weather, input performance • Market risk – prices for the product and prices of the inputs, product hazards and law suits • Policy risk – will policy changes cause costs to increase, will environmental policies limit production • Competition – will competitors take away my market

10. Basic Business Model • Income Statement Receipts = Price (P) * Quantity (Q) Expenses = Fixed Costs + [Variable Cost * Quantity (Q)] + Interest Net Cash Income (NCI) = Receipts – Expenses • Cash Flow Statement Inflows = NCI + Other Income + Interest Earned Outflows = Dividends + Owner Withdrawals + Taxes + Machinery Replacement Outlays + Repay Cash Flow Deficits Ending Cash = Inflows - Outflows • Balance Sheet Assets = Ending Cash + Land + Machinery + Livestock Liabilities = Land Debt + Machinery Debt + Livestock Debt + Cash Flow Deficits Net Worth = Assets - Liabilities

11. Where Does Risk Enter the Business • Income Statement Receipts = Price (P) * Quantity (Q) Expenses = Fixed Cost + Variable Cost * Quantity (Q) + Interest Net Cash Income (NCI) = Receipts – Expenses • Cash Flow Statement Inflows = NCI + Other Income + Interest Earned Outflows = Dividends + Owner Withdrawals + Taxes + Machinery Replacement Outlays + Repay Cash Flow Deficits Ending Cash = Inflows - Outflows • Balance Sheet Assets = Ending Cash + Land + Machinery + Livestock Liabilities = Land Debt + Machinery Debt + Livestock Debt + Cash Flow Deficits Net Worth = Assets - Liabilities

12. Simulation is the Best Method to Analyze Risk for Business Decisions • Over the past 20 years more businesses have come to rely on Monte Carlo simulation to analyze risk • Simulation used to require massive computers and special languages. Excel changed all of that!!! • Simulation is best tool for risk analysis because: • Simulates the business as it is and how it could be • Simulation results resonate well with manages • Many different forms risk can take and simulation can handle all of them. Limitation is your imagination. • Incredibly flexible, adapts to any type of problem • Bottom line it is the methodology that answers the question … What if……?

13. What Does Our Business Model Look Like When We Include Risk? • Income Statement = * Expenses = Fixed Cost + Interest + * Net Cash Income (NCI) = Receipts – Expenses • Cash Flow Statement Inflows = NCI + Other Income + Interest Earned Outflows = Dividends + Owner Withdrawals + Taxes + Machinery Replacement + Short Term Cash Flow Deficits Ending Cash = Inflows - Outflows • Balance Sheet Assets = Ending Cash + Land + Machinery + Livestock Liabilities = Land Debt + Machinery Debt + Livestock Debt + Cash Flow Deficits Net Worth = Assets - Liabilities

14. Steps for Modeling a Business • Know the business you are analyzing • Determine the Key Output Variables (KOVs) the manager/owner wants to know • Determine the risky variables affecting business • Obtain historical data for the risky variables and the business pro forma financial statements • Determine the “What if ….? Question really is the manager/owner wants answered -- • Often times this is not what the owner is asking but a more basic or underlying question • Given this information we build a simulation model to fit the problem at hand

15. What is a Simulation Model? • A simulation Model is a mathematical representation of a business • When you think through the many steps to solve a problem you are constructing a virtual model • Computer games are simulation models • Forecasting equations will be part of a model • We build computer models …. • So we do not have to experiment on the actual economic system • So we can test many different management scenarios rapidly. For example: • Will the business be successful if we change management practices from A to B to C?

16. Organization of Models in Excel • Sheet 1 (Model) • Assumptions and all Input Data • Control variables for managing the system • Logical flow of all calculations • Table of intermediate results • Pro Forma financial tables of results • Key Output Variables (KOVs) Table to send to SimData • Sheet 2 (Stoch) • Historical data for all random variables • Calculations to estimate the parameters for all random variables • Simulate all random values to be used in the Model • Sheets 3-N (SimData, Stoplite, SERF, STODOM, etc) • Simulation results tables and charts • Rank the risky scenarios

17. Design Build KOVs Intermediate Results Tables and Reports Equations and Calculations to Get Values for Reports Stochastic Variables Exogenous and Control Variables Model Design Steps • Model development is like building a pyramid • Design the model from the top down • Build from the bottom up

18. Steps for Model Development • Write out the equations by hand or at least in Word • This organizes your thoughts and the model’s structure • Avoids problem of forgetting important sections • Example of equations to simulate receipts: • Output/hour = a stochastic variable • Hours Operated = management control value (scenario variable) • Production = Output/hour * Hours Operated • Price = forecast mean each year with a risk component • Receipts = Price * Production • Define types of input variables • Exogenous variables that are not controlled by management and are deterministic; usually policy driven • Stochastic variables management can not control and are random in nature: weather, input & output prices, interest rates • Control variables the manager can manipulate and are usually used for sensitivity and/or scenario analyses

19. Steps for Model Development • Identify key random variables that affect the system • Estimate parameters for the assumed distributions • Normality – means and standard deviations • Empirical – sorted deviates and probabilities • Other distributions should be tested • Use the best possible econometric model to forecast deterministic part of stochastic variables to reduce risk • Model validation starts here • Use statistical tests of the simulated stochastic variables to insure that random variables are simulated correctly • Correlation tests, means tests, variance tests • CDF and PDF charts to compare history to simulated values • Key to validating model are statistical tests

20. More About Stochastic Variables • Why include stochastic variables? • To get a more robust simulation answer • By including stochastic variables we can assign probabilities to KOVs • We can incorporate risk in our decisions of selecting between scenarios • We do not have to forecast stochastic variables with a perfect model because we are including the risk component

21. More About Stochastic Variables • Production of agricultural products is stochastic due to many factors • Weather, producers’ response to prices (acres planted, inputs used in production, etc.) Output Y Input X1

22. Prices are Stochastic Due to Demand Being Stochastic • Supply and Demand Model • You learned there is one Demand and one Supply • But there are many, due to risk in the market Qx = a + b1Px +b2Y + b3Py gives a single line for Demand Qx = a + b1Px +b2Y + b3Py + ẽ gives infinite Demands • After harvest Supply is a constant, so we get an infinite number of Prices as we draw ẽ values at random Price/U Supply • Demand is stochastic so we can have an infinite number of Demand functions passing through the QD distribution Demand Quantity/UT

23. Simulation Model Output

24. Simulation Model Output

25. Simulation Model Output

26. Summary • Do you want to make multiple million dollar decisions using a point forecast of net income? Or calculating the “best case” and the “Worst case?” • Or do you want to make business decisions based on all possible outcomes with probabilities for success and failure? • Simulation techniques covered in class will teach you how to build risk based business models

27. Forecasting REVIEW Notes • The following is a mathematical review of the forecasting techniques we have covered in class • We will not cover these slides in class • They are for your benefit as a summary of the math all in one place

28. Calculate and simulate as Normally distributed, Forecast Techniques - Moving Average Example of a 3 period MA model Simulate it for a future period, say, year 16 as Stochastic Comp Deterministic Component

29. Simulate for a future period, say, 25 as: Forecasting Techniques - Simple Exponential Smoothing Example is: Deterministic Component Stochastic Comp

30. Use the residuals to simulate the risk in the forecast Forecasting Techniques - Regression Models · Trend Regression · Multiple Regression · Non-Linear Trend Regression · Harmonic Regression For example, if we had used OLS to estimate a cycle Y= a + b T + b Sin(2*PI()*T/CL) + b COS(2*PI()*T/CL) Where CL = No. of Years * SL SL = 12 for monthly data, 4 for quarterly data, and 1 for annual data

31. · Annual forecast for year t is · To make this stochastic need to add risk on the index I and on - Risk on annual forecasts component is from the residuals on the annual forecast ) or use a MVE for the Deviations from mean). - Risk on the monthly index is from the index for month i. Forecast Techniques - Using a Seasonal Price Index for Forecasting: · Seasonal index for each month Ii,i = 1, 2, …, 12 · Deterministic monthly forecast for month 6 · Stochastic monthly forecast for month 6 if assume residuals are normally dist.

32. · Calculate the Stochastic Index Value for each year as: Forecast Techniques -- Seasonal Forecast Finding the risk measure for the monthly index, or · Calculate the Seasonal Index Table to get index values Iij • Calculate parameters for a Multivariate Empirical Distribution as a Fraction of the Mean – using the values in the Index table ( the 12 months and N years of prices or sales numbers) • Correlation matrix using unsorted deviations from the mean • Sorted deviations from the mean as a fraction • Probabilities for the sorted deviates · Calculate CUSD’s using the correlation Matrix. Calculate a separate 12x1 vector for each year to forecast · Seasonal forecast value in year i, month j is:

33. where is the std. dev. of the residuals for the AR( ) model Forecast Techniques - Times Series Stochastic Forecasts - AR and VAR models can be estimated and deterministic forecasts can be developed - The one period ahead forecast can be simulated stochastic by adding risk - This is a stochastic application of the Chain Rule forecasting formula

34. Time Series Stochastic Forecasts - The second and third periods ahead stochastic forecasts from the AR Model become more complex as: and