Additional Case Study Two: Property Risk Assessment: A Simulation Approach
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1 Additional Case Study Two: Property Risk Assessment: A Simulation Approach This case study focuses on analyzing the risk of investing in income properties. The key point is that measures of central tendency, applied through probability analysis using Monte Carlo simulation, can be effectively used to evaluate investment property risk. This case study, prepared by Barrett A. Slade, PhD, MAI, can be read in entirety in The Appraisal Journal (Fall 2006), pages The subject matter is of particular interest to developers, commercial Realtors, real estate investors, appraisers and real estate consultants, but the statistical tools employed are of universal interest. Whereas Additional Case Study one assesses risk associated with dwellings, this case study uses statistical analysis to analyze risk associated with income properties. Although this case study applies the simulation tool Monte Carlo analysis, that has not been presented in this course, it also includes tools that have been presented such as: mean, median, mode, standard deviation, variance, skewness, range, and standard error 1. Simulation analysis leads to greater insights into the risk characteristics of investment properties by explicitly recognizing that many input assumptions are uncertain. It allows the analyst to realistically model this uncertainty and estimate the likelihood of an investment outcome. Compared to traditional risk assessment techniques, simulation analysis allows the investment decision maker to be much more informed. By applying modern simulation analysis to the investment analysis of an apartment property, this article illustrates the comparative advantages of modern risk assessment techniques over traditional methods. Business schools teach students that risk is the possibility that an investment s actual return may be different than expected, including the possibility that some or all of the original investment may be lost. Therefore, prudent investment analysis requires that this uncertainty be examined so that appropriate steps can be taken to mitigate potential loss. Risk assessment in real estate investment requires both qualitative as well as quantitative analysis, which is often referred to as the art and science of real estate investment analysis. Although the art, i.e. human judgment aspect, of investment analysis is an important part of the investment decision, the objective of this study is to illustrate the advantages of simulation analysis so that the science of risk assessment can be improved. Therefore, an important aspect of this study is to provide the reader with an introduction into the characteristics and benefits of simulation analysis for assessing risk in real property investments. Spreadsheet Construction Conventional risk assessment techniques generally begin with the construction of a spreadsheet that presents the expected future cash flows from an investment property. The spreadsheet in Table 1 below illustrates the expected cash flows from an apartment complex. 1 Monte Carlo Methods are techniques based on random numbers. Monte Carlo methods have been applied to a great variety of problems in the physical, social, and biological sciences. Monte Carlo methods have been used to simulate such things as the spread of cholera epidemics, the collision of photons with electrons, the scattering of neutrons in a nuclear reactor, traffic congestion on freeways, air turbulence and its effect on airplane wings, to mention but a few. In this way, methods based on random numbers make it possible to simulate the experiments which either cannot be performed in the laboratory (such as the spreading of an epidemic) or which would otherwise require prohibitively expensive equipment. Monte Carlo methods have also found wide application in business research, where they are used for solving inventory problems, or questions arising in connection with the allocation or resources, advertising, competition, and over-all planning and organization. UBC Real Estate Division 1
2 Table 2 below presents the reversion calculation. Table 3 shows important spreadsheet assumptions that are applied in Tables 1 and 2. Table 4 includes three important return measures critical to the overall acquisition decision, including the going-in capitalization rate, free and clear internal rate of return (IRR) after fees, and the leveraged equity IRR after fees. Don t concern yourself overly with the methodology of the discounted cash flow procedure as your primary interest is in the application of statistical analysis that follows the estimate of value flowing from the spreadsheet. UBC Real Estate Division 2
3 Traditional Scenario Analysis Traditionally an analyst will examine three scenarios: best-case, most-likely case (as shown in tables 1 and 2), and worst-case. These typical scenarios are shown on the following tables 5 and 6. In this traditional analysis there is no insight into the likelihood or probability of actually obtaining any of the three outcomes, which is not particularly comforting for the decision maker. Simulation Analysis At this point the power of statistical analysis for probability assessment and risk analysis is applied. Application of a Monte Carlo simulation analysis permits the analyst to simultaneously examine thousands of alternative scenarios and subsequently estimate the probability of an outcome. The analyst uses probabilistic input assumptions to generate forecasts or outcomes that can be analyzed statistically. Advancement in simulation software, both in technology and economy, have made simulation analysis much more practical for real estate investment risk analysis. The simulation software applied below is Crystal Ball, a Microsoft Excel add-in 2. For a simulation analysis, the analyst must first determine which input values are uncertain and then define the distributional assumptions associated with these values. An example of the way inputs are established is shown below in Figure 1. The analyst has forecast that market rents will grow from 1% to 6% annually and that the most likely growth rate is 3%. If the distributional characteristics of rent growth rates are unknown, the triangular distribution shown is applicable. This shape allows for identification of minimum, most likely and maximum values. The height of the triangle is least at the 1% and 6% points and highest at the 3% point. This tells the simulation program that values near 3% have a greater probability of occurrence; thus, when the simulation begins to run, values near 3% will be selected more frequently than values near the minimum and maximum points. 2 For more information on this software see UBC Real Estate Division 3
4 Other triangular distributions, with various degrees of skewness, are presented below in Figure 2 that provides the assumptions and relevant ranges for each uncertain input variable. Once the input variables have been identified and ranged, the output variables are specified as: going-in capitalization rate, free and clear IRR after fees, and the leveraged equity IRR after fees. At this point the number of trials is specified and the simulation started. Simulation results, after 1,000 iterations, are shown below in Figure 3. UBC Real Estate Division 4
5 The simulation results in Figure 3 illustrate the likelihood (probability) of a particular outcome. For example, with reference to the last chart Leveraged Equity IRR After Fees, the minimum and maximum leveraged equity IRR after fees are 4.66% and 24.68%, respectively. The mean and median are 15.52% and 15.54%, respectively. The proximity of the median to the mean suggests that the distribution is highly symmetrical, making statistical inference more reliable. The percentiles show that there is an 80% probability of achieving a leveraged equity IRR after fees of at least 12.55%. In addition to the foregoing, this simulation can also calculate the likelihood (probability) of obtaining a specific IRR. As shown below on Figure 4, there is a 66.97% probability of obtaining a leveraged equity IRR after fees that is greater than 14%. UBC Real Estate Division 5
6 Conclusion Simulation analysis leads to greater insights into the risk characteristics of investment properties by explicitly recognizing that many input assumptions are uncertain. The statistics accompanying the charts in Figure 3 permit the analyst to assess risk associated with each of the selected outputs and fine-tune the investment decision. See also: Arnold, Tom & Henry, Stephen "An Excel Application for Valuing European Options with Monte Carlo Analysis". Journal of Financial Education. 31 (Spring 2005). p This article illustrates the basic intuition of Monte Carlo simulation within an Excel spreadsheet framework, demonstrating the use of Monte Carlo simulation techniques to price options without additional sophisticated software. The skills and intuition developed also provide the basis for much more complex simulation techniques. UBC Real Estate Division 6
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