HowBad Is. Mark Zoellertakes a common, Commercial Real Estate

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1 Commercial Real Estate HowBad Is Mark Zoellertakes a common, often overlooked, problem and offers a path toward a workable solution. In this first of two articles, Zoeller feels that risk analysts are missing the boat by neglecting an important aspect of steering it. It s the old question of having the data to show risk probabilities but not having the tools to interpret it in a way that dictates an action. In this article, he encourages bankers to adapt an Excel spreadsheet model to fit the needs of their institutions and to help them correct course when needed. Next month, Zoeller offers technical rationale and some of the alternatives used within the financial community to estimate risk in commercial real estate by RMA, Mark Zoeller has worked as a credit analyst, loan officer, and departmental and regional credit administrator at a large bank; as a loan collection officer at a smaller regional bank; and as an examiner with the OCC. He is now a banking consultant with community banks, mostly in the San Francisco area.nk and 86 The RMA Journal May 2007

2 Bad? Estimating Risk Probabilities in Commercial Real Estate Commercial Real Estate by Mark Zoeller Do you stress test your commercial real estate loans? Do you test cash flows and debt service coverage? What about collateral values and loan-to-value ratios? Will the adequate coverage you show today withstand the test of time? With what probability? Cash flows, debt service coverage (DSC), collateral values, and loan-to-values (LTVs) are dynamic. Although many banks stress test by showing how interest rate changes affect the DSC, few discuss the results in terms of probability. The testing seems to be informational only it does not convey any sense that it affects loan decisions or structure. Such phrases as most likely, worst case, and best case often accompany stress tests. These descriptions, though, seem arbitrary. How probable is the worst case? Would it make a difference in your loan structure, price, or risk rating if, at the end of five years, your initial 80% LTV has a 15% probability of increasing to 95%? What if your initial 1.10x DSC has a 20% probability of being less than 1.0x? 1 The model presented in this article calculates those probabilities and can help you understand the dynamics of the LTV and DSC probabilities. It uses common techniques within the most common financial modeling tool, Excel. It incorporates some methods already used in the banking community to measure value-at-risk (VaR). The investment community also uses some of the methods to value stocks. I have adapted them for use in CRE. I present the model not as a turnkey spreadsheet fully fleshed out for you to use as is. Rather, it is an example of how you can use the methods to construct your own models to meet your circumstances. (To download a live copy of the model in Excel, see As you work with this model, I hope you can continue to improve it. Statistics Many of us took a statistics course in college and may remember, vaguely, some of the concepts. In our day-to-day work as lenders, we may see no benefit to the concepts we did learn. The relevance is just not there. Most college-level statistics courses have little relevance to what we do in credit. We may even disdain a statistical approach to lending because it is too mechanical. With years of experience, successful lenders may be more comfortable with the touch and feel of lending. Statistics is not touch and feel. More important, statistics is not destiny. It is not intended to be destiny. If we use statistical methods judiciously, however, they can give us information and insight that allow us to be better informed about risk. A model, such as the one presented in this article, can help us understand the risk (probability) that the DSC might decrease or that the LTV might increase beyond critical levels. Monte Carlo Monte Carlo simulation is a statistical/mathematical technique using random numbers. Developed 87

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4 How Bad Is Bad? Statistics is not destiny. It is not intended to be destiny. If we use statistical methods judiciously, however, they can give us information and insight that allow us to be better informed about risk. during World War II for other purposes, banks have come to use it for value-at-risk calculations. CreditMetrics, 2 for example, uses Monte Carlo simulation. Stock analysts use it to study potential movements in stock price. By using random numbers, it shows how changing the subparts of a system affects the end product or amount over time. Thus, it is adaptable to stress testing in many different situations. For example, we could use it with commercial and industrial financial statements to study the effects of potential changes in sales, profit margins, and interest rates. Real estate appraisers already use it in consulting on large-scale developments. It allows the consultant to test various alternatives against expected outcomes and their probabilities. 3 A true Monte Carlo simulation uses 10,000 or more trials. Using Excel with this model would produce a big spreadsheet. For our purposes, a smaller number, perhaps 500, should suffice. The 30 trials presented in this article are not enough, but do illustrate the mechanics. Useful Concepts In statistics, the standard deviation is usually represented by the Greek letter. It is a measure of how much each number in a series differs from the arithmetic average (A) of those numbers. In the normal statistical curve, 67% of the curve covers one standard deviation with the mean (μ) also being the A. Two standard deviations cover 95% of the curve. For, I used the following Excel function: =STDEV(beginning cell:ending cell). The μ in the first part of the model is the A of the natural logarithm of annual changes of national rental rates, occupancy rates, and adjusted 10-year Treasury rates (the 10-year Treasury rate plus 3% is a proxy for capitalization [cap] rates). The historical in the model is the standard deviation of the natural logarithm of 1 + the annual percentage changes. The historical changes allow us to estimate future changes. By using Excel s function, =NORMINV(RAND(),μ, ), 4 we can generate random numbers within the normal (bell-shaped) statistical curve. These random numbers based on the historical μ and allow us to simultaneously randomly vary possible future rental rates, occupancy rates, and cap rates. For example, we can generate future rental rates (RR) by using the NORMINV(RAND()) function with the μ and of the natural logarithm of 1 + the percentage change [LN(1 + % change)]. I discuss why I used LN(1 + % change) in greater detail in next month s issue. I have modified the Excel function slightly to create the following equation: RR t = RR 0 *[1 + NORMINV(RAND(),μ*t, *t 0.5 )] where RR t is the rental rate after year t, and RR 0 is the beginning rental rate, that is, the last historical year. NORMINV(RAND(),μ, )] is the Excel function creating random numbers with an average of μ and standard deviation of. The t is the number of years since the last historical year. I added the time aspect to allow us to create trials for any year within the loan period. In modern portfolio theory, is a measure of risk because a higher represents a higher level of uncertainty. In one manifestation of the theory, changes directly with longer periods by t = *t 0.5 where t is the number of periods. This is the cumulative standard deviation. For example, if for one year is 3, the fifth year is (3 * ). The standard normal variate allows us to derive probabilities of whether the DSC and LTV are likely to exceed critical limits. It takes the following form: z = (x - μ)/ In this basic form, z measures how many standard deviations the number you want to measure (x) is from μ. Tables convert the z into a probability. As a short example, if cash flow (x) needs to be 0.8 or larger when the historical average cash flow (μ) is 1 and 89

5 rates. For your market, you will likely need to obtain the historical-average data from private sources. A true Monte Carlo simulation uses 10,000 or more trials. Using Excel with this model would produce a big spreadsheet. is 1, then z is The probability that x will be 0.8 or larger is 57.9%. Conversely, the probability that x will be less than 0.8 is 42.1%. We can use this concept to measure the probability that our projected future DSCs and LTVs will be larger or smaller than critical limits. A better tool than manual tables is the Excel function, =NORMDIST(x,μ,, true). In the NORMDIST function, the true states that the probability is cumulative, meaning it includes all probabilities up to the x. When calculating probabilities using the NORMDIST function, however, I used the geometric mean (GM) as μ rather than the A. 5 While Monte Carlo normally uses over 10,000 trials, I present only the following trials as appendices: 30 trials projecting the first year into the future (Appendix B). 30 trials projecting the fifth year into the future (Appendix C). One trial projecting 25 years, year by year, into the future (Appendix D). For day-to-day purposes, though, 500 trials will likely provide reasonably stable probabilities. The small number of trials I use causes considerable fluctuations with each push of the F9 key. Pushing F9 creates new random numbers and recalculates everything in the spreadsheet. The historical data is in Appendix A. Users of the Monte Carlo method recommend that models contain as few random variables as possible. The larger the number of random variables, the more complex and less reliable a model becomes. For the random variables in the model, I have limited them to rental rates, occupancy rates, and cap Model Background and Assumptions The model assumes that the CRE has multiple tenants with short-term leases. The basic calculations are per square foot per year. I have not fitted the model to any particular building s square footage or number of tenants. The historical national rental rates and vacancy rates used as the model s base are from 1980 through 2005 (estimated). 6 To modify the model to fit your needs, you should use your local data rather than the national data I have used. While the model s data will not fit your market, you could still use some of the methodology. If the leases are with credit tenants, are long term, have built-in rent increases, or are net/net/net, for example, or if your loan payments are tied to prime, you need to change the model. Effective gross income (EGI) is gross rental income minus vacancy and collection losses. To calculate projected EGI, I used the random generated rental rates and vacancy rates (occupancy rate = 1 minus vacancy rate). The national vacancy rate in the historical table (Appendix A) is much higher than the 5% normally assumed in appraisals. By using the higher vacancy rate, the model s projected DSC will likely be lower than what you might think. I did not tie the vacancy or occupancy rates to rental rates because the statistical correlation is only moderate at 48%. These future calculations of rental rates, occupancy rates, and cap rates rely on their A (as μ) and of their historical numbers used in the NORMINV(RAND()) function. Net operating income (NOI) is EGI minus operating expenses. Appraisers often show operating expenses at 25% of EGI. The model divides this 25% into two parts. It ties 12% to EGI while the other, initially 13% of EGI, increases at a 3% inflation rate. expenses will change with the structure of the leases, the cost structure of the particular property, and the rate of cost inflation. Subtracting the operating expenses from the random EGI generates random NOI. 90 The RMA Journal May 2007

6 How Bad Is Bad? Dividing NOI by the fixed loan payment produces a random DSC. Dividing each random generated NOI by a random generated cap rate generates random collateral values. Dividing the random value by the average loan balance outstanding during the year produces the random LTV. The model uses the annual 10-year Treasury rate 7 plus 3% as a proxy for cap rates. One study shows that cap rates tend to correlate well with the 3% add-on. 8 I did make the cap rate as an exception to the rule of using the A of LN(1 + % change), however. The A is a minus 2.73%, which is strongly negative, and the model produces, after a few years, cap rates as low as 1%. I therefore changed the A (as μ) used in the NORMINV function to 0%. Using the 0% as μ created more understandable and realistic future cap rates. To calculate the probabilities that future DSCs and LTVs will meet critical limits, I used their randomly generated GM as the μ in the NORMDIST function. 9 I discuss the reasons for using the GM rather than the A when calculating probabilities in next month s issue. For the loan payments, I used the calculated historical estimated 2005 value (NOI cap rate) and assumed a 75% LTV, which I then amortized at an 8% fixed rate over 25 years. Multiple trials of randomly calculated DSCs and LTVs allow the standard normal variate to show the probabilities that they will exceed critical limits. Although Appendix B shows 30 trials for one year in the future, you will have information about what is likely to happen to the CRE in your market. Consequently, you should adjust the model to include local near-term forecasts. Clarity of foresight (which is never perfectly clear) decreases with the length of the forecast period. Beyond the one-year horizon, you would want to stay more with the historical μ and. Model Results DSCs and LTVs can vary from year to year sometimes in the direction that we expect, but sometimes not. The graphs on the following page are from Appendices B and C and show the results of only one set of 30 trials. Remember, a true Monte Carlo requires hundreds, if not thousands, of trials. The graphs are for illustration only. Other sets of trials can produce considerably different results, although the shape of the graphs seems to stay relatively constant. The results show risk probabilities. Comparing first-year with fifth-year probabilities is interesting. For example, the first-year trials show that the beginning 1.05x DSC has a 26.8% probability within one year of falling below 1.00x. The fifth-year trials, however, show a larger 50.5% probability within five years of falling below 1.00x. Meanwhile, the first-year trials show a 77.9% probability of being below 1.10x while the fifth-year trials show a smaller 73.6%. Given the beginning LTV of 75%, the fifth-year trials show LTV as 24.1% probable within five years to be above 85%, while the first-year trials show LTV as only 5.7% probable within one year to be above 85%. Both show small probabilities that the LTV will be above 100% with the fifthyear trials showing the higher probability. In Appendix D (the 25-year sequential trial), I do not include averages and probabilities. This is primarily because, after several years, the loan balance decreases to a level that more than compensates for any decrease in net operating income or any increase in the cap rate. Although the single presented trial does not show it, the LTV can increase substantially through several years before the rapidly decreasing loan balance dominates. Summary and Conclusions The model demonstrated in this article uses Excel and several of its functions applied to historical office rental rates, occupancy rates, and cap rates to calculate the probabilities that DSC and LTV will be above or below critical limits at different times in the future. This model calculates those probabilities; it does not calculate certainties. The model, though, would have to be much larger than the one presented here to generate statistically valid results. The model can be applied to individual CRE collateral or it can be applied to a larger class of CRE collateral that has similar characteristics. The national data and consequent probabilities shown here will not fit your market. You will need to obtain local data from private sources. In hot markets, you might also think that rental rates and real estate values always increase. Rapid 91

7 How Bad Is Bad? Probability 120% 100% 80% 60% 40% 20% 0% First-Year DSC Probabilities DSC < DSC < DSC < DSC < DSC < DSC < 1.00x 1.05x 1.10x 1.15x 1.20x 1.25x DSC Levels Probability 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% Fifth-Year DSC Probabilities DSC < DSC < DSC < DSC < DSC < DSC < 1.00x 1.05x 1.10x 1.15x 1.20x 1.25x DSC Levels Probability 40% 35% 30% 25% 20% 15% 10% 5% 0% First-Year LTV Probabilities DSC < DSC < DSC < DSC < DSC < DSC < 75% 80% 85% 90% 95% 100% LTV Levels Probability 50% 45% 40% 35% 30% 25% 20% 15% 10% 5% 0% Fifth-Year LTV Probabilities DSC < DSC < DSC < DSC < DSC < DSC < 75% 80% 85% 90% 95% 100% LTV Levels increases in rental rates and values, however, will likely return to the mean. Nothing grows rapidly forever, at least not without some hiccup. The return to the mean implies that what is now growing more rapidly than the historical average will, eventually, grow more slowly than the average and may even decrease. The methods in the model include the potential for the growth rate to become negative. The model encourages you to ask: How probable is that? That, in turn, allows for another question: If the probabilities show relatively high risk, how do you mitigate or price for that risk? Contact Mark Zoeller by at Note: To download a live copy of the model in Excel, go to the following Web site: Notes 1 For additional information about stress testing CRE, refer to Mike Newett and Don Gilliam, Commercial Real Estate Stress Testing, The RMA Journal, November 2006, pp A product of RiskMetrics, which spun off from JPMorgan in It claims to have 700 banking customers. 3 The Appraisal of Real Estate, Tenth Ed., The Appraisal Institute, pp Winston, Wayne L., and S. Christian Albright, Practical Management Science: Spreadsheet Modeling and Applications, Duxbury, 1997, p Kritzman, Mark, The Portable Financial Analyst: What Practitioners Need to Know, Irwin, 1995, p Lynford, Lloyd, What s Happening in Office and Apartment Leasing, The RMA Journal, November 2005, p Federal Reserve Web site ( gov). 8 Krauch, William K., Inflation, Cap Rate, and Interest : Historical Relationships and What They Tell Us About Buying and Selling in Today s Environment, Real Estate Investing, Spring 2005, p Ibid. 92 The RMA Journal May 2007

8 Year Appendix A Rental ($) Per Square Foot 10-Year Treasury Note Historical Effective Rental Rate % Change Natural Log 1 + % Change Historical Vacancy Rate Historical Rate Rate % Change Natural Log 1 + % Change EGI Variable Costs at 12% of 2005 EGI Fixed Costs at 13% 2005 EGI 2005 NOI Annual Average Annual Average + 3% % Change Natural Log 1 + % Change % 93.00% 11.43% 14.43% % 13.90% 8.50% 91.50% -1.61% -1.63% 13.92% 16.92% 17.62% 15.92% % -0.77% 13.00% 87.00% -4.92% -5.04% 13.01% 16.01% -5.38% -5.53% % -0.05% 15.40% 84.60% -2.76% -2.80% 11.10% 14.10% % % % 0.46% 15.80% 84.20% -0.47% -0.47% 12.46% 15.46% 9.65% 9.21% % -5.59% 18.00% 82.00% -2.61% -2.65% 10.62% 13.62% % % % -1.70% 19.40% 80.60% -1.71% -1.72% 7.67% 10.67% % % % -1.95% 19.10% 80.90% 0.37% 0.37% 8.39% 11.39% 6.75% 6.53% % -0.56% 18.70% 81.30% 0.49% 0.49% 8.85% 11.85% 4.04% 3.96% % -1.19% 18.90% 81.10% -0.25% -0.25% 8.49% 11.49% -3.04% -3.09% % -0.98% 19.10% 80.90% -0.25% -0.25% 8.55% 11.55% 0.52% 0.52% % -2.99% 19.30% 80.70% -0.25% -0.25% 7.86% 10.86% -5.97% -6.16% % -2.41% 18.70% 81.30% 0.74% 0.74% 7.01% 10.01% -7.83% -8.15% % -0.49% 17.30% 82.70% 1.72% 1.71% 5.87% 8.87% % % % 2.12% 15.30% 84.70% 2.42% 2.39% 7.09% 10.09% 13.75% 12.89% % 3.65% 13.50% 86.50% 2.13% 2.10% 6.57% 9.57% -5.15% -5.29% % 6.50% 11.70% 88.30% 2.08% 2.06% 6.44% 9.44% -1.36% -1.37% % 7.92% 10.00% 90.00% 1.93% 1.91% 6.35% 9.35% -0.95% -0.96% % 8.27% 9.30% 90.70% 0.78% 0.77% 5.26% 8.26% % % % 2.23% 8.90% 91.10% 0.44% 0.44% 5.65% 8.65% 4.72% 4.61% % 11.77% 8.10% 91.90% 0.88% 0.87% 6.03% 9.03% 4.39% 4.30% % -7.75% 13.60% 86.40% -5.98% -6.17% 5.02% 8.02% % % % -7.60% 16.00% 84.0% -2.78% -2.82% 4.61% 7.61% -5.11% -5.25% % -5.28% 16.90% 83.10% -1.07% -1.08% 4.01% 7.01% -7.88% -8.21% % -1.14% 16.20% 83.80% 0.84% 0.84% 4.27% 7.27% 3.71% 3.64% 2005 (estm) % 2.12% 15.00% 85.00% 1.43% 1.42% % 7.29% 0.28% 0.27% $ =2005 value =$13.06/7.29% Arithmetic Average (A) Standard Deviation % 0.74% 14.72% 85.28% -0.34% -0.36% 7.69% 10.69% -2.29% -2.73% $ % LTV % 5.38% 3.76% 3.76% 2.17% 2.16% 2.80% 2.80% 9.04% 9.07% $1.037 Correlation with Rental =monthly pmt 8%, 25 years $12.45 =annual pmt 1.05 =2005 DSC 93

9 Appendix B (First-Year Simulation) t=1 Inflation Rate = 3.0-% Year Rental Scheduled Rate EFI Effective Variable Costs 12% of EFI Inflation- Adjusted Fixed Costs at 3.0% NOI Loan Payment Debt Service Coverage (DSC) Cap Rate (NOI/Cap Rate) Value Average Loan Balance in Year Average Loan to Value (LTV) % % 81.97% % % % % 89.62% % % % % 84.00% % % % % 85.92% % % % % 83.39% % % % % 85.51% % % % % 84.04% % % % % 85.49% % % % % 86.32% % % % % 84.91% % % % % 83.98% % % % % 83.82% % % % % 83.14% % % % % 84.88% % % % % 86.44% % % % % 82.57% % % % % 85.78% % % % % 86.50% % % % % 83.62% % % % % 84.28% % % % % 86.37% % % % % 82.35% % % % % 82.28% % % % % 87.12% % % % % 84.43% % % % % 87.44% % % % % 86.03% % % % % 83.82% % % % % 88.63% % % % % 87.76% % % 94 The RMA Journal May 2007 DSC Probabilities 2005 DSC = 1.05x Geometric Mean (GM) = Standard Deviation ( ) = Geometric Mean (GM) = Standard Deviation ( ) = 71.5% 8.5% Minimum = 0.87 Minimum = 90.5% DSC < 1.00x 26.8% LTV > 75% 34.0% DSC < 1.05x 52.9% LTV LTV > 80% 15.9% DSC < 1.10x 77.9% Probabilities LTV > 85% 5.7% DSC < 1.15x 92.8% 2005 LTV = LTV > 90% 1.5% DSC < 1.20x 98.4% 75% LTV > 95% 0.3% DSC < 1.25x 99.8% LTV >100% 0.0%

10 Appendix C (Fifth-Year Simulation) t=5 Inflation Rate = 3.0-% 2.62 Year Rental Scheduled Rate EFI Effective Variable Costs 12% of EFI Inflation- Adjusted Fixed Costs at 3.0% NOI Loan Payment Debt Service Coverage (DSC) Cap Rate (NOI/Cap Rate) Value Average Loan Balance in Year Average Loan to Value (LTV) % % 81.12% % % % % 87.70% % % % % 85.37% % % % % 88.28% % % % % 74.04% % % % % 78.21% % % % % 78.31% % % % % 83.77% % % % % 86.62% % % % % 79.93% % % % % 84.74% % % % % 91.83% % % % % 79.63% % % % % 89.64% % % % % 81.78% % % % % 83.57% % % % % 78.68% % % % % 84.92% % % % % 83.42% % % % % 86.80% % % % % 78.18% % % % % 78.68% % % % % 83.03% % % % % 88.35% % % % % 88.36% % % % % 81.25% % % % % 88.80% % % % % 88.40% % % % % 82.93% % % % % 86.55% % % DSC Probabilities 2005 DSC = 1.05x Geometric Mean (GM) = Standard Deviation ( ) = Geometric Mean (GM) = Standard Deviation ( ) = % 17.8% Minimum = 0.63 Minimum = 102.8% DSC < 1.00x 50.5% LTV > 75% 44.5% DSC < 1.05x 62.6% LTV LTV > 80% 33.7% DSC < 1.10x 73.6% Probabilities LTV > 85% 24.1% DSC < 1.15x 82.6% 2005 LTV = LTV > 90% 16.3% DSC < 1.20x 89.4% 75% LTV > 95% 10.3% DSC < 1.25x 94.0% LTV >100% 6.1%

11 Appendix D (Twenty-Fifth Year Simulation) Inflation Rate = 0.03% Year Rental Scheduled Rate EFI Effective Variable Costs 12% of EFI Inflation- Adjusted Fixed Costs at 3.0% NOI Loan Payment Debt Service Coverage (DSC) Cap Rate (NOI/Cap Rate) Value Average Loan Balance in Year Average Loan to Value (LTV) Loan Balance Beginning of Year % % 85.37% % % % % 83.35% % % % % 86.83% % % % % 84.39% % % % % 86.82% % % % % 87.79% % % % % 82.01% % % % % 85.41% % % % % 87.03% % % % % 87.18% % % % % 85.39% % % % % 86.32% % % % % 86.36% % % % % 81.50% % % % % 85.46% % % % % 84.41% % % % % 81.88% % % % % 83.77% % % % % 84.39% % % % % 83.03% % % % % 88.41% % % % % 86.32% % % % % 86.00% % % % % 85.40% % % % % 86.50% % % The RMA Journal May 2007