# Application of Portfolio Theory to Commercial Real Estate

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1 h Application of Portfolio Theory to Commercial Real Estate Eric Hines John Hopkins University December 10 th, 2009 h

2 Executive Summary: Goals of Model: Commercial real estate portfolios are not typically analyzed with a quantitative risk measurement. The goal of this practicum is to build a model to assess risk and return for individual real estate assets that would provide investment managers another tool in assessing commercial real estate portfolios and construction of these portfolios. Additionally, a subject portfolio managed by LaSalle Investment Management is used to display model capabilities and results. Method: The model is built in excel and aims to analyze risk and return for two situations: (1) Asset/Property level decisions such as the impact of termination options, credit risk, key discounted cash flow variables and lease structure and (2) Portfolio construction decisions including appropriate debt levels, product type allocation, and risk profile of private portfolios vs public securities. The model uses Monte Carlo simulations in which key uncertainty variables 1 in a discounted cash flow analysis are run thru the model 10,000 times to produce 10,000 IRR results. The process takes into account uncertainty of future outcomes and each variable has a defined probability distribution based on historical market volatility. The model has uncertainty variables including: market rent growth, expense growth, downtime, and residual cap rate. In each of these 10,000 scenarios a random number from the probability distribution is selected for each variable. The final results have 10,000 return outcomes that can be plotted, and typically ends up distributed similarly to a normal distribution or bell curve. The model is built to apply Modern Portfolio Theory (MPT) 2 and Post Modern Portfolio Theory (PMPT) 3 to commercial real estate portfolios. MPT was born out of the idea that investment returns should be viewed in light of quantitative risk assessment, and makes the assumption that investors are risk adverse and prefer the highest return for a level of risk (or lowest risk for a level of return). The statistic used in MPT to assess risk is standard deviation. Standard deviation makes the assumption that a set percentage of results are within a range of the mean. For instance, 68.2% of the results are captured within +/ one standard deviation of the mean. (Ie. If you had an asset with an expected return of 8% and a standard deviation of 3%, there is an expected 68.26% chance the asset s return will be in the range of 5% 11%. And there is an expected 95.4% chance you would be within +/ 2 standard deviations of the mean which would be between 2% 14%.) The larger the standard deviation, the more risk inherent in the expected returns. The criticism with MPT surrounds the assumptions that the 1 Uncertainty variables are those that do not have a certain result and are used in arriving at expected returns. 2 MPT was developed in the 1950 s and 1960 s. Was introduced by Harry Markowitz in PMPT was developed as an improvement in MPT as it appropriately accounts for non-normally distributed data sets. 1 Eric Hines Practicum Johns Hopkins University

3 expected investment performance always fits a normal distribution. Standard deviation analysis and the normal distribution are both limited in the fact that they are symmetrical. Using standard deviation implies that there is an equal chance of a worse than expected return than there is of a better than expected return. Furthermore, using the normal distribution to model the pattern of potential investment returns makes investment results with more upside than downside appear more risky than they really are, with the opposite true as well. This leads to potential for investors to misunderstand the potential upside or downside of a particular investment when considering only typical MPT methodology. To take into account these criticisms of MPT, PMPT has gained traction among the investment community. PMPT aims to overcome the limitations of MPT by redefining the concept of risk. PMPT recognizes that standard deviation is a poor proxy for investment risk and risk to an investor is the failure to achieve a certain financial goal. PMPT incorporates a metric entitled Downside Risk that was developed to incorporate an investor s goal and defines risk as those outcomes that do not achieve that goal. The statistic is calculated in a similar manner as standard deviation, however only accounts for results that lie below the investors desired return hurdle. The metric measures the volatility of results below the target return. To integrate return and risk into one statistic, the Sortino ratio can be applied. This statistic is similar to the Sharpe Ratio and measures how many units of excess return are expected for every unit of downside risk. This ratio incorporates the concept of downside risk and is calculated by subtracting the target return from the assets expected return and dividing the result by the previously mentioned downside risk metric. The result is a single number that incorporates expected return results for every unit of risk. The Sortino ratio provides investors a comparison tool to use as a measuring stick for making decisions between different assets and portfolios on a risk/return basis. Portfolio Analyzed: The subject portfolio is composed of six assets managed by LaSalle Investment Management. To prevent any disclosure of confidential information, the names of the assets and tenants are not being disclosed as well dividing all asset numbers in the analysis by a prime number. The analysis start date is January 1 st, Uncertainty Variables: The uncertainty variables that influence the model are: Market Rent Growth, Downtime, Subject Portfolio Asset Size Date of Construction Occupancy Comments Suburban Orlando Office 230,000 SF Late 1990's Mid 80%'s Multi Tenanted. Aprox 40% of bldg w/ two strong tenants on long term leases Southern New Jersey Industrial Portfolio 1,000,000 SF 1980's / early 1990's 100% 4 buildings all single tenanted. Lease term remaining ranges from Q to Q Suburban Chicago Neighborhood Retail 138,000 SF Mid 1990's 90% Grocery Anchored with grocer taking 40% of space Suburban Atlanta Neighborhood Retail 88,000 SF Late 1990's 98% Grocery Anchored with grocer taking 60% of space Suburban San Diego Office 75,000 SF Mid 2000's 55% Some spaces are in shell condition Northern New Jersey Apartments 115 Units Early 1990's Mid 90%'s In desirable submarket, 25% of units are affordable and eligible to be converted to market during hold period Variable Data Source Comments Market Rent Growth REIS/Toro Wheaton/ LIM Uncertainty Variables Historical data sets for each submarket were used to create distribution. Downtime CoStar / LIM Data Office and Industrial downtime datasets are gathered from CoStar and based upon the local market and segmented by size. Retail is obtained from LIM portfolio performance of neighborhood centers. Renewal Assumptions REITS / LIM Data Renewal data gathered from REIT supplemental reports for Office and Industrial. Retail renewal is based upon LIM historical renewal ratios at neighborhood centers. Expense Growth BOMA Expenses are broken into CAM, Real Estate Taxes, Insurance and Utilities in the model. Historical growth rates derived from BOMA Experience and Exchange report with data dating back to Credit Impact Moody's All tenants are assigned a credit assumption (% chance of bankruptcy) based on historical Moody's data. Tenants with public credit rating are assigned the appropriate credit assumption, while all private tenants are assigned a BBB rating. Residual Cap Rate Historical Data Calculation to arrive at residual cap rate = Forward Looking 10 Yr Treasury Rate + Risk Premium for Product Type + Age/Osolesce Premium. The risk premium is an uncertainty variable and is based on historical data between the difference in going in cap rates and the 10 year treasury. Correlations Historical Data All market rent growth on a local and national level, expense growth, GDP and inflation are all correlated. 2 Eric Hines Practicum Johns Hopkins University

4 Renewal Assumptions, Expense Growth, Credit Impact, Residual Value and Correlations. See body of paper for more depth on methodology and appendix for relevant data sets. Results: 10 Yr Unleveraged Results The results show an expected portfolio return of 8.49% for a 10 year hold with a standard deviation of 3.21% and downside risk of (at a 7.5% target return) of 0.81%. The portfolio has a the following Sortino ratio for return expectations: 10 Year Unleveraged: 1.26; 10 Year Leveraged: 2.44; 20 Year Unleveraged: 1.42; 20 Year Leveraged: % 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% Orlando Office New Jersey Industrial Chicago Retail Atlanta Retail San Diego Office New Jersey Portfolio Apartments (E) IRR Standard Deviation Downside Risk The results show a few highlights: (1) Diversification is of clear benefit. Portfolio risk metrics are lower than weighted average of assets and portfolio distribution has a positive skew (2) Assets with NNN leases (retail and industrial) exhibited the strongest Sortino ratio s, and thus the best risk/expected return tradeoff. (3) Leverage for the subject portfolio at the existing levels (~30%) adds expected return without sacrificing significant downside risk. Asset Management Impacts: Termination o The subject portfolio was analyzed assuming all vacant spaces are given tenant termination options three years into the term at both unamortized (at 9%) capital costs (Scenario #1) and 50% of unamortized (at 9%) capital costs (Scenario #2). Tenants are assumed to terminate the lease when it would be financially preferable (costs to continue lease term at market plus termination fee are below remaining obligation) o The San Diego Office asset has the most vacancy and shows the greatest impact: Scenario #1: 23% chance of termination; reduction in expected return of 12 basis points; and increase in downside risk of 7 basis points. Scenario #2: 50% chance of termination; reduction in expected return of 42 bp; and increase in downside risk of 30 bp. o The impact of termination options on expected return and risk is going to vary for each asset. The outcome is based upon: (1) Projected rental rate volatility (2) Negotiated termination payment and (3) Downtime and amount of capital to release tenant spaces. o This tool can quantitatively assess the risk in agreeing to tenant termination options. This could be especially helpful in negotiations with large tenants requesting such options or underwriting an asset with Credit Scenarios an existing termination option. 8.80% Credit o The subject portfolio has a weighted average annual default rate of 1.34%. Sensitivity scenario s were run in 2% intervals from 0% 6% annual default rates. Portfolio (E) IRR 8.60% 8.40% 8.20% 8.00% 7.80% 7.60% 7.40% 0% CL Base Run 2% CL 4% CL 6% CL 2.40% 2.50% 2.60% 2.70% 2.80% 2.90% 3.00% 3.10% 3.20% Portfolio Downside Risk 3 Eric Hines Practicum Johns Hopkins University

5 o Credit quality matters, there is a basis point difference in expected return from moving the credit loss assumption up by 2%. o The increase in downside risk along with the decrease in expected return is a fairly linear tradeoff. Uncertainty Variables Impact o Scenarios were run on the subject portfolio Variable Analysis Return Volatility 4.50% isolating each uncertainty variable to gauge 4.00% it s impact on expected return volatility. 3.50% 3.00% o Residual cap rate risk premium and market Market Rent Growth 2.50% Downtime rent growth have the largest impact on the 2.00% Renewal Ratio 1.50% Expense Escalation volatility of expected returns for the portfolio. 1.00% o Gross lease structures see significantly more 0.50% 0.00% expected return volatility than the NNN Orlando Philadelphia Chicago Atlanta Retail San Diego New Jersey Portfolio Office Industrial Retail Office Apt leased assets. The office and apartment assets have an average of 0.7% standard deviation attributed to expense escalation compared to 0.2% for the retail and industrial assets. Portfolio Impacts Leverage Impact o The debt level of this portfolio is fairly low as Leveraged Scenarios Measured by Sortino Ratio 2.5 the LTV for the portfolio is ~30%. Sensitivity scenarios were run assuming debt levels for 2 each asset and the portfolio in 10% increments 1.5 from 30% 80%. All the debt was assumed to 1 be interest only and at a rate of 6.5%, with the 0.5 one exception of the apartment asset at 6.0%. 0 At the 70% and 80% debt levels, an additional Unlev IRR 30% Lev IRR 40% LEV IRR 50% LEV IRR 60% LEV IRR 70% LEV IRR 80% LEV IRR 50 and 100 basis points are added to interest rates. o Increasing use of debt can be an effective strategy to boost expected return. This portfolio is maximized on a risk/return basis at debt levels in the range of 50% 70%. At the 70% 80% leverage level, the additional expected return for this portfolio is not justified given the return benchmark and by the additional downside risk that leverage creates. Standard Deviation Residual Cap Risk Premium Product Type Summary o Office Volatile rent growth patterns, gross leases with narrowing net margins, and high risk premium on resale lead to most volatile return expectations. Market pricing for office assets may be too aggressive given the risk, as this product type has the lowest expected returns and most volatility. 4 Eric Hines Practicum Johns Hopkins University

6 o o o Apartments Low rent growth volatility and smallest risk premium on sale lead to low expected return volatility. Investors targeting stability should focus on apartments due to attractive return for every level of risk on a long term perspective. Retail NNN leases and minimal tenant capital obligations lead to an excellent return/risk tradeoff. The assets analyzed are well located, grocery anchored neighborhood centers, poorly situated retail would have a different result. Industrial NNN leases and minimal tenant capital obligations help to offset volatile market rent growth patterns. With 100% occupancy and low lease rollover until 2013, this portfolio benefits from stable in place dynamics. Comparative Asset Types o The subject portfolio has been compared to Asset Type Efficient Frontier other product type s historical return and 12.00% Base Port Leveraged volatility. The assets types analyzed include: 11.00% 80% 10.00% Base Port 50% Lev US Stocks: S&P 500; US Investment Grade Base Portfolio Leveraged S&P % NCREIF Base Port Unleveraged Bonds: Barclays Aggregate Bond Index; US 8.00% 7.00% Government Bond: 10 Yr Treasury (held until Barclays Bond Index 6.00% maturity); Private Real Estate Returns: 5.00% NCREIF. The comparative benchmarks annual 4.00% 10 YR Treasury 3.00% return results were complied by compounded 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% annual growth rate and the downside Downside Deviation deviation is the amount of volatility on a 10 year basis below the compounded annual growth. To arrive at the downside deviation, continuous ten year results were analyzed for each comparative benchmark. o The results show that the subject portfolio of real estate assets is efficient from a return/risk basis as compared to NCREIF and S&P 500. The bond data points show the lowest risk, while the subject portfolio along with NCREIF were shown to have lower downside volatility compared to the S&P 500. Future Applications This model has the ability to analyze all product types and has the ability to incorporate analytical capability that are unavailable in the market accepted valuation software. Investors and investment managers can benefit from understanding it s expected risk/return profile for their existing assets and location on the efficient frontier. Given the level of detail in the model, many different types of analytical decisions made in the real estate industry can benefit from this type of risk analysis. Annual Return 5 Eric Hines Practicum Johns Hopkins University

7 Problem in need of solution Quantitative Real Estate Risk Analysis Commercial real estate portfolios are not typically analyzed with quantitative risk measurement. Arriving at a model to assess risk and return would provide investment managers another tool in assessing commercial real estate portfolios and construction of these portfolios. Assessing risk has largely been a qualitative assessment in assigning values and making investment decisions for commercial real estate. Investment decisions are typically made with a benchmark return in mind, however it is unusual to see quantitative analysis done to compare risk levels of potential investments with similar expected returns. A potential improvement to the existing model is to introduce elements of Modern Portfolio Theory (MPT) and Post Modern Portfolio Theory (PMPT) into quantitative real estate investment analysis. MPT is based on the assumption that investors are risk adverse, suggesting that if an investor is given the choice of two assets with the same expected return, the investor would prefer the less risky asset. Quantitative modeling results do not solely make a real estate investment decision; however they do give the decision maker another data point to fully assess an investment decision. Issues Surrounding Problem and Current Applications The current standard valuation analysis for real estate is composed of three methods: cost approach, comparable sales approach and discounted cash flow approach. The cost and comparable sale approaches are static and do not account for future projections in performance or cash flow. The discounted cash flow analysis provides the opportunity to analyze projects based on expected results that are determined by market assumptions. The current standard for this analysis is the Argus software. The limitation with the current standards for valuation is that there is no account for the uncertainty of the future projected cash flows. The inputs for Argus are all static and are successful in arriving at a value based on an qualitative input of key assumptions. Inputs in Argus do not account for the potential variability of the assumptions. Current methods include running multiple discounted cash flow scenario s including an upside and downside to understand the potentially volatility. This method, while effective in showing returns based on adjustment of inputs, it is not able to deliver a quantitative assessment of risk level reflective of all potential outcomes to compare investments. Quantitative assessment of risk for investment level decisions is not typical in both an asset level and a portfolio level: Asset Analysis Many decisions made on a property level involved some component of uncertainty. Such examples include leasing decisions with credit as a concern, the risk of a termination option, and below market or fixed renewal options. Such key determinants to the value of leases to tenant and landlord are not currently analyzed to take quantitative risk into consideration in providing the landlord perspective on the additional risk such provisions add or reduce risk. 6 Eric Hines Practicum Johns Hopkins University

8 Portfolio Analysis Investment managers could benefit from understanding of risk and return trade off in construction of portfolios. Portfolio construction does not typically assess quantitative risk of the assets individually compared to the aggregate portfolio. This model can help investment managers select assets that fit the desired risk/return profile of the investor. Analysis Method Theoretical Underpinning To understand Modern Portfolio Theory, it is essential to understand the statistical underpinning of major assumptions. Statisticians have found that naturally occurring data tends to follow a natural distribution (or Bell Curve ) pattern. The normal distribution has its mean, median and mode as an identical value. This suggests that the mean lies at a point that divides the distribution exactly in half with 50% of the scores lying above the mean and 50% lying below the mean. Since the curve is symmetrical, what holds true on one side of the mean also holds true on the other side. Therefore in the case of a normal distribution, the data becomes easier to analyze by statisticians using the concept of standard deviation of the distribution. The range of scores for a normal distribution of one standard deviation is 34.13% (which holds true on both sides of the mean). This results in that 68.26% of all results under a normal distribution would occur within one standard deviation of the mean % of results are within two standard deviations of the mean. A potential improvement to the existing commercial real estate analytical model is to introduce elements of Modern Portfolio Theory and Post Modern Portfolio Theory. Harry Markowitz s work in the 1950 s introduced the concept of analyzing expected risk in turn with expected return. Markowitz suggested a mathematical risk/return framework for investment decision making based on the assumption that investors are risk adverse. MPT is as investment theory that attempts to explain how investors can maximize expected return and minimize expected risk. The theory is a qualitative assessment of the diversification in investing. MPT models a portfolio as a weighted combination of assets so that the return of a portfolio is the weighted combination of the assets return. Risk in this situation is the standard deviation of return. By assembling portfolio s of different assets whose returns are not completely correlated, MPT seeks to reduce the total expected standard deviation, and therefore risk, of the portfolio. MPT also makes the key assumptions that: Asset returns are normally distributed Correlations are stable All investors are rational and risk adverse All investors aim to maximize economic utility The criticism with MPT surrounds the assumptions that the expected investment performance always fits a normal distribution. Standard deviation analysis and the normal distribution are both limited in the fact that they are symmetrical. Using standard deviation implies that there is an equal chance of a worse than expected 7 Eric Hines Practicum Johns Hopkins University

9 return than there is of a better than expected return. Furthermore, using the normal distribution to model the pattern of potential investment returns makes investment results with more upside than downside appear more risky than they really are, with the opposite true as well. This leads to potential for investors to misunderstand the potential upside or downside of a particular investment when considering only typical MPT methodology. To take into account these criticisms of MPT, a theory entitled Post Modern Portfolio Theory (PMPT) has gained traction among the investment community. PMPT aims to overcome the limitations of MPT by redefining the concept of risk. PMPT recognizes that standard deviation is a poor proxy for investment risk and risk to an investor is the failure to achieve a certain financial goal. In some cases this goal is to completely avoid a loss, sometimes it is tied to a relevant benchmark, for institutional investors it may be to line up assets and liabilities appropriately. PMPT incorporates this redefined sense of risk in a statistical manner by introducing the statistic Downside Risk (DR). Downside Risk incorporates an investor s goal and defines risk as those outcomes that do not achieve that goal. The differences between downside risk and standard deviation are that: (1) Downside risk can differentiate between good and bad results (2) Non normal distributions can be analyzed effectively. Downside risk is calculated by downside deviation or the following calculation (where t = target return, r = asset return and f(r)dr = the probability density of r): The probability density is the likelihood of the specific return to occur on a defined point within the distribution. In the case of this analysis, there are 10,000 results compiled from the Monte Carlo scenario, and the likelihood of each result is thusly 1/10,000. To integrate return and risk into one statistic, one can use the Sortino Ratio. This statistic is similar to the Sharpe Ratio (which uses standard deviation). The ratio measures how many units of active excess return are expected for ever unit of downside risk. It defines risk in a way that investor s perceive risk, where the greater the positive value, the better the expected return in relationship to risk. A negative value is a signal that the investment would be a poor choice for the desired benchmark. The ratio is calculated as follows (where T = target return, R = asset return, DR = Downside Risk): The Sortino ratio statistic provides investors a comparison tool to use as a measuring stick for making decisions between different assets and portfolios on a risk/return basis. Another measure used by PMPT is Skewness, which the ratio of a distributions s percentage of total variance from returns above the mean, to the percentage of distributions total variance from returns below the mean. If a distribution is symmetrical, it has a skewness of zero. Values greater than zero indicate positive skewness (slant to values above the mean); values less than zero indicate negative skewness (slant to values below the 8 Eric Hines Practicum Johns Hopkins University

10 mean). The importance of skewness lies in the fact that the more non normal a return series is, the more it s true risk will be distorted by the traditional MPT measures. Modeling Methods The simulations will be run with Monte Carlo analysis 4 in excel with the help of the Crystal Ball software package. The software applies the Monte Carlo simulation on each of the variables 10,000 times to yield 10,000 expected IRR results. The process takes into account uncertainty of future outcomes and each variable is given a probability distribution based on market data. For example, downtime for a vacant space could be anywhere from 0 to infinity. Everytime a lease rolls over, the space is subject to an uncertainty variable regarding renewal, the tenant either renews or vacates. If the tenant vacates, then the space is subjected to a downtime that is based on a random selection on a number based on the individual probably distribution. With 10,000 expected IRR results plotted in a distribution, assets can be analyzed for investment by mean IRR as well as risk metrics such as: standard deviation, downside risk and skewness. Working Model and Results The model built to analytically review risk and return on an asset and portfolio basis was written in excel and uses the software application Crystal Ball to perform the Monte Carlo simulations. The analysis start date is January 1 st, The portfolio is composed of the following assets: Suburban Orlando Office Asset 230,000 SF multi tenanted building built in the late 1990 s. Currently 90% occupied with strong anchor tenants with significant lease term remaining. Southern New Jersey Industrial Portfolio 4 building industrial portfolio composed of nearly 1 million SF. Fully occupied with single tenants occupying each of the 4 buildings. Lease term remaining ranges from Q to Q Suburban Chicago Neighborhood Retail Center 138,000 SF neighborhood shopping center anchored by grocer. 40% of the space is occupied by the grocer. The center is 90% occupied. Suburban Atlanta Neighborhood Retail Center 88,000 SF neighborhood shopping center anchored by dominant local grocer. 60% of the space is occupied by the grocer. The center is 98% occupied. Orange County California Office Asset 75,000 SF multi tenanted building built in the mid 2000 s. Currently 55% occupied. Northern New Jersey Apartments 115 unit apartment complex in desirable submarket built in Currently has 23 units tagged as affordable that will be eligible to be converted to market rent in Unit size ranges from 583 1,113 SF. Uncertainty Variables 4 Monte Carlo methods are useful for analyzing potential outcomes with significant uncertainty in inputs. The greater number of sources of uncertainty, the greater the benefit of this method. Monte Carlo simulations are used in many fields such as: physical sciences, design, and telecommunications. 9 Eric Hines Practicum Johns Hopkins University

11 The following are the key assumptions that are subject to uncertainty in the subject properties. See appendix for relevant data sets. Market Rent Growth Historical data for each product type and submarket was compiled to create a probability distribution based on the volatility of market rents. Each probability distribution for each submarket was correlated with a growth rate for a specified product type. For example the Orlando office distribution is correlated with the National Office distribution 5. Given that each market is subject to different local economic drivers, short term and long term projections take into account supply and demand expectations and well as assumptions that market rents will trend towards replacement cost over the longer term. After the 2 4 year time horizon, rents are assumed to be stabilized and will follow a long term projection. Downtime: For the office and industrial assets, a CoStar study was performed to create a downtime data set for each submarket of Class A & B buildings. Data points were also segmented to yield appropriate distributions based on the size of the available vacancy. For retail assets, a study from 2000 to 2009 of 17 neighborhood/community centers yielded downtime data points to create a probability distribution. See property pages in Appendix A for the distribution results. The distribution for all product types and sizes is a lognormal distribution, which is characteristically positively skewed, with most of the data points near the lower limit. Apartment downtime data was incorporated with a vacancy allocation based on submarket historical data. Renewal Assumptions: Each product type was reviewed for renewal rates. For office and industrial, data was generated from REITS via supplemental reports produced quarterly. The office REITS that provided renewal data and were reviewed were: COPT, BDN, HRPT, CLI and MPG. The industrial REITS that provided renewal data and were reviewed were: AMB, DCT, EGP and PLD. Retail data was compiled thru a study of 17 neighborhood / community centers in LIM portfolios from Downtime Probability Distributions (Data in Months) Market Mean Median Range Data Source Orlando Office CoStar 0 5,000 SF ,001 10,000 SF ,001 20,000 SF ,001 SF Philadelphia Industrial CoStar Chicago Retail LIM Data Atlanta Retail LIM Data San Diego Office CoStar 0 3,000 SF ,001 7,500 SF ,500 SF Renewal Ratio Product Type Ratio Data Source Office 60% REITS Industrial 70% REITS Retail 70% LIM Expense Growth Expenses in the model have been broken into: CAM, Real Estate Taxes, Insurance and Utilities. Historical data series of growth rates have been analyzed and fit into probability distribution curves (see Appendix A). The best source of product type data is the BOMA Experience and Exchange Report that specifically reports on office product. The data set gathered from the BOMA Experience and Exchange Report dates back to The probability distributions for CAM, Real Estate Taxes and Insurance expense growth were all derived from the BOMA data set and used for each of the product types. While not ideal, there is no other applicable data source with an extended history. (Discussion on this topic is included in data limitations heading). The probability distribution for utilities was derived from Bureau of Labor Statistics, which dated back to At a local level, the Metropolitan Statistical Area s (MSA) utility data is highly correlated with the national average. See Appendix A for all probability distributions. 5 The correlation between Orlando office and national office is Eric Hines Practicum Johns Hopkins University

12 Credit Impact Current analytical methods used to account for potential credit loss are static and do not typically account for the full scope of ramifications of a tenant going bankrupt. When a tenant vacates early, the landlord will experience downtime in the space as well as retenanting costs including tenant allowance and leasing commission. Using a monte carlo simulation, the model makes an annual assumption for each tenant and the probably of default. Upon an instance of default, downtime will be experienced in the space along with retenanting costs. Default rates were gathered from Moody s. Tenants with debt ratings were assigned their appropriate annual default rate. Tenants without public debt were all given an assumed BB rating and given an annual default probability based on that rating. Residual Value The mathematical method used to arrive at a residual cap rate is as follows: Expected forward looking 10 Yr Treasury Rate + Risk Premium for Product Type + Age/Obsolesce Premium. Risk Premium uses a product specific probability distribution that is correlated with the other product types. The risk premium for product type is arrived at by creating a Moody's Default Rates Debt Default Rating Probability AAA 0.00% AA 0.03% A 0.08% BBB 0.24% BB 0.99% B 4.50% CCC 25.67% Product Type Residual Risk Premium Market Mean Median Range Office 2.64% 3.01% 14.1% 21.5% Industrial 2.06% 2.36% 11.9% 18.0% Retail 2.26% 2.62% 13.5% 7.3% Apartments 1.58% 2.03% % probability distribution of historical data of the difference between going in cap rate and the 10 year treasury rate. The data set analyzed is from 1984 to The forward looking 10 year treasury rate is derived from using a bootstrapping 6 technique on the current yield curve. Hold Period Maximization Multiple hold periods were analyzed in generating IRRs. The two periods analyzed are 10 year and 20 year. The 10 year term is consistent with a typical assumed hold period for a core asset and is the standard term length for normal underwriting. A 20 year analysis is completed as well to reduce the impact of the residual cap rate. Assets that have a likelihood of concentrated rollover in a cap year need to be adjusted based on the most realistic sale projection. Taking this into consideration, the maximum IRR is selected for the three years surrounding the target hold period. Correlations To fully account for risk, correlations of key variables need to be considered. Market rent growth on a local and national level, expense growth, GDP and inflation are all correlated. See appendix A to see correlation matrix among inputs. 6 Calculated by: ((1+20 yr)^20 / (1+10 Yr)^10)^(1/10)-1. The results are for the implied forward looking 10 year treasury as of 2020 is: 5.04% and the forward looking 10 year treasury as of 2030 is: 4.33%. 11 Eric Hines Practicum Johns Hopkins University

13 Results The results show an expected portfolio return of 8.49% for a 10 year hold with a standard deviation of 3.21% and downside risk (at a 7.5% target return 7 ) of 0.81%. 10 Yr Unleveraged Results 20 Yr Unleveraged Results 12.00% 12.00% 10.00% 10.00% 8.00% 8.00% 6.00% (E) IRR 6.00% (E) IRR Standard Deviation Standard Deviation 4.00% Downside Risk 4.00% Downside Risk 2.00% 2.00% 0.00% 0.00% Orlando Office New Jersey Industrial Chicago Retail Atlanta Retail San Diego New Jersey Office Apartments Portfolio Orlando Office New Jersey Industrial Chicago Retail Atlanta Retail San Diego New Jersey Office Apartments Portfolio The portfolio exhibits a positive skew, evidenced by a 9.39 skewness results on the 10 year Portfolio IRR distribution. As you can see in the distribution, the results have a longer tail on the upside. Skewness Results YR Skewness 20 Yr Skewness Orlando Office New Jersey Chicago Retail Atlanta Retail San Diego Office New Jersey Portfolio Industrial Apartments The portfolio has a Sortino ratio of the following for following return expectations: Sortino Ratio Year Unleveraged: Year Leveraged: Year Unleveraged: Year Leveraged: Yr Unlev 10 Yr Lev 20 Yr Unlev 20 Yr Lev Orlando Office New Jersey Chicago Retail Atlanta Retail San Diego Office New Jersey Portfolio 2.00 Industrial Apartments The following are some high level takeaways: The results show an obvious benefit of diversification. Portfolio risk metrics are lower than the weighted average of the assets, and the portfolio distribution exhibiting a strong positive skewness. The retail and industrial assets exhibited the strongest scores from the Sortino ratio, highlighting the impact of NNN leases. 7 Downside risk is based off this investor s benchmark for the portfolio of a 5% real return. Assuming inflation of 2.5%, the assumed desired outcome is a 7.5% aggregate return. All downside risk calculations in this paper are made with the assumption the investor has a 7.5% target return. 12 Eric Hines Practicum Johns Hopkins University

14 Leverage for this portfolio at the existing levels (~30%) adds expected return without sacrificing significant downside risk. To continue the analysis on a more micro level to gain insight into risk in a variety of scenarios, the results have been analyzed to consider a variety of asset level and portfolio level considerations. Asset Management Impacts Termination Option Tenants with termination options add additional risk to potential returns. The portfolio analyzed has two significant tenants that have termination options written into their leases: 27,000 square feet at the Orlando office property and 198,000 square feet in the Philadelphia Industrial portfolio. Each of these termination options has been modeled into excel with the likelihood of tenant termination dependent upon the tenant s ability to reduce their rent over the remaining term when taking into consideration the termination penalty. Eliminating these two options has a positive impact for each of these assets. Expected IRRs for both tenants are flat, however we see a reduction in downside risk for both assets: Orlando 7 basis points; Philadelphia 5 basis points. The likelihood of a termination is dependent upon market rent fluctuations. Markets with higher rent growth variability are at more risk of these options being exercised then markets with more stable growth patterns. As market rent growth is one of the uncertainty variables in the model, landlords can use this tool to determine how much additional risk and reduction in expected return there is in giving a tenant a termination option. To analyze the impact of giving termination options to new tenants, a scenario has been run assuming all the vacant space in the portfolio among office, industrial and retail assets will have termination options attached to new leases on the existing vacancy in which the tenant will have the option of terminating at the end of three years 8 for the remaining unamortized (at 9%) principal balance of the leasing Market Termination Options Termination Termination Date Penalty Remaining Obligation % of Remaining Obligation % Chance of Termination Philadelphia Industrial 12/31/ ,927 2,599, % 38.4% Orlando Office 4/30/ , , % 97.7% Scenario #1: Termination Options Vacant Space Unamortized Capital Costs Market Total SF Vacancy % AVG Probabily Change in of Term Asset IRR 10 YR Change in Asset Downside Risk Change in Sortino Ratio Orlando Office 35, % 1.0% 0.02% 0.02% 0.01 Chicago Retail 25, % 0.7% 0.10% 0.17% 1.11 San Diego Office 33, % 23.0% 0.12% 0.07% 0.05 Portfolio 94, % 0.06% 0.02% 0.03 Scenario #2: Termination Options Vacant Space 50% Unamortized Capital Costs Market Total SF Vacancy % AVG Probabily Change in of Term Asset IRR 10 YR Change in Asset Downside Risk Change in Sortino Ratio Orlando Office 35, % 27.8% 0.04% 0.10% 0.02 Chicago Retail 25, % 11.9% 0.11% 0.03% 0.00 San Diego Office 33, % 50.3% 0.42% 0.30% 0.16 Portfolio 94, % 0.07% 0.06% 0.16 commissions and tenant improvements (Scenario #1). A sensitivity scenario was run at 50% of the unamortized capital costs as well to gauge the sensitivity of the termination payment (Scenario #2). The portfolio sees a moderately lower expected return and moderate increase in risk. The results on an asset basis are impacted by: Orlando Office: For Scenario #1 there was a nominal adjustment in expected return and risk. Scenario #2 showed a slight decrease in expected return and increase in risk. Due to the marginal amount of vacancy, the impact on this asset for either scenario is not substantial. 8 San Diego lease length assumption is 7 years and the potential termination would be after year Eric Hines Practicum Johns Hopkins University

15 Chicago Retail: The expected rent volatility of this asset is the lowest among the assets, yielding low probabilities of tenant termination in these hypothetical situations. Also contributing to the minor risk and return movements is the lower amount of capital needed to for release in comparison to office. As shown in the results, there is a minimal impact on risk and return. San Diego Office: The asset sees the greatest hypothetical impact as the Sortino ratio declined by.05 (Scenario #1) and.16 (Scenario #2). This asset saw the largest impact due to a large amount of vacancy and a volatile market rent assumption. Conclusions from simulations: The impact of tenant termination options is fairly significant when applicable to a large amount of space, the asset is in a market with significant rent volatility, and the penalty is less than standard unamortized cost. When the landlord is adequately compensated (unamortized capital balance) for the termination risk, there is little expected difference in return and risk. The impact of termination options on expected return and return volatility is based on: amount of capital needed to lease tenant spaces, rent volatility and the negotiated amount of payment tenant is obligated to pay to exercise the option. Credit Analysis Historical public debt default rates were gathered from Moody s and tenants with debt ratings were assigned their appropriate annual default rate in the base scenario. Tenants without public debt were all given an assumed BB rating and assigned an annual default Credit Scenarios probability based on that rating. The weighted average annual default 8.80% 0% CL 8.60% Base Run rating for the portfolio is 1.34%. As the chart shows, and 8.40% 2% CL 8.20% unsurprisingly, an increase in credit risk reduces the expected return. 8.00% 4% CL 7.80% On a portfolio basis, if the office, retail and industrial assets increase 7.60% 6% CL 7.40% credit risk from the in place annual default rate to 6% annual default 2.40% 2.50% 2.60% 2.70% 2.80% 2.90% 3.00% 3.10% 3.20% Portfolio Downside Risk rate, there is an decrease in expected return of 89 basis points and an increase in risk of 49 basis points. Credit risk should be a key determinant in any Credit Analysis 0 % Credit Loss 2 % Credit Loss 4 % Credit Loss 6 % Credit Loss Market Base Annual Default Delta IRR Delta Delta DR Sortino Ratio Delta IRR Delta Delta DR Sortino Ratio Delta IRR Delta DR Delta Sortino Ratio Delta IRR Delta DR Delta Sortino Ratio Orlando Office 1.19% 0.43% 0.27% % 0.14% % 0.77% % 1.19% 0.44 Philadelphia Industrial 1.54% 0.16% 0.12% % 0.01% % 0.15% % 0.26% 0.93 Chicago Retail 0.60% 0.30% 0.01% % 0.19% % 0.64% % 0.89% 3.29 Atlanta Retail 1.00% 0.01% 0.03% % 0.04% % 0.05% % 0.36% 0.42 San Diego Office 0.83% 0.13% 0.10% % 0.19% % 0.52% % 0.80% 0.40 Portfolio 1.34% 0.15% 0.12% % 0.04% % 0.32% % 0.49% 1.17 leasing decision. Asset managers should not necessarily completely avoid credit risk, as there is a point of potential expected return indifference if the tenant with credit risk is willing to pay a premium rental stream. Accepting a higher rental stream as an offset for credit risk would shift the expected outcome to a higher expected return as an offset for additional risk. Conclusions: Credit quality matters, there is a basis point difference in expected return from moving the credit loss assumption up by 2%. As investment managers underwrite assets, this benchmark can be helpful to gauge appropriate impact to discount rate or required return. 14 Eric Hines Practicum Johns Hopkins University Portfolio (E) IRR

16 An increase in rental rate can offset the impact of credit risk on expected return. Investment managers can use this tool to help negotiate appropriate rental requirements for taking credit risk. Variable Impact Residual cap rate and market rent growth have the largest impact on the volatility of expected returns for the portfolio. Uncertainty variables downtime, renewal ratio s and expense growth all have a fairly minor impact on expected return volatility. Variable analysis conclusions: 0.00% Rent growth has a significant impact on Orlando Philadelphia Chicago Atlanta Retail San Diego New Jersey Portfolio Office Industrial Retail Office Apt expected return volatility. This is especially important to core buyers that are aiming to invest in an asset for stability. Downtime has a relatively small impact on volatility. Each of the product types all have fairly similar downtime patterns. Gross lease structures see more expected return volatility than the NNN leased assets. In aggregate, the expense growth projections have a significant impact on expected return volatility. The office and apartment assets have an average of 0.7% standard deviation 9 attributed to expense escalation compared to 0.2% for the retail and industrial assets. Residual Cap Rate assumptions have a large impact on expected returns. The risk premium is most volatile for office and industrial product. Apartments see the lowest volatility in risk premium. Given the magnitude of volatility, it suggests that timing for real estate investors is vital to create strong returns. Investors should look to sell when risk premium is on the low end of the volatility curve, and buy when there is a large spread. Historical data shows this range is approximately 4% to 5% with the bulk of the data points falling around 2% 3%. Portfolio Implications Standard Deviation 4.50% 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% 1.00% 0.50% Variable Analysis Return Volatility Market Rent Growth Downtime Renewal Ratio Expense Escalation Residual Cap Risk Premium Volatility of Debt Returns The debt level of this portfolio is fairly low as the LTV for the portfolio is ~30%. Using leverage can be a strategy to boost potential returns, but the potential risk each asset and the portfolio undertakes with placing leverage on the asset is important to quantify. All the debt was assumed to be interest only and at a rate of 6. 5%, with one exception in the apartment asset assumed to be at 6.0%. At the 70% and 80% debt levels, an additional 50 and 100 basis points are added Expected Return 11.50% 11.00% 10.50% 10.00% 9.50% 9.00% 8.50% 8.00% 7.50% 7.00% 40% Leverage 30% Leverage Unleveraged Portfolio Leverage Risk and Return 50% Leverage 60% Leverage 70% Leverage 0.75% 1.25% 1.75% 2.25% 2.75% 3.25% Downside Risk 80% Leverage 9 The San Diego office asset assumed a fixed 2% annual tax increase in taxes consistent with California tax law. If this was not the case, more volatility attributed to expense escalations would have been seen. 15 Eric Hines Practicum Johns Hopkins University

17 to interest rates. Increasing use of debt can be an effective strategy to boost expected return. This portfolio is maximized on a risk/return basis at debt levels in the range of 50% 70%. At the 70% 80% leverage level, the additional return for this portfolio is not justified given the return benchmark and the additional downside that the leverage creates. Comparative Asset Types Leveraged Scenarios Measured by Sortino Ratio Unlev IRR 30% Lev IRR 40% LEV IRR 50% LEV IRR 60% LEV IRR 70% LEV IRR 80% LEV IRR Office Returns lags the remainder of asset types, and returns have the highest level of volatility. As a result the Sortino ratio for the office properties lag the remaining assets in the portfolio. Driving Factors: Volatile rent growth patterns on the two office assets due to large swings historically in their local markets Gross leases with narrowing net margins over time as expected expense growth outpaces rent growth Highest risk premium on resale (thus highest residual cap) of all asset types along with the greatest volatility in risk premium. Conclusions: Core buyers looking for return stability should favor other property types. Given the volatile nature, office can make sense for opportunistic buyers if market is timed correctly. Market pricing currently for office assets may be too aggressive given the risk. Prices will have to fall to give investors an attractive return for the risk taken. Apartments Asset return in portfolio is on the lower end for 10 year but stronger under 20 year hold. Expected return volatility (as measured by standard deviation) is the lowest among all of the assets. 10 Driving Factors: Rent growth volatility is lowest among property types. Apartments have the smallest risk premium on resale National rent growth is highest for apartments among all property types, leading to less margin reduction over time suggesting improved performance over longer hold periods. Conclusions: Investors looking for stability should focus on apartments due to the attractive return for every level of risk on long term perspective. Further analysis is needed to gauge the risk return trade off on apartment assets, as this particular property has unique characteristics that impact expected results. 10 Only one apartment asset was analyzed and is unique in the fact that it has the ability to transform rent controlled units to market rent and is in a highly desired submarket. These two factors have played a role in the assumed purchase price and has greater impact on the 10 year hold. 16 Eric Hines Practicum Johns Hopkins University

18 Retail Strong, well located retail assets have attractive returns with low volatility. The retail assets in this portfolio are attractive on a risk/return basis. Driving Factors: NNN leases minimize margin reduction over lease term, helping to reduce return volatility Minimal capital expenditures for leasing helps minimize risk. Conclusions: The assets analyzed are well located, grocery anchored neighborhood centers. This product type provides an excellent return/risk tradeoff. Further analysis would be needed to understand lesser located retail or the mall sector. Industrial The industrial portfolio analyzed performs well on a return/risk profile with the second highest expected return and minimal volatility. Driving factors: NNN leases minimize margin reduction over lease term, helping to reduce return volatility Minimal capital expenditures for leasing helps minimize risk. Higher volatility comes from market rent growth and risk premium. Conclusions: With 100% occupancy and low lease rollover until 2013, this portfolio benefits from stable in place dynamics. With four tenants in the portfolio, credit risk is concentrated. This is typical in warehouse portfolios and focus on credit is thusly more important on a individual tenant basis. Comparative Asset Types Institutional investors with long term liabilities are concerned with long term asset performance and risk levels. The portfolio analyzed is compared to other product types to compare the efficiency of the expected returns. Other asset types analyzed are: US Stocks: S&P 500; US Investment Grade Bonds: Barclays Aggregate Bond Index; US Government Bond: 10 Yr Treasury (held until maturity); Private Real Estate Returns: NCREIF. Annual Return Asset Type Efficient Frontier 12.00% Base Port Leveraged 11.00% 80% 10.00% Base Port 50% Lev Base Portfolio Leveraged S&P % NCREIF Base Port Unleveraged 8.00% 7.00% Barclays Bond Index 6.00% 5.00% 4.00% 10 YR Treasury 3.00% 0.00% 0.50% 1.00% 1.50% 2.00% 2.50% 3.00% 3.50% 4.00% 4.50% 5.00% Downside Deviation Historical data for each segment are analyzed with the comparative results incorporating the expected results for the base portfolio analyzed in this paper, and historical results for the remainder of the data sets. The comparative benchmarks annual return results were complied by compounded annual growth rate and the downside deviation is the amount of volatility on a 10 year basis below the compounded annual growth. To arrive at this statistic, continuous ten year results were analyzed for each comparative benchmark. The downside deviation is calculated based upon these continuous 17 Eric Hines Practicum Johns Hopkins University

19 10 year results. This method was selected as it gave the best comparison to the expected results in the base portfolio on a 10 year hold basis. The results show that the portfolio of real estate assets analyzed is efficient from a return/risk basis as compared to NCREIF and the S&P 500. The bond data points showed the lowest risk, while the commercial real estate portfolio s along with NCREIF were shown to have lower downside volatility compared to the S&P 500. How this moves the ball forward and issues This model creates a tool to analyze commercial real estate decisions on a quantitative basis. Being able to understand both the return and risk profiles from a quantitative perspective will provide another tool in the decision making process. Over the past few decades, real estate has become a more accepted asset class by institutional investors. As many of these institutional investors are looking to line up long term liabilities with long term assets, real estate provides an excellent vehicle to do so. By taking a quantitative look at risk and return, institutional investors can integrate projected real estate risk and return profiles as well as correlation with their stock and bond portfolio s. Given the ability to understand risk real estate investment managers have the ability to further develop their solicitation of investment capital by showing the benefit of increasing their allocation to direct real estate and the ability of the investor and investment manager to adapt to a desired risk return level based upon how the assets/portfolio is capitalized and managed. The big issues surrounding the current use of the model are data limitations and the speed of excel/crystal ball. The data limitations are due to a lack of reliable historical data points in the real estate industry. As real estate has increasingly become an Data Limitations Market Data Source Date Range Comments Market Rent Growth REIS, TWR Based on asking rents and not achieved rents. Volatility is based on historical metrics. Expense Growth BOMA / BLS Based on office data from BOMA. Unable to obtain reliable data sets for other office types as it's either unavailable or unreliable. Downtime CoStar / Product Tracking CoStar details are rarely completely accurate. Data is compiled based on when space was added to CoStar and when it was taken off; which is not an exact match to downtime REIT Data and LIM product tracking does not incorporate a large amount of history. Renewal Ratio's REITS / Product Tracking Credit Ratings Moody's Privately owned tenants have a global credit assumption. accepted investment class over the past decades, data availability has increased, however this provides a minor data set to analyze historical variability. 18 Eric Hines Practicum Johns Hopkins University

20 Appendix A 19 Eric Hines Practicum Johns Hopkins University

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