Office Building Capitalization Rates: The Case of Downtown Chicago

Transcription

1 J Real Estate Finan Econ (2009) 39: DOI /s Office Building Capitalization Rates: The Case of Downtown Chicago John F. McDonald & Sofia Dermisi Published online: 26 March 2008 # Springer Science + Business Media, LLC 2008 Abstract This paper is an empirical study of the capitalization rates for 132 office building sales in downtown Chicago from 1996 to The capitalization rate is hypothesized to be a function of the classic capital asset pricing model variable and variables intended to capture the expectation that the real market value of the building will change. The results show that the capitalization rate for office buildings incorporates a very low value for beta. A lower capitalization rate was associated with a smaller risk-free rate, a lower borrowing rate, class A buildings, newer buildings, buildings that had been renovated, a reduction in the vacancy rate in the downtown Chicago office market, and an increase in employment in the financial sector of the metropolitan area. Keywords Office capitalization rates. Office asset markets This paper is an empirical study of the capitalization rates that were used to convert net operating income into the price at which office buildings were sold in downtown Chicago during 1996 to The sample includes 132 transactions of large office buildings, some of which are among the most prominent structures in the nation. The study is based on the capital asset pricing model, supplemented by variables that real estate investors use as proxies for expected changes in the market value of an office building. These variables include features of the buildings and changes in the local market for office space. A search of the literature on office building capitalization rates reveals that there is no published study of individual office building capitalization rates, so apparently this study is the first of its kind. The capitalization rate has a critical role in property valuation. Potential buyers of commercial real estate typically convert the expected or current net operating income J. F. McDonald (*) University of Illinois at Chicago, Chicago, IL 60607, USA mcdonald@uic.edu S. Dermisi Roosevelt University, Chicago, IL 60605, USA sdermisi@roosevelt.edu

2 Office Building Capitalization Rates: The Case of Downtown Chicago 473 into asset value using an overall capitalization rate. The goal of this study is to investigate in more detail than has been done previously the variables that influence the choice of the capitalization rate. Miller and Geltner (2005, pp ) provide an illuminating textbook discussion of factors that influence capitalization rates, including income growth, risk, economic obsolescence, interest rates, market conditions, and property age. This study finds, in the case of office buildings in downtown Chicago, empirical confirmation for most of their hypotheses. Previous Literature Previous research on office building capitalization rates falls into two broad categories. Onetypeofstudy,suchasNourse(1987), Froland (1987), Evans (1990), Ambrose and Nourse (1993), and Jud and Winkler (1995), examined the movement of an overall average capitalization rate over time as it depends upon the capital market and other variables. A second group of studies investigated the cross-section variation in capitalization rates for example, across property types or metropolitan areas. These studies include Ambrose and Nourse (1993), Sirmans et al. (1986), Sivitanides and Sivitanidou (1996), and Sivitanidou and Sivitanides (1999). However, only Sirmans et al. (1986) used the individual property as the unit of observation. Nourse (1987) studied a time series of national capitalization rates for multifamily and nonresidential properties (provided by the American Council for Life Insurance), with the result that the debt service payment had a positive effect and the percentage of the loan that had been amortized had a negative effect on the capitalization rate. These findings are consistent with the view that the capitalization rate is the weighted average of the equity yield and the mortgage constant (adjusted for equity build-up and expected changes in value). Froland (1987) studied the same data and found that the capitalization rate had positive correlations with debt yields and inflation expectations. Evans (1990) also conducted a time-series analysis of the ACLI data, and found that the capitalization rate series is auto-correlated and positively related to the earnings-price ratio in the stock market with a lag of one quarter. Ambrose and Nourse (1993) used ACLI national data on individual property types, and estimated a time-series, cross-section model in which the capitalization rate is a function of financial variables the spread between the long-term treasury bond and treasury bill rates, the earnings/price ratio for the S&P 500, the cost of debt (loan-to-value ratio times the mortgage constant), and the percentage equity investment. The coefficients of the debt and equity variables were found to be highly statistically significant with the correct orders of magnitude, but the coefficient of the spread variable is only marginally statistically significant, and the coefficient of the earnings/price ratio was found to be negative and highly statistically significant. The study also estimated differences in capitalization rates by property type and region, but made no attempt to interpret these results. The study by Jud and Winkler (1995) represents a significant step forward in that they developed a financial model based on the capital asset pricing model (CAPM) that includes the variables the earlier studies had employed. In this model the capitalization rate minus the risk-free interest rate is a function of the spread between the long-term debt and risk-free rate, the expected return to the market

3 474 J.F. McDonald, S. Dermisi portfolio minus the risk-free rate (the traditional CAPM variable), and the expected growth rate of the income stream. This model is derived in the next section. The data for the study consist of capitalization rates for four property types from 21 metropolitan areas for 15 time periods from 1985 through The results show that the estimated coefficients for both of the financial variables are statistically significant, and that the traditional CAPM variable affects the dependent variable with a lag, a finding that is consistent with the earlier result from Evans (1990) and suggests inefficiency in real estate markets. The study made no attempt to explain the differences in capitalization rates by property type or across metropolitan areas. Sivitanides and Sivitanidou (1996), in a study of average office building capitalization rates across metropolitan areas, found that the vacancy rate and the lagged capitalization rate had positive effects, and absorption and the size of the stock of office space had negative effects on the capitalization rate. Sivitanidou and Sivitanides (1999), in a more elaborate time-series, cross-section study, found that the average capitalization rate in a metropolitan area was negatively related to local demand variables absorption, growth stability, rent growth, tenant diversity and percentage of government tenants. Inflation and stock returns were positively related to, and the central business district share of the office market had a negative effect on, the capitalization rate. The study by Sirmans et al. (1986) is based on market-extracted capitalization rates for apartment buildings in the Chicago metropolitan area. This study found that location with the metropolitan area and physical characteristics of the property were related to the capitalization rate, but did not examine the effects of local market characteristics. The previous studies indicate that capitalization rates depend upon financial variables, and the model developed by Jud and Winkler (1995) provides the needed theoretical framework. In addition, the studies of cross-section variation in capitalization rates provided evidence of the importance of local market conditions and individual property characteristics. This study of office buildings in downtown Chicago employs variables of all three types. Model of Capitalization Rates The current value of a commercial real estate property can be written as V 1 ¼ X. inoi i ð1 þ rþ i ; ð1þ where NOI i is net operating income received at the end of time period i and r is the risk-adjusted cost of capital. Equation 1 is a statement of market equilibrium. The corporate income tax is ignored in this presentation on the grounds that real estate investors are exempt from this tax because they are organized as real estate investment trusts, limited-liability companies (LLC), or other entities that are exempt from this tax. Multiplication by (1+r) produces ð1 þ rþv 1 ¼ NOI 1 þ V 2 : ð2þ

4 Office Building Capitalization Rates: The Case of Downtown Chicago 475 This equation can be written as V 1 ¼ ½NOI 1 þ $VŠ r; ð3þ where NOI 1 is current net operating income ΔV is the expected change in real market value. McDonald (2005) provides a detailed derivation of this equation. Equation 3 can be solved for the capitalization rate ρ: ρ ¼ NOI 1 V 1 ¼ r ð$v=v 1 Þ: ð4þ Equation 4 is simply a rewriting of Eq. 1, and is therefore also a statement of market equilibrium; the capitalization rate for the current period equals the riskadjusted cost of capital minus the expected percentage change in the real value of the asset. Following Jud and Winkler (1995), we note that the cost of capital (r) in the traditional band-of-investment method is the weighted average of cost of debt and equity, written r ¼ dr ð d Þþð1 dþr e ; ð5þ where d is the proportion debt financing, r d is the interest rate on debt, and r e is the cost of equity. Using the capital asset pricing model (CAPM), the cost of equity is r e ¼ r f þ b r m r f ; ð6þ r f is the risk-free interest rate, r m is the expected rate of return for the entire capital market, and β is the equity beta of the real estate asset in question. Substitution of Eqs. 5 and 6 into Eq. 4 produces the model that is estimated empirically: ρ r f ¼ drd r f þ ð1 d Þβ rm r f ð $V=V1 Þ: ð7þ This is the same model specified by Jud and Winkler (1995). In their empirical study they assumed that ΔV/V 1 is a constant term that may vary by property type and metropolitan area. They did not include variables that might be thought to influence the expected change in real asset prices. In Eq. 7 the market return is the total rate of return (annualized) for the S&P 500 stocks for the quarter in which the office building was sold, the risk-free rate is the 3-month (annualized) treasury bill rate for the quarter in question, and the interest rate on debt is the interest rate on conventional home mortgages for the quarter. (We experimented with other interest rates on debt, and these results are reported below.) All interest rates are stated in real terms. A constant term is added to Eq. 7 because the borrowing rate available to real estate investors typically is different from the interest rate on conventional home mortgages, so: ρ r f ¼ α þ drd r f þ ð1 d Þβ rm r f ð $V=V1 Þ: ð8þ Here α=d(r b r d ), where r b is the borrowing rate for real estate investors.

5 476 J.F. McDonald, S. Dermisi The expected change in the real value of the property is assumed to be a function of characteristics of the building the class of the office building (A or B), the age of the property, and whether the property had been renovated and changes in local market conditions, represented by the change in employment in the financial sector over the past year, and the change in the vacancy rate in the downtown Chicago office market over the past year. While the model is based on the capital asset pricing model, the inclusion of several variables that may signal a change in the market value of office buildings means that the model is also intended to describe the behavior of office building investors and how they form expectations of property value changes. 1 Data The data for the study are the records of 132 office building transactions that took place in downtown Chicago from 1996 to The data include selling price, capitalization rate, class of the building (A or B), rentable square feet, age of the building, whether the building had been renovated, occupancy rate, date of sale, and other features of the building. With the exception of the capitalization rate, all of these variables are available from commercial real estate services such as CoStar. The capitalization rates were compiled by Zeller Realty based on building income data provided to potential buyers. Other variables added to the data are the risk-free rate (3-month Treasury bill rate for the quarter in which the building was sold), the total return to the S&P 500 for that quarter, the interest rate on conventional home mortgages, financial sector employment for the Chicago metropolitan area for the year of sale (from the Bureau of Labor of Statistics), and the office vacancy rate in downtown Chicago for that year as provided by CoStar Group. Means and standard deviations for these variables are shown in Table 1. The mean capitalization rate in the sample is 8.39%, the mean risk-free rate is 3.51%, the mean mortgage interest rate is 6.67%, and the mean (annualized) return for the S&P 500 is 10.07%. The mean value of risk, calculated as the total return to the S&P 500 minus the risk-free rate, is 6.57% on an annualized basis. Half of the transactions (49%) involved class A buildings, the mean age is 31 years, and 41% of the buildings had been renovated. The mean square footage for the buildings is 734,000, and the mean price per square foot is $ The mean for the change in the vacancy rate was 0.48% for the year. The vacancy rate fell from 10.2% in 1996 to 8.2% in 1998, then increased steadily to 16.2% in 2005, and fell to 12.8% in Employment in the financial sector of metropolitan Chicago increased from 295,000 in 1995 to 336,000 in 2007, with small interruptions in growth in 2002 and The mean annual financial employment increase in the metropolitan area for the 132 transactions was 1, Building characteristics and current market conditions such as the vacancy rate level and the employment level affect net operating income. The variables included in the model of the capitalization rate are intended to signal changes in the real value of the asset.

6 Office Building Capitalization Rates: The Case of Downtown Chicago 477 Table 1 Variables, means, and standard deviations Variable Mean Standard Deviation Data Source Cap rate 8.39% 1.61 Zeller Realty Group Risk-free rate 3.51% month T bill rate Mortgage rate 6.67% 0.79 Federal Reserve Cap rate R f (real) 7.40% 2.21 Mortgage rate T bill rate 1.41% 1.28 Federal Reserve S&P return (annualized) 10.07% S&P 500 total return Risk (R m R f ) 6.57% S&P 500 total return Risk lagged one quarter -5.39% Class A building 0.49 CoStar Group Age CoStar Group Renovated building.41 CoStar Group Change in financial Bureau of Labor Statistics employment (1,000 s) Change in vacancy rate 0.49% 1.48 CoStar Group Building size (square foot) 734, ,510 CoStar Group Price per square foot Zeller Realty Group and John Buck Co. Quarterly Report Sample size 132 Empirical Model As indicated above, the dependent variable is the capitalization rate for the building minus the real risk-free rate for the quarter in which the building was sold. The independent variables in the model include the spread between the interest rate on long-term debt and the risk-free rate and the classic variable for the capital asset pricing model the expected market return (as estimated as the actual return for the quarter in question) minus the risk-free rate. Jud and Winkler (1995) found that the latter variable influenced the capitalization rates for commercial properties with a lag of one quarter, so both the contemporaneous and lagged values of the expected market return minus the risk-free rate are included in the model. Table 2 displays the mean capitalization rates (and sample sizes) for each year from 1996 to 2007, along with the mean risk-free rate and the mean mortgage rate for the same years. Sample sizes are small for 1996 and 1997, but the data show that the capitalization rate moved with the risk-free rate during However, the Federal Reserve began to lower short-term interest rates aggressively in The mean for the risk-free rate fell from 6.00% in 2000 to 1.03% in 2003, but the mean capitalization rate declined only from 9.56% to 8.63% and the mortgage rate fell from 8.06% to 5.82% over these years. After 2003 the risk-free rate increased to a mean value of 4.84% in 2006 and 5.00% in the first half of In contrast, the mean capitalization rate continued to decline to 6.24% in 2006 and the mortgage rate increased from 5.82% to 6.41%. (The sample size for 2007 is very small.) In short, the spread between the risk-free rate and the mean capitalization rate widened as the risk-free rate fell precipitously, and then narrowed as the risk-free rate increased to more normal levels. The mean capitalization rate reported in Table 2 follows closely the national average capitalization rates for office buildings provided by

7 478 J.F. McDonald, S. Dermisi Table 2 Capitalization rate and borrowing rates Year Capitalization rate (Mean) Sample size Risk-free rate (3-month T bill) Conventional mortgage rate Real Capital Analytics (RCA). RCA reports in the Wall Street Journal (2008) that the capitalization rate declined almost continuously from 9.0% in 2001 to 6.3% in It is hypothesized that expected change in the market value of an office building depends upon the following variables. Investors may expect that class A buildings (the buildings with the most up-to-date facilities) will appreciate in real value more rapidly than class B buildings. The age of the building affects the percentage change in building value directly (and negatively) because an older building has fewer years of useful life remaining. For example, if a building is expected to last 60 years, then a new building loses 1/60 of its remaining life when it is new and loses 1/30 of its remaining life at age 30. The life a building can be extended by renovation, so a dummy variable for renovation is included. Office building investors pay close attention to the vacancy rate in the market. A reduction in the vacancy rate is hypothesized to signal an increase in market value and therefore a reduction in the capitalization rate. A simple model of the vacancy rate is presented in the appendix that shows how the vacancy rate changes with changes in demand and supply. This model shows that changes in the vacancy rate unambiguously reflect changes in the demand for office space. Lastly, the growth in office employment also may be another signal for an increase in market value. The most important office employment category is hypothesized to be the financial sector. Table 3 is the correlation matrix for the variables included in the estimated models. We note that the dependent variable (capitalization rate minus real risk-free rate) is highly positively correlated with the mortgage rate minus the risk-free rate and the change in the downtown office vacancy rate. Other high correlations are between the change in the vacancy rate and the mortgage rate minus the risk-free rate and between the age of the building and the renovation dummy. The interaction between these two variables (age times the renovation dummy) has a simple correlation with age of 0.87 and with the renovation dummy of Eleven other correlations shown in Table 3 exceed the 1% critical value of 0.22 for simple correlations with a sample of 132. Multiple regression results are displayed in Table 4. The first model includes only a constant term and the financial variables; the mortgage rate minus the risk-free rate

8 Office Building Capitalization Rates: The Case of Downtown Chicago 479 Table 3 Simple correlation matrix Mort. r f Risk Risk lag Class Age Renov ΔVac rate ΔFin empl Age Renov Cap rate r f Mortgage r f Risk Risk lagged Class Age Renovated ΔVac rate ΔFin empl 0.06 and expected market return minus the risk-free rate (current and lagged). This model mimics the model estimated by Jud and Winkler (1995). The standard errors of the coefficients are corrected for heteroskedasticity using the White (1980) procedure. The adjusted R square for the ordinary least squares estimate is The estimated coefficient of the mortgage rate minus the risk-free rate is 1.218, which is highly statistically significantly different from zero (and from 1.0). Recall from Eq. 8 that this coefficient is an estimate of the percentage of debt financing, so this estimated coefficient is larger than expected. The coefficients of both market risk variables are negative (contrary to expectations) and not statistically significantly different from zero. The estimated constant term is 3.55 (with t value of 10.25). However, this model omits variables that measure the expected change in the real value of the asset. The second estimated model in Table 4 includes the variables that measure the characteristics of the buildings and the changes in local market conditions. The Table 4 Multiple regression results (dependent variable is capitalization rate minus real risk-free rate or capitalization rate) a Independent variable Model 1 ρ r f Model 2 ρ r f Model 3 ρ r f Model 4 ρ Constant (10.25) (12.27) (11.10) (9.87) Mortgage rate minus risk-free (11.77) (6.11) (6.74) rate Risk ( 1.16) (2.35) (1.92) (2.01) Risk lagged one quarter ( 0.49) (2.54) (2.79) (2.51) Class A ( 3.43) ( 2.66) ( 2.87) Age of building (2.01) (3.51) (3.38) Renovated building ( 2.46) Age renovated ( 3.50) ( 3.44) Change in vacancy rate (6.09) (6.20) (6.30) Change in financial employment ( 1.84) ( 1.74) ( 1.93) Real risk-free rate (3.19) Real mortgage rate (1.95) R square for OLS (adjusted) Sample size a T values are in parentheses. Standard errors of estimated coefficients corrected for heteroskedasticity by the White (1980) procedure

9 480 J.F. McDonald, S. Dermisi adjusted R square for the ordinary least squares estimate of the model is Standard errors used in the computation of the t statistics have been corrected for heteroskedasticity by the White (1980) procedure. The results for the model show that the coefficient of the mortgage rate minus risk-free rate is and highly statistically significant. As indicated above, this coefficient is an estimate of the proportion of debt financing. The market risk measure and its lagged value are statistically significant with coefficients of and As shown in Eq. 8, these coefficients are estimates of (1 d)β. If the proportion debt is 69.7% (or 80%), the estimated equity betas are and (or and 0.045). This result is consistent with the hypothesis that real estate investment has a low beta value and therefore usefully adds to a diversified investment portfolio. The statistical significance of the coefficient of the lagged risk variable is consistent with the findings of Evans (1990) and Jud and Winkler (1995). Note that the estimated constant term is 5.369, and that it is highly statistically significantly different from zero. In the equilibrium CAPM this coefficient is hypothesized to be equal to the difference between the home mortgage rate and the borrowing rate for real estate investors. However, in this study of capitalization rates the right-hand-side of Eq. 8 includes the expected change in the real asset value. The presence of a statistically significant constant term also may mean that the model fails to explain fully the expectation of the change in the real asset value. The coefficient of the dummy variable for class A buildings is negative as expected with a value of 0.913, and the coefficient attains the conventional level of statistical significance. The age of the building has the expected positive effect on the capitalization rate minus the risk-free rate. The coefficient means that an added ten years increased the capitalization rate by 0.12%. Also, the coefficient of renovation has a negative sign, which indicates that renovation reduced the capitalization rate (i.e., extended the economic life of the building). The next variable included in the model is the change in the vacancy rate over the previous year. This variable had a large and statistically significant impact on the capitalization rate of An increase in the vacancy rate from the previous year of 0.49% (the mean value) is estimated to have increased the capitalization rate minus the risk-free rate by 0.33%. As we suggested, it is evident that office building investors are paying close attention to the direction and magnitude of the recent change in the vacancy rate to signal when building values can be expected to change. The last variable in the model is the change in financial sector employment, another variable that is used as a signal for an increase in office building value. The coefficient of this variable is marginally statistically significant and has the expected negative value. The coefficient of indicates that an increase in financial sector employment of 2,000 was associated with a reduction in the capitalization rate of 0.14% The renovation variable has a statistically significant negative effect on the capitalization rate as expected, but it may be that the impact of renovation depends upon the age of the building. In particular, it is possible that renovations have a larger impact on extending the life of older buildings. A variable that captures this idea is age of the building times the renovation dummy variable. However, we note in Table 3 that the simple correlation between this variable and building age is 0.87, indicating a possible collinearity problem. The third estimated model shown in

10 Office Building Capitalization Rates: The Case of Downtown Chicago 481 Table 4 replaces the renovation dummy with this new variable. The estimated coefficient of building age increases from to (with a t value of 3.51), and the coefficient of the age-renovation interaction variable is (with a t value of 3.50). These coefficients have the expected signs, and their magnitudes appear to be reasonable. In particular, the coefficients indicate that the effect of renovation on the capitalization rate is equal to times the age of the building; a 40-year old building that has been renovated is estimated to have a capitalization rate that is 0.96% lower than a 40-year old building that has not been renovated. The old building that is not renovated has a capitalization rate that is estimated to be 1.20% lower than the rate for a new building, while the renovated old building has an estimated capitalization rate that is 0.24% lower than the rate for a new building. Unfortunately, we do not have data on the extent of the renovations. Nevertheless, the importance of office building renovation is confirmed in this study. One potential problem with the estimated models suggested by a reviewer is that the coefficients may be biased by the presence of the risk-free rate on both sides of the equation. Equation 8 can be rewritten as: ρ ¼ α þ ð1 d Þr f þ dr d þ ð1 dþβ r m r f ð $V =V1 Þ: ð9þ The real risk-free rate and the real mortgage rate are entered as separate variables (replacing the spread between the mortgage rate and the risk-free rate). The dependent variable now is the capitalization rate. Results are shown in Table 4 as the fourth model. The estimated coefficient of the real risk-free rate is (with t= 3.19), which is statistically significantly greater than zero. This coefficient is an estimate of the proportion of equity invested (implying that the proportion of debt is 0.657). The estimated coefficient of the mortgage rate has dropped to 0.314, and this coefficient is marginally statistically significantly different from zero (t = 1.95). It was expected that this coefficient would be an estimate of the percentage borrowed to purchase the real estate assets, but the two estimates of the proportion debt (0.657 and 0.314) are statistically significantly different. 2 Although the coefficient of the real mortgage rate has the expected sign and attains marginal statistical significance, this result suggests that the real mortgage rate is not a good proxy for the borrowing rate for real estate investors. However, the coefficients of all of the other variables are not affected appreciably by this change in empirical specification. The coefficients of the market risk variables, the building characteristics, and the changes in local office market conditions are stable. All of the models reported in Table 4 were estimated with two other proxies for the borrowing rate that have been used in previous studies the 10-year treasury bond rate, and the Baa corporate bond rate but neither of these rates performed as well as the mortgage rate. For the model in column 4 of Table 4, the estimated coefficient of the real 10-year Treasury bond rate is (t = 1.08), and coefficient of the real Baa corporate bond rate is (t = 1.90). Additional research should 2 The statistical test is computed as t ¼ ð1 0:343 0:314Þ= ½0:0157 þ 0:0320 þ 20:0173 ð ÞŠ¼ 0:343= :0823¼ 4:17:The numerator is the difference between the two estimates of the proportion debt ( ). The denominator is the sum of the variances of the two regression coefficients minus two times their covariance. The test rejects the hypothesis that the difference between the two estimates is zero.

11 482 J.F. McDonald, S. Dermisi include better measures of the borrowing terms faced by commercial real estate investors. Several other models were estimated that produced no change in the basic nature of the results. The omission of the ten observations from 1996, 1997, and 2007 resulted in very little change in the estimated coefficients. Estimated coefficients for the occupancy rate in the building, the size of the building (square feet of rentable space), a dummy variable for parking in the building, and time since 1996 were found to be statistically not significant and the inclusion of these variables had no appreciable impact on the other estimated coefficients. Time was entered to test the possibility that the capitalization rate followed a time path that may have been generated by variables other than the variables in the model. The change in the downtown vacancy rate was entered as a quadratic variable to capture the possibility of a non-linear response, but the quadratic term has a statistically insignificant coefficient as well. In summary, the capitalization rate is found to be related to variables that are signals for an expected change in the value of office buildings in downtown Chicago. Those variables include the class and age of the building, whether it has been renovated, and the changes in the downtown vacancy rate and financial sector employment. The capitalization rate is related to the classic measure of risk (and its lagged value), but with very small coefficient values, suggesting that downtown office buildings in Chicago were considered to be essentially zero beta investments. The real risk-free rate had the expected positive effect on the capitalization rate. The study used the mortgage interest rate as a proxy for the borrowing rate for real estate investors, but the numerical value of the estimated coefficient suggests that it is not a very good proxy for the borrowing terms faced by commercial real estate investors. The risk-free rate and the change in the downtown vacancy rate were found to be the most important factors associated with changes in the capitalization rate over time. The model in column 4 of Table 4 can be used to compute a predicted value Table 5 Predicted and actual mean capitalization rates (predictions based on model 4 in Table 4; see text for equation) Year Risk-free rate(%) Mortgage rate (%) CPI (%) Vacancy change (%) Financial empl. change (1,000 s) CAPM risk (%) Cap rate, predicted (%) Cap rate, actual mean (%)

12 Office Building Capitalization Rates: The Case of Downtown Chicago 483 for the capitalization rate over time for a given type of building. Table 5 has been prepared using mean values for building class, age, and renovation. The equation is: ρ* ¼ 6:539 þ 0:035 þ 0:343ðreal riskfree rate þ 0:669ðchange in vacancy rate þ 0:016ðaverage CAPM risk for the yearþ: Þþ0:314ðreal mortgage rateþ Þ0:073ðchange in financial employmentþ Table 5 shows that this predicted capitalization rate increases from 1998 to 2001, declines from 2001 to 2006, and then increases in These movements follow the actual mean capitalization rate for the sample. The increase in the capitalization rate from 1998 to 2001 is associated with increases in the vacancy rate, which countered the effects of reductions in the two real interest rates. After 2002 to 2005 the continued declines in real interest rates overcame the effect of further increases in the vacancy rate, so the capitalization rate fell. Real interest rates increased in 2006, but the decline in the vacancy rate and strong increase in financial sector employment pushed the capitalization rate down. These trends continued into Conclusion This study is an empirical examination of the capitalization rates that were used to convert net operating income into selling prices for 132 office buildings in downtown Chicago during the period 1996 to The sample of transactions includes some well-known office buildings. The study is based on a basic model of the capitalization rate, and combines the traditional capital asset pricing model with variables that are hypothesized to signal expected changes in market values of office buildings in downtown Chicago. The results of the study show that the estimated beta for these buildings was quite low, although statistically significantly different from zero. The real risk-free rate was found to have (approximately) the expected positive effect on the capitalization rate, but the mortgage interest rate was found not to be a good proxy for the borrowing rate faced by real estate investors. (However, the mortgage rate appears to be a better proxy than the 10-year treasury bond rate or the Baa corporate bond rate.) The other results are that the capitalization rate was associated with building characteristics (class, age and whether the building had been renovated) and market forces (changes in the downtown office vacancy rate and changes in financial sector employment). An increase in the vacancy rate of 0.49% (the mean change for the period) was associated with an increase in the capitalization rate of 0.33%. It is well known that real estate investment professionals pay close attention to movements in the vacancy rate, a variable that can be measured with considerable accuracy and represents a good statistic for the state of the market, at least in the short run. This paper provides one important reason for this focus on vacancy rates. Acknowledgement The authors thank Mr. Bob Six, Senior Vice President of Zeller Realty Group for access to data, the John Buck Company Quarterly Report for recent transaction information, and the two anonymous referees for their very helpful comments on an earlier draft.

13 484 J.F. McDonald, S. Dermisi Appendix This appendix presents a simple linear model of an office market in which changes in the vacancy rate capture changes in underlying demand variables. Suppose that the demand for occupied space Q is Q ¼ Q 0 ar; ð10þ where R is rent. Coefficient a is greater than zero. Following McDonald (2000), further assume that the demand for the inventory of vacant space on the part of building owners is V ¼ V 0 ar: The total stock of space K equals Q+V. Substituting V=K Q in Eq. 11 and solving for R produces ð11þ R ¼ ½1= ðα þ aþšðq 0 þ V 0 KÞ: ð12þ Substitution for R in Eq. 11 yields an equation for the vacancy rate: V=K ¼ ð1=kþf½av 0 = ða þ αþš½αðq 0 KÞ= ða þ αþšg: ð13þ This equation shows that: The vacancy rate increases with an increase in the demand for vacant space (increase in V 0 ). The vacancy rate declines with increases in the demand for occupied space (increase in Q 0 ). The change in the vacancy rate with respect to a change in the stock of space is dv=k ð Þ=dK ¼ ð1=kþf½α= ðα þ aþšðv=kþg. The vacancy rate increases with the stock of space K provided that α= ðα þ aþ > V=K. In words, this condition is that the change in the quantity of vacant space demanded with respect to a change in rent divided by the sum the changes in vacant and occupied space with respect to a change in rent exceeds the vacancy rate. It is likely that this condition holds at normal vacancy rates of less than 15%, but the change in the vacancy rate can be an ambiguous signal when the stock of space is expanding (and demand is constant). References Ambrose, B., & Nourse, H. (1993). Factors influencing capitalization rates. Journal of Real Estate Research, 8, Evans, R. D. (1990). A transfer function analysis of real estate capitalization rates. Journal of Real Estate Research, 5, Froland, C. (1987). What determines cap rates in real estate? Journal of Portfolio Management, 13, Jud, D., & Winkler, D. (1995). The capitalization rate of commercial properties and market returns. Journal of Real Estate Research, 10, McDonald, J. (2000). Rent, vacancy, and equilibrium in real estate markets. Journal of Real Estate Practice and Education, 3, McDonald, J. (2005). The Q theory of investment, the capital asset pricing model, and real estate valuation: A synthesis. Journal of Real Estate Literature, 13,

14 Office Building Capitalization Rates: The Case of Downtown Chicago 485 Miller, N., & Geltner, D. (2005). Real estate principles for the new economy. Mason, OH: South-Western. Nourse, H. (1987). The Cap Rate, : A test of the impact of income tax changes on income property. Land Economics, 63, Sirmans, C. F., Sirmans, S., & Beasly, B. (1986). Income property valuation and the use of market extracted overall capitalization rates. The Real Estate Appraiser and Analyst, Sivitanides, P., & Sivitanidou, R. (1996). Office capitalization rates: Why do they vary across metropolitan areas? Real Estate Issues, 21, Sivitanidou, R., & Sivitanides, P. (1999). Office capitalization rates: Real estate and capital market influences. Journal of Real Estate Finance and Economics, 18, Wall Street Journal (2008). Some cap rates inch up. Wall Street Journal January 30, 2008:B6. White, H. (1980). A heteroskedasticity consistent covariance matrix estimator and a direct test of heteroskedasticity. Econometrica, 48,