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Deconstructing overall capitalization rates.

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This article examines the relation of the substitution principle and overall capitalization rates. Although investors may substitute between low- and high-quality investment-grade property of the same type and within the same market, differences in property quality can cause large variations in overall capitalization rates. This study finds overall capitalization rates for apartments, office, industrial, and retail property to be cointegrated, suggesting that the principle of substitution applies across property types. Variation in rates by property type is attributed to the equity capitalization rate and the loan-to-value ratio rather than to the mortgage capitalization rate. The overall capitalization rate for real estate is not cointegrated with capital market yields, indicating that real estate is not a good substitute for stocks and bonds.

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Theory and common sense suggest that equity investors will pay no more for an asset than they would pay for a similar asset that generates equal cash flows with equivalent risk. In appraisal this concept is referred to as the substitution principle; economists frequently refer to it as the law of one price. The substitution principle helps us to understand many of the most critical aspects of real estate value. For this reason, it may be the most important concept in appraisal theory.

This article examines three dimensions of real estate overall capitalization rates ([R.sub.o]s) and their relation to the substitution principle. The first dimension is the effects of quality segmentation on overall capitalization rates within the market for a given real estate type. Higher overall capitalization rates frequently include a market premium reflecting the greater risk associated with low-quality investment-grade property. The second dimension is differences in overall capitalization rates for high-quality, investment-grade property types suitable for institutional investment portfolios. This dimension is explored by using American Council of Life Insurance (ACLI) data for a 23-year period. Presumably the substitution principle applies not only within a property type but across investment categories such as apartments, retail, office, and industrial property in a more broadly defined, multitype real estate market. The third dimension is substitution across asset classes. Typically this dimension tests the market integration of real estate with capital market assets such as stocks and bonds.

Band-of-investment Techniques

In direct capitalization, real estate value ([V.sub.o]) is estimated by capitalizing net operating income ([I.sub.o]), usually the new owner's first-year income, with an overall capitalization rate ([R.sub.o]) using the following formula:

[V.sub.o] = [I.sub.o]/[R.sub.o]

The [R.sub.o] can be extracted from market (sales) data or calculated using the band-of-investment technique. (1)

[R.sub.o] = M x [R.sub.M] + (1-M) x [R.sub.E]

where:

M = the loan-to-value ratio

[R.sub.M] = the mortgage capitalization rate

[R.sub.E] = the equity capitalization rate (equity dividend rate)

Ideally, overall capitalization rates derived by applying the band-of-investment technique should be the same as rates extracted from market sales data. Because of variation in the method of estimating overall capitalization rates, however, Francis (2) emphasizes the need for appraisers to be clear in their discussion of the methodology used to develop market-derived capitalization rates.

Possible Reasons for Differences in Overall Rates

Assuming reliable market data, a persistent difference between overall capitalization rates extracted from market sales and those derived using the band-of-investment technique suggests that lenders have either failed to adjust mortgage terms to make them consistent with market conditions or that the equity capitalization rate ([R.sub.E]) is incorrect. Research suggests that regional segmentation in mortgage markets could, at one time, account for fairly large differences in overall capitalization rates calculated by the band-of-investment technique. However, deregulation and financial innovation, especially securitization, have contributed to a mortgage market that is national in scope and have tended to eliminate variation in mortgage rates attributable to regional imbalances in the supply of and demand for mortgage funds. There may still be differences in overall capitalization rates that are caused by location, but these differences are usually attributed to local imbalances in the supply of and demand for property rather than to the rationing of mortgage funds. Therefore, equity capitalization rates must be investigated to account for differences in overall capitalization rates.

The First Dimension: Quality Segmentation

Much real estate literature suggests that even within a given market there may be both time-series and cross-sectional differences in overall capitalization rates that can be attributed to quality segmentation. Hendershott and Kane (3) argue that apparent distortions in the office component of the NCREIF Office Index may occur because of differences in the character and condition of the office property that is traded at different stages of the real estate cycle.

There are also cross-sectional variations in overall capitalization rates that can be attributed to quality differences. Bullock (4) finds that significantly higher overall capitalization rates are justified for low-quality, investment-grade apartments relative to median-grade property and that the appropriate rate will tend to rise when property characteristics such as lower-quality construction and advanced property age exist. Bullock attributes the differences in overall capitalization rates to the added risk associated with the relatively high operating expense ratios for low-quality property and the increased variability of the income stream because changes in gross income or expenses have a greater relative impact on net operating income when the rent levels are low.

Higher overall capitalization rates may also be justified for lower-quality apartments because of more frequent tenant lawsuits, higher insurance costs, more intense management, and the greater likelihood of negative external influences. Low-quality properties frequently have shorter economic lives than other properties and a greater allowance for replacements. Bullock estimates that low-quality, investment-grade apartments that have most of these characteristics will sometimes sell with capitalization rates that are 50% to 100% higher than those of median-grade projects.

When an appraiser applies the sales comparison approach, common sense dictates that when the quality difference between properties becomes too large, the properties cease to be comparable substitutes for investors. Given the 50%-100% differences in rates identified by Bullock, one might argue that median-grade apartments are more comparable to other real property types (e.g., retail, office) than to low-quality, investment-grade apartments.

The Second Dimension: Property Type

While appraisers are familiar with overall rate differences attributable to quality segmentation, they tend to be less concerned with explaining variations across property types. Table 1 shows overall capitalization rates, mortgage capitalization rates, loan-to-value ratios, and equity capitalization rates for apartments, industrial, office, and retail real estate as reported by the American Council of Life Insurance (ACLI) for the first quarter of 1975 through the second quarter of 1997. Because ACLI does not report equity capitalization rates, these rates were extracted from the ACLI data using the band-of-investment technique.

Essentially, the data reported in Table 1 is a time-series decomposition of the band-of-investment equation. The table shows the mean as well as the standard deviation (in parentheses) for all four components of the mortgage-equity band-of-investment equation. These statistics indicate little variation across property types. Graphical presentation of that data, however, provides a visual explanation of the rates' behavior by property type over time.

Graphical Comparison of Data

The data summarized in Table 1 is graphed in Figures 1 through 4 for the period 1975-1997. Figure 1 shows the fluctuation in overall capitalization rates for each quarter of that period. The most obvious feature of the period is the sharp decline in capitalization rates for all property types during the mid-1980s. The decline reflects the increase in real estate values and the sharp reduction in interest rates. Since the mid-1980s, overall capitalization rates have fluctuated within a narrower range, with rates for apartments at the low end of the range.

[FIGURES 1-4 OMITTED]

Figure 2 is a graph of mortgage capitalization rates ([R.sub.M]s) for the four real estate property types. Although there has been substantial variation in rates over the period examined, there is very little variation in mortgage capitalization rates across property types. This lack of variation suggests that where there are unique differences in credit risk by property type, lenders tend to use loan terms such as the amortization period and loan-to-value ratio rather than mortgage capitalization rates to manage credit risk.

Figure 3 shows loan-to-value ratios by property type. During the late 1970s, loan-to-value ratios were virtually flat, with much more variation across property types occurring in the 1980s and 1990s. The data indicates very low loan-to-value ratios for apartments during the early 1980s and very high loan-to-value ratios for office property in the early 1990s. In their research, Weber and Devaney (5) find that changes in regulatory standards during the 1980s had a significant influence on real estate lending and credit standards. They maintain that high loan-to-value ratios for office properties during the early 1990s occurred as a consequence of duress and loan restructuring rather than because of an easing of credit terms.

Figure 4 is a graph of equity capitalization rates that were extracted from the ACLI data using the band-of-investment technique. This graph shows much more variation in the equity capitalization rates than in any of the other variables in the band-of-investment equation. In other research, Devaney (6) performs a test of market segmentation among equity capitalization rates for apartment, industrial, office, and retail properties based on a statistical procedure known as cointegration and error correction. The results indicate that unit changes in the rates for apartment, industrial, and retail properties in the current period (t) act to remove disequilibrium in the previous period (t-1). In other words, these three types of real estate were good substitutes for each other during the period examined. In contrast, the equity capitalization rates for office property did not respond, indicating that office property was largely segmented from other property types. Seck (7) also finds office property a weaker substitute for other real estate asset classes.

As mentioned earlier, Henershott and Kane attribute the behavior in the office component of NCREIF data to distortions caused by qualitative differences in character and condition of office property traded at different stages in the real estate market cycle. Office property appears to be more prone to market imbalances in supply and demand conditions and, therefore, to greater variation in overall capitalization rates. The apparent segmentation may also be influenced by the periodic need for significant capital expenditures for tenant improvements in office property. To avoid these expenditures some investors may simply choose not to participate in the market for office property.

Cointegration Regression

A preliminary test for establishing evidence of substitution in the four time series for overall capitalization rates is found by estimating a cointegrating regression, which is explained in the Appendix. This test determines whether or not the rate for one property type influences a change in the rate for any of the other property types in the subsequent period, thus suggesting that the series share a long-run equilibrium relationship and are substitutes. However, even if the series for the four real property types are cointegrated, it is not possible to determine the exact nature of the relationship between each (the lag structure) or whether the so-called cointengrating vector can be used to forecast overall capitalization rates for all four property types without implementing a more detailed error correction model such as the one used by Devaney.

This finding of cointegration in overall capitalization rates by property type and the evidence in Figures 1 through 4 support the band-of-investment technique findings that differences in overall capitalization rates ([R.sub.o]s) across property types are explained primarily by differences in equity capitalization rates ([R.sub.E]s), followed by differences in loan-to-value ratios. Although there was substantial variation in mortgage capitalization rates ([R.sub.M]s) over time, there was little difference in these rates among the property types investigated.

The Third Dimension: Asset Class

The third dimension of the substitution principle is substitution between real estate and other classes of assets, such as stocks and bonds. The studies cited below typically characterize their objective as testing real estate integration with national capital markets. Using ACLI data, Froland (8) and Evans (9) find that overall capitalization rates are related to national capital markets, while Ambrose and Nourse (10) find that the rates are segmented from capital markets. Jud and Winkler (11) conclude that there was no relationship between capitalization rates and returns for stocks and bonds. Two problems typically arise in many of these studies: one is the statistical method used to test market integration and the other is data that mixes returns with capitalization rates.

Cointegration Methodology

Cointegration tests have become the preferred statistical method for determining whether two time series share a long-run equilibrium relationship. (12) If time series are not cointegrated, the hypothesis of market integration (substitution) is typically rejected. Many of these real estate integration tests compare capitalization rates with stock and bond returns or use real estate yields rather than overall capitalization rates.

Stock and Bond Earnings and Capitalization Rates

Overall capitalization rates for real estate are a single year's net operating income ([I.sub.o]) divided by real estate value ([V.sub.o]); they are conceptually similar to the ratio of earnings before interest and taxes divided by share price (EBIT/[P.sub.o]) in the stock market. This data is not available in aggregate for major stock market indices (such as the S&P 500), so most researchers use the earnings yield (earnings divided by stock price [[E.sub.o]/[P.sub.o]]) or the dividend yield (dividends divided by stock price [[D.sub.o]/[P.sub.o]]). Of course, the difference between earnings and dividends is retention. The cash flow that accrues to the firm and is available to the owner is more akin to earnings. However, a minority stockholder does not exercise control over earnings in a publicly traded firm, and the stockholder's cash flow is represented by dividends and capital gain on sale. For this reason, traditional textbook stock valuation models tend to capitalize dividends.

Ten-Year Treasury Bond Yield and Capitalization Rates

In the bond market, overall capitalization rates are most similar to the yield to maturity. For consistency most studies use the constant maturity yield on the ten-year Treasury bond; it is free of default risk and is calculated as the interest rate that makes the present value of the ten-year bond's coupon and principal equal to the market price.

Table 2 lists quarterly statistics for overall capitalization rates during 1975-1997, both the earnings and dividend yields on the S&P 500 and the yield to maturity on the ten-year Treasury bond. The real estate overall capitalization rate is an equally weighted average of the rates for the four property types in the ACLI reports. The standard deviations for the earnings yield and the Treasury bond yield are much larger than for either the real estate overall capitalization rate or the dividend yield.

The greater volatility of earnings and bond yields is evident in Figure 5 and Figure 6. Figure 5 is a graph of the overall capitalization rate and the earnings and dividend yields for the S&P 500 from 1975-1997; Figure 6 graphs the capitalization rate and the yield to maturity on the ten-year Treasury bond in the same period. Unlike the graphs in Figures 1 through 4, Figures 5 and 6 reveal no clear relationship between the overall capitalization rate and the stock or bond market yields.

[FIGURE 5 & 6 OMITTED]

The Appendix shows augmented Dickey-Fuller (ADF) tests for stationarity of an aggregated overall capitalization rate. This rate is a weighted average of the overall capitalization rates of the four property types discussed in the previous section and the earnings yield, the dividend yield, and the yield to maturity on the ten-year Treasury bond. None of the cointegration tests supported cointegration between the real estate capitalization rate and capital market yields. This result supports the assertion that real estate and capital markets are not good substitutes for one another.

Conclusions

This paper discusses the substitution principle and how it relates to differences in overall capitalization rates ([R.sub.o]s) within a property type, among different property types, and across asset classes. Although low-quality property competes with conventional investment-grade properties, overall capitalization rates can differ by a substantial margin. Similarly, overall capitalization rates can vary among property types, but the evidence indicates they are cointegrated and share a common, long-run equilibrium relationship. Finally, despite conflicting literature, tests indicate that capital market yields are not cointegrated with an aggregated real estate overall capitalization rate. This suggests that real estate and capital market assets are not good substitutes for one another.

Appendix

Estimating a Cointegrating Regression

Unit Root Tests

The stationarity of a time series can be examined using the augmented Dickey-Fuller (ADF) test to determine the order of integration. To illustrate this test, consider an AR(1) process:

[y.sub.t] = [delta] + [alpha][y.sub.t-1] + [[epsilon].sub.t]

where [delta] and [alpha] are parameters and [[epsilon].sub.t] is assumed to be white noise. In this equation y indicates a stationary series if -1<[alpha]<1, but y indicates a nonstationary series if [alpha] = 1. The hypothesis that the series is stationary is evaluated by testing whether the absolute value is less than one. The ADF test is implemented by estimating the following equation, where y is the series to be tested.

[DELTA][y.sub.t] = [delta] + [lambda][y.sub.t-1] + [[epsilon].sub.t]

Dickey and Fuller (a) show that the estimated [lambda] for testing the unit root does not follow the t-distribution and simulate the MacKinnon critical values for selected sample sizes. More recently, MacKinnon critical values have been used in many statistical software packages and are reported in the tables in this Appendix. The following ADF tests use four lags and indicate that all eight of the series are nonstationary in level form and that nonstationarity is removed by first differencing. The series are integrated of order one I(1).

Because all series are integrated of the same order, cointegration tests are appropriate. (b) The results of the Johansen test for cointegrating equations among the overall capitalization rates for the four property types discussed in the article--apartment, industrial, office, and retail--are shown following the ADF tests. These results indicate that the rates for the four property types are cointegrated, while critical values for the Johansen test indicate no cointegration between real estate overall capitalization rates and stock market yields or the yield to maturity on the ten-year Treasury bond.
Table A-1 ADF Tests for Unit Root

 Augmented Augmented
 Dickey-Fuller Dickey-Fuller
 Test (4) Test (4)
Variable (Level From) (First Difference)

Apartment [R.sub.0] -1.27 -4.61 *
Industrial [R.sub.0] -1.57 -3.98 *
Office [R.sub.0] -1.40 -4.86 *
Retail [R.sub.0] -1.49 -5.37 *
[R.sub.0] -1.37 -3.66 *
Earnings yield -1.44 -4.67 *
Dividend yield -0.74 -5.21 *
Ten-year Treasury bond yield -1.34 -4.61 *

MacKinnon critical values for rejection of the unit root hypothesis
at 1% *, 5% **, and 10% *** are -3.507, -2.895. and -2.584.

Table A-2 Johansen Test for Cointegration
Among Apartment, Industrial, Office, and
Retail [R.sub.O]s

 Hypothesized
 Five % No. of
 Likelihood Critical Cointegrating
Eigenvalue Ratio Value Equations

0.362 64.57 47.21 None **
0.263 29.90 29.68 At most 1 *
0.071 6.33 15.41 At most 2
0.007 0.61 3.76 At most 3

* (***) denotes rejection of the hypothesis at 5%
(1%) significance level.

Likelihood ratio test indicates 2 cointegrating
equation(s) at 5% significance.

Table A-3 Johansen Test for Cointegration among
[R.sub.O], Earnings Yield, and Dividend Yield

 Five %
Eigenvalue Likelihood Critical Hypothesized
 Ratio Value No. of CEs

0.110 15.10 29.68 None
0.046 4.90 15.41 At most 1
0.008 0.72 3.76 At most 2

Table A-4 Johansen Test for Cointegration between
[R.sub.O] and Ten-Year Treasury Bond Yield

 Five % Hypothesized
 Likelihood Critical No.
Eigenvalue Ratio Value of CEs

0.046 7.59 15.41 None
0.038 3.44 3.76 At most 1

Likelihood ratio test rejects any cointegration
at 5% significance.


(a.) D. Dickey and W. Fuller, "Distribution of the Estimators for Autoregressive Time Series with the Unit Root," Journal of the American Statistical Association, 74 (1979): 427-431

(b.) See Enders, Applied Economic Time Series, for a detailed discussion of the cointegration method.
Table 1 American Council of Life Insurance Data
for Apartment, Industrial, Office, and Retail,
1975-1997-Mean and Standard Deviation (Std. Dev.)

 Apartment Industrial

Overall capitalization rate, mean 9.75 10.10
 (Std. Dev.) (1.00) (0.97)
Mortgage capitalization rate, mean 10.11 10.11
 (Std. Dev.) (1.77) (1.77)
Loan-to-value ratio 0.71 0.72
 (Std. Dev.) (0.03) (0.02)
Equity capitalization rate,* mean 7.17 7.13
 (Std. Dev.) (1.84) (1.77)

 Office Retail

Overall capitalization rate, mean 10.07 9.93
 (Std. Dev.) (0.94) (1.20)
Mortgage capitalization rate, mean 10.11 10.09
 (Std. Dev.) (1.66) (1.76)
Loan-to-value ratio 0.72 0.71
 (Std. Dev.) (0.03) (0.03)
Equity capitalization rate,* mean 7.78 7.34
 (Std. Dev.) (2.03) (1.70)

* Extracted from ACLI data

Table 2 Real Estate Overall Capitalization Rate ([R.sub.o]), Earnings
and Dividend Yields on the S&P 500, and the Yield to
Maturity on the Ten-Year Treasury Bond, 1975-1997--Mean and
Standard Deviation (Std. Dev.)

 [R.sup.o] Earnings Dividend Yield on
 for Real Yield Yield Ten-Year
 Estate for S&P 500 for S&P 500 Treasury Bond

Mean 10.08 8.16 3.79 8.85
(Std. Dev.) (1.09) (2.92) (1.04) (2.29)


(1.) For a detailed discussion of the band-of-investment technique, see Appraisal Institute, The Appraisal of Real Estate, 12th ed. (Chicago: Appraisal Institute, 2001), 534-537.

(2.) John M. Francis, "The Elusive Definitions of NOI and OAR," The Appraisal Journal (January 1998): 56-61.

(3.) Patric H. Hendershott and Edward J. Kane, "U.S. Office Market Values During the Past Decade: How Distorted Have Appraisals Been?" Real Estate Economics 23, no. 2 (1995): 101-116.

(4.) Stephen R. Bullock, "Appraising Low-Investment-Grade Apartments," The Appraisal Journal (January 1996): 34-43.

(5.) William Weber and Michael Devaney, "Bank Efficiency, Risk-Based Capital, and Real Estate Exposure: The Credit Crunch Revisited," Real Estate Economics 27, no.1 (1999): 1-25.

(6.) Michael Devaney, "The Long-run Equilibrium Relationship among Equity Capitalization Rates for Retail, Apartment, Office, and Industrial Real Estate," in Real Estate Valuation Theory, ed. Ko Wang and Marvin L. Wolverton, 373-387 (Boston: Kluwer Academic Publishers, 2002).

(7.) Diery Seck, "The Substitutability of Real Estate Assets," Real Estate Economics 24, no. 1 (1996): 75-95.

(8.) Charles Froland, "What Determines Cap Rates on Real Estate," Journal of Portfolio Management 13, no. 4 (1987): 77-83.

(9.) Richard Evans, "A Transfer Function Analysis of Real Estate Capitalization Rates," Journal of Real Estate Research 5, no. 3 (1990): 371-380.

(10.) Brent Ambrose and Hugh O. Nourse, "Factors Influencing Capitalization Rates," Journal of Real Estate Research 8, no. 2. (1993): 221-237.

(11.) G. Donald Jud and Daniel T. Winkler, "The Capitalization Rate of Commercial Properties and Market Returns," Journal of Real Estate Research 10, no. 5. (1995): 509-518.

(12.) For a detailed review of the cointegration method, see Walter Enders, Applied Econometric Time Series (New York: John Wiley & Sons, Inc., 1995), 65-69.

Michael Devaney, PhD, MAI, received his doctoral degree from the University of Arkansas and is a professor of finance at Southeast Missouri State University. Devaney is a Chartered Financial Analyst and has published in The Appraisal Journal, Real Estate Economics, Journal of Real Estate Research, and Journal of Real Estate Finance and Economics, among others. Contact: T 573-651-2319; E-mail: C587bua@semo.ed
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Date:Jan 1, 2005
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