Real options: An alternative valuation model for the U.S. REIT Market.

Dubreuille, Stephane ; Cherif, Mondher ; Bellalah, Mondher 等

ABSTRACT

REITs are alternative investments that offer asset managers high returns and diversification opportunities. In an active management process, securities selection and more specifically their valuation is a key component of future performance. In this paper, we propose a model that combines a Discounted Cash Flow model with real options in order to take into account the different drivers of real estate investment value, such as net asset value, future rentals income and capital expenditures policy. Our theoretical model for Real Estate Investment Trusts provides an average spread around 16% compared with the market value.

JEL Classifications: G11, G13, R32

Keywords: real estate investments; DCF; real options; asset valuation

I. INTRODUCTION

Institutional investors began to take interest in real estate markets at the beginning of the 1980s due to their potential for growth, their risk diversification benefits and as inflation hedging instruments. Real estate is traditionally considered as a safe haven when financial markets are unstable. Investors can access the real estate market directly by purchasing buildings, land, shopping centers, office space; or indirectly by investing in real estate investment trusts. Direct investment in real estate is characterized by a lack of liquidity, significant transaction sizes, a degree of opacity, and high levels of heterogeneity. On the contrary, real estate investment trusts provide investors with exposure to the real estate sector without liquidity constraints given that they are stocks listed on financial market. This relative lack of liquidity in real estate investments tends to smooth performance and reduce volatility levels (Fisher, Gatzlaff, Geltner, and Haurin, 2003). In a portfolio management strategy, real estate is considered as an alternative investment. Westerheide (2006) shows that REITs are a class of assets on their own that evolves differently from stocks and bonds. These features have justified real estate investment to spread the risk inherent in a portfolio made up entirely of traditional assets (stocks, bonds and cash). Simon and Ng (2009) show that real estate plays this role in spreading risk even more when the stock market is bearish. Real estate distinguishes itself by its defensive character, being less sensitive to the macro-economic environment than traditional classes of assets. According to Hoesli, Lekander, and Witkiewicz (2004), real estate leads to a reduction of 5-10% in total portfolio risk, and nearly 20% when international real estate investments are taken into account.

In a "top down" analysis, the selection of the best stocks in the real estate industry is a key performance factor. The selection of stocks to include in a portfolio is traditionally based on classic discounted or multiple valuation models. Real estate investments include options such as the utilization of property reserves, extension, renovation (brownfield sites) or the renewal of leases. These options ought to be included in valuation models. In practice, managers react to events and modify their strategy with the use of additional information. Such flexibility is lacking in standard discounted models, which make their valuation based on a single scenario for future cash flow. Flexibility based on monitoring investments with regard to incoming information is rather like an option. According to Copeland, Koller, and Murrin (2000), the development of option theory is a real innovation in the field of corporate valuation. Options take into account the ambiguous, dynamic features of financial projects. Our article proposes a valuation model of REITs that adds real options to traditional discounted cash flow. Using securities that are on both the FTSE/EPRA NAREIT North America index and the S&P 500 Index, we analyze price differences between our theoretical model with options and the market. Our paper is organized as follows. The first section reviews traditional theoretical models for valuing real estate assets. The second section describes our sample and discusses the results of DCF models based on realistic assumptions. The third section introduces real options and analyzes the main results. Finally, we conclude by presenting the theoretical and practical contribution of our research.

II. THEORETICAL MODELS FOR VALUING REAL ESTATE ASSETS

Three main methods are used to value real estate investments. The first is based on the adjusted net asset value, the second on a comparison with similar assets and the third is based on discounted future operating cash flows. The net asset value (NAV) is an adjustment of the value of real estate assets based on the fair value of assets in the balance sheet. The value of the shareholders' equity is calculated by subtracting revalued liabilities from the fair value of assets. Capozza and Lee (1995) define the value of the net assets of REITs using the following formula:

NAV = Market Value of properties + Other assets - Total Liabilitie s/Number of shares(1)

For REITs, the major challenge is to account for investment property. The EPRA (European Public Real Estate Association) has drawn up recommendations for best practice in the accounting and financial reporting of listed firms in the real estate sector. Its aim is to ensure comparability and transparency throughout the European real estate sector. EPRA uses the IAS 40 standard, which allows the valuation of investment property using historical cost or fair value. Historical cost records the property asset at its initial cost of acquisition. When using this method, EPRA recommends that the amortization method and lifetime used should be indicated. In fair value accounting, the variation in value of property investment is recorded in the income statement when the fluctuations occur.

The choice of fair value is not without consequences for the financial statements and for their transparency. On a sample of 45 real estate firms in 16 countries, Edelstein et al. (2012) show that adopting fair value resulted in an average increase of net income of more than 50% during the year 2005. These results confirm the conclusions of Fortin et al. (2011), who show that the IFRS standards tend to magnify the consequence of economic cycles in the financial statements of real estate companies. In the multiples approach, the investor will compare the price of buildings that have recently been sold with similar features to the real estate to be valued. The existence of differences between the property sold and the building that is to be valued is taken into account during the valuation process: the investor adjusts the price on the basis of the disparities observed. The hedonist method uses the fact that a property transaction is motivated by the nature of the property and its intrinsic characteristics. Investing in property gives a certain degree of satisfaction, and this depends on the different features of the asset. By regression of the data linking the market price to these features, it is possible to quantify the value of each of these determinants. Regression analyses are performed on the price, represented as y, and different independent variables ([x.sub.i]). Date of construction, location, size, rate of occupancy and economic environment are examples of independent variables (Equation 2):

y = [n.summation over (i=1)][[beta].sub.i][x.sub.i]+[[epsilon].i] (2)

Hedonist regressions use a linear model. A variation in the price of the asset is a consequence of an increase of one unit of value, represented by [[beta].sub.i], of one or more variables. This method has been widely discussed in the academic literature (see Sirmans et al., 2005, for a review). Finally, the third method of valuing direct and indirect real estate is based on an estimation of future rents related to the real estate investment. The model discounts projected cash flows according to the risk of the asset. The first discounted model for a property asset takes up Irving Fisher's (1930) model, which assumes a constant and perpetual Net Operating Income (NOI):

[V.sub.0] = NO[I.sub.1]/[R.sub.0] (3)

The operating income is discounted at a rate, [R.sub.0], known as the capitalization rate. This rate corresponds to the cost of equity capital when the real estate investment is internally funded or to the average cost of funding sources (WACC) when the firm uses financial leverage for its investment decisions. The net operating income (NOI) measures all the rents received less taxes, insurance, maintenance and repair costs and losses due to vacancy. The NOI corresponds to the EBITDA in the income statement of REITs.

Because of the simplified hypotheses it introduces, the previous model has been neglected in favor of the DCF (Discounted Cash Flow) approach. This consists in discounting at the weighted average cost of capital the net operating income over an explicit period of time rather than to infinity, and a terminal cash flow.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The operating income is estimated using different hypotheses of growth, rate of occupancy, economic and fiscal environments. The terminal value ([TV.sub.n]) is the selling price of the property at the end of the planning period. It is a function of the hypotheses on the level of inflation and the valuation model selected (NAV, multiple or perpetual rental). The discounting rate (k) is based on the return on equity capital, the yield curve and the credit spread. The international valuation standards committee, or IVSC 2005, recommends in its note no. 9 the use of DCF to determine the fair value of real estate investments. We first choose this model to value REITs and give details of our assumptions in the next section.

III. US EMPIRICAL EVIDENCE BASED ON DCF VALUATION

In this section, we carry out an intrinsic valuation of property companies based on the book value and discounted approaches presented in the previous section. We then extend these traditional models, by considering real options.

A. Presentation of the Sample

The sample is made up of fourteen firms listed on both the FTSE/EPRA NAREIT North America Index and the S&P 500 Index. The real estate market is analyzed by investors in terms of sub-sectors. The most important are retail, offices, residential and industrial property. The components of our sample are presented in Table 1.

The choice of stocks operating in the real estate industry was based on the FTSE/EPRA NAREIT North America index, which serves as a benchmark for numerous investment strategies targeting the real estate sector. The firms selected operate mainly in the United States of America and cover all the different real estate sub-sectors to guarantee a diversified portfolio. The major player in our sample is Simon Property Group with real estate assets estimated at more than $25 billion.

B. Net Asset Valuation

The property companies are valued based on their real estate assets. We analyzed the "Price-to-book" multiples of each of the fourteen firms in our sample between 12/31/2000 and 12/31/2013, and compared them with the S&P 500 Index. For the book value, we selected the adjusted net assets, published annually in the financial statements. This year-end asset valuation has been compared with the market value displayed on Bloomberg for the same period.

The real estate industry valuation, based on the P/B multiple, appears slightly higher than other sectors, with an average ratio of 2.9 vs 2.5 for the S&P 500 Index. This valuation is related to organic growth rates, nearly 5% on average in our sample, attractive yields around 3% higher than US government bond yields, and relatively low interest rates to leverage real estate investments. According to our sample, financing costs have fallen by more than 20% over the last four years in the real estate sector, due to improved ratings. These perspectives have turned into a rise of 36% for the EPRA index between 2000 and 2013. In the following sub-section we propose to value property companies using a DCF model that takes account of future operating cash flows and financing costs.

C. Discounted Cash Flows (DCF)

Companies in the real estate industry have several features that have to be taken into account when determining their intrinsic value via a discounting model. The real estate sector is closely correlated to the economic environment and to interest rate levels. Subsectors such as retail property and offices are very cyclical and depend on the consumer confidence levels and household spending. This dependence on the economic environment is even more marked when the assets held by property companies are not located in so-called "prime" areas, which are always attractive. The quality of the valuation depends on the relevance and realism of the hypotheses made for future forecasts. We list below the principal assumptions used in the DCF model:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

* To forecast operating cash flows ([NOI.sub.t]), we use the average of operating margins (EBITDA/Sales) over a thirteen-year period (01/01/2000 to 31/12/2013). The operating income is considered before adjustment for changes in the value of property investment (IAS 40 standard) to limit their volatility. The revenue is made up of gross rental income. Rents are very volatile, being linked to both economic cycles and prime investment projects. We have used an average growth in sales corrected from seasonal changes over the last 13 years;

* CAPEX is a significant component of the activity of REITs, which constantly modify their assets by developing new projects and selling off mature assets. In some years, CAPEX exceeds sales, making the notion of Free Cash-Flow inconsistent. The property companies are valued on the operating cash flow considering only investments in net working capital requirements.

* The real estate industry uses significantly the leverage to finance assets. Today these financing operations are stimulated by low interest rates, strategic refocusing on "prime" property and improved ratings. In our sample, average net financial debt stands at more than [euro]5.5 billion. Five companies over fourteen have more than [euro]10 billion of debt in their balance sheet. Simon Property Group shows financial debts close to [euro]22 billion on our date of valuation (12/31/2013). The net debt ([D.sub.0]) amount will reduce significantly the intrinsic value of the stocks.

* We used the weighted average cost of capital (WACC) as the discount rate (k) for operating cash flow. The WACC was obtained from Bloomberg on 12/31/2013 and adjusted for the cost of debt depending on the credit risk of the firms in our sample.

* At the end of the Thirteen-year forecasting period, we compute the terminal value ([TV.sub.n]) based on the Gordon Growth Model. We assume a growth to perpetuity of 2.35 %. This rate was chosen to reflect the economic growth in the United States where the REITs in our sample mainly operate. The figure is the average of the last 2 years (2013 and 2012). The assumptions used for our valuation model are summarized in Table 2. Using these assumptions, we present in Table 3 the intrinsic value of the companies in our sample and the differences with the market value at the valuation date (12/31/2013).

The stock market overvalues the property firms. The market value is higher than the theoretical DCF valuations for all companies of the sample. The average premium is 24.8% with a standard deviation of 47%. The largest market premium is for General Growth Properties with a premium paid by the market equals to 182.28%. This company presents a tremendous amount of debt. Investors agree to overpay in the real estate sector for reasons that are both tangible and intangible. We have highlighted the impressive performance of the real estate sector during the period of our study, which can be explained by attractive rental yields and favorable financing conditions. Every investor agrees on the importance of psychology in investment decisions. Research into behavioral finance shows the sometimes irrational and illogical behavior of investors in terms of choices and decision-making. The influence of emotional factors, but also a certain number of cognitive biases in information processing lead to errors of evaluation and judgment. Tetlock (2007) has shown that investors' "feeling" affects their asset valuation. This emotional interference might explain to some extent the differences between theoretical and market values highlighted by our study. Kyle (1985) described these investors guided by their feeling as "noise traders".

The next section examines the persistent overvaluation by the markets of property firms. We propose to improve discounted cash flow model by adding real options.

IV. VALUATION OF REITS BY REAL OPTIONS

Real options deal with tangible assets and make it possible to adjust the course of an investment project during its lifecycle. Real options capture the value of uncertain growth opportunities.

A. Theoretical frame of real options

Real options have been widely used to analyze decisions to develop/abandon physical property (Chan et al., 2012) and financing opportunities (Changwen et al., 2007). The conditions for the existence of real options in an investment project are irreversibility, uncertainty and flexibility explained below:

* With irreversibility, it is impossible to turn back without losing a significant amount of the funds already expensed. If the decision can be altered without cost, the real option has no value.

* Uncertainty will encourage managers to wait and keep the investment opportunity in order to benefit from the release of new information (Yavas and Sirmans, 2005).

* Flexibility represents the possibility of making or not making an investment, in other words of exercising or abandoning the option depending on market conditions. It takes its value from the uncertainty and flexibility of the environment surrounding the holder of the property investment project (Sebehela and Tumellano, 2008). Different categories of real options exist in real estate investment projects by property firms, such as options to postpone, develop, abandon or sell assets (see Grovenstein et al., (2011) and Paxson (2007) for a review) When valuing real estate firms, these options should naturally be considered as future sources of value creation. Real options premiums are valued using Black and Scholes' model (1973). Assuming fixed interest rate, constant volatility and no transaction costs, the premium of a European-type call option is calculated using the following formula:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (6)

with

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

where S is the rate of the underlying stock; K, the exercise price; Rf, the risk-free rate; t, the life of option; a, the underlying volatility and N(d), the cumulative normal function. The assumptions used to value property firms with real options are presented in the next section.

B. Hypotheses in the Real Options Model

We follow the procedure proposed by Rappaport and Mauboussin (2003), which consists in quantifying the value of a firm's implicit real options on the basis of the investments carried out or planned for in the business model. The performance of the property companies is directly related to their investment strategy and their assets turnover. Such firms sell off mature assets to refocus their portfolio on more profitable sectors, develop new projects or improve their financing conditions. In our procedure, and in line with the recent work by Tsekrekos (2013), we value property firms by combining discounted cash flow model and real options. The firm's value is the sum of its economic value (discounted cash flow model) and the value of its investment opportunities (real option model). According to the Black and Scholes method (1973), the premium of an option depends on five parameters: the value of the underlying stock, the exercise price, the volatility, the maturity date and the interest rate. We have formulated the following hypotheses to determine the parameters of the model:

* The intrinsic value of the underlying stock, expressed as S, is equal to the CAPEX. Investment opportunities create value. The CAPEX is the expense carried out over the year 2013;

* In line with the hypotheses of Rappaport and Mauboussin (2003), we suppose that S/K = 100 %. It means the Net Present Value (NPV) of the project at the time of decision is zero;

* Maturity is the time that a company can defer an investment decision without losing an opportunity. The length of time is five years;

* For the risk-free rate, we have retained the yield-to-maturity on US medium term government bonds;

* Volatility measures the potential variability of a project's cash flow and future value. We have retained the historic annualized volatility of real estate firm performance for the period of our study (2000 to 2013).

The value of the parameters in our real options is indicated in Table 4.

C. Results

The results obtained by a real options model are presented in Table 5. The use of real options allowed us to refine the intrinsic value and move closer to the market value. Indeed, by including the investment options of these property firms, we have reduced the average gap between the theoretical value and the market value from 24.8% to 16.2% with a standard deviation of 27.5%. The range of value is more homogeneous with our combining valuation. Compared to the previous DCF intrinsic values, the market does not automatically overvalue the REITs. We value 4 companies with theoretical prices higher than market prices (Apartment Investment and Management, Boston Properties Inc., Health Care REIT Inc., Kimco Realty Corp.). Considering investment opportunities in the valuation process make market value and intrinsic value to converge. Our combined approach resulted in differences of less than two dollars for seven of the fourteen companies in our sample. The use of real options can in no way be reduced to a process of simple technical calculation. These options reflect the strategic and financial constraints that real estate firms face. They try to invest in "premium" assets to generate stable income and manage debt that can cast doubt on the profitability of their future projects. We recommend an approach combining a discounted model and real options to value alternative investments such as real estate companies. Indeed, the value of listed real estate firms depends simultaneously on the quality of their assets, the rental income generated by the business, their future development projects and their asset turnover policy.

V. CONCLUSION

In this research, we have stressed the importance for fund managers to consider investing in the real estate sector to improve their performance. During the period we have studied, the real estate sector performed on average 7.65% per year. However, we have underlined the problem of valuing property companies, given their specific features. Property investments depend to a great extent on the economic environment for their rental income, the value of the assets and the development of new projects. The main contribution of this research is that it proposes a theoretical frame for valuation that combines discounted cash flow models and real options. In the "stock picking" process, managers should favor the discounted approach to the NAV approach with an exit hypothesis estimated based on perpetual growth rate rather than a multiple. To this should be added options that are justified by the company's asset turnover policy. Considering options results in an average difference of 16.2% between the intrinsic value and market values. The conclusions of our research are based on a relatively small sample, which could be extended to other countries and other market environments.

REFERENCES

Black, F., and M, Scholes, 1973, "The Pricing of Options and Corporate Liabilities." Journal of Political Economy, 81, 637-654.

Capozza, D., and S., Lee, 1995, "Property Type, Size, and REIT Value." Journal of Real Estate Research, 10, 363-379.

Chan, S., K., Wang, and J., Yang, 2012, "Presale Contract and its Embedded Default and Abandonment Options." Journal of Real Estate Finance & Economics, 44,116-152.

Changwen, K., W., Zongjun, and C, Guo, 2007, "The Financing and Abandonment Options in Chinese Real Estate Development Projects." Journal of Corporate Real Estate, 9, 111-124.

Copeland, T., T., Koller, and J., Murrin, 2000, Valuation: Measuring and Managing the Value of Companies, John Wiley and sons, Inc., New York.

Edelstein, R., S., Fortin, and D., Tsang, 2012, "An International Exploration of Financial Reporting Practices in the Real Estate Industry." International Real Estate Review, 15,347-372.

Fisher, J., D., Gatzlaff, D., Geltner, and D., Haurin, 2003, "Controlling for the Impact of Variable Liquidity on Commercial Real Estate Price Indices." Real Estate Economics, 31, 269-303.

Fortin, S., W.B., Thomas, D., Tsang, 2011, "Value Relevance of Fair Value Gains and Losses of Investment Properties: Evidence From the IFRS Countries." Working Paper, McGill University and University of Oklahoma.

Fisher, I., 1930, The Theory of Interest, The MacMillan Company, New York.

Georgiev, G., B., Bhaswar Gupta, and T., Kunkel, 2003, "Benefits of Real Estate Investment - Some Diversification Benefit in Particular Allocations." Journal of Portfolio Management, 29, 28-33.

Grovenstein, R., J., Kau, and H., Munneke, 2011, "Development Value: A Real Options Approach Using Empirical Data." Journal of Real Estate Finance and Economics, 43,321-335.

Hoesli, M., J., Lekander, and W., Witkiewicz, 2004, "International Evidence on Real Estate as a Portfolio Diversifier." Journal of Real Estate Research, 26, 161-206.

Kyle, A.S., 1985, "Continuous Auctions and Inside Trading." Econometrica, 53, 1315-1335.

Paxson, D.A., 2007, "Sequential American Exchange Property Options." Journal of Real Estate Finance & Economics, 34, 135-157.

Ratcliff, U., 1972, Valuation for Real Estate Decisions. Santa Cruz, CA: Democrat Press.

Simon, S., and W.L., Ng, 2009, "The Effect of the Real Estate Downturn on the Link between REITs and the Stock Market." Journal of Real Estate Portfolio Management, 15, 211-219.

Sirmans, G.S., D.A., Macpherson, and Zietz E.N, 2005, "The Composition of Hedonic Pricing Models." Journal of Real Estate Literature, 13, 1-44.

Tetlock, P., 2007, "Giving Content to Investor Sentiment: The Role of Media in the Stock Market." Journal of Finance, 62, 1139-1168.

Tsekrekos, E., and G.F., Kanoutos 2013, "Real Options Premia Implied from Recent Transactions in the Greek Real Estate Market." Journal of Real Estate Finance and Economics, 47, 152-168.

Westerheide, P., 2006, "Cointegration of Real Estate Stocks and REITs with Common Stocks. Bonds and Consumer Price Inflation - An International Comparison." Discussion paper Nr. 06-057, Centre for European Economic Research.

Yavas, A., and S.F., Sirmans, 2005, "Real Options: Experimental Evidence." The Journal of Real Estate Finance and Economics, 31, 27-52.

Stephane Dubreuille (3), Mondher Cherif (b), Mondher Bellalah (c)

(a) Corresponding author, NEOMA Business School 59 rue Pierre Taittinger, 51100 Reims, France

Stephane, [email protected]

(b) University of Reims

mondherc@gmail. com

(c) University of Cergy-Pontoise and ISCParis

mondher.bellalah@gmail. com

Table 1
Characteristics of the property firms in the sample as at 31/12/2013

Companies                  Sectors


1. Apartment Investment    Multifamily Apartment
& Management               Properties
2. Avalonbay               Multifamily
Communities Inc            Communities
3. Boston Properties Inc   Office Properties


4. Equity Residential      Apartment Complexes
5. Essex Property Trust    Multifamily Residential
Inc                        Properties, Commercial
                           Properties
6. General Growth          Shopping Mall Centers
Properties
7. HCP Inc                 Senior Housing, Life
                           Services, Medical Offices,
                           Hospital, Skilled Nursing Homes
8. Health Care REIT Inc    Senior Housing &
                           Health Care Real Estate
9. Host Hotels & Resorts   Upscale and Luxury
Inc                        Hotel Lodging
                           Properties

10. Kimco Realty Corp      Shopping Center

11. Macerich Co            Shopping Center
12. Public Storage         Self-storage Facilities
13. Simon Property         Regional Mall, Outlet
Group                      Centers,
                           International Properties,
                           Lifestyle Centers
14. Vornado Realy Trust    Office and Retail
                           Properties


Companies                 Geographical presence             NAV
                                                        (in million USD)

1. Apartment Investment   USA, Puerto Rico                  5391
& Management
2. Avalonbay              USA                              14284
Communities Inc
3. Boston Properties Inc  Boston, Washington DC,           15817
                          Midtown Manhattan, San
                          Francisco
4. Equity Residential     USA                              21993
5. Essex Property Trust   California & Washington           4239
Inc                       DC

6. General Growth         USA                              21113
Properties
7. HCP Inc                USA                              10627


8. Health Care REIT Inc   USA                              20277

9. Host Hotels & Resorts  USA, Canada, Mexico,             11168
Inc                       Chile, Italy,
                          Spain, Poland, Belgium,
                          UK, Netherlands
10. Kimco Realty Corp     USA, Canada, Puerto Rico          7519
                          Mexico, Chile, Brazil, Pen
11. Macerich Co           USA                               7622
12. Public Storage        USA                               8240
13. Simon Property        USA & International              25059
Group


14. Vornado Realy Trust   New York City,                   14944
                          Washington DC,
                          California, Puerto Rico

Table 2
Assumptions of the DCF model

                          Sales   Operating  Terminal
Companies                 Growth   Margin     Value    Net Debt   WACC
                          Rate

1. Apartment Investment
& Management                5%     55.73%     10270     4332.43   6.77%
2. Avalonbay
Communities Inc            10%     63.40%     26381     5863.85   7.00%
3. Boston Properties Inc    9%     58.62%     31314     8976.37   6.51%
4. Equity Residential       3%     63.93%     29464    10712.72   6.18%
5. Essex Property
Trust Inc                  11%     64.27%     14262     3023.08   6.72%
6. General Growth
Properties                  3%     67.58%     27917    15301.37   6.50%
7. HCP Inc                 15%     82.46%     41160     8361.07   8.63%
8. Health Care REIT Inc    10%     49.94%     32452    10493.23   6.90%
9. Host Hotels &
Resorts Inc                13%     23.59%     20704     3898.00  10.12%
10. Kimco Realty Corp       8%     60.98%     15359     4072.63   7.67%
11. Macerich Co            14%     58.69%     14471     4513.02   8.06%
12. Public Storage          9%     68.11%     33364      819.88   8.60%
13. Simon Property Group   11%     72.50%     83032    21871.68   7.30%
14. Vornado Realy Trust    15%     52.18%     32242     9395.43   7.78%

Table 3
Spreads between theoretical and market valuations

Companies                     Market  Intrinsic  Spread   Market
                              Value     Value             Premium

1. Apartment Investment
& Management                   25.91   25.08      -0.83    3.31%
2. Avalonbay Communities Inc  118.23  111.05      -7.18    6.47%
3. Boston Properties Inc      100.37   98.67      -1.70    1.72%
4. Equity Residential          51.87   34.07     -17.8    52.25%
5. Essex Property Trust Inc   143.51  123.86     -19.65   15.86%
6. General Growth Properties   20.07    7.11     -12.96  182.28%
7. HCP Inc                     36.32   32.43      -3.89   12.00%
8. Health Care REIT Inc        53.57   50.98      -2.59    5.08%
9. Host Hotels & Resorts Inc   19.44   16.04      -3.40   21.20%
10. Kimco Realty Corp          19.75   19.24      -0.51    2.65%
11. Macerich Co                58.89   45.81     -13.08   28.55%
12. Public Storage            150.52  146.11      -4.41    3.02%
13. Simon Property Group      143.06  137.22      -5.84    4.26%
14. Vornado Realy Trust        88.79   81.76      -7.03    8.60%

Table 4
Parameters of real options

Companies                           Volatility  CAPEX    S/K   US YTM

1. Apartment Investment Management  32.05%      350.34   100%   1.5%
2. Avalonbay Communities Inc        29.32%      2151.80  100%   1.5%
3. Boston Properties Inc            25.25%      1098.98  100%   1.5%
4. Equity Residential               21.97%      625.70   100%   1.5%
5. Essex Property Trust Inc         24.36%      470.74   100%   1.5%
6. General Growth Properties        27.73%      982.47   100%   1.5%
7. HCP Inc                          18.61%      259.55   100%   1.5%
8. Health Care REIT inc             16.92%      3981.35  100%   1.5%
9. Host Hotels & Resorts Inc        36.23%      488.00   100%   1.5%
10. Kimco Realty Corp               27.75%      485.72   100%   1.5%
11. Macerich Co                     40.86%      726.60   100%   1.5%
12. Public Storage                  18.96%      1323.59  100%   1.5%
13. Simon Property Group            24.30%      1707.75  100%   1.5%
14. Vornado Realy Trust             24.25%      923.18   100%   1.5%

Table 5
Results of the theoretical valuation using real options (RO)

Companies                     Market  Real Options   DCF     Spread
                              Value   Premium        + RO    (USD)

1. Apartment Investment
Management                     25.91   1.13          26.21   -0.30
2. Avalonbay Communities Inc  118.23   6.47         117.52    0.71
3. Boston Properties Inc      100.37   2.92         101.59   -1.22
4. Equity Residential          51.87   1.48          35.55   16.32
5. Essex Property Trust Inc   143.51   1.21         125.07   18.44
6. General Growth Properties   20.07   2.82           9.93   10.14
7. HCP Inc                     36.32   0.54          32.97    3.35
8. Health Care REIT inc        53.57   7.70          58.68   -5.11
9. Host Hotels & Resorts Inc   19.44   1.75          17.79    1.65
10. Kimco Realty Corp          19.75   1.39          20.63   -0.88
11. Macerich Co                58.89   2.88          48.69   10.20
12. Public Storage            150.52   2.79         148.9     1.62
13. Simon Property Group      143.06   4.39         141.61    1.45
14. Vornado Realy Trust        88.79   2.37          84.13    4.66