1. Yale School of Management Introduction to Real Estate History and Concepts

2. Yale School of Management The Dynamics of Real Estate Markets Real Estate Finance Spring 2005

3. Yale School of Management From Pro Forma to Stochastic Processes Pro Forma risk analysis Cash flows depend upon: –Scenarios –Probability assessments Discount rates depend upon –Systematic vs. unsystematic risk drivers Is there any way to incorporate all of this?

4. Yale School of Management Simulation Tools Value drivers: –Rents –Vacancies –Expenses Drivers of value drivers: –

5. Yale School of Management Simulation Methods Requires structure/model –Rent processes –Vacancy processes –Interest rates –Covariance estimates Model: Sivitanides, Torto, Wheaton (2003) –MSA/aggregate structural relationships

6. Yale School of Management Forward Looking? Rational Model: Efficient markets –Agents anticipate future conditions and trends Myopic model –Agents react to immediate conditions –Rational explanation? –Muth model

7. Yale School of Management Are Cycles Rational?

8. Yale School of Management Cobweb Model 1

9. Yale School of Management Cobweb Model 2

10. Yale School of Management STW Analysis Interest rates matter Spreads and Cap Rates not forward-looking No trend towards efficiency

11. Yale School of Management Rents and Vacancies

12. Yale School of Management Patterns: Autocorrelation Inter-dependence Mean reversion

13. Yale School of Management Cap Rates and Interest Rates C = NOI/P e.g. Before Tax Yield Why Negative? Why Positive?

14. Yale School of Management Hypotheses Inflation hedge. Lower future growth. GDP changes. Recent trends: dropping since 2000 –9.5 to 8.5 RCA –8.5 – 7.5 NREI –NCREIF no change What about diversification? Trends in the equity market? Sentiment?

15. Yale School of Management Survey of Institutional Investors

16. Yale School of Management STW Analysis Cap Rates moved by interest rates Historical analysis remains reliable Other factors that could explain structure? –Strategy? –Other investments?

17. Yale School of Management Back to Simulation CF depends on: –Rents, vacancies Prices depend upon –interest rates –Growth expectations – inflation

18. Yale School of Management Simple Simulation: Rents follow a random walk R(t) = R(t-1) + e(t) E(t) is a random error Spreadsheet simulation straightforward Take last qtr rent, add a normal error term to it, then move forward one cell for ten cells. Do this 100 different times and look at range of outcomes.

19. Yale School of Management Problems Random walk assumption Normal errors and positive rents Don’t know std of error Don’t know if random walk makes sense What to do?

20. Yale School of Management More Complex Recipe If rents autocorrelated –Estimate an autoregression: –R(t) = a + bR(t-1) + e(t) SAVE ERRORS –Take R(0) as today’s rents –R(1) = a+bR(0) + e* where * means random draw from saved errors. –Move to the next cell

21. Yale School of Management Ultimate Recipe Include other variables in estimation stage Vector auto-regression –Allows rents to depend on past vacancies –Allows vacancies to depend on past rents –Allows them to depend on past interest rates Also allows simulation of extreme cases

22. Yale School of Management VAR Forecasts