1. European Real Estate Society - Milan - 2010 Combining Monte-Carlo Simulations and Options to manage Risk of Real Estate Portfolios Amédée-Manesme Charles-Olivier, BNP Paribas Real Estate Investment Services Baroni Michel, Essec Business School Barthélémy Fabrice, THEMA, University of Cergy-Pontoise Dupuy Etienne, BNP Paribas Real Estate Investment Services

2. European Real Estate Society - Milan - 2010 Research overview Objective: Taking real estate risk into account, in particular the risk inherent in the (European) lease structures Methodology: Combination of Monte-Carlo simulations and option theory Conclusion: The approach allows a better Portfolio valuation and numerous and nurturing risk measurements

3. European Real Estate Society - Milan - 2010 Literature Pyhhr, S.A., 1973 French, N. and Gabrielli, L., 2005 Hoesli, M., Jani, E. and Bender, A., 2006 Kelliher, C.F. and Mahoney, L.S., 2000 Baroni, M., Barthélémy, F. and Mokrane, M., 2001; 2007a; 2007b Dupuy, E., 2003; 2004 Barthélémy, F. and Prigent, J-L., 2009

4. European Real Estate Society - Milan - 2010 Continental Europe lease contract: the structure Lease structures vary across countries Long lease (5 to 10 years) Usually tenants have options to leave during the course of the lease: Break- Option “BO” At the time of a Break-Option the tenant has two possibilities: Staying Leaving At the time of a Break-Option the Landlord has no decision to take but can enter a negotiation

5. European Real Estate Society - Milan - 2010 Continental Europe lease contract: the rent In Europe, Rents usually indexed Inflation Country specific index Fixed indexation

6. European Real Estate Society - Milan - 2010 European Lease contract: Risk Traditionally, tenants cannot negotiate the rent during the course of the contract whatever is the level of the Market rental value.

7. European Real Estate Society - Milan - 2010 Taking lease structure risk and global systematic risk into account = Monte-Carlo + Options

8. European Real Estate Society - Milan - 2010 Simulation of the Price & Market Rental Values (I)

9. European Real Estate Society - Milan - 2010 Break-Option: Analogy with option’s theory (I) The owner of a call option has the right but not the obligation to buy an underlying asset at a predefined price K The tenant of a European lease contract is the owner of an option: at the time of a break option, a tenant has the right but not the obligation to terminate the lease vs

10. European Real Estate Society - Milan - 2010 Break-Option: Analogy with option’s theory (II) A rational player will exercise its option at maturity as soon as it is “in the money” S t > K The value of a European call at maturity is A rational tenant will exercise its option to leave as soon as it is “in the money” R t > MRV t By analogy, the value of a BO can be written: =>

11. European Real Estate Society - Milan - 2010 MRV + Tc > MRV t (MRV + Tc) > Rt: No exercise of break-options 0,000 2,000 4,000 6,000 8,000 10,000 12,000 12345678910111213141516 Time Rent

12. European Real Estate Society - Milan - 2010 Option should be exercised

13. European Real Estate Society - Milan - 2010 In our implementation The tenant vacates and the landlord has to find another tenant for a new rent. Given the necessary time to find a new tenant, the possible advantageous financial conditions granted by the landlord and the state of the market a void period corresponding to one year is applied in the cash-flow. The tenant stays in the premises (same rent). The tenant’s rent stands between the Market Rental Value and the Market Rental Value plus the transaction costs: in this case we consider both the tenant and the landlord adopt a rational behaviour and start negotiating. For simplification we consider they will concord to the market rental value.

14. European Real Estate Society - Milan - 2010 The Model

15. European Real Estate Society - Milan - 2010 The Model

16. European Real Estate Society - Milan - 2010 Net operating income with our model for one scenario Net operating income when three leases are signed and two break-options are exercised 0,00 2,00 4,00 6,00 8,00 10,00 12,00 14,00 12345678910111213141516

17. European Real Estate Society - Milan - 2010 Hypothesis of the implementation

18. European Real Estate Society - Milan - 2010 Sensitivities: Level of inflows

19. European Real Estate Society - Milan - 2010 Sensitivities: Level of inflows

20. European Real Estate Society - Milan - 2010 Sensitivities: Valuation of the Portfolio

21. European Real Estate Society - Milan - 2010 Questions? ?

22. European Real Estate Society - Milan - 2010 European Lease contract: Risk For the owners, risk concentrated in the lease structure The inflows received are based on the rents indexed and not on the market rental values, the rents can be overvalued or undervalued A fixed 10 year lease is “safer” than a 10 years lease with an option to break at the fifth year. Likely to cause vacancy  Risk

23. European Real Estate Society - Milan - 2010 Monte-Carlo Methods averaging results from a large number of samples to provide meaningful results Sampling a universe of possible outcomes. Require computational implementation Monte Carlo methods are based on the analogy between probability and volume. Useful when significant uncertainty in inputs Useful for risk analysis (reliable and rational)

24. European Real Estate Society - Milan - 2010 Monte-Carlo methods Estimate the inputs Generate random numbers Perform a deterministic computation Aggregate the results of the scenario into a final result Repeat the last two steps several times Aggregate the results

25. European Real Estate Society - Milan - 2010 Simulation of the Price & Market Rental Values (II) Together correlated with a fixed correlation parameter

26. European Real Estate Society - Milan - 2010 MRV > R t

27. European Real Estate Society - Milan - 2010 BO should be exercised

28. European Real Estate Society - Milan - 2010 European Lease = Option We do not need to value the premium of the option We only need to estimate if the option will be exercised or not Therefore at the time of a break-option each simulated Market Rental Value will be compared to the rents and the best tenant’s rational decision will be taken