Combining Monte-Carlo Simulations and Options to manage Risk of Real Estate Portfolios

1. 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. 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. 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. 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. Continental Europe lease contract: the rent In Europe, Rents usually indexed • Inflation • Country specific index • Fixed indexation

6. 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. Taking lease structure risk and global systematic risk into account=Monte-Carlo + Options

8. Simulation of the Price & Market Rental Values (I)

9. 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. 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” St > 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” Rt > MRVt By analogy, the value of a BO can be written: =>

11. (MRV + Tc) > Rt: No exercise of break-options 12,000 10,000 8,000 Rent 6,000 4,000 2,000 0,000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Time MRV + Tc > MRVt

12. Option should be exercised

13. 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. The Model

15. The Model

16. Net operating income when three leases are signed and two break-options are exercised 14,00 12,00 10,00 8,00 6,00 4,00 2,00 0,00 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Net operating income with our model for one scenario

17. Hypothesis of the implementation

18. Sensitivities: Level of inflows

19. Sensitivities: Level of inflows

20. Sensitivities: Valuation of the Portfolio

21. Questions? ?

22. 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. 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. 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. Simulation of the Price & Market Rental Values (II) Together correlated with a fixed correlation parameter

26. MRV > Rt

27. BO should be exercised

28. 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