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

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

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

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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

- 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

- 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

- 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

In Europe,

Rents usually indexed

- Inflation
- Country specific index
- Fixed indexation

Traditionally, tenants cannot negotiate the rent during the course of the contract whatever is the level of the Market rental value.

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

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:

=>

(MRV + Tc) > Rt: No exercise of break-options

12,000

10,000

8,000

Rent

6,000

4,000

2,000

0,000

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Time

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.

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

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?

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

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)

- 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

Together correlated with a fixed correlation parameter

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