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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

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Combining monte carlo simulations and options to manage risk of real estate portfolios

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


Research overview
Research overview of Real Estate Portfolios

  • 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


Literature
Literature of Real Estate Portfolios

  • 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


Continental europe lease contract the structure
Continental Europe lease contract: the structure of Real Estate Portfolios

  • 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


Continental europe lease contract the rent
Continental Europe lease contract: the rent of Real Estate Portfolios

In Europe,

Rents usually indexed

  • Inflation

  • Country specific index

  • Fixed indexation


European lease contract risk
European Lease contract: Risk of Real Estate Portfolios

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




Break option analogy with option s theory i
Break-Option: Analogy with option’s theory (I) account

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


Break option analogy with option s theory ii
Break-Option: Analogy with option’s theory (II) account

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 mrv t

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

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



In our implementation
In our implementation account

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.


The model
The Model account


The model1
The Model account


Net operating income with our model for one scenario

Net operating income when three leases are signed and account

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

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7

8

9

10

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Net operating income with our model for one scenario






Questions
Questions? account

?


European lease contract risk1
European Lease contract: Risk account

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


Monte carlo methods
Monte-Carlo Methods account

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)


Monte carlo methods1
Monte-Carlo methods account

  • 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


Simulation of the price market rental values ii
Simulation of the Price & Market Rental Values (II) account

Together correlated with a fixed correlation parameter


Mrv r t
MRV > R accountt



European lease option
European Lease = Option account

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


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