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

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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

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

  • 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

  • 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

  • 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

In Europe,

Rents usually indexed

  • Inflation

  • Country specific index

  • Fixed indexation


European lease contract risk

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.


Taking lease structure risk and global systematic risk into account monte carlo options

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


Simulation of the price market rental values i

Simulation of the Price & Market Rental Values (I)


Break option analogy with option s theory i

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


Break option analogy with option s theory ii

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:

=>


Mrv tc mrv t

(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


Option should be exercised

Option should be exercised


In our implementation

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.


The model

The Model


The model1

The Model


Net operating income with our model for one scenario

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


Hypothesis of the implementation

Hypothesis of the implementation


Sensitivities level of inflows

Sensitivities: Level of inflows


Sensitivities level of inflows1

Sensitivities: Level of inflows


Sensitivities valuation of the portfolio

Sensitivities: Valuation of the Portfolio


Questions

Questions?

?


European lease contract risk1

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


Monte carlo methods

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)


Monte carlo methods1

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


Simulation of the price market rental values ii

Simulation of the Price & Market Rental Values (II)

Together correlated with a fixed correlation parameter


Mrv r t

MRV > Rt


Bo should be exercised

BO should be exercised


European lease option

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


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