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

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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

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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

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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

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Continental Europe lease contract the rent

• In Europe,
• Rents usually indexed
• Inflation
• Country specific index
• Fixed indexation

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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.

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Taking lease structure risk and global systematic
risk into accountMonte-Carlo Options

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Simulation of the Price Market Rental Values (I)
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Break-Option Analogy with options 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
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Break-Option Analogy with options theory (II)

• A rational player will exercise its option at
  maturity as soon as it is in the money
• St gt 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 gt MRVt
• By analogy, the value of a BO can be written

gt
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MRV Tc gt MRVt
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Option should be exercised
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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 tenants 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.

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The Model
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The Model
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Net operating income with our model for one
scenario
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Hypothesis of the implementation
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Sensitivities Level of inflows
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Sensitivities Level of inflows
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Sensitivities Valuation of the Portfolio
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Questions?

• ?

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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

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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)

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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

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Simulation of the Price Market Rental Values
(II)
Together correlated with a fixed correlation
parameter
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MRV gt Rt
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BO should be exercised
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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 tenants rational decision
  will be taken