european real estate society - milan - 2010 combining monte-carlo simulations and options to manage...
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European Real Estate Society - Milan - 2010
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
European Real Estate Society - Milan - 2010
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
European Real Estate Society - Milan - 2010
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
European Real Estate Society - Milan - 2010
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
European Real Estate Society - Milan - 2010
Continental Europe lease contract: the rent
In Europe,
Rents usually indexed
• Inflation
• Country specific index
• Fixed indexation
Possible rent's indexation
Year 1Year 2
Year 3Year 4
Year 5Year 6
Year 7Year 8
Year 9
Year 10
Year 11
Fixed indexation
CPI
capped indexation (max3,5%)
European Real Estate Society - Milan - 2010
European Lease contract: RiskTraditionally, tenants cannot negotiate the rent
during the course of the contract whatever is the level of the Market rental value.
MRV higher than rents paid
Year 1Year 2
Year 3Year 4
Year 5Year 6
Year 7Year 8
Year 9
Year 10
Year 11
Possible Market Rental Values
capped indexation (max3,5%)
MRV below rents paid
Year 1Year 2
Year 3Year 4
Year 5Year 6
Year 7Year 8
Year 9
Year 10
Year 11
Possible Market Rental Values
capped indexation (max3,5%)
European Real Estate Society - Milan - 2010
Taking lease structure risk and global systematic risk into account
=Monte-Carlo + Options
1 6 11 16 21 26 31 36 41 46 51 56 61
European Real Estate Society - Milan - 2010
Simulation of the Price & Market Rental Values (I)
PtP
Pt
t
t dWdtP
dP
PP
PPttt UttPP
2exp1
MRVtMRV
MRVi
t
t dWdttMRV
dMRV
MRVMRV
MRVMRVitt UtttMRVMRV
2exp1
tP
PPtt WtPP
2exp0
i
ttiif
ttiif
ti
ttiPi 1,,0
1,,
1 1;
j
ttjif
ttjif
t
j
ttiMRVj 1,,0
1,,
1 1;
European Real Estate Society - Milan - 2010
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
Premium of a standard call option
0
5
10
15
20
25
70 80 90 100 110 120 130
vs
European Real Estate Society - Milan - 2010
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:
=>
)0;max( rTT KeSC )0;max( tt MRVRBO
European Real Estate Society - Milan - 2010
MRV + Tc > MRVt
(MRV + Tc) > Rt: No exercise of break-options
0,000
2,000
4,000
6,000
8,000
10,000
12,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Re
nt
European Real Estate Society - Milan - 2010
Option should be exercised
Exercice of break option possible between the 6th observation date and the 11th
0,000
2,000
4,000
6,000
8,000
10,000
12,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Ren
t
European Real Estate Society - Milan - 2010
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.
)(tTMRVR ctt
tt MRVR
)(tTMRVRMRV cttt
European Real Estate Society - Milan - 2010
The Model
11
1200
2
2
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000 )1()1(
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)1(
)1(
)1(
)1(
TT
tt
t
ii
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jj
k
PK
k
IICF
k
ICF
k
ICFP
European Real Estate Society - Milan - 2010
The Model
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00100
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2001003
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22
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121
12
221
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k
IICF
k
IICF
k
IMRV
k
MRV
k
MRV
k
IICF
k
IICFK
k
IIMRV
k
IIMRV
k
IMRV
k
MRV
k
MRV
k
IIMRV
k
MRVK
k
IIMRV
k
IIMRV
k
IIMRV
k
MRV
k
IIMRV
k
MRV
k
IIMRV
k
MRVK
K
European Real Estate Society - Milan - 2010
Net operating income with our model for one scenario
Net operating income when three leases are signed and two break-options are exercised
0,00
2,00
4,00
6,00
8,00
10,00
12,00
14,00
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
European Real Estate Society - Milan - 2010
Hypothesis of the implementation
Years MRV Lease 1 to 6 Rent Lease 1 Lease 2 Lease 3 Lease 4 Lease 5 Lease 6
2010 -3,0% 1,5% 1,5% 1,5% 1,2% 1,5% 1,5%2011 -1,0% 1,0% 1,0% 1,5% 0,8% 1,0% 1,0%2012 0,0% 1,2% 1,2% 1,5% 1,0% 1,2% 1,2%2013 1,0% 3,7% 3,5% 1,5% 3,0% 3,7% 3,7%2014 2,0% 4,0% 3,5% 1,5% 3,2% 4,0% 4,0%2015 2,5% 3,8% 3,5% 1,5% 3,0% 3,8% 3,8%2016 3,0% 3,5% 3,5% 1,5% 2,8% 3,5% 3,5%2017 3,5% 3,6% 3,5% 1,5% 2,9% 3,6% 3,6%2018 2,8% 3,1% 3,1% 1,5% 2,5% 3,1% 3,1%2019 2,3% 2,6% 2,6% 1,5% 2,0% 2,6% 2,6%2020 2,0% 2,2% 2,2% 1,5% 1,8% 2,2% 2,2%2021 2,0% 1,8% 1,8% 1,5% 1,4% 1,8% 1,8%2022 1,5% 1,8% 1,8% 1,5% 1,4% 1,8% 1,8%2023 1,5% 1,8% 1,8% 1,5% 1,4% 1,8% 1,8%2024 1,5% 1,8% 1,8% 1,5% 1,4% 1,8% 1,8%
MRV's Volatility: 8%
MR
V's
Tre
nd
Ren
t's
ind
exat
ion
YearsPrice trend
Price volatility
2010 2% 6%2011 2% 6%2012 2% 6%2013 3% 6%2014 3% 6%2015 3% 6%2016 3% 6%2017 2% 6%2018 2% 6%2019 2% 6%2020 2% 6%2021 2% 6%2022 2% 6%2023 2% 6%2024 2% 6%
European Real Estate Society - Milan - 2010
Sensitivities: Level of inflows
-4,0
% -2,8
% -1,5
%
-0,3
% 1,0% 2,
3% 3,5%
2009
2012
2015
2018
2021
4
5
6
7
8
9
10
Level of inflows
changes in the MRV's trend
Horizon
Level of inflows according to the changes in the market rental value's trend
European Real Estate Society - Milan - 2010
Sensitivities: Level of inflows
-4,0
% -2,8
% -1,5
% -0,3
% 1,0% 2,
3% 3,5%
2009
2012
2015
2018
2021
4
5
6
7
8
9
10
Level of inflows
Changes in indexation
Horizon
Level of inflows according to changes in the indexation
European Real Estate Society - Milan - 2010
Sensitivities: Valuation of the Portfolio
-4,0
%
-3,3
%
-2,5
%
-1,8
%
-1,0
%
-0,3
%
0,5%
1,3%
2,0%
2,8%
3,5%
2009 20
13 2017 20
21
80
85
90
95
100
105
110
115
120
125
Portfolio Level
Changes in the trend Horizon
Valuation of the Portfolio according to the changes in the market rental value's trend
European Real Estate Society - Milan - 2010
Questions?
?
European Real Estate Society - Milan - 2010
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
European Real Estate Society - Milan - 2010
Monte-Carlo Methodsaveraging 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)
European Real Estate Society - Milan - 2010
Monte-Carlo methods30 trajectories simulation for 60 steps
and their average
1 6 11 16 21 26 31 36 41 46 51 56 61
Average of the 30 simulated paths
• 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
European Real Estate Society - Milan - 2010
Simulation of the Price & Market Rental Values (II)
Price
80
90
100
110
120
130
140
150
160
170
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57
MRV
3
5
7
9
11
13
15
1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58
Together correlated with a fixed correlation parameter
European Real Estate Society - Milan - 2010
MRV > Rt
MRV > Rt: No exercise of break-options
0,000
2,000
4,000
6,000
8,000
10,000
12,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Ren
t
European Real Estate Society - Milan - 2010
BO should be exercised
Exercice of break option possible between the 2nd observation date and the 12th
0,000
2,000
4,000
6,000
8,000
10,000
12,000
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Time
Ren
t
European Real Estate Society - Milan - 2010
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