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

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 ServicesBaroni Michel, Essec Business SchoolBarthélémy Fabrice, THEMA, University of Cergy-PontoiseDupuy Etienne, BNP Paribas Real Estate Investment Services


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

• 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

• 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

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 9Year 10

Year 11

Fixed indexation

CPI

capped indexation (max3,5%)


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 9Year 10

Year 11

Possible Market Rental Values


MRV below rents paid

Year 1Year 2

Year 3Year 4

Year 5Year 6

Year 7Year 8

Year 9Year 10

Year 11

Possible Market Rental Values



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


Simulation of the Price & Market Rental Values (I)

PtP

Pt

t

t dWdtPdP

PP

PPttt UttPP

2

exp1

MRVtMRV

MRVi

t

t dWdttMRVdMRV

MRVMRV

MRVMRVitt UtttMRVMRV

2exp1

tP

PPtt WtPP

2exp0

ittiifttiif

ti

ttiPi 1,,0

1,,1 1;

jttjif

ttjif

tj

ttiMRVj 1,,0

1,,

1 1;


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


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


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

Ren

t


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

Rent


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


The Model

11

1200

2

2

1

00

000 )1()1(

)1()1()1(

)1(

)1()1(

TT

tt

t

ii

i

jj

kPK

kIICF

k

ICF

kICFP


The Model

100100

1

11

1200100

3

11

1

11

12

2

1121

12221

1121

1212

1222

2222

2221

11

1

)1()1()1(

)1()1()1(

)1()1(

)1(

)1(0

)1()1()1(

)1()1()1(

)1()1()1(

)1()1()1(

)1()1(

)1(

)1(0

)1()1()1(

)1(

)1()1()1(

)1()1()1(

)1()1()1(

)1(

)1()1()1(

)1(0

)1()1()1(

)1(0

TT

TT

TTT

TT

TT

TT

tt

TTtt

TTtt

TTT

TT

TT

TTtt

tt

TTtt

tttt

TTtt

tt

TTtt

tt

tttt

tt

kIICF

kIICF

kIMRV

kMRV

kMRV

kIICF

kIICF

K

kIIMRV

kIIMRV

kIMRV

kMRV

kMRV

kIIMRV

kMRV

K

kIIMRV

kIIMRVk

IIMRVk

MRVk

IIMRVk

MRV

kIIMRV

kMRV

K

K


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


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

Tren

d

Ren

t's in

dexa

tion

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%


Sensitivities: Level of inflows

-4,0

% -2,8

% -1,5

% -0,3

% 1,0% 2,

3% 3,5%

20092012

2015

20182021

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


Sensitivities: Level of inflows

-4,0

% -2,8

% -1,5

% -0,3

% 1,0% 2,

3% 3,5%

200920122015

20182021

4

5

6

7

8

9

10

Level of inflows

Changes in indexation

Horizon

Level of inflows according to changes in the indexation


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


Questions?

?


European Lease contract: RiskFor the owners, risk concentrated in the lease

structureThe 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 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)


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


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


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

Rent


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

Rent


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

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

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