Real Options Applications in Real Estate

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Real Options Applications in Real Estate
Infrastructure

• Gordon Sick
• Haskayne School of Business
• University of Calgary

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Real Estate Real Options
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Real Estate Development Options

• Consider the basics of real estate development
  option, which is a call option.
• The volatility is the volatility of the value of
  a developed project.
• The convenience dividend is the earnings from
  developed real estate.

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Real Estate

• The exercise cost is the capital cost of
  development plus the opportunity cost of the next
  best use of the land, which is often its value as
  an agricultural property.
• The option is often perpetual, which often
  simplifies the analysis.

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Aside Operating Cost

• We often assume lognormal distributions
  geometric Brownian motion (GBM).
• Fixed operating costs (in real estate or any
  other project) ruin the GBM property.
• Consider modeling the PV of revenue as GBM and
  add the PV of fixed op costs into the capital
  development cost (exercise price).

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Real Estate Decisions

• When to develop
• What scale to develop to

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Development Scale

• For each potential development scenario (hurdle
  price), choose an optimal scale.
• Decreasing returns to scale higher density costs
  more per incremental unit of size than lower
  density.
• Without sufficiently decreasing returns to scale,
  the model often blows up to an infinite size.

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Development Hurdle

• Given the solution to the scale problem for each
  potential development hurdle, solve for the
  optimal development hurdle.
• The hurdle is a threshold developed property
  value.
• If there is a finite window of opportunity for
  development, the optimal threshold also depends
  on time to option maturity.

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Real Estate Monopolist

• It is often simplest to think of the holder of a
  real option as being a monopolist.
• His decisions do not affect other holders of real
  options.
• Their decisions do not affect his.

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Multiple Developments

• Assume that the monopolist has multiple
  properties to develop.
• Now, we cannot take the developed property value
  or revenue stream as an exogenous stochastic
  variable.
• The revenue for each property depends on how many
  other properties the developer has already
  developed.

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Demand Shocks

• We need an exogenous variable, such as a market
  demand shock, X.
• Model an inverse demand curve where price P
  depends on the shock and amount of property
  already developed, Q.
• P f(X, Q) is increasing in X and decreasing in
  Q.

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Exogenous Shock and Convenience

• We lose the nice convenience dividend
  interpretation, because the exogenous shock is
  not a cash flow.
• Use a risk-neutral shock growth rate.
• Subtract a risk premium from the growth rate,
  determined by the CAPM.

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CAPM and Risk Premia

• The Capital Asset Pricing Model (CAPM) says that
  the growth rate, g, plus the notional convenience
  dividend yield, y, is total return and equals the
  riskless rate, r, plus the beta risk premium, RP
• g y r RP
• y r RP - g is the convenience yield.

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Demand Curve

• The demand curve affects the scale choices for an
  individual development.
• It affects the number of properties that the
  developer will start at one time.
• Each development decision is a sequential
  optimization, given the number of properties
  already developed.

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Real Estate Cycles

• As the exogenous shock variable reaches new
  highs, new developments are started.
• When the shock variable falls, development ceases
  and property prices or rent fall.
• The developer anticipates the possibility of a
  drop and sets the hurdle higher to compensate.

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Real Estate Games

• Introducing multiple developers requires game
  theory.
• Your option exercise affects other players real
  options and their decisions affect yours.

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Pre-Leasing

• A commercial real estate developer usually
  pre-leases much of the development before
  starting.
• This is a binding contract between lessee and
  lessor, so the lessee requires penalties if the
  lessor is late or performs poorly.

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Pre-emption

• The pre-leasing preempts the lessee from signing
  a lease contract with another developer.
• The developers want to develop earlier in order
  to fill their building.
• This works like the convenience yield to induce
  early development.

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Possible Equilibria

• Grenadier shows that this leads to a simultaneous
  or sequential (leader and follower) two-player
  development game.
• It also leads to cascades of development.
• Grenadier, S. R. (1996). The strategic exercise
  of options Development cascades and overbuilding
  in real estate markets. Journal of Finance,
  51(5)1653 1679.

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Building Cascades

• Grenadier characterizes a building cascade as a
  situation where the follower enters very soon
  after the leader.
• Cascades are more likely to occur in volatile
  markets.

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Recession-Induced Construction Booms

• Grenadier also notes that the simultaneous
  development can result in a construction boom
  even in a recession.
• It is more likely to occur when the time to build
  is large and demand volatility is high.

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Perfect Competition

• When there are more developers, they do not
  consider the impact of their decision on the
  overall market.
• They have earlier development thresholds.
• The competition bids away much of the real option
  premium.

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Differentiation

• Novy-Marx shows that one can modify the Grenadier
  model in a sequential equilibrium where
  developers build and subsequently redevelop.
• Since different developers have property at
  different density of development, their
  opportunity cost differs and they do not develop
  simultaneously.

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Real Option Premia

• Since the developers are distinguished by their
  current level of development, they are not
  perfect substitutes in the decision to develop.
• Real option premia do not get bid to zero in this
  setting.
• Novy-Marx, R. (2007). An equilibrium model of
  investment under uncertainty. Review of Financial
  Studies, 20(5)14611502.

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Infrastructure Real Options
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Infrastructure Games

• Infrastructure options involve a game between the
  provider and the user
• The user can demand too much or too little
  infrastructure.

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A Car Leasing Puzzle

• Why are daily rental rates for a car from a
  rental agency like Hertz signi?cantly greater
  than the per diem equivalent of the monthly rate?

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• Someone renting a car on a daily basis has the
  ?exibility of only having to rent the car when
  and where it is needed.
• This ?exibility option is valuable, so the renter
  is willing to pay a higher daily rate.
• It is also costly to provide, since the provider
  must carry excess or idle capacity.

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Pricing Access

• We have seen that a competitive equilibrium would
  have users of a facility (such as a car, road or
  processing facility) paying for the option to use
  the facility only when they need it.

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How to Structure Payment?

• An option premium must be added to avoid
  distortions, but simply adding it when the
  facility is used causes distortions.
• The provider is not compensated for the cost
  incurred if the facility is never accessed.

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• Increasing the usage payment only when the
  facility is accessed to compensate for cost when
  it is not used simply drives users away from
  using the facility in good times.
• The user must pay a standby fee for the right to
  use the facility even if the facility is not used.

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Take or Pay Tolls

• In the gas pipeline and electricity businesses,
  it is common to have a take-or-pay toll.
• The buyer has to pay for the gas even if it is
  not taken sometime in the delivery interval.
• The buyer still has flexibility of when to access
  the facility, but the builder is compensated for
  providing the real option.

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Deregulation

• Many industries have been deregulated by
  declaring the production facility to be accessed
  by competitive suppliers, who then compete in
  consumer markets with the facility owner.
• The regulation is moved to determining the
  appropriate toll for facilities access.

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• But regulators missed the point in two ways.
• They often forgot to compensate the facility
  owner for the flexibility options they had to
  create, which were valuable to the entrant
  telecom access, for example.
• Even if they allowed a real option premium, they
  only had it paid when the facility was accessed.

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Two-part Tariffs

• The correct solution is to provide a two-part
  facilities access tariff.
• A fixed part would be a standby fee that
  compensates for the provision of a real access
  option even when not used.
• A usage part would pay for actual usage when the
  facility is accessed.

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Determining Tariffs

• There does not seem to be a simple way of setting
  the two-part tariffs.
• The appropriate solution is to solve for optimal
  behaviour by the provider and user for a given
  tariff and then compare social surplus to what
  would occur if the provider and user are the
  same, avoiding distorted decisions.

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Summary
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• Real estate options involve a tradeoff of the
  risk of a developed project against the benefit
  of owning a developed project.
• The benefits of a developed project include
• Revenue or dividends from developed project.
• The benefit of preempting competors.

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• Real estate options with multiple developers need
  a risk-neutral growth rate on a stochastic demand
  shock variable.
• A cash dividend is not readily observable, but
  can be inferred from the CAPM risk premium.

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• In access to common facilities, non-distorting
  tariffs must compensate the facility provider for
  costly flexibility options of excess capacity
  that are valuable to the user.
• The tariff structure must have two parts.
• Fixed standby fee for the right to access.
• Usage fee for actual use of facility.