Yale School of Management

Real Options in Real Estate

Theory and Evidence

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Overview

• Options

• Real Options

• Development Option

• Empirical Evidence

• Applications

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Options

• Call option: The right (not the obligation) to purchase a share of stock at a date T in the future for price P.

K

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Option Valuation

• Stock price

• Strike price

• Interest rate

• Volatility of stock return

• Time to maturity

• Black-Scholes formula: C ( S, K, r, σ, T)

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Volatility and Call Option

• No downside cost, so no downside risk.• Upside payoff, so risk is good.• Method of valuation:

– Call option payoff can be locally matched by borrowing, and holding some amount of the stock.

– As S changes, this “replicating portfolio” must be adjusted.

– We know the price of the stock and the bond at each moment, so we can calculate the equivalent price of the option.

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Real Options

• Fisher’s NPV criterion: take any project that project that provides a positive Net Present Value.

• Suppose, however, that taking one project costs you the opportunity to take another positive NPV project?

• Take the highest NPV of the two.

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Example: Plant Construction

• Cost of Plant: $100 million

• Net after-tax cash flow/yr. in perpetuity from plant: $3 million.

• Cot of capital = current interest rate.

• Current cost of capital today: 3%.

• NPV = $3 m/ .03 = $100 m.

• Build the plant?

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Stochastic Interest Rates

• Interest rates go up or down each year by 100 BP. • If they are certain to go to 2% next year: • NPV = [$3 m/.02 - $100m]/(1.03) = $48.54 m• Wait one year to build!• Each project competes with itself delayed by one

period.• But ONLY if both projects cannot be undertaken!• Irreversible investment.

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Implications

• Irreversible investment involves a timing decision.

• Relevant stochastic variables:– Interest rates– Demand– Investment cost

• Autocorrelation of variables are relevant.

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Real Estate Example

• Rents vary through time, with some momentum.• Rents are locked in for 10 years when you lease.• Costs to build are fixed (as are interest rates): $

400/square foot. Build and lease instantaneously.• Current rents are $40/square foot.• Current cost of capital is 10%.• Rents are trending up: prob 60% of rents going to

$50/sq.foot and 40% chance of $30/square foot.

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Build or Wait?

• NPV = $40/.1 - $400 = 0• Exp. Value: .6($500-$400)/(1.1) + .4(0)= $90.9• Optionality premium = $90.09• What if rent (t) = a + b*rent(t-1)+e ?• Wait for rents to tip and then build?• Issues:

– Construction time.

– Build but hold vacant.

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Do Real Options Matter?

• Laura Quigg (JF, 1993)

• Examines Seattle market for undeveloped land.

• Estimates building prices, development costs and models development costs as stochastic.

• Value with and without std of DC = 0.

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Optionality Premium

0

0.05

0.1

0.15

0.2

0.25

0.3

1977 1978 1979

Bus.premiumInd-premiumHD residential prem.

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Evidence from Office Construction

• Rena Sivitanidou & Petros Sivitanides (RE Econ 2000)

• Construction starts should depend upon option value.

• Higher volatility of rents should cause delay of construction.

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Approach

• Time-series of commercial property completions in U.S. Office markets: CC

• Data: Torto-Wheaton Research: 1982 – 1998.• Model:• Completions = a+ a1*Completions t-1 +

a2*Income + a3*EmpGrowth+ a4*EmpVolatility +a5*Interest +a6*Cost + a7*Commute +a8 Temperature

• Also used Rents and Vacancies in other models

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Results

A = constant: + insignificantA1 = Lag Comp: + significantA2 = Income: + significantA3 = EmpGrowth + significantA4 = Volatility -- significantA5 = Interest Rate -- significantA6 = Cost -- insignificantA7 = Commute -- significantA8 = Climate + significant

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More

• Other variables: Income and Rents both are positive and significant in other models. Vacancies are negative and significant in other models

• Some evidence that development in 1990’s took optionality more into account.– Conservatism or increased volatility

expectation?

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Applications

• Empirical results suggest that developers already value optionality:

• Land prices are higher than simple present values.

• Volatility in demand causes construction delay.

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Application to Development

• Vacant land represents an option.• Option exercise triggered by peak valuation

– Demand, construction costs, financing.– Strategic considerations.– Rents.

• Complex issues– Time to build.– Competitor decisions.

• Steven Grenadier (Stanford) “Construction Cascades.”– One exercise, all exercise.

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Application to Leasing

• Each floor is a separate option.• High volatility of rents implies value in short-term

lease/ vacancy.• Peaking rents a sign to lease up.• Low rents a sign to keep vacant space.• Low rents + vacancy = negative economic sign –

or not?• Low vacancy + high rents = positive sign – or not?

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Agency Theory and Real Estate

Theory, Insights and Applications

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Background

• Ross (1973) "The Economic theory of agency: the principal's problem.“

• “Agency relationship when one, designated as the agent, acts for, on behalf of, or as representative for the other, designated the principal, in a particular domain of decision problems.”

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Structure of Analysis

• Agent and Principal agree on a fee structure.

• Agent takes actions that are not directly monitored or observable.

• Fees determined by outcomes and external events, perhaps.

• Agent motivated to act in his/her own interest.

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Why is it Interesting?

• Imperfect information

• Management

• Complex organizations

• Co-operative ventures

• Negotiation

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Issues in Analysis

• What fee structure will best align interest of P & A?

• Is it possible to find something that achieves a “first best” solution which maximally motivates the Agent?

• What additional mechanisms exist to align interests/motivate Agent?– Costly auditing/ monitoring an option

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General Analytical Results

• There are agency costs– Shirking– Pilferage– Risk-shifting

• Near alignment of interests possible– Stock option programs a major solution

• Solutions must be incentive-compatible and individually rational.

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Examples in Real Estate

• Real Estate Agents– Local knowledge essential (before web)– Commission earned on transaction.– Effort unobservable.– Result: Realtors leave their own home on the market

longer and get higher adjusted prices for it.

• Home-ownership and urban quality– Home ownership aligns upkeep incentives.– Rental home are not well-maintained.– Externalities imposed.

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Real Estate Portfolios

• Real estate development and management is local.

• Real estate portfolios are diversified.

• Principal = national owner, Agent = local manager.

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Approach

• Understand differing motivations– Where will conflicts arise?

• Understand differing strengths– These provide the gains to trade.

• Understand the IR and IC constraints on both– This means the deal will not fall through in the

future.

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Contracting

• A solution should be possible (Ross result) for a wide range of agents and principals.

• Negotiation process should help reveal the relative strengths and motivations (Raiffa result).

• Use the power of incentive alignment– Equity sharing.

• Look for judicious use of monitoring.