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.
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