# Yale School of Management Real Options in Real Estate Theory and Evidence.

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Yale School of Management Real Options in Real Estate Theory and Evidence

Yale School of Management Overview Options Real Options Development Option Empirical Evidence Applications

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

Yale School of Management Option Valuation Stock price Strike price Interest rate Volatility of stock return Time to maturity Black-Scholes formula: C ( S, K, r, σ, T)

Yale School of Management 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.

Yale School of Management 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.

Yale School of Management 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?

Yale School of Management 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.

Yale School of Management Implications Irreversible investment involves a timing decision. Relevant stochastic variables: –Interest rates –Demand –Investment cost Autocorrelation of variables are relevant.

Yale School of Management 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.

Yale School of Management 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.

Yale School of Management 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.

Yale School of Management Optionality Premium

Yale School of Management 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.

Yale School of Management 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

Yale School of Management Results A = constant: + insignificant A1 = Lag Comp:+ significant A2 = Income: + significant A3 = EmpGrowth+ significant A4 = Volatility-- significant A5 = Interest Rate-- significant A6 = Cost-- insignificant A7 = Commute-- significant A8 = Climate + significant

Yale School of Management 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?

Yale School of Management Applications Empirical results suggest that developers already value optionality: Land prices are higher than simple present values. Volatility in demand causes construction delay.

Yale School of Management 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.

Yale School of Management 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?

Yale School of Management Agency Theory and Real Estate Theory, Insights and Applications

Yale School of Management 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.”

Yale School of Management 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.

Yale School of Management Why is it Interesting? Imperfect information Management Complex organizations Co-operative ventures Negotiation

Yale School of Management 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

Yale School of Management 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.

Yale School of Management 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.

Yale School of Management Real Estate Portfolios Real estate development and management is local. Real estate portfolios are diversified. Principal = national owner, Agent = local manager.

Yale School of Management 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.

Yale School of Management 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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