Real Options in Real Estate

1. Real Options in Real Estate Theory and Evidence

2. Overview • Options • Real Options • Development Option • Empirical Evidence • Applications

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

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

5. 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.

6. 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.

7. 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?

8. 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.

9. Implications • Irreversible investment involves a timing decision. • Relevant stochastic variables: • Interest rates • Demand • Investment cost • Autocorrelation of variables are relevant.

10. 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.

11. 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.

12. 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.

13. Optionality Premium

14. 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.

15. 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

16. 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

17. 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?

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

19. 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.

20. 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?

21. Agency Theory and Real Estate Theory, Insights and Applications

22. 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.”

23. 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.

24. Why is it Interesting? • Imperfect information • Management • Complex organizations • Co-operative ventures • Negotiation

25. 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

26. 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.

27. 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.

28. Real Estate Portfolios • Real estate development and management is local. • Real estate portfolios are diversified. • Principal = national owner, Agent = local manager.

29. 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.

30. 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.