Week 11: Real Estate Cycles and Time Series Analysis The dynamic behavior of the 4-Q model: stability versus oscillations. Real Estate Pricing

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1 Week 11: Real Estate Cycles and Time Series Analysis The dynamic behavior of the 4-Q model: stability versus oscillations. Real Estate Pricing Behavior: backward or forward looking? Development Options and Competition Forecasting markets: Univariate analysis, Vector Auto regressions, structured models. The definition and evaluation of risk

2 What are Real Estate cycles A reaction to a shock in the underlying economic demand for the property: national or regional recessions and economic boom periods. [e.g. single family residential, industrial, apartments] A periodic overbuilding of the market - excess supply that originates from capital or development activity and is not necessarily linked to demand movements. [e.g. office, hotels, retail?] Which markets/property types exhibit which? Are Markets changing?

3 U.S. Single-Family Market Completions Rate vs. Home Price Appreciation 7% 6% 5% 4% 3% 2% 1% 0% -1% -2% -3% -4% -5% Completions Rate Employment Growth Home Price Index (2002 $)

4 National Multi-Housing Forecast 6.00% 5.00% Permits vs. Real Rent $ Per Sqft Forecast 4.00% % % 1.00% % % -2.00% Total Employment Growth (L) Real Rent (R) Completion Rate (L)

5 National Industrial Forecast 6.00% Completions Rate vs. Real Rent $ Per Sqft % Forecast % % % % % % % Total Employment Growth (L) Real Rent (R) Completion Rate (L)

6 8.00% National Office Forecast Completions Rate vs. Real Rent $ Per Sqft Forecast % % % % % Total Employment Growth (L) Real Rent (R) Completion Rate (L)

7 National Hotel Forecast 8.00% Supply Growth Rate vs. Real ADR Forecast 6.00% % % % % % Total Employment Growth (L) Real ADR (R) Supply Growth Rate (L)

8 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00% 0.00% -1.00% -2.00% National Retail Forecast Completion Rate vs. Real Rent $ Per Sqft Forecast % Total Employment Growth (L) Real Rent (R) Completion Rate (L)

9 Dynamic 4-Q Model 1). Office Demand t = α 1 E t R t E t = office employment -β1 Rt = rent per square foot β1 = rental elasticity of demand: [%change in sqft per worker/% change in rent] 2). Demand t = Stock t = S t 3). Hence: R t = (S t / αe t ) 1/β1

10 4). Office Construction rate: β2 C t-n /S t = α 2 P t P t = Asset Price per square foot β 2 = price elasticity of supply: [Perfect competition Q investment theory with n-period delivery lag. Projects begun n-periods back are based the expected value of asset prices at the time of delivery.]

11 5). Replacement version: E= fixed S t /S t-1 = 1- δ + C t-n /S t-1 6). Steady Demand growth version: E t = [1+ δ] E t-1 S t /S t-1 = 1 + C t-n /S t-1 [δ can represent the sum of employment growth and replacement demand]

12 7). Myopic (backward) behavior: P t = R t-n / i i = interest rate (discount rate) [Extrapolate the future from the current/past] 8). Forward looking behavior (the efficient market theory): P t = R t /(1+r) t -t t =t+1, or: P t+1 P t = i P t -R t

13 9). Solution: P t, R t P t+1 R t+1 (the supply equation), etc. As long as the initial price is efficient and you know E t. = the steady state solution. 10). Rational Expectations : you can t predict the future with certainty, but if you use all the info your mistakes are only random. 11). A random shock to rent should not influence price much since its only temporary (definition of random).

14 Efficient Market: Prices less volatile than income, cap rate is low when market is down (mean reversion). Inefficient Market: Prices more volatile than income, cap rate is high when market is down (extrapolation). Cap Rate ( %) Index, 1977:4 = 10 Cap Rate Capital Value Index (R) NOI Index (R)

15 12). Market steady state solution [the uncertain variable E t grows as we think it will = at the rate δ] δ = C t-n /S t-1, P 1/β2 t = (δ/α 2 ), S t /S t-1 = 1+ δ R t = ip t+1 = ip t 13). What happens if E t increases Randomly for one period and then resumes its long term growth rate?

16 Impulse response to demand shock with stable market parameters. Holds for either efficient or extrapolative pricing: Intrinsic mean reversion (Image removed due to copyright considerations.)

17 Impulse response to demand shock with unstable market parameters. Holds only for extrapolative pricing rules: mean over-reversion. (Image removed due to copyright considerations.)

18 What makes the model unstable? More elastic supply (β 2 ). and less elastic demand (β 1 ). A high rate of demand growth or rapid obsolescence of properties (δ) Long Delivery lags (n) Extrapolative (backward) as opposed to forward, efficient expectations by investors/developers. Variation by property type? In any case, all models above have mean reversion and are not a random walks [Shiller].

19 Historic Real Estate Price volatility: Source: NCREIF R&D Office Retail Warehouse

20 What if market participants wait = slow adjustment? Gradual adjustment of space demand to changes in employment and rents. Why? Only 20% or so of tenants can move each year given lease contracts. Gradual adjustment of rent to vacancy. Why? Lease contracts make the leasing decision like an investment there are option values to waiting [Grenadier]. Example: the Rental Adjustment process. R t -R t-1 = λ 0 - λ 1 V t (Rosen, 1980s). λ 0 / λ 1 = structural vacancy rate R t -R t-1 = λ 0 - λ 1 V t - λ 2 R t-1 (Wheaton, 1990s). R* = (λ 0 - λ 1 V t )/ λ 2 rent at which landlords indifferent to leasing versus waiting

21 Waiting = Development as a Real Option Competitive model (Tobin s Q): develop as soon as when Prices equal replacement cost. But what if prices are stochastic, uncertain? If wait and they go down little lost. If wait and they go up a lot gained! Hence wait. Until Prices cross a hurdle = replacement cost + option value = exercise price Greater uncertainty = higher option value = longer wait since exercise price is higher.

22 Development Options and Development Lags Lags are delays between when you exercise the option (commit) and when you realize the Price. Lags mean that the impact of uncertainty on waiting is less than without lags. For a given level of uncertainty the hurdle is lower with lags. The value of waiting is less because if good times occur, and it take you several years to build, by the time you build they may have vanished. Without lags you can always realize the good times value!

23 Development Options and Overbuilding When we all wait, its more likely that multiple players exercise the option at the same time. Exercising at the same time = a building Cycle (Grenadier). When there are more players (increased competition), the option value of waiting is eroded. Why? Because competitors can take your place and pre-empt you. If you are a monopolistic developer there is no fear of this! Are property types with more competition, or locations with more competition less prone to overbuilding, since no player waits? (Somerville). The Dynamic 4-Q model assumes competitive supply

24 Can models be estimated empirically and used to make forecasts and assess risk? Option #1: reduced form forecast just evaluate and forecast rents with a model that has no other variables. Option #2: forecast rents and construction together. Do you assume market clearing as in the 4-Q model? Option #3: add in vacancy and assume that markets clear slowly = more variables and more equations. Better forecasts?

25 Model #1: Unconditional Univariate (quarterly Boston data, 1979:1-2002:4) R = R T (2.5) (22.1) (.6) R 2 =.933 No trend in real office rents (.09 is not significant). Rents depend an awful lot on last periods rents! R* = ( T)/ (1-.92) = $39! (steady state rents in real dollars) How does this equation work?

26 Model #1: Rental Adjustment R = R T, is the same as: R - R -1 =.08 [ ( T)/.08 - R -1 ] =.08 [ R* - R -1 ] Rents adjust slowly to random shocks (8% quarterly or about 28% annually) to a negative real trend (if significant) More rent lags = more zigs and zags in the adjustment process, but around what? Nice and clean, but what have we learned?

27 Model #2: Conditional Rent/Construction Multivariate R = R FIRE +.02SER S -1 (2.9) (17.1) (2.1) (3.2) (-3.9) R 2 =.976 C = R S -1 (.9) (2.9) (-2.2) R 2 =.41 S = S -1 + C Who forecasts FIRE and SER? That s what is meant by conditional. Note that rents still adjust slowly, but now to changes in employment or stock ( 6% quarterly or 22% annually). Not like the theoretical model.

28 Model #2: Rent Conditional Multivariate Behavioral implications: (continued) For every 1000 FIRE jobs added to the economy, if we develop 307,000 more square feet then real rents will be stable. For every 1000 Business Service jobs added to the economy, if we develop 157,000 more square feet then real rents will be stable. If rents are at $30 real, the construction will average about 600,000 square feet each quarter or 2.4m annually. FIRE growth of 7,500 jobs annually or Business service growth of 15,000 jobs annually would justify this. This is just about what is forecast!

29 Model #3: Conditional Rent/Construction/ Vacancy Multivariate OC = R FIRE SER +.91OC -1 (2.1) (-3.4) (2.6) (1.9) (30.6) R 2 =.997 C = R S V -18 (.9) (2.5) (-2.0) (-3.4) R 2 =.54 R = R V -1 (6.0) (20.1) (-6.9) R 2 =.958 S = S -1 + C; V = 1.0 OC/S Absorption = OC OC -1

30 Behavioral implications: Model #3 (continued) Each 1000 FIRE workers needs 310,000 square feet and each Business Service worker 135,000. Adding this much square feet keeps vacancy constant (occupied square feet). To get to these targets, occupied square feet responds slowly 9% quarterly or 30% yearly. At rents of $30 and vacancy rate of 10%, construction will add about 500,000 square feet quarterly (2.0m annually) This is about what the job forecast is! But at 10% vacancy rents will rise above $30 until they stabilize at $43. This would add more construction than is justified.

31 55 MIT Center for Real Estate Boston Office Market. Red: Univariate(#1); Green: Rent- only(#2); Blue: Rent & Vacancy(#3). FITTED FOREAB Office Absorption

32 enter for Real E MIT C state Boston Office Market: Rent only forecast(#2): green; Rent & vacancy(#3): blue.

33 Boston Office Market: Full model (#3).

34 Distribution of Forecast Outcomes A forecast is the mean value of the variable(s) being forecast. Any forecast has a probability distribution surrounding it. A wide distribution (high std. Error) implies not a very good model, or a lot of uncertainty exists about the outcome. Variables that are random walks are forecast with simulations wherein the starting value plays no role. With mean reversion, real estate forecasts obviously depend on where the market currently is. Historic volatility not enough.

35 What is Risk: Historic Variability vs. Forecast Uncertainty Historic Variability NOI Forecast TIME Uncertainty

36 San Diego Office Income and Value Confidence Bands [+2 to -4] (against a loan) $ (Thous) $ (Mils) NOI BaseLine Debt Service V alue BaseLine Balance

37 Atlanta Office Equity Risk Metrics Yield = 7.1%, expected IRR = 7.3% (base case) Std Deviation in IRR = 5.0 Standard Avera ge Errors NOI Ave rage Away from Growth Appre ciation IRR Base Case % -20.9% -15.1% % -15.1% -8.7% % -9.7% -3.0% % -4.8% 2.3% 0 1.6% -0.2% 7.3% 1 5.2% 4.2% 12.0% 2 8.6% 8.4% 16.6% % 12.4% 21.0% % 15.4% 24.4%

38 Debt Risk Metrics PD: Conditional (to getting there) Probability of Default. Area in the NOI probability distribution that represents outcomes< debt service. Loss at each outcome = Debt service - NOI Expected Loss: probability of outcome x outcomes loss at that outcome Severity (Loss Given Default, LGD) = EL/PD Value-at-Risk: Loss (e.g. Loan Balance value) associated with a particular range of outcomes in the probability distribution (e.g. 95% confidence = 5% worst outcomes).

39 Debt Risk Metrics (continued) What about time? There are 10 years in which loan can default. D t : Unconditional likelihood of Default at time t. The likelihood that the loan defaults and that the default occurs in year t. D t = S t-1 x PD t. S t = S t-1 x (1- PD t ), S 0 = 1. (recursive equations) Hazard function: a competing risk over time. Lifetime Default = D t

40 PD = area to left of orange line LGD = green sloping downward line Expected Loss = integral of PD x LGD 100% 75% Probability (%) 50% 25% 0% Probability Point (standard deviations)