MIT OpenCourseWare http://ocw.mit.edu 11.433J / 15.021J Real Estate Economics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MIT Center for Real Estate 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” MIT Center for Real Estate 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? MIT Center for Real Estate 3.2 4 2.8 3 2.4 2 2.0 1 1.6 0 1.2 -1 0.8 -2 0.4 -3 0.0 New Jobs (L) Sources: BLS, BOC, TWR. Total Housing Starts (R) Total housing starts, millions of units 5 1960 1962 1964 1966 1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 Year-over-year change in total employment, millions Prefect Historic correlation between economic recessions and Housing Production – except for the last 5 years MIT Center for Real Estate National Office Market: Completions Rate, Real Rent, Job Growth $ Per Sqft Forecast 34.00 8.00% 32.00 6.00% 30.00 28.00 4.00% 26.00 2.00% 24.00 0.00% 22.00 Total Employment Growth (L) Real Rent (R) Completion Rate (L) 2007 2005 2003 2001 1999 1997 1995 1993 1991 1989 1987 1985 1983 1981 1979 1977 1975 1973 20.00 1971 -2.00% MIT Center for Real Estate National Hotel Market (full service): Supply Growth Rate, Real ADR, Job Growth 8.00% Forecast 110.00 Total Employment Growth (L) Real ADR (R) Supply Growth Rate (L) 2007 2006 2005 2004 2003 2002 2001 2000 1999 80.00 1998 -4.00% 1997 85.00 1996 -2.00% 1995 90.00 1994 0.00% 1993 95.00 1992 2.00% 1991 100.00 1990 4.00% 1989 105.00 1988 6.00% MIT Center for Real Estate Dynamic 4-Q Model (t=time Period) 1). Office Demandt = α1EtRt-β1 Et= office employment Rt = rent per square foot β1 = rental elasticity of demand: [%change in sqft per worker/% change in rent] 2). Demandt = Stockt = St [Market clearing] 3). Hence: Rt = (St/ α1Et)–1/β1 MIT Center for Real Estate 4). Office Construction rate: Ct-n/St = α2Ptβ2 Pt = Asset Price per square foot β2 = 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.] MIT Center for Real Estate 5). Replacement version: E= fixed St/St-1= 1- δ + Ct-n/St-1 6). Steady Demand growth version: Et = [1+ δ] Et-1 St/St-1= 1 + Ct-n/St-1 [δ can represent the sum of employment growth and replacement demand] MIT Center for Real Estate 7). Myopic (backward) behavior: Pt = Rt-n / i i = interest rate (discount rate) [Extrapolate the future from the current/past] 8). Forward looking behavior (the efficient market theory): Pt = ∑Rt’/(1+i)t’-t t’=t+1,∞ or: Pt+1 – Pt = i Pt - Rt (if R is changing) MIT Center for Real Estate 9). Market steady state solution: all variables are constant over time or are changing at the same rate as Et grows. St/St-1= 1+ δ δ = Ct-n/St-1 , Pt = (δ/α2)1/β2, Rt = iPt+1 = iPt with either pricing model 10). What happens if Et increases “Randomly” for one period – and then resumes its long term growth rate? Or interest rates decline? 11). Much depends on the pricing model. MIT Center for Real Estate Valuing Property: Efficient Asset Pricing Principles • Use future rent and income forecasts that are based upon the “model” (i.e. assume all market participants use the “model” to evaluate the change in E) • Future Residual values are DCF from the residual date forward • Since today’s value is DCF until residual date plus residual value, the hold period is irrelevant: today’s value is the in-perpetuity DCF. • Result: Price Volatility low and less than income volatility since income volatility is only temporary (with mean reversion) MIT Center for Real Estate Valuing Property: The traditional way (Myopic). • Extrapolate current, past or “average” rent/income growth (what’s wrong with ARGUS?) • Residual value is capped Future NOI with cap at 50bps over initial period. • Result: Price Volatility High and greater than income volatility. MIT Center for Real Estate Implication: when are Cap rates lowest? • FINANCE 101: Cap rate = i-g+r i = risk free rate + capital expenditures g = expected future value/income growth r = real estate risk premium • Efficient prices are lowest when the market is most down. With mean reversion, that’s when expected rent/income growth is highest! • With traditional or extrapolative pricing, cap rates are lowest when the market is strongest (continued rent/income growth) and highest when the market is down (continued decline). MIT Center for Real Estate 180 9.50 9.00 8.50 8.00 7.50 7.00 6.50 6.00 5.50 160 140 120 100 80 78 80 82 Cap Rate 84 86 88 90 92 Capital Value Index (R) 94 96 98 NOI Index (R) Index, 1977:4 = 100 Cap Rate (%) 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). MIT Center for Real Estate The “Shiller Test” • If market pricing is “rational” cap rates should correlate negatively (if imperfectly) with actual future (subsequent) growth. Efficient markets can at least partially anticipate the future. • Why weren’t cap rate spreads higher in the late 1980s anticipating the tanking of the market, and lower in the early 1990s – anticipating the market recovery? • The implied growth in today’s cap rates: g (3.5%) = i (5.0%) + Capex (2.0%) + r (3.0%) – Cap (6.5%) MIT Center for Real Estate Pricing seems always based on expected growth that just matches inflation - not actual subsequent appreciation (good for 100 years, but not 10!) Percent 20 1991: 5.7%=7.8%+5.0%-7.1% 2004: 2.0%=4.5%+5.0%-7.5% 15 10 5 0 -5 TWR Forecast -10 implied future growth US Office Investment data. 3-Year Forward Appreciation CPI inflation 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996 1995 1994 1993 1992 1991 1990 1989 -15 MIT Center for Real Estate Hence across the EU, 2000 cap rates did not reflect subsequent (2001-2005) growth in Fundamentals European Cities, Average Annual Office Rent Growth % 2000q4 - 2005q4 8 Brussels 6 Degree of Under Pricing 4 2 0 -2 -4 -6 Paris -8 4.5 5.5 6.5 7.5 8.5 2000 q4 Prime Yield Source: Torto Wheaton Research 9.5 10.5 11.5 MIT Center for Real Estate Impulse response to demand shock (increase in E) with “stable” market parameters. Holds for efficient pricing and may hold for extrapolative pricing: Intrinsic “mean reversion” Market reaction to a 50% demand shock (lag: n = 5; depreciationgrowth: δ = 0.05: demand elasticity = 1.0; supply elasticity = 1.0). 600 Price Stock/Employment 800 500 600 400 300 400 200 200 100 0 0 10 20 30 40 50 60 70 Period from shock 80 90 100 0 0 10 20 30 40 50 60 70 Period from shock 80 90 100 Figure by MIT OpenCourseWare. MIT Center for Real Estate Impulse response to demand “shock” with “unstable” market parameters. Holds only for extrapolative pricing under certain situations: “mean over-reversion”. Market reaction to a 50% demand shock (lag: n = 8; depreciationgrowth: δ = 0.05: demand elasticity = 0.4; supply elasticity = 2.0). 600 Stock/Employment 1200 500 900 400 600 300 200 300 100 0 Price 0 10 20 30 40 50 60 70 Period from shock 80 90 100 0 0 10 20 30 40 50 60 70 Period from shock 80 90 100 Figure by MIT OpenCourseWare. MIT Center for Real Estate What makes the model unstable? • More elastic supply (β2). and less elastic demand (β1). • A high rate of demand growth or rapid obsolescence of properties (δ) • Long Delivery lags (n), “slow adjustment”, delayed responses (regulation?) • 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]. MIT Center for Real Estate Historic Office Rent Volatility by Market: “Barriers to Entry” = more volatility! (Barriers = lower supply elasticity or longer lags?) 140 120 100 ATL ANT B O S TO N P HO E NI S F R ANC 80 60 40 20 2014 2012 2010 2008 2006 2004 2002 2000 1998 1996 1994 1992 1990 1988 1986 1984 1982 1980 0 MIT Center for Real Estate Historic Real Estate Price volatility: 1978-1998 By Property Type (Source: NCREIF) 205 185 165 145 125 105 85 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 R&D Office Retail Warehouse MIT Center for Real Estate What if market participants “delay”? “Slow adjustment” increases instability • 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. Lease contracts make the leasing decision like an “investment” – there are option values to both parties to waiting [Grenadier]. Waiting pushes the supply response further into the future • Example: the “Rental Adjustment” process. Rt-Rt-1 = λ0 - λ1Vt (Rosen, 1980s). λ0 / λ1 = “structural vacancy rate” Rt-Rt-1 = λ0 - λ1Vt - λ2Rt-1 (Wheaton, 1990s). R* = (λ0 - λ1Vt )/ λ2 “rent at which landlords indifferent to leasing versus waiting” (R constant) MIT Center for Real Estate “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 delay to development since exercise price is higher. MIT Center for Real Estate 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 the option value is less than without lags (develop sooner). – The option 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 immediately realize the good times value! • However, for a given level of uncertainty the hurdle value is higher with lags than in a model with no construction lag (develop later). – Intuitively, the further into the future the realization of your investment return, the smaller its present value. Therefore, you optimally wait until the Price is higher (all else equal) in order to commence development when there are lags between exercise and realization of Price as opposed to instantaneous realization of Price upon exercise. MIT Center for Real Estate 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! (Schwartz and Torous) • 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 MIT Center for Real Estate Models be estimated empirically using real estate data together with Economic data • Option #1 and #2: reduced form forecast – just evaluate and forecast rents with a model that has either a trend or Economic Demand variables. • Option #3: forecast rents and new supply together. Assume market clearing. Base forecast conditional on Economic variables. • Option #4: add in vacancy and assume that markets clear slowly = more variables and more equations. Better forecasts? MIT Center for Real Estate Model #1: Unconditional Univariate (quarterly Boston data, 1979:1 - 2002:4) R = 3.23 + .92R-1 - . 01T • • • • (2.5) (22.1) (.6) R2 = .933 No trend in real office rents (.09 is not significant). Rents depend an awful lot on last periods rents (.92)! R* = (3.23-.01T)/ (1-.92) = $(40-.12T) (long term steady state rents in real dollars) How does this equation “work” when there is a lagged dependent variable on the right hand side? MIT Center for Real Estate Model #1: Implied Rental Adjustment R = 3.23 + .92R-1 - .01T, is the same as: R - R-1 = .08 [ (3.23 - .01T)/.08 - R-1 ] = .08 [ R* - R-1 ] • Rents adjust slowly (8% quarterly or about 28% annually) to gap between: Steady state rent ($40-.12T) – current rent • More rent lags = more zigs and zags in the adjustment process, but around what? • Nice and clean, but what have we learned? Trend! • How accurate from 2002:4 through 2005:4 (Red)? MIT Center for Real Estate Model #2: Conditional Univariate (quarterly Boston data, 1979:1 - 2002:4) R = 13.2 + .94R-1 - .06 FIRE + .023 SER • • • • • • (4.1) (36.2) (3.6) (2.9) R2 = .942 Trend is replaced with office employment. Does that work? Rents still depend an awful lot on last periods rents! Why is it that growth in FIRE jobs creates negative rent growth? Could FIRE firms build their own space? Why does Service grow have positive impact? Who forecasts FIRE and SER (and how?) Assumption: supply responds quickly MIT Center for Real Estate Model #3: Conditional Multivariate: Rent and Supply (like 4 Q) • Suppose space Demand = 62,500 + 330FIRE + 155SER 500R-1 • Suppose Rent equates space demand to last period’s stock (market clearing – as in 4Q diagram, dynamic model). • Call that R* = 125+.66FIRE+.33SER - .002S-1 • But then Suppose Rents adjust gradually: • R-R-1 = .06 [(125+.66FIRE +.33SER - .0021S-1) -R-1 ] • Note that real rents still adjust slowly, but now to changes in employment or stock ( 6% quarterly or 22% annually). Also FIRE now has correct sign! MIT Center for Real Estate Model #3: Conditional Rent/Construction Multivariate (continued) • The estimated demand side or rent equation becomes: • R = 7.6 + .94R-1 + .04FIRE + .02SER - .00013S-1 (2.9) (17.1) (2.1) (3.2) (-3.9) R2 = .976 • Also need a supply side equation: • C = 449 + 39.7R-10 -.007S-1 (.9) (2.9) (-2.2) R2 = .41 • S = S-1 + C • System will forecast rents and construction and the stock of space – given FIRE and SER forecasts. Who forecasts FIRE and SER? That’s what is meant by conditional. MIT Center for Real Estate Model #3: Conditional Rent Multivariate • R-R-1 = .06 [(125+.66FIRE +.33SER - .0021S-1) -R-1 ] • For every 1000 FIRE jobs added to the economy, if we develop 307,000 more square feet then long term steady state real rents will be stable . • For every 1000 Business Service jobs added to the economy, if we develop 157,000 more square feet then long term steady state real rents will be stable. • Rents adjust to gap: Steady State - current rent • If rents are at $35 real, then 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. But the forecast is for each to grow about ½ of these! Hence new supply exceeds demand, rents stagnate (Green) MIT Center for Real Estate Model #4: Multivariate: Rent, Supply and Vacancy (slow response) • Suppose firms desired occupied stock is: OC* = 4109 + 283FIRE + 118SER - 76R-1 • But leasing constrains tenants so that only 10% can get to their desired stock in a period. Hence: OC - OC-1 = AB = .10 [(4109 -76R-1 + 283FIRE + 118SER) - OC-1 ] (30.6) (2.1) (-3.4) (2.6) (1.9) R2 = .99 • V = 1.0 – OC/S • Or rent determines vacancy. MIT Center for Real Estate Model #4: Multivariate with Vacancy • But Landlords also determine rents as a function of vacancy. Why (bird in hand = 2 in bush)? R = 6.5 +.81R-1 - .34V-1 (6.0) (20.1) (-6.9) R2 = .958 So in theory, with the pair of equations, there is a rent where vacancy is fixed (stable). And for supply: • S = S-1 + C; C = 1339 + 32.4R-10 -.006S-1 – 75.6V-18 (.9) (2.5) (-2.0) (-3.4) R2 = .54 Now the system is complete with both vacancy and rent also determining new supply. MIT Center for Real Estate Model #4 (continued) • Behavioral implications of slow adjustment: • Each 1000 FIRE workers needs 283,000 square feet and each Business Service worker 118,000. Adding this much square feet per new worker would also keeps vacancy (occupied square feet) constant in the long run. • To get to these “targets”, occupied square feet responds slowly – 10% quarterly or 35% yearly (leases). • At current rents of $30 and vacancy of 16%, construction will add only 50,000 square feet quarterly (.2 m annually) • And at 16% vacancy rents will fall below $30. • This is far less than job forecast demand is! • Hence market goes down and eventually recovers (blue). MIT Center for Real Estate Boston Office Market. Red: Univariate(#2); Green: Rentonly(#3); Blue: Rent & Vacancy(#4). Forecast from 2002:4 Actual and fitted values of real rents 60 RRENT FOREVVAR FORESVAR FORE FITTED 55 50 2007:4 45 40 35 30 25 20 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 MIT Center for Real Estate Boston Office Market: Rent only forecast(#3): green; Rent & vacancy(#4): blue. Forecast from 2002:4 Multi tenant Completions 3000 CC FOREVPER FORESPER 2500 2000 2007:4 1500 1000 500 0 -500 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 MIT Center for Real Estate Boston Office Market: Full model (#4). Forecast from 2002:4 Office Absorption 3000 FOREAB Vacancy 20 VAC FOREVAC 2000 15 % 1000 10 0 -1000 5 2007:4 -2000 0 -3000 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 1970 1974 1978 1982 1986 1990 1994 1998 2002 2006 2010 MIT Center for Real Estate Additional criteria for evaluating models: “back testing” This is a forecast for Boston house prices using a Univariate model (#2). Why does this model work well here – but not for office? Boston Boston 2006:4 2006:4 1998:4 983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 2011 2013 Forecast from 2006 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Forecast from 1998 MIT Center for Real Estate Forecasting Lessons • When supply adjusts quickly to prices or rents, then little is to be gained from a model that jointly forecasts the two – Just use a Univariate model (#2) (Single Family Housing ) • The slower supply responds and the more gradual prices and rents adjust, then the more you need to forecast both sides of the market (#3 or #4) to capture its momentum and cyclic swings. (Apartments, Office. Hotels, Retail) MIT Center for Real Estate Distribution of Forecast Outcomes • A “forecast” is the mean value of the variable(s) being forecast. Any forecast has a probability distribution surrounding it. • The further out you go the wider is the forecast probability distribution of possible outcomes. Why? • 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 to estimate “risk”. MIT Center for Real Estate What is Risk: Historic Variability vs. Forecast Uncertainty (Notice true risk grows over time) Historic NOI Variability Forecast Uncertainty TIME MIT Center for Real Estate Forecasts give “standard errors” which can be used to generate confidence bands or the probability distribution of future income Collateral Income $250,000 $200,000 $150,000 $100,000 $50,000 $0 0 1 2 3 4 5 Years 6 7 8 9 10 MIT Center for Real Estate What determines confidence band width? • A market with wide historic swings will tend to generate wider confidence bands in the future – unless you can “explain” these swings accurately. • A “poor” model (low fit) means you do not understand the forces affecting the market. What you don’t know = risk. • Low quality data, missing observations, a short historic data series, no variables that capture what really drives the market = a “poor” model. MIT Center for Real Estate Atlanta Office Risk Calculated along probability “paths” Yield = 7.1%, expected IRR = 7.3% (base case) Std Deviation of IRR = 5.0 Standard Errors Away from Base Case Average NOI Growth 2002-2007 Average Appreciation 2002-2007 IRR 2002-2007 -4 -3 -2 -1 0 1 2 3 4 -16.6% -11.3% -6.6% -2.3% 1.6% 5.2% 8.6% 11.9% 14.0% -20.9% -15.1% -9.7% -4.8% -0.2% 4.2% 8.4% 12.4% 15.4% -15.1% -8.7% -3.0% 2.3% 7.3% 12.0% 16.6% 21.0% 24.4% MIT Center for Real Estate Is “forward risk” reflected in pricing? Industrial markets: 2005-2012 y = -0.6016x + 10.134 R 2 = 0.0331 Ra w Re g re ssio n 18 16 Expected Return 14 12 10 8 6 4 0.0 0.5 1.0 1.5 2.0 Ris k 2.5 3.0 3.5 MIT Center for Real Estate Confidence Bands can be compared to the Loan Obligations of a Commercial Mortgage Collateral Income $250,000 $200,000 $150,000 $100,000 $50,000 $0 0 1 2 3 4 5 6 7 8 9 Years +/- 2 Standard Deviations +/- 1 Standard Deviation Baseline Income Debt Service 10 MIT Center for Real Estate The probability of Default is then the probability that your forecast predicts insufficient NOI to cover Debt service! Debt Service Delinquent Probability Full Payment Probability Shortfall: Loss Given Default -2 SD -1 SD Base +1 SD NOI Probability Distribution +2 SD MIT Center for Real Estate 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 point in the probability distribution (e.g. 95% confidence = 5% worst outcome). MIT Center for Real Estate Debt Risk Metrics (continued) • What about time? There are 10 years in which loan can default. • Dt: Unconditional likelihood of Default at time t. The likelihood that the loan defaults and that the default occurs in year t. • Dt = St-1 x PDt . • St = St-1 x (1- PDt), S0 = 1. (recursive equations) • “Hazard” function: a competing risk over time. • Lifetime Default = ∑ Dt • The Basel Agreement is coming! MIT Center for Real Estate Forecast Risk Metrics: The next wave of Risk Management (and Basel Compliance) Risk measures over 3-year term Future default frequency Loss given default Expected loss Unexpected loss at 95% Rating Yeld degradation 0.98% $ 100,295 $ 983 $0 2 10 Risk measures by year Year Default frequency 1 0.86% $ 98,934 $ 851 $0 2 3 4 5 6 7 8 9 10 0.77% 1.29% 1.43% 1.24% 0.94% 0.44% 0.35% 0.32% 0.20% $ 97,794 $ 102,695 $ 120,935 $ 149,784 $ 138,057 $ 112,738 $ 104,450 $ 89,791 $ 85,301 $ 753 $ 1,325 $ 1,729 $ 1,857 $ 1,298 $ 496 $ 366 $ 287 $ 171 $0 $0 $0 $ 92,547 $ 93,931 $ 94,043 $ 94,145 $ 94,239 $ 94,327 Loss given default Expected loss Unexpected loss at 95% Figure by MIT OpenCourseWare. MIT Center for Real Estate Application: Future Annual Default and loss expected to be small Compared to history (and current CMBX)! Default Rates (60+ Days) 8% History and TWR Forecast Loss Rates (Charge-off) 2.00% 7% 1.75% 6% 1.50% CMBX Implied 5% 1.25% 1.00% 3% 0.75% 2% 0.50% 1% 0.25% 0% 0.00% 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 4% Com m ercial Banks' Charge-off/Loss Rate (R) 2007 Vintage (R) CMBS Universe (R) ACLI Default Rate (L) CMBS Default Rate (L) Sources: ACLI, FDIC, Trepp , Moody’s, CBRE Torto Wheaton Research