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Real Estate and Risk: Time to Rethink What You Thought You Knew
PresenterRichard B. GoldMarch 16, 2017
“Just because we can doesn’t mean we should”
Dr. Ian Malcolm (Jeff Goldblum) Jurassic Park
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What/Who Is Northfield? A Speaker’s Self-Serving Introduction
2
Page 35
“I turned to a man named Dan diBartolomeo. Dan is the founder of Northfield, a collection of math whizzes who provide sophisticated analytical and statistical risk management tools to portfolio managers.
Dan is an eccentric, bow-tie-wearing East Coast surfer with a photographic memory that revels in math.”
UNFORTURNATELY FOR YOU, I AM NOT DAN
diBARTOLOMEO!
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Statistics Less Than Glorious Past
A regulatory innovation in 16th century Italy
The “Problem of the Points”
Geralamo Cardano to the rescue
• Typhoid
• Other less advertised “cures”
The “Book on Games of Chance”
• Published 1663
• First modern treatment of probability theory
• Also contained extensive sections on how to cheat at cards
Slide 3
“Uncertainty is a salient feature of
security investment. Economic forces
are not known well enough for
predictions to be beyond doubt.”
Harry M. Markowitz
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Correlation Is Not Causality
“Even trained statisticians often fail to appreciate the extent to which statistics are vitiated by the unrecorded assumptions of their interpreters... It is easy to prove that the wearing of tall hats and the carrying of umbrellas enlarges the chest, prolongs life and confers comparative immunity from disease. A university degree, a daily bath, the owning of thirty pairs of trousers, a knowledge of Wagner's music, a pew in church, anything, in short, that implies more means and better nurture... can be statistically palmed off as a magic spell conferring all sorts of privileges...
The mathematician whose correlations would fill a Newton with admiration, may, in collecting and accepting data and drawing conclusions from them fall into quite crude errors by just such popular oversights as I have been describing.”
George Bernard Shaw, The Doctor's Dilemma
Slide 4
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Parameter Estimation Error
Testing on In-Sample Data• How to always be right• What In-Sample tests can do
Meaning of T-Stats• Spurious Correlation
Validity of parametric statistics• Mean-Variance utility functions• The not-so-efficient frontier
Bayesian statistical adjustments• “To thine own self be true”
• Bootstrap re-sampling: Monte Carlo or Las Vegas?
“In war, you have the known unknowns and the unknown unknowns”
US Defense Secretary Donald Rumsfeld
Slide 5
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What is Risk?Statisticians believe that risk is the uncertainty of return:
• Imagine you accept a gift of a lottery ticket with the condition that you cannot give away or sell the ticket.
According to statisticians, you just did something very risky:
• The uncertainty of the economic outcome of a lottery drawing is very high, even though you had nothing to lose.
You jump off the Empire State Building:
• In this case the “potential for loss” is total: your life
• However, the uncertainty of the outcome is very low.
DO NOT CONFUSE THE OUTCOME ITSELF WITH THE PROBABILITY OF IT ACTUALLY HAPPENING
RISK IS A SECOND, NOT FIRST, MOMENT PROBLEM
• Most real estate analysis is first moment
• What will be my return?
• Even VAR is not an appropriate metric of risk
• Short-term: Appropriate for banks not RE
• Incoherent answers possible
• Benchmark versus Absolute Returns
• Central limit theorem
• Diversified portfolio normally distributed
6
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So Why Should You Care?
• Going forward assume that virtually every thing you have learned about real estate risk has been “wrong“ or not obtainable
• Investors do not buy markets they buy assets
• What does a Toronto office building look like?
• How many does it take to buy the market, what tenants & credit ratings, duration of leases, gearing or no gearing and how much, capital needs?
• Distance is not diversification
• Diversification possible in a single market except for idiosyncratic risk
• Real estate cycles do they matter? – real estate is illiquid and lumpy
• Appraisals are not robust metrics for return or risk
• Auctions generally suboptimal
• We can always adjust rent growth or cap rates
• You cannot “fine turn” a real estate portfolio
• Incremental not marginal change
• Buildings - composite assets with bond & equity components
Slide 7
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Current Risk Measures: Insufficient
• Current indices (NCREIF, IPD, etc.) do not use observable prices:
• Appraisal-driven & therefore appraisal-biased
• Suffer from serial correlation
• Smoothed and dampened
• BACKWARD LOOKING
• You do not drive a car looking in the rearview mirror.
• “Willing” buyer and “willing” seller mythology
• Sample size issues
• Tells nothing about individual asset risk
• Current indices:
• Good for:
• Long-term trends
• Absolute Returns
• Not good for:
• Short-term analysis
• Uncertainty of returns
• Components of risk and their contribution at the property or portfolio levels
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Why Indices Just Don’t Work
• Main benefit: Simple aggregate view of the world
• Main problem: Simple aggregate view of the world
– Users are constrained by the Index’s characteristics• Levered? If so how much? Building size & quality, etc.
• How many properties does it take to represent a market?
– Appraisal not transaction-based• Bottom line appraisal-based return series overstate absolute returns and
underestimate volatility and cross asset class correlations. Leads to artificially inflated allocations and unreliable and biased factor exposures.
– Covariance matrix unstable• A pair-wise correlation confidence level of two de-smoothed
models each with a confidence level of 90% is 81% when combined (.9 X .9) and decays rapidly after that.
• At the security level, the estimation errors diversify and become negligible at the portfolio level.
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Public Versus Private Property Returns
10
-50%
-40%
-30%
-20%
-10%
00%
10%
20%
30%
40%
78:1 81:3 85:1 88:3 92:1 95:3 99:1 02:3 06:1 09:3 13:1 16:3
NCREIF vs. NAREIT Quarterly Returns(1978:1 – 2016:4)
NCREIF NAREIT
Appraisal Smoothing or Are REITs Real Estate or Both?
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By economic intuition as well as mathematically, real estate and bonds returns are not independent.
1. They are driven by the same factors (interest rates, economy), co-varied movements in a one period setting can only be captured using techniques such as factor risk models
2. However, this does not mean that a linear relationship of appraisal-based real estate and bond returns is the one that holds over multiple periods; hence using regression/correlation rather than the changes in appraised values vs. changes in interest rates or the stock market should be done with great caution.
Bottom line: real estate can’t have it both ways:1. Either it has bond-like and equity-like characteristics
2. Or the math of cap rates and cash flows is wrong
3. We choose the former
Volatility of less risky asset cannot be greater than riskier asset in the long-run1. Value = NOI / Cap Rate
2. Cap Rate = Risk-Free Rate + Spread
3. Ergo Change in Risk-Free Leads to ?????
Another View of Appraisal Smoothing
Slide 11
2012-2016 QUARTERLY STANDARD DEVIATION –
TOTAL RETURNS
1.58% BARCLAYS AGGREGATE BOND INDEX
0.46% NCREIF UNADJUSTED
1.55%
NCREIF ADJUSTED FOR SERIAL
CORRELATION
.1 CORRELATION: NCREIF & BARCLAYS
Observed Variance = True Variance * [(1- ρ)/(1+ ρ)]
NCREIF Std Dev only 8 bps more than 10 Year Treasuries between 2012-2016
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Examples of Previous Correlation Findings
• Real estate’s purported low/negative correlation of real estate with other asset classes has been the impetus for adding property to investment portfolios
• A publication by Merrill Lynch in 2012 indicated that using quarterly returns, the correlation between direct real estate was -.14 with the Barclays Agg Bond Index and .19 with the S&P between 2002 and 2011.
• Same conclusions by Clarion Partners in 2011 and Pepperdine University in 2009.
• The Pension Real Estate Association’s own study using annual data:
Slide 12
-0,4 -0,3 -0,2 -0,1 0 0,1 0,2
Large Cap
Mid Cap
Small Cap
Treasuries
Investment Grade
High Yield
NCREIF Annual Correlations: 1978 - 2014Source: PREA
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Appraisal Bias Remains an Issue
13
,00 ,10 ,20 ,30 ,40 ,50 ,60 ,70 ,80 ,90
T-1
T-2
T-3
T-4
Return Persistence - Lagged NCREIF Correlations
1979-2016 2007-2016
2012-2016 Rho Values T-1NCREIF = .75BARCLAYS = .02
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If It’s too Good to Be True…..
• Taken at face value indices such as NCREIF and IPD seem to suggest that real estate is a good diversifier
• Low or negative correlation with other asset classes
• Low volatility and high absolute returns relative to equities and bonds
• Appraisal smoothing impacts risk and return metrics
• Correlations between real estate and bonds estimated in previous studies are counterintuitive.
• Real estate should be positively correlated with treasury securities due to their inverse relationship with interest rates. Also improving credit spreads diminish the discount rates on both property cash flows and bond coupons making higher positive correlation between real estate and corporate bonds the most plausible outcome.
• Equity returns should also be positively correlated with real estate
• Improving economy leads to better cash flows and lower risk
Slide 14
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Portfolio Risk
• Typical institutional investor: multiple asset types
– Stocks, bonds, private, public, etc.
– Some liquid, some illiquid
• Many countries, regions, market, submarkets
• However, factor models are designed specifically for this task
– Any asset class is exposed to various economic factors plus exchange rates
– A subset of factor exposures relevant each asset
– Plus… idiosyncratic / asset-specific risk
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One Solution - Factor Models
• Factor models
– Relate the returns of each asset to a set of underlying economic drivers
– Once factor sensitivities are determined it is possible to infer cross-asset relationships
• Law of One Price: Changes in Prices of Similar Things Must Move Similarly
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Factor Models
• Possible to estimate correlations for a large number of assets from a small number of common economic drivers
• Each asset’s risks expressed as a series of exposures to a set of common drivers plus idiosyncratic/asset-specific risk
• No need for appraisals to determine volatility/risk as well as future cash flow (CF) and Net Operating Income (NOI)
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Northfield’s Factor Model
• Factors include:– Six economic sectors
• Consumer• Technology & Health• Interest Rate Sensitive• Industrial• Energy• Non-Energy Minerals
– Five geographic regions – global coverage• Also shapes future economic and real estate demand
– Investor outlook/sentiment factors:• Relative returns of large cap to small cap stocks• Relative returns of developed to emerging country stocks• Relative returns of “value” stocks (high dividend) with “growth”
stocks (no-dividend)– 57 Currencies
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Northfield’s Factor Model (cont)
• Changes in oil prices
• Changes in bond market index returns
• Changes measures of the interest rate yield curve:
– “Shift” the average level of interest rates
– “Twist” the spread between long-term and short-term rates
– “Butterfly” the curvature of the yield curve
• EE incorporates a very detailed binomial model of the range of possible future interest rate conditions. This is important for working out possible mortgage pre-payment scenarios
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Northfields’ Factor Model
• Credit Risk
– EE tracks credit related yield spreads for each economic and each rating agency level
– Credit risk equivalent to a partial exposure to the firm’s equity
– Credit spread has an implied default rate
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Northfield’s Property Risk Approach
• A “bottom-up” property-by-property model
• Each property is treated as a composite asset with:
– Risks based on “steady-state” Cash Flow (CF) assumptions for existing and expected leases
– Risks related to mortgage financing (if property is levered)
– Risks of future fluctuations in rents
• Each component has risk exposures to the EE common factors plus idiosyncratic risks
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Real Estate Model Structure
22
MORTGAGEFINANCING
(SHORT)
STEADY STATE
CASH FLOW(LONG)
RENTVOLATILITY
TIME VALUE OF
MONEY
CREDITRISK/LEAS
E ROLLOVER
% CHANGE
RENT
EE MODEL
PROPERTY/ PORTFOLIORISK
EE
FACTORSEE
FACTORS
EE
FACTORS
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Steady State Cash Flow
23
Integrating real estate investment positions into a factor model starts with modeling risk from cash flows without considering rent volatility (Steady State Cash Flow)
A convenient framework:
• Consider lease units within properties to be long credit bonds bringing in rent cash flows or Property Asset Securities
• Each tenant determines aggregate quality of the cash flow
• Represent mortgage financing as short bonds generating outgoing cash flows - interest and principal repayments or Financing Securities
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Steady State Cash Flow
24
• Assume property life – 50 years • Named lead tenants and then all others collectively
� For current lease period, consider operating expenses and expected losses from defaults given the credit of the tenant
� Generic tenants have credit rating of market• Forecast volatility in steady-state cash flow growth:
� CF adjusted for probability of lease renewal. Non-renewed leases are assumed to be taken over by a “generic” tenant
� CF adjusted for potential tenant default� Expected downtime between leases incorporated into CFs for non-
renewals� Adjust least default rates losses for the probability of generic tenant in
second and subsequent leases
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Steady State Cash Flow
25
Property Asset Securities - Cash Flows
• Cash flows are based on projected NOI (Net Operating Income) which changes with projected inflation
• NOI estimation should take into consideration changing projected vacancy (normally vacant space is more expensive to landlord)
• Vacancy is projected to move from current to a long term equilibrium structural vacancy
• Renewal rate of existing tenants is inversely related to vacancy
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Steady State Cash Flow
Repeat yearly for the useful life of the building to form expected CF stream
– Different discount rates apply to each year’s CF according to the current or assumed yield curve
– All CF streams exposed to the three factors that describe changes in yield curve conditions (time value of money)
– Each CF stream’s idiosyncratic risk is a function of its location, property condition, and vacancy time between leases
Idiosyncratic risks diversify.
– A complex of 200 apartments may have less property-specific risk than an office building with three investment grade tenants even though the individual office tenants have much better credit
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Steady-State Cash Flow Inputs
27
Inputs for Forecasting Steady-State Cash Flows:
• Tenant quality
• Credit ratings of lead tenants and “generic” tenants
• Current rent (tenant-level)• Lease resets – how often is are rental rates adjusted within a
lease term• Critical in determining how bond or equity-like is a building is
• Operating expenses as % of rents
• Current occupancy / vacancy
• Structural vacancy & reversion
• Probability of lease renewal
• Down-time between leases
• Useful life of building
All Inputs Taken Directly From Argus/Similar Source
OrGeneric Assumptions Are
Made
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Rent and Occupancy Volatility
• Demand volatility function local employment profile;– In London, Tokyo and NY, financial businesses have an above
average share of local employment. • Popping of financial bubbles hits office demand hard
– Houston is dominated by the energy industry and employment in that sector impacts office demand - unlike Boston which has virtually no employment in the energy sector
– All the risk exposures related to rent/occupancy risks are scaled to reflect the nature of a property
• A property that has a triple net lease for 100 years will have zero exposure, while an apartment complex with short-term leases would have its exposures scaled accordingly. This scalar is roughly the annual percentage of lease turnover
– The frequency at which a building’s leases are exposed to the market, the more equity-like it is.
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Metro Employment Profiles Differ
29
EMPLOYMENT SHARES BY SECTOR AND REGION - 2011Q1
Sector U.S. San Jose D.C.
Interest Sensitive 23.5% 14.6% 29.0%
Technology 15.9% 28.7% 10.9%
Energy 0.6% 0.0% 0.0%
Non-Energy Minerals 1.8% 1.3% 0.2%
Industrial 9.3% 7.0% 6.6%
Consumer 48.9% 48.4% 53.3%
Different Employment Profiles Generate Different Weightings & Exposures to EE Factors
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Components of Property-Level Risk
30
Rent Risk
Interest Rate Risk
Credit Risk
Specific Risk
TOTAL RISK
Risk is not additive unless using variance.
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Components of Portfolio Risk
31
Rent RiskInterest
Rate Risk
Credit Risk
TOTAL RISK
Risk is not additive unless using variance.
Idiosyncratic Risk Still Present ButLargely Diversified Away as
Portfolio Size Increases
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Model Results
32
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Model Results – Portfolio Profile
Portfolio:
• “Core” portfolio
• Conservative leverage (<15%)
• 14 properties
• Apartment, industrial, office, and retail
• 10 metro areas
• Boston, New York, Washington, D.C., Miami, Seattle, Sacramento, San Jose, Inland Empire, San Diego, Phoenix
33
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Model Results – Portfolio Profile
34
PORTFOLIO PROFILE
Metro Apartment Office Industrial Retail
Boston 1
DC 2
Inland Empire 1
Miami 1 1
New York 1 1 1
Phoenix 1
Sacramento 1
San Diego 1
Seattle 1
San Jose 1
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Model Results: Model Output
35
Portfolio Risk Report
Subject Portfolio
Factor PortExp BenchExp ActiveExp FactorVar VarContr
ENGLISH-SPEAKING COUNTRIES 0.1133 0 0.1133 339.108 5.7848
INDUSTRIAL SECTOR 0.0007 0 0.0007 446.687 0.0475
CONSUMER SECTOR 0.0045 0 0.0045 211.55 0.2336
TECHNOLOGY&HEALTH SECTOR 0.0007 0 0.0007 239.033 0.0375
INTEREST RATE SENSITIVE SECTR 0.0008 0 0.0008 357.689 0.0447
NON-ENERGY MINERALS 0.0085 0 0.0085 774.214 0.4068
ENERGY MINERAL SECTOR 0 0 0 450.202 0
S B WORLD GOVT BOND INDEX -0.0041 0 -0.0041 69.4732 -0.0168
OIL PRICES IN USD -0.0013 0 -0.0013 1106.85 0.0189
DEVELOPING MARKET 0.0402 0 0.0402 169.136 -0.584
SIZE -0.0249 0 -0.0249 55.0837 -0.5048
VALUE/GROWTH -0.1033 0 -0.1033 6.8313 -0.3732
TREASURY CURVE FACTOR1 -27.3504 0 -27.3504 0.3925 295.7643
TREASURY CURVE FACTOR2 -232.3808 0 -232.3808 0.0037 170.6205
TREASURY CURVE FACTOR3 -1754.4193 0 -1754.4193 0 -93.3204
Factor Tracking Variance 378.1592
Stock Specific Tracking Variance 0.4298
Total Tracking Variance 378.589
Tracking Error 19.4574
Total Risk of Portfolio 19.4574
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Model Results: Model Output
36
Individual Property Risk Report
Apartment Building - San Diego, CA
Factor PortExp BenchExp ActiveExp FactorVar VarContr
ENGLISH-SPEAKING COUNTRIES 0.1961 0 0.1961 339.108 14.686
INDUSTRIAL SECTOR 0.0012 0 0.0012 446.687 0.1011
CONSUMER SECTOR 0.0084 0 0.0084 211.55 0.5707
TECHNOLOGY&HEALTH SECTOR 0.0011 0 0.0011 239.033 0.072
INTEREST RATE SENSITIVE SECTR 0.0014 0 0.0014 357.689 0.1116
NON-ENERGY MINERALS 0.0001 0 0.0001 774.214 0.0053
ENERGY MINERAL SECTOR 0 0 0 450.202 0.0001
S B WORLD GOVT BOND INDEX -0.0117 0 -0.0117 69.4732 -0.0469
OIL PRICES IN USD -0.0027 0 -0.0027 1106.85 0.0342
DEVELOPING MARKET 0.0626 0 0.0626 169.136 0.7945
SIZE -0.0341 0 -0.0341 55.0837 -0.9026
VALUE/GROWTH -0.1605 0 -0.1605 6.8313 -0.8097
TREASURY CURVE FACTOR1 -17.1647 0 -17.1647 0.3925 116.1395
TREASURY CURVE FACTOR2 -319.564 0 -319.564 0.0037 244.5631
TREASURY CURVE FACTOR3 -2452.5646 0 -2452.5646 0 -102.3807
Factor Tracking Variance 272.9382
Stock Specific Tracking Variance 24.9445
Total Tracking Variance 297.8826
Tracking Error 17.2593
Total Risk of Portfolio 17.2593
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Model Results – Risk by Source
37
Interest Rate Risk
Rent RiskCredit Risk
Total Risk
16.1%
XX%
3.9%5.1%
17.3%
Risk Profile: Apartment Building – San Diego, CA
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Model Results – Incremental Risk
38
Average Incremental Contribution to Risk by Location(All Leverage Removed)
Incremental Risk by Metro Area
Metro Area Std Dev # Props Properties
San Diego 2.12 1 Apartment
Phoenix 2.14 1 Apartment
NYC 2.44 3 Apartment, Office, Retail
DC 2.55 2 Office
Miami 2.58 2 Industrial, Office
Sacramento 2.60 1 Retail
San Jose 2.65 1 Retail
Seattle 2.65 1 Industrial
Inland Empire 2.65 1 Industrial
Boston 2.85 1 Office
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Effects of Leverage
0
20
40
60
80
100
120
140
160
0,2 0,4 0,6 0,95 1,5
Sta
nd
ard
De
via
tio
n
NYC Office BuildingRisk (Std Dev) Per Percent Debt/Equity Ratio
Debt as a Percent of Asset/Portfolio Value
For every 1% increase in leverage between 60%-90%, risk increases by
As leverage exceeds 95%, negative equity quickly accumulates and predicted variance in values falls. Leading to a decline in the expected variability of net value.
39
Why President Trump Simultaneously Loves and Hates Real Estate
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Model Results – Incremental Risk
40
Industrial
Retail
Office
Apartment
2,61%
2,54%
2,35%
2,08%
Incremental Risk by Property TypePer Percent of Portfolio Share
(All Leverage Removed)
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Model Results: Portfolio Risk by Acquisition
41
Portfolio Acquisition Schedule and Impact on Risk (Standard Deviation)
Location Property Type
Individual
Property Total
Risk
Individual
Property
Specific Risk
Portfolio
Total Risk
Portfolio
Specific Risk
New York City Multifamily 13.1 16.9 13.1 16.9
Inland Empire Industrial 18.9 4.6 15.3 6.2
Seattle Industrial 18.9 4.5 16.2 3.5
Miami Office 18.3 1.8 17.0 1.6
Miami Industrial 19.0 9.8 17.1 1.4
New York City Office 32.1 10.8 19.3 1.3
New York City Retail 19.7 2.9 19.4 1.0
San Jose Retail 18.9 1.6 19.3 0.7
San Diego Multifamily 17.3 24.9 18.8 1.0
Boston Office 22.5 4.7 19.3 0.8
D.C. Office 18.5 3.1 19.1 0.6
Sacramento Retail 18.6 0.7 19.1 0.5
D.C. Office 30.3 3.7 19.8 0.5
Phoenix Multifamily 12.8 8.1 19.5 0.4
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0
2
4
6
8
10
12
14
16
18
1 2 3 4 5 6 7 8 9 10 11 12 13 14
16 6, 3, 1, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0,
Ris
k -
Std
De
v
Number of Properties &Standard Deviation
Incremental Idiosyncratic Risk
Trendline
Specific Risk
0
5
10
15
20
25
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Ris
k -
Std
De
v
Number of Properties
Systematic Does Not Diversity Away &Is Asset-Specific. However, Incremental
Impact Smaller as Portfolio Size Increases
Incremental Total Risk
Model Results: Incremental Risk
42
Idiosyncratic Risk Quickly Disappears Total Risk Can Still Increase as Portfolio Grows
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Risk by Asset Class
43
Expected One Year Annualized Risk as of 2011Q3Bond Index: Historic Barclay’s 30 Year Treasury Bellweather Bond IndexExpected NIS-Generated 30-Year Bond Index
0% 5% 10% 15% 20% 25% 30% 35%
Subject Portfolio
All NCREIF
ODCE NCREIF
NAREIT
Bond Index
S&P 500
Annualized Risk by Asset Class
Hist (06Q3 - 11Q2)
Hist Adjusted
Expected
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Summary
• Propose methodology:
– Puts real estate risk assessment on par with other asset classes
– Data requirements not burdensome
– Each property analyzed by cash flow, rent volatility, and financing
– Factor model relates behavior of each asset to a set of common economic drivers
– Infer relationships between investment assets
– Integrated and consistent risk measurement across asset classes now possible
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Summary: Lies, Damned Lies and Statistics
• Statistics like most things in life have a light side and a dark side
• Private equity real estate has ridden a wave of popularity in part based on mythology rather than fact
– If you paint a cantaloupe red, you will probably win the prize for the largest tomato:
• Properties sell near appraised value because investors assume that appraised values are correct not necessarily because they are
• Real estate risk cannot rationally be less than that of risk-free assets
• Forward, not backward looking, risk metrics valuable
– Forecasting is easy especially the past
– Property’s value and volatility determined by cash flow, rent volatility, and financing
– Factor model relates behavior of each asset to a set of common economic drivers
– Infer relationships between investment assets
– Integrated and consistent risk measurement across asset classes now possible
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Conclusions
46
• Factor model relates behavior of each asset to a set of common economic drivers
• Infer relationships between investment assets
• Integrated and consistent risk measurement across asset classes
• Results are consistent with expectations
• Real estate riskier than fixed income but less than equities
• Interest rate risk dominates –long-term cash flow stream: similar to bond behavior
• Credit risk represents significant percent of total risk: similar to real world experience during recent downturn
• Leverage risk a function of term, call option, coupon rate, fixed versus floating
• Results show higher expected risk than historic NCREIF or ODCE but:
• Adjusted NCREIF and ODCE risk much higher than published data suggest
Appendix I: Some Comments on VaR and IRR
Slide 47
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Value at Risk (VaR)
Slide 48
While Northfield’s models can be used to produce VaR estimates, Northfield is not an enthusiastic advocate of the VaR methodology. A few reasons:
1. There is no economic theory that Northfield knows that rationally links VAR to returns in terms of any sort of investor utility function.
2. Northfield could compute VAR numbers just for reporting, but that seems counterproductive, as it draws attention from Variance values that do have real economic meaning in terms of tradeoffs against returns and trading costs.
3. Equity portfolio problems normally have large numbers of assets involved. As such, the Central Limit Theorem of statistics guarantees that the portfolio returns will be normally distributed even if the return distributions of individual assets have distributions with high levels of skew or kurtosis. In any case where the portfolio returns are normally distributed, VAR is just a scalar multiple of the volatility. We just have to establish the frequency of event against which we are trying to protect. VaR values are appropriate phrased as:
There is a less than P% likelihood that we will lose more than Y dollars in this portfolio on this one day. The value of P isselected by the investor (say 5%) and then we can calculate Y as follows:
Y (VaR) = V * N(p) * S / (D^.5)
V is the portfolio value N is the number of standard deviations from the mean of a normal distribution (one tailed test) to have cumulative density equal to (1-p) S is the standard deviation of portfolio return (annual portfolio volatility) D is the number of trading days in a year
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Value at Risk (VaR) Con’t
Slide 49
4. However, most asset management firms are concerned about relative return compared to a benchmark, not absolute return, so it is unclear how much VaR helps anybody on the buyside.
5. VaR has been shown to not be a "coherent" measure of risk. This means that in certain cases, VaR actually produces irrational results. Here is a wonderful example of how it breaks. This is from a paper by Claudio Albanese from the University of Toronto:
Giving a VaR value can be expressed as "in (100 - X)% of cases your probable loss is less than Y$." So if I set X to 5, then I would be saying that it is our expectation that in 95% of cases your loss will be Y or less.
Now let’s imagine a $1,000,000 bond that pays 2% interest and has a 1% probability of default. Since the chance of default is just one percent, if we set X to 5, we are interested in what happens in 95% of cases. In 95% of cases the bond won't default so the bond will just pay you the interest of $20,000, so the VaR risk value is actually negative. There appears to be no risk at all at X = 5
Now imagine we diversify our risk by buying $1,000 each of 1,000 different bonds in different companies. Each bond still pays 2% interest and the default probability of 1%. However, if we compute the joint probabilities we will see that it is possible that in 5% of the cases, a significant number of the 1000 different bonds will default. In fact with default probability of 1% each, and 1000 different bonds, we would expect at least 10 different bonds to default and possibly more. As such, the VaR at the 5% level will be positive, and obviously much greater than the "no risk" answer we got for just one bond.
Obviously, in the real world it is much safer to loan money to 1000 different borrowers than it is to lend money to just one if everyone is of equal likelihood of default. In such a case VaR, gets precisely the wrong answer: a concentrated portfolio is not risky, and a well diversified portfolio is risky.
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Internal Rate of Return (IRR)
• IRR is the opposite of NPV where the NPV is the discounted value of a stream of cash flows generated by an investment
• IRR is the discount rate below which an investment’s NPV is positive
• All else being equal, a project with a higher IRR is preferred to a project with a lower IRR
• In reality IRRs are much more complex, suffer from a number of issues, and investors must answer a number of questions before they can choose the optimal investment given their risk tolerance
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IRR – The Basic Formula
The formula for IRR is as follows:
However, algebraically solving for IRR is not possible, it must be done iteratively (trial and error).
Where PV = Amount invested in year 0
PV =CF1
(1+ IRR)+CF2
(1+ IRR)2
+ ...+CFn
(1+ IRR)n
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IRR – Solving
To solve for IRR you set the NPV of an investment to zeroand use the following formula:
Where:
NPV = Net Present ValueCash Flow = Cash Flow in Period “n”r = IRR
NPV =Cn
(1+ r)n
n=0
N
∑ = 0
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IRR – Excel Example I
A simple example of abuilding held for 5 yearsand sold at the end of thefifth year. All the cash flowswere positive and there wereno major Cap Ex dollars putinto the project.
The resulting IRR is 7.44%and the Excel formula isstraightforward and in thiscase no “guess” was needed.
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IRR – Excel Example II
But what happens if you are not so lucky and you loose control of a project afterredeveloping it?
The IRR function does not work without a little help from the user in the form of a guess.
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IRR – Same Cash Flows But ….
DIFFERENT BORROWING AND INVESTMENT PATTERNSCAN PRODUCE MULTIPLE ANSWERS
Problems with IRR typically occur in real estate in development/redevelopment schemes when there are:
• Large initial investments• Followed by capital expenditures• Variable cash flows because of
redevelopment
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Multiple IRR Solutions Example II
GENERAL RULE:IRR does not do well with more than one sign change
including the initial investment!
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IRR – It’s All in the Math!
Blame the Quadratic Equation. It Has Two SolutionsCalled Roots. These Solutions May or May Not Be
Unique as Can Be Seen Below.
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And if You Do Not Believe Me….
Assume the following Cash Flow pattern:
Internal rate of return is the value of IRR below:
Divide both sides by 1,000:
Multiply both sides by (1+IRR)2 :3.2(1+IRR) - 2.4 - (1+IRR)2 = 0
Rearrange and we have our old friend the quadratic equationwhere x = (1+IRR)
x2 - 3.2x - 2.4 = 0
3,200
(1+ IRR)−2,400
(1+ IRR)2
−1,000 = 0
01IRR1
42
IRR1
23
2=−
+−
+ )(
.
)(
.
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Finally the Answer(s) Is(Are)……
Our friend the quadratic root says:
And that’s all folks!!
x =
−b ± b2− 4ac
2a
=3.2 ± 3.2
2− 4(1)(2.4)
2(1)
=3.2± 0.8
2
= 2.0 or 1.2
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IRR - Is Not God’s Gift to Investors
IRR is not perfect and suffers from a number of problems:a. Sometimes there is no solution b. Sometimes there are multiple solutionsc. Very short-term solutions can lead to distorted
resultsd. Economies of scale distortions (sometimes it is
better to take the lower IRR solution) e. Sometimes you will reject higher IRR solutions for
lower IRR options. Do not confuse percentage change with wealth creation.
The “Internal” part of IRR refers to the returns earned
on capital while it is invested in a project. When it
is reinvested…Adios
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IRR – What Is It?
a. Dollar-weighted average return, not time-weighted
b. Reflects the impact of the amount invested in each time period
c. Reflects how capital is invested in a project over time
d. Investors who put money in a project at the right time and exit at the right time are rewarded
e. Those who do not are not rewarded
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IRR – Size Doesn’t Matter!
EXAMPLE I
Another Shortcoming of IRRs Is Economies of Scale
Imagine I am willing to give you $400 after a year forlending me $100. That’s a 300% return! But don’tdon’t be fooled by percentages!
Wouldn’t you rather take a 200% return if I gave you $900 after a year for lending me $300?
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IRR – Size Doesn’t Matter! (con’t)
EXAMPLE II
I have a machine that makes widgets
Case I: I upgrade immediately by investing $10,000 andearn $25,000
or
Case II: Spend $25,000 and receive $50,000 next year?
Given a discount rate of 8% which is the better deal?
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IRR – Size Doesn’t Matter! (Con’t)
Which one would you choose assuming they areequally risky?
EXAMPLE II
Case I: IRR = 150% but is worth only $24,348
Case II: IRR = 100% but is worth $39,438
Clearly Case II generates higher absolute returns. Percent change does not put more food on the table.
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A Tale of Two Projects
Note: Project B has a higher IRR but it has a lower NPV.Also note that investments with delayed capital outlayswill have lower IRRs, ceteris paribus. Of course, theopposite is true for deals that have capital outlays earlyand positive CFs thereafter.
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One Final Twist of the IRR Screw
IRR assumes:
All positive CFs are immediately paid and reinvestedBut for institutional investors they are held by a manager
Modified Internal Rate of Return (MIRR) assumes:
That positive CFs are immediate re-invested with the interest rate on these investments equal to the investor’s WACC
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