Real Estate and Risk: Time to Rethink What You …...Real Estate and Risk: Time to Rethink What You...

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

www.northinfo.comwww.northinfo.com

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!


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


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


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


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


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

www.northinfo.comwww.northinfo.com 8

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


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.


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?


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


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


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


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


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


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


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)


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


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


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


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


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


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



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



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



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


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


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.


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


Components of Property-Level Risk

30

Rent Risk

Interest Rate Risk

Credit Risk

Specific Risk

TOTAL RISK

Risk is not additive unless using variance.


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


Model Results

32


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


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


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 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


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 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


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


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


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


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)


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


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


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


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


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


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


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


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.


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

50


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

51


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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