private real estate investment data analysis and decision making

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Private
Real Estate Investment
Data Analysis and Decision Making
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Private
Real Estate
Investment
Data Analysis and Decision Making
Roger J. Brown, PhD
Director of Research
Real Estate and Land Use Institute
San Diego State University
San Diego, California
Amsterdam Boston Heidelberg London New York Oxford
Paris San Diego San Francisco Singapore Sydney Tokyo
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Elsevier Academic Press
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‘‘Is life mathematics or is it poetry?’ ’
Roger Mague
´
re
`
s
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CONTENTS
Preface xiii
Acknowledgements xix
1. Why Location Matters: The Bid Rent Surface and
Theory of Rent Determination

Introduction 1
Classical Location Theory 2
Notation Guide 2
The Model 3
Example #1—Two Competing Users in the Same Industry 3
Example #2—Several Competing Users in Different Industries 5
Is the Bid Rent Curve Linear? 7
Empirical Verification 8
An Economic Topographical Map 12
Relaxing the Assumptions 13
A Window to the Future 16
References 17
2. Land Use Regulation
Introduction 19
Who Shall Decide—The Problem of Externalities 20
The Idea of Utility 23
The Model 24
Optimization and Comparative Statics 27
A Graphic Illustration 28
Implications 32
A Case Study in Aesthetic Regulation 32
vii
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Conclusion 36
References 37
Appendix: Comparative Statics for Chapter 2 37
3. The ‘‘Rules of Thumb’’: Threshold Performance Measures
for Real Estate Investment
Introduction 39

Threshold Performance Measures 40
A General Caution 42
The Gross Rent Multiplier (GRM) 43
What Not to Do 44
What Should be Done 45
Capitalization Rate (CR) 49
The Three Bad Assumptions 49
Capitalization Rate and Discounted Cash Flow Analysis 50
Monotonic Growth 52
The Expense Ratio and the ‘‘Honest’’ Capitalization Rate 54
The Normal Approach to Data 56
Questioning the Assumption of Normality 60
The Stable Approach to Data 62
Linear Relationships 62
Linear Transformations 64
Spurious Relationships 64
Cash-on-Cash Return (C/C) 67
Price Per Unit (PPU) 67
Other Data Issues 71
References 72
4. Fundamental Real Estate Analysis
Introduction 73
The Role of Computational Aids 73
Deterministic Variables of Discounted Cash Flow Analysis 75
Single Year Relationships and Project Data 76
Multi-Year Relationships 78
Sale Variables Relationships 79
The Net Present Value 81
Insight into the Analysis 82
An Illustration of Bargaining 87

Another Growth Function 90
Data Issues 93
Conclusion 98
References 98
viii Contents
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5. Chance: Risk in General
Introduction 99
Objective and Subjective Risk 100
Games of Chance and Risk Bearing 101
The Utility Function Revisited 104
The ‘‘Certainty Equivalent’’ Approach 107
Multiple (More than Two) Outcomes 111
The Continuous Normal Case 112
Conclusion 116
References 117
6. Uncertainty: Risk in Real Estate
Introduction 119
Non-normality—How and Where Does it Fit? 119
The Continuous Stable Case 121
Producing a Stable pdf 123
Still More Distributions? 126
Enter Real Estate 127
Determinism 128
Determinism and House Prices 131
Determinism and Real Estate Investment 135
Risk and Uncertainty 138
Rolling the Dice 141
Real Estate—The ‘‘Have it Your Way’’ Game 145

The Payoff 147
Data Issues 150
Conclusion 152
References 153
7. The Tax Deferred Exchange
Introduction 157
Taxes are Less Certain for Real Estate Investors 158
Variable Definitions 160
The Structure of the Examples 161
The Base Case: Purchase–Hold–Sell 162
Example 1—Modifying the Growth Projection 163
Example 2—The Tax Deferred Exchange Strategy 167
Exchange Variable Definitions 168
The Value of Tax Deferral 173
The Sale-and-Repurchase Strategy: Tax Deferral as a Risk Modifier 176
The Sale-and-Better-Repurchase Strategy: The Cost of Exchanging 178
Contents ix
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Example 3—Exchanging and The Plodder 182
Data Issues 185
Conclusion 186
References 188
8. The Management Problem
Introduction 189
The Unavoidable Management Issue 189
The Property Manager’s Dilemma 190
Is Building Size Really Important? 193

The Property Owner’s Dilemma 195
The ‘‘No Vacancy Rate’’ Approach 195
Enter the Vacancy Rate 197
Reconciling the Two Problems 198
Data Issues 201
Conclusion 202
References 203
Appendix: A Caution On the Use of Data to Construct Theories 204
Making Vacancy and Rental Rates Reasonable 204
The Model to End all Models 205
9. The Lender’s Dilemma
Introduction 209
Lenders and their Rules 209
Appraisal Techniques 210
The Capitalization Rate Approach Versus the Mortgage Equity
Approach 210
The Lender’s Perspective 212
The Borrower’s Perspective 212
Irrational Exuberance and the Madness of Crowds 213
Bubble Theory—How High is Up? 217
Positive Leverage 217
The Lender as Governor 221
Resolving the Conflict 222
Three Two-Dimensional (2D) Illustrations 224
Endgame 227
Data Issues 231
Conclusion 235
References 235
x Contents
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10. The Private Lender
Introduction 237
The ‘‘Hard Money’’ Loan Versus the ‘‘Purchase Money’’ Loan 238
The Diversification Problem 238
Other Possibilities 239
Did We Make a Loan or Did We Buy the Property? 240
The Installment Sale 242
The Motivation of the Parties 244
The Buyer 244
The Seller 245
The Installment Sale Transaction 248
Is the Seller’s Financing a Good Deal for The Buyer? 248
The NPV Test 249
An IRR Test 250
A Simple ‘‘Tax Blind’’ Test 250
A Prepayment Penalty 253
Conclusion 255
Reference 257
11. Creative Financing
Introduction 259
Retirement and Creative Financing 259
A Life Estate 260
A Zero Coupon Bond 261
The Retiree’s Dilemma 261
The Conventional Arrangement 262
The Reverse Amortization Mortgage 265
Intra-Family Alternatives 267
The Income Viewpoint 268
The Larger House Viewpoint 269

The Remainderman’s Position 271
The Income Case 271
The Larger House Case 272
Conclusion 273
References 274
Index 279
Contents xi
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PREFACE
This book is designed as a supplementary text for upper division under-
graduate and graduate real estate investment courses. The CD-ROM included
with the book contains spreadsheets for data analysis tailored specifically
to real estate settings. The major thrust is to bridge the gap between theory
and practice by showing the student how to implement his real estate
education in the real world.
The study of real estate follows long traditions grounded in Urban
Economics and Finance. There is, however an inherent conflict between the
twin realities that the finance market is efficient and the real estate market is
not. Practitioners in the real world know, or at least act as if they know, that
real estate is very different from finance. No investment real estate broker gets
up in the morning and does anything even remotely resembling what a
stockbroker does. While anecdotal evidence suggests that the two activities
are different, until very recently academic theory supporting such a belief has
been underdeveloped and has suffered from a lack of data to test hypotheses.
The data are growing around us every day as the industry converts real

estate information into digital form. It may be that this will improve real estate
market efficiency. It may also lead us to conclude that real estate is different
from finance for reasons we previously had not considered.
Three significant ideas motivate this book:
1. Until recently, data on real estate was available only for large,
institutional grade properties and its use limited to those who work in
that market. Now, robust databases are available for many different
types of real estate. For the first time, databases covering private real
estate investment have breadth (large number of observations in
relatively small geographic areas) and depth (long histories of data
covering the same property).
xiii
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2. Closed-form analytical techniques for risk modeling either (a) have
been exhausted and/or (b) because of institutional factors are inappli-
cable to real estate. Hence, risk modeling using fast, numerically
intensive simulation with bounded datasets offers a significant
improvement over the present ad hoc real estate methods.
3. Considerable recent progress has been made in mathematical software
and algorithms that permit one to access, combine, and integrate real
estate databases in ways that make possible visual, spatial represen-
tations. Such demonstrations are now accessible to a much larger, and
at times less sophisticated, audience.
It has been estimated that one-half of the world’s wealth is in real estate.
A book such as this offers tools to enhance decision-making for consumers
and researchers in market economies of any country interested in land use
and real estate investment. Empirical risk analysis improves the under-
standing of markets in general. Real estate is not different in this regard. Each

day thousands of bright, entrepreneurial souls arise and make dramatic
contributions to our built environment, heretofore without data or database
analysis techniques. This book hopes to add a suite of tools that will sharpen
their vision and understanding of that process.
READERS OF THIS BOOK
Academic
1. Undergraduate students will find the narrative and examples in the
text manageable without higher mathematics or an understanding of
programming. The assumption is that students have had at least a
semester of calculus and have for reference a primary real estate
investment text.
2. Graduate students with some background in statistics will take the
sample data provided and exercise their empirical skills in the context
of real estate data limitations. This will enhance understanding of how
real estate adds to and fits into the overall economic picture.
Practitioners
1. Lenders and managers of large real estate portfolios, many of whom
originate real estate data, will be able to incorporate these tools into
their daily real estate risk management activities.
2. The most sophisticated investors and their advisors will use these tools
for due diligence in an environment of professional liability and a
rising standard of care.
xiv Preface
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3. Investment real estate brokers in the MAI and CCIM category will find
the narrative and illustrations helpful in explaining investment risk/
return tradeoffs to clients.

Investors
For investors (and all others) familiar with the spreadsheet environment,
numerical analysis and sensitivity testing is often done via example for which
a spreadsheet is well suited. The use of the tools provided here can enhance
the investor’s experience by providing better understanding of his advisor’s
recommendations.
However, all should recognize the inherent limitations of any
spreadsheet approach.
1. The use of a spreadsheet implies (but does not require) two
dimensions. Certainly the graphics produced by the average spread-
sheet program model only two variables.
2. Very often spreadsheet use in limited to linear models or models that
exhibit non-decreasing functions. These are misleading as the world is
neither linear nor do the economic variables in the real world
constantly increase.
3. There is a static aspect to spreadsheets that fail to fully consider the
time dimensions of any model.
These three limitations are partially overcome by higher mathematics and
symbolic computing software that extends beyond spreadsheets and the
scope of this book. The reader is urged to develop an appreciation for these
advanced tools and recognize the elementary nature of spreadsheet
modeling and the complexity such simplification overlooks.
A PRACTICAL GUIDE TO INVESTMENT
REAL ESTATE
Perhaps the first manual for the private real estate investor was William
Nickerson’s How I Turned $1,000 into a Million in Real Estate in My Spare Time
based on his real estate investments in the 1930s. Despite the complexities of
modern day life, thousands of real estate investors still practice his teachings
each day.
This book updates Nickerson’s timeless message and elaborates it in a

rigorous framework that describes how individual real estate investors make
decisions in the 21
st
Century. Underlying most successful folklore is a sound
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theory. Private real estate investors follow well-developed and widely
respected micro-economic theory in that they are profit seeking, risk
averse, utility maximizers. However, their approach differs from that of
their brethren in financial assets. Privately owned real estate offers an
opportunity to add the value of one’s entrepreneurial effort to one’s portfolio.
Such a process provides an avenue to success quite different from the route
taken by the average stock market investor.
After decades of thinking of a database as three comparable sales, real
estate investors today suddenly find that they have access to plentiful data.
Large data sets light the way to a host of objective ways of viewing real estate.
Until now, the thorny issue of risk has been real estate’s crazy aunt in the
basement, either completely ignored or dealt with subjectively in a variety of
ad hoc ways. Despite this, over the long run the monetary performance of real
estate investments appears to compete favorably with that of financial assets,
an outcome that could not have been achieved without addressing risk along
the way. However, little analysis of this process exists beyond applying
mainstream finance models, often with apologies for how poorly the square
peg of real estate fits through the round hole of finance.
Private real estate investment opportunities offer a different kind of risk, a
non-linear variety characterized by observations often far from the mean. The
persistence of such outliers bespeaks of a need for a new approach to risk.

Also, as a result of (1) a fixed supply of land, (2) an adjustment in holding
period when needed, and (3) the addition of labor, real estate investors live in
a market where the size of their return may be uncertain but the sign is likely
to be positive. With empirical support for the maxim ‘‘You can’t go wrong in
real estate’’ comes a different view of risk in this unique market.
The goal of this book is, therefore, threefold: First, updating Nickerson’s
widely respected work, it will apply mathematical rigor to the various
homilies and truisms that have characterized private real estate investment for
decades. Second, at a time when the industry is digitizing and databases
deliver more objective information about the private real estate investment
market, it will incorporate appropriate yet innovative ways to use this new
data. Third, combining the first two, it will uncover a way of viewing risk in
real estate that is intuitively appealing, theoretically sound and supported by
empirical evidence.
WHAT THIS BOOK IS NOT
As a supplementary text, this book cannot cover in detail the myriad aspects
of real estate investment that come before or run along side the need to
understand risk and use data. Early chapters lay foundation to some degree
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but the reader is cautioned not to take the contents of a book this short as
exhaustive.
Some fundamentals of probability and statistics are discussed but there is
no attempt here to provide what excellent texts in those subject areas offer.
The subtleties of such topics as leptokurtosis, ergodicity and the asymptotic
properties of likelihood functions, pervade the subject of statistics. While
practitioners can often get by without an intimate knowledge of such things,
they exist and should not be ignored. Practical limitations prevent a thorough

discussion of these subtleties here.
The illustrations in this book offer guidelines about locating a path, they
are not a road map with a certain destination. Indeed the subject of risk and
data is about uncertainty. The most a book such as this can offer is a
framework for thinking about problems involving uncertainty. Hopefully the
illustrations stimulate thinking about how people, property and numbers can
be combined in the presence of uncertainty to make good decisions.
A FINAL THOUGHT ON PURPOSE
There is an undertone of indifference and occasional hostility between
academics and practitioners. At times each side considers the other to be
either irrelevant or the enemy. This behavior is not productive. Academics
need practitioners mucking around in a messy real world producing
observations that in the aggregate provide empirical evidence to support or
contradict theory. Practitioners need academics to articulate theory that
constitutes a base of knowledge from which to launch successful careers. One
of the most ambitious goals of this book is to speak the language of both sides
in a way that the separate camps understand each other and appreciate the
importance of each other’s contribution.
To that end, I counsel patience on the part of practitioners who quickly
grow weary of the pedantic formalism of mathematics and on the part of
academics who become impatient with examples that may seem superficial
and anecdotal.
These sentiments may be summarized in a metaphor from another field.
Very few people are interested in the inner workings of the highly
mathematical model that sequences the human genome. Even fewer under-
stand it. Similarly, only a few people are interested in models describing the
general nature of how real estate markets work. On the other hand, we all
have a common and usually strong interest in being healthy. Thus, after the
doctor listens very carefully to the patient’s description of his symptoms, the
patient, otherwise disinterested in biology, listens very carefully as a doctor

explains how a particular form of gene therapy may preserve and extend his
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life. In the spirit of this analogy it may be equally well for academics to
observe how real world investors make money as it is for practitioners to learn
the mathematics that underlies whatever science there is in real estate
investing.
Now let us begin sequencing the genome of real estate investing.
Roger J. Brown
Alpine, CA
January, 2005
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ACKNOWLEDGMENTS
When this book is made into a movie and wins an Academy Award, my
acceptance speech will be long:
At the end of a project like this there are so many people to thank. I hope
I don’t leave anyone out. The order of mention is more about chronology than
importance for all were vital to my education and intellectual development.
All, in some way, made an important contribution to this book
From my earliest childhood days I was inspired and guided by wonderful
math teachers from Sister Fridolene, my first grade teacher through Monty
Fones in high school. I was twice blessed when it all had to be done again
thirty years later at Penn State. Ed Coulson and Herman Bierens were both

patient and talented professors who, in restoring my ancient math skills, gave
more of their time than I deserved.
Four people made important contributions to the sort of business
understanding one can only obtain in the real world. Chilton and Bryan
Jelks provided years of practical guidance outside of real estate. I have
Dr. David K. Hostetler and Jim Darr to thank for keeping me on the right
track over three decades of real estate practice. For me, these four were Deans
of the School of Hard Knocks without whom the knocks would have been a
lot harder.
The graduate school part of this quest began in 1992 at San Diego
State University under the wise guidance of Bob Wilbur, Andy Do, and
Milton Chen. In 1995 these fine academics breathed a sigh of relief and
handed me off to Professors Ken Lusht and Jeff Sharp at Penn State, two
superb gentlemen did their best, given the raw material they had to
work with, to finish the job. While at Penn State I was also fortunate to
receive vital help at crucial times from Cemile Yavas, Tom Geurts, Jim Jordan,
xix
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Norm Swanson, and Paul Claar. Since I left PSU the help and thoughtful
comments of Richard Graff, Colin Rose, Stephen Roulac, Hu McCulloch,
Tim Riddiough, Norm Miller, George Matysiak, and Ted Ersek were also
appreciated.
The technical aspects of this book, especially the inclusion of very
artful Mathematica code that produced many of the insights, most of the
graphics and a number of the technical goodies on the CD-ROM, would
not have been possible without the tireless efforts of Marlyn L. Hicks
whose clear-headed, agnostic view of mathematics is reflected in every
chapter. Marlyn was a wonderful sounding board, a voice of reason never

swayed by academic history or politics. A book of this nature needs a
real mathematician and Marlyn played that role magnificently.
Tom Zeller and Andreas Lauschke are two very talented Mathematica
programmers at Wolfram Research who always came through with important
assistance when I needed it.
The inspiration for the Risk in Real Estate models of Chapter 6 comes
from John Nolan whose help over many years enriched my understanding
of the strange world of Stable Distributions. This area in the book also
benefited from the long discussions of life, investing, probability and
mathematics with Robert Rimmer, MD, who very generously gave of his
time, providing important interpretations that may have been missed and also
assisting in the Mathematica programming. This book is supported by an
interactive web site, www.mathestate.com, where many of the routines
described here can be immediately implemented. My thanks to the World
Famous Cosmo Jones and his more talented sidekicks, Lorenzo Ciacci and
Chris Sessions for building that site and to Tom Compton and D. Jacob
Wildstrom for their help in maintaining it.
My contemporaries in the business world were also very supportive. John
Boyle, Terry Moore, Richard Schneider, Howard Wiggins, Chuck Wise, and
several anonymous reviewers either read portions of the book or provided
helpful suggestions. Data provided by the CoStar Group was made possible
through the gracious assistance of Craig Farrington. Craig and I spent many
a lunch over most of a decade dreaming about new and different ways in
which data will be used in future real estate decisions. Pat Barnes and Bruce
Howe provided vital data for Chapter Two that made the case study at the end
of that chapter possible.
No book ever sees the light of day without a superb editor who believes
in the project. Scott Bentley was that person for me. His easy-going manner
and always helpful suggestions made this process a pleasure.
Many books leave some innocent soul waiting. No married author ever

reaches the end of a process like this without owing yet another un-repayable
xx Acknowledgments
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debt of gratitude to a long-suffering spouse. This author is no different.
Without the world’s most perfect woman exhibiting the sort of understanding
that passes all understanding this book would not exist. Thank you most of
all, Bonnie Jean.
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CHAPTER
1
Why Location Matters
The Bid Rent Surface and Theory of
Rent Determination
If you do not rest on the good foundation of nature, you will
labor with little honor and less profit.
Leonardo da Vinci (1452–1519) quoted in Mathematics
for the Non-Mathematician (Kline, p. 204)
INTRODUCTION
One of the oldest cliche
´
s we hear is: ‘‘The three most important things in real
estate are location, location and location.’’ Most cliche
´

s become truisms for a
good reason. If the value of location is universally acknowledged, there may
be some strong underlying theory that can be represented mathematically.
That theory is found in the construction of a ‘‘bid rent curve.’’ The general
notion is that land users ‘‘bid’’ or ‘‘offer’’ to pay rent to land owners based
on the renters’ ability to efficiently use the land. Those who can use it
most efficiently offer to pay the highest rent. If value is based on income,
the highest land values should occur where users are willing to pay the
highest rent.
In this chapter we will:
 Determine how the market allocates land between consumers.
 Build a model that tells us who will locate where.
 Compute the bid rent curve, the rate at which rents fall for a particular
use as one moves away from the center of the city.
 Consider how the appropriate use of real estate data permits us to
confirm the actual shape of the rent gradient.
 Reach conclusions about another commonly used term in real estate: the
path of progress.
 Discuss how the use of data improves the location decision.
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CLASSICAL LOCATION THEORY
Certain tenants, categorized by the way they use land, have certain needs.
Common to all of them is the need to locate in a specific place. That specific
place may be dependent on proximity to their customers, suppliers, raw
material, transportation arteries, or any number of other attributes of a land
market. The key word here is ‘‘proximity.’’ Hence, location obtains its value
from the notion of ‘‘closeness.’’ We need an analytical way to determine how
one parcel of land is better or worse than another by virtue of its location,

its closeness to some particular desirable other place.
Theory predicts that rents (and therefore values) will be highest where
economic activity is most intense and productive, hence profitable. Profits are
what we observe when land is used efficiently. Therefore, if one land
consumer can achieve a greater profitability on a parcel of land than another
can, the consumer who can use the land most profitably pays the highest
price. Efficient outcomes are achieved as property rights in land gravitate
to the highest bidder. To illustrate this theory and build a workable model,
we make several simplifying assumptions:
 The urban area is monocentric, that is, all activity takes place at the
center. There are no suburbs.
 The land is a flat, featureless, uniform plane over which movement is
equally possible in all directions. The only variation between different
places is the distance from the center of the city.
 No input substitution or scale economies are possible. For instance, you
can’t substitute cheaper capital for expensive labor; neither can you
reduce transportation costs per unit by carrying larger loads.
 Transportation costs are uniform in all directions. These costs are linear
in distance based on a cost per unit with no initial fixed cost.
 The urban area contains the textbook competitive market (many sellers,
all price takers, identical products, no monopoly, no transaction costs,
no economic profits).
These are, admittedly, very restrictive assumptions. We will relax some of
them later, but for now this is what is required to establish a baseline
understanding of how location relates to value.
NOTATION GUIDE
R ¼ Rent, formally ‘‘Ricardian Rent’’ after David Ricardo who first
observed the nature of rent determination
2 Private Real Estate Investment