text: Expected Returns
  An Investor’s Guide to Harvesting Market Rewards
  For other titles in the Wiley Finance Series please seeﬁnance
  Expected Returns
  An Investor’s Guide to Harvesting Market Rewards
  Antti Ilmanen
  A John Wiley and Sons, Ltd, Publication
  This edition ﬁrst published 2011
  # 2011 Antti Ilmanen
  Registered oﬃce
  John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom
  For details of our global editorial o trade
  marks-119-99072-7
  A catalogue record for this book is available from the British Library.
  Projec; t management by OPS Ltd, Gt Yarmouth, Norfolk
  Typeset in 10/12pt Times
  Printed in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire
  Contents
  Foreword by Cliﬀord Asness
  xi
  Acknowledgments
  xvii
  Abbreviations and acronyms
  xix
  PART I
  OVERVIEW, HISTORICAL RETURNS, AND
  ACADEMIC THEORIES
  1
  1
  Introduction
  1.1
  Historical performance
  1.2
  Financial and behavioral theories: A brief history of ideas
  1.3
  Forward-looking indicators
  1.4
  View-based expected returns
  1.5
  General comments about the book
  1.6
  Notes
  3
  7
  9
  13
  15
  16
  20
  2
  Whetting the appetite: Historical averages and forward-looking returns
  2.1
  Historical performance since 1990
  2.2
  Sample-speciﬁc results: Dealing with the pitfalls
  2.3
  Forward-looking return indicators
  2.4
  Notes
  23
  24
  27
  32
  35
  3
  The historical record: The past 20 years in a longer perspective
  3.1
  Stocks
  3.2
  Bonds
  3.3
  Real asset investing and active investing
  3.4
  FX and money markets
  3.5
  Real return histories
  3.6
  Notes
  37
  39
  43
  47
  50
  52
  52
  4
  Road map to terminology
  4.1
  Constant or time-varying expected returns?
  4.2
  Rational or irrational expectations formation?
  57
  57
  58
  vi
  Contents
  4.3
  4.4
  4.5
  4.6
  4.7
  Return measurement issues
  Returns in what currency?
  Risk-adjusted returns
  Biased returns
  Notes
  59
  60
  61
  63
  63
  65
  66
  68
  81
  83
  5
  Rational theories on expected return determination
  5.1
  The old world
  5.2
  The new world
  5.3
  Detour: a brief survey of the eﬃcient markets hypothesis
  5.4
  Notes
  6
  Behavioral ﬁnance
  6.1
  Limits to arbitrage
  6.2
  Psychology
  6.3
  Applications
  6.4
  Conclusion
  6.5
  Notes
  87
  87
  89
  98
  106
  107
  7
  Alternative interpretations for return predictability
  7.1
  Risk premia or market ineﬃciency
  7.2
  Data mining and other ‘‘mirage’’ explanations
  7.3
  Notes
  111
  111
  112
  115
  PART II
  8
  9
  A DOZEN CASE STUDIES
  117
  Equity risk premium
  8.1
  Introduction and terminology
  8.2
  Theories and the equity premium puzzle
  8.3
  Historical equity premium
  8.4
  Forward-looking (ex ante objective) long-term expected return
  measures
  8.5
  Survey-based subjective expectations
  8.6
  Tactical forecasting for market timing
  8.7
  Notes
  119
  119
  120
  122
  Bond
  9.1
  9.2
  9.3
  9.4
  9.5
  9.6
  9.7
  153
  153
  157
  160
  161
  164
  174
  177
  risk premium
  Introduction, terminology, and theories
  Historical average returns
  Alternative ex ante measures of the BRP
  Yield curve steepness: important predictive relations
  Explaining BRP behavior: ﬁrst targets, then four drivers
  Tactical forecasting—duration timing
  Notes
  128
  141
  144
  149
  10 Credit
  10.1
  10.2
  10.3
  10.4
  10.5
  10.6
  10.7
  10.8
  Contents
  vii
  risk premium
  Introduction, terminology, and theory
  Historical average excess returns
  Focus on front-end trading—a pocket of attractive reward to risk
  Understanding credit spreads and their drivers
  Tactical forecasting of corporate bond outperformance
  Assessing other non-government debt
  Concluding remarks
  Notes
  179
  179
  183
  188
  191
  198
  199
  204
  205
  11 Alternative asset premia
  11.1 Introduction to alternatives
  11.2 Real estate
  11.3 Commodities
  11.4 Hedge funds
  11.5 Private equity funds
  11.6 Notes
  207
  207
  210
  219
  226
  241
  245
  249
  249
  251
  258
  261
  13 Currency carry
  13.1 Introduction
  13.2 Historical average returns
  13.3 Improvements/reﬁnements to the baseline carry strategy
  13.4 Why do carry strategies work?
  13.5 Carry here, carry there, carry everywhere
  13.6 Notes
  271
  271
  272
  276
  282
  288
  290
  14 Commodity momentum and trend following
  14.1 Introduction
  14.2 Performance of simple commodity momentum strategies
  14.3 Tweaks
  14.4 Why does momentum—such a naive strategy—work?
  14.5 Momentum in other asset classes
  14.6 Notes
  293
  293
  294
  298
  299
  301
  305
  15 Volatility selling (on equity indices)
  15.1 Introduction
  15.2 Historical performance of volatility-trading strategies
  307
  307
  311
  265
  267
  268
  viii
  Contents
  15.3
  15.4
  15.5
  15.6
  Tweaks/Reﬁnements
  The reasons volatility selling is proﬁtable
  Other assets
  Notes
  314
  315
  319
  319
  16 Growth factor and growth premium
  16.1 Introduction to underlying factors in Chapters 16–19
  16.2 Introduction to the growth factor
  16.3 Theory and evidence on growth
  16.4 Asset market relations
  16.5 Time-varying growth premium
  16.6 Notes
  321
  321
  327
  328
  331
  338
  338
  17 Inﬂation factor and inﬂation premium
  17.1 Introduction
  17.2 Inﬂation process—history, determinants, expectations
  17.3 Inﬂation sensitivity of major asset classes and the inﬂation
  premium
  17.4 Time-varying inﬂation premium
  17.5 Notes
  341
  341
  345
  18 Liquidity factor and illiquidity premium
  18.1 Introduction
  18.2 Factor history: how does liquidity itself vary over time?
  18.3 Historical evidence on average liquidity-related premia
  18.4 Time-varying illiquidity premia
  18.5 Note
  359
  359
  362
  365
  370
  374
  375
  375
  378
  PART III
  399
  BACK TO BROADER THEMES
  20 Endogenous return and risk: Feedback eﬀects on expected returns
  20.1 Feedback loops on the direction of risky assets
  20.2 Feedback loops on less directional positions
  20.3 Agenda for market timers and researchers
  20.4 Notes
  350
  356
  356
  380
  389
  392
  395
  396
  401
  401
  403
  405
  407
  Contents
  ix
  21 Forward-looking measures of asset returns
  21.1 Popular value and carry indicators and their pitfalls
  21.2 Building blocks of expected returns
  21.3 Notes
  409
  410
  413
  416
  22 Interpreting carry or non-zero yield spreads
  22.1 Introduction
  22.2 Future excess returns or market expectations?
  22.3 Empirical horse races for various assets
  22.4 Conclusions
  22.5 Notes
  419
  419
  420
  424
  428
  429
  23 Survey-based subjective expected returns
  23.1 Notes
  431
  435
  24 Tactical return forecasting models
  24.1 Introduction
  24.2 What type of model?
  24.3 Which assets/trades?
  24.4 Which indicator types?
  24.5 Enhancements and pitfalls
  24.6 Notes
  437
  437
  438
  441
  442
  443
  444
  25 Seasonal regularities
  25.1 Seasonal, cyclical, and secular patterns in asset returns
  25.2 Monthly seasonals and the January eﬀect
  25.3 Other seasonals
  445
  445
  446
  453
  26 Cyclical variation in asset returns
  26.1 Typical behavior of realized returns and ex ante indicators through
  the business cycle
  26.2 Typical behavior of realized returns and ex ante indicators across
  diﬀerent economic regimes
  26.3 Notes
  457
  27 Secular trends and the next 20 years
  27.1 Contrasting 1988–2007 with 1968–1987
  27.2 Reversible and sustainable secular trends
  27.3 The next 20 years
  27.4 Notes
  467
  467
  468
  474
  478
  28 Enhancing returns through managing risks, horizon, skill, and costs
  28.1 Introduction: how can investors enhance returns?
  28.2 Risk
  28.3 Investment horizon
  28.4 Skill
  28.5 Costs
  28.6 Notes
  479
  479
  482
  492
  496
  499
  501
  458
  461
  465
  x
  Contents
  29 Takeaways for long-horizon investors
  29.1 Key takeaways from theory
  29.2 Empirical return sources
  29.3 My take on key debates
  29.4 Know thyself: large long-horizon investors’ natural edges
  29.5 Institutional practices
  29.6 Notes
  503
  504
  504
  506
  512
  513
  514
  APPENDICES
  515
  A
  World
  A.1
  A.2
  A.3
  515
  516
  516
  518
  B
  Data
  B.1
  B.2
  B.3
  B.4
  B.5
  B.6
  wealth
  Global total
  Asset class detail
  Notes
  sources and data series construction
  Asset class and sector returns
  Strategy style returns
  Factor proxies
  Forward-looking yields and spreads
  Survey data and expected inﬂation
  Miscellaneous other
  519
  519
  521
  522
  523
  523
  524
  Bibliography
  527
  Index
  551
  Foreword
  The ﬁrst time I met Antti Ilmanen I thought he was insane. I was right. But, I was to
  discover quickly he was insane in a good way. The incident in question was at a new
  Ph.D. student mixer, about as exciting as it sounds, where seconds after being intro
  duced to Antti he asked me ‘‘who do you rate in the top-ﬁve academics in ﬁnance and
  why?’’ He had his own answers on a set of Post-it notes. By the way, Antti has become
  famous for these Post-it notes. Suﬃce it to say if he consults the Post-its, and says you
  said something 17 years ago that turned out to be disproved in the latest Journal of
  Finance paper, just assume he’s right and move on.
  Getting back to my story, he couldn’t understand how I couldn’t name ﬁve. Truth be
  told I probably could have named maybe three academics in total, and as to justifying
  my choices with ‘‘why?’’, I was stuck at zero. I had not chosen ﬁnance because, like
  Antti, I was already obsessed with it. I chose it as my dad, a lawyer, forbade me to go to
  law school, I had some mild ability at mathematics, I recognized that ﬁnance might be
  both intellectually interesting and provide a good living, and ﬁnally I chose a Ph.D. as
  being a professor seemed like a nice life (little did I know the Sirens of Wall Street would
  soon call me away . . .) Antti looked at me with a ‘‘what the heck are you doing in the
  Ph.D. program’’ confused stare, and I politely ran away from the very intense, very
  ﬁnance-obsessed young Finn. Now, 20þ years later, and after countless similar inci
  dents, I no longer run away (he ﬁnds me anyway), but he’s still intense and obsessed with
  ﬁnance. Over the years, and speciﬁcally through this book, those traits of his have made
  us all better oﬀ.
  One more aside before my foreword begins in earnest. I brieﬂy considered not writing
  this foreword in protest or as a rearguard action. Antti gives away a lot in this book.
  Perhaps few true secrets (though there are some!), as this is more a textbook than
  original research. But he makes much of what has become called ‘‘quantitative ﬁnance’’
  easily (OK, 300þ dense pages, in original format, of ‘‘easily’’) accessible in one place.
  Long term, that can’t be good for people like me who make their livings from this stuﬀ
  being at least a bit secret. But being skilled at game theory I quickly determined that if
  I didn’t write the foreword somebody else would, so refusal would not accomplish much.
  With that strategy shot down, I very ﬂeetingly considered having him killed, but this
  seemed to entail too much ‘‘tail risk’’ (see Chapters 15 and 19) and, anyway, is at least
  somewhat morally ambiguous. Besides, Antti’s just the type to have stashed a Post-it at
  his lawyer with a note ‘‘in the event of my untimely . . .’’ So in the end I decided to smile
  xii
  Foreword
  and write the foreword, and just resolve to work harder (along with many others at my
  ﬁrm and others throughout the ﬁeld) to give Antti material for a sequel 20þ years from
  now!
  Now let’s talk about the title subject.
  Expected returns are how much you make on average over time on an investment or
  strategy. Risk is the possibility that, over any time horizon, you never get your expecta
  tion, as once again the world interferes with a perfectly good plan. Risk can make you
  fail to reach your expectations because of the simple uncertainty around expectations it
  brings, or because, as in 2008 for many, bad realizations call into question long-term
  survival or at least the ability to stick with a plan. Still, expected returns are incredibly
  important. If you survive and stick to a good plan, they add up nicely.
  Antti has chosen to write a book on expected return in the Age of Risk. Risk, and
  particularly risk in the sense of survival, is all the rage in these days following a major
  ﬁnancial crisis. This wide-ranging discussion of risk is right and proper. If some
  investors took too much risk and that caused or exacerbated the ﬁnancial crisis, that’s
  a pretty important event to learn from. If some investors thought risk was simple and all
  ﬁgured out, and got a black swan dropped on their heads, it is important to learn from
  that too. However, it’s not the whole story.
  While perhaps diﬀering from the vast majority of risk-focused researchers and
  authors these days, I’d argue that the study of expected returns deserves more of our
  attention, even just after one of the biggest ‘‘left tails’’ in history. For one thing, as scary
  as the world got, some of our much maligned simple ‘‘normal’’ models actually did OK
  for all assets other than highly structured and/or levered ones, or over the very short
  term (see
  market-of-2008.html ). For another thing, in a theme Antti returns to again and again
  in his book, expected returns don’t have to stay the same throughout time. Part of what
  we see as ‘‘risk’’ materializing during events like the 2008 ﬁnancial crisis, and the 1999–
  2000 tech bubble, are more accurately seen as investors misunderstanding or mis
  estimating expected returns. In both those cases the extreme dénouement that followed
  occurred, at least according to many (and me), because before the disaster, investors
  were willing to accept far too low an expected return, ﬁrst on stocks and speciﬁcally on
  technology stocks, and then a decade later on credit and real estate. In both the theory
  and the reality of these globe-shaking events, the discussions of risk and expected return
  are intimately linked.
  So why so much more discussion of risk than expected return these days? Well,
  obviously the magnitude of recent events makes all of us greatly value the chance we
  could have avoided that pain. But again, a careful study of expected return might have
  easily, perhaps even more easily, led to the same protection by avoiding certain invest
  ments on the ground that their expected returns were too low. Frankly, I think a lot of
  the answer is that discussing risk is inherently sexier than discussing expected returns.
  Good forecasts of expected return add up over the long term, but don’t matter for squat
  next week. Risk can kill you, or make you a hero, in the time it takes you to say ‘‘ﬂash
  crash’’. Would you rather write about a tsunami or erosion? More speciﬁcally, from a
  safe perch, say the hindsight of authoring a book, which event would be more dramatic
  to narrate? The analogy, forced though it may be, continues to work as erosion, or
  expected return, might be mind-numbingly boring at any one moment, but it has a heck
  of a lot to say about how the future will be shaped.
  Foreword
  xiii
  For perspective, you want to see a black swan? Try making nothing on your equities
  in your ﬁnal 20 years until retirement because you bought them at an extremely high
  price (low expected return). That is one pile of ebony long-necked bird. If risk is about
  surviving the short term, expected return is about whether, after surviving, you think it
  was worth it.
  Here’s another secret. Besides being at least as important, estimating expected returns
  is much harder than estimating risk. Now, estimating risk is no easy task. But at least
  ﬁnance wears its insecurity on its sleeve here. Are returns ‘‘normal’’ or do we have to
  worry about ‘‘black swans’’, ‘‘fat tails’’, and all that? This worry and eﬀort is worth
  while, but those trying to estimate the expected return on various assets smile at those
  taking on the comparatively easy task of estimating risk. Basically, you need a heck of a
  lot more data to estimate expected returns than to estimate risk. In geek-speak, the ﬁrst
  moment laughs at and taunts the second moment (which I’m going to pretend for a
  second is all you need for risk). The second moment gives up its secrets reluctantly, but
  far more readily than that more covert ﬁrst moment. To estimate risk we lament (as
  statisticians not humanitarians) that we don’t get to see a few more disasters. To
  estimate expected return we lament we don’t get to see a few more centuries.
  Now that the motivation behind and the diﬃculty of Antti’s task is clear, let’s talk
  about how one might actually try to forecast expected returns. Starting with the very big
  picture, why is there a positive expected return (let’s make that positive relative to some
  riskless rate or, in other words, a positive risk premium) on any asset or investment
  strategy? Well, there are two possible reasons. First, in a rational world you should get
  paid a positive expected return for bearing a risk others don’t wish to bear. As an aside,
  Antti repeatedly hammers home the poorly understood point that you should get paid
  particularly well for bearing risks that hurt you exactly when it is most painful to be
  hurt, and less or not at all for risks that only bring you harm when all is well. Second, in
  a world that permits some irrationality, you can also get paid for someone else’s
  systematic mistakes (or pay for your own).
  While this parsing is useful, and Antti makes great use of it throughout the book, he
  takes it further, examining expected returns along three diﬀerent dimensions (and asking
  the rational vs. irrational question for each part):
  (1) The expected return you get paid for owning any of the major asset classes (stocks,
  bonds, commodities, etc.).
  (2) The expected return you get from pursuing well-known strategies such as value
  investing, momentum investing, and carry-based investing. These are fundamentally
  diﬀerent from the returns in (1) as, for instance, in examining value investing you
  don’t count the expected return from just being long stocks, but rather the extra
  return that has historically accrued to value stocks vs. the universe of all stocks.
  These strategies also tend to be far more dynamic than the asset classes in (1),
  changing their portfolio holdings more often through time.
  (3) The expected return you get from being willing to take the risk of being exposed to
  economic or other risks (e.g., shocks to growth, shocks to inﬂation, liquidity risk,
  etc.).
  These are all connected and overlapping. For instance, passive ownership of equities
  exposes you more to risk of poor real economic growth than does passive ownership of
  bonds, which exposes you more to risk of higher-than-expected inﬂation. Small stocks
  xiv
  Foreword
  expose you to more liquidity risk than large ones. The overlapping descriptions go on
  and on. Antti doesn’t mean for these three ways to look at expected returns to be a
  clean decomposition, rather he ﬁnds use for all three at once (remember, he calls this
  art and science). He continually stresses that there is no perfect way to examine (or
  later forecast) expected returns. You want to use every framework that is useful and
  brings anything new to the study. In this sense his three-way examination succeeds
  handily.
  OK, let’s recap. So there are two ways you can get a positive expected return, by
  taking a risk you get paid for (roughly, ‘‘beta’’), or by outsmarting someone else
  (‘‘alpha’’). There are three useful perspectives to examine the source of expected returns:
  asset classes, systematic strategies, and risk factors such as economic growth and
  liquidity. Exposure to any of these three can generate a positive return for either of
  the ﬁrst two reasons (rational compensation for risk, or outsmarting of others who are
  less than rational). Now we’re cooking. All we need now—assuming we have identiﬁed
  one or more of the three categories of sources of expected returns (from the overlapping
  categories of asset class, strategy, and risk factor exposure) and have a theory as to why
  an investor gets paid this expected return (rational vs. irrational)—is a way to estimate
  the size of that expected return going forward. Here, you guessed it, Antti gives us not
  one but three very useful methods. They are again complementary—not competitors. In
  order from weakest to strongest (Antti’s ordering which I agree with): (1) you can
  forecast the future from looking purely at how something has done in the past,
  (2) you can forecast the future based solely on your theory of how the world should
  work without examining data, (3) you can jump straight to current measures (e.g., the
  P/E of the stock market, the nominal or real yield on bonds) and use them to forecast.
  Like Antti, for reasons you’ll have to get from the book, I favor (3), but even using
  current measures like P/E and yield you still need history and theory. You would like
  some theory to guide why you think today’s stock market P/E should be related to its
  future return, and probably would like some evidence that this has historically been an
  eﬀective tool.
  So, remember, there are two reasons you might get paid an expected return, three
  overlapping ways to parse the diﬀerent sources of expected returns, and three non
  mutually exclusive methods to estimate the expected return going forward, all probably
  containing part but not all the truth, so all must be strongly considered, but none
  blindly, and all at once. You got that?
  Well, I didn’t promise you this would be simple, did I? In fact, I told you the opposite.
  Expected returns are interesting precisely because they are hard (and very important)!
  This means there is no easy answer. But, it also means that eﬀort on this front is
  potentially highly valuable. Understanding easy but very important problems is also
  important, but the barriers to entry are low, and getting an advantage from such an easy
  understanding is usually diﬃcult because the understanding is so widespread. (On the
  other hand, the investing public’s continued failure to understand basic ideas like
  diversifying widely, keeping average costs low, and realizing that it is hard to beat
  the market, etc., makes even this eﬀort worthwhile to the marginal investor.) But,
  understanding deeply, if imperfectly, what many don’t understand at all or even get
  backwards (like the common error of thinking expected returns are especially high going
  forward after realized returns have had an exceptionally good run), well, that is great
  stuﬀ !
  Foreword
  xv
  Antti’s book is complicated and dense. The best compliment I can pay it is that it’s not
  more complicated than it has to be. It chooses to take on a hard question and is honest
  about this degree of diﬃculty. It chooses to oﬀer multiple overlapping methods at each
  point, as there truly is not one certain method, and each brings some value. Another, far
  weaker, even harmful, book could tell you that forecasting long-term future returns is
  easy. That all you have to do is listen to the author’s simple formula and prosper (Dow
  36,000 anyone?). Antti tells you it’s hard. He says if you follow our best minds, and use
  the best data we have, you probably have an edge, or at least your mistakes are not silly,
  but he says it is art and science, and makes no guarantees.
  If I can leave you with advice that applies directly to Antti’s book, but is actually far
  more general, it’s to listen to people who take on diﬃcult problems boldly. Listen to
  people who are honest that our best hope is improved but not perfect understanding.
  Listen to people who aren’t afraid to tell you the world is a complicated place, but then
  are damned talented at making it as simple as possible (but no simpler).
  In other words, read this book. Listen to Antti.
  Cliﬀord S. Asness
  AQR Capital Management LLC oﬀer or solicitation of an oﬀer, or any advice or recommendation, to purchase any
  securities or other ﬁnancial instruments, and may not be construed as such. This document
  is intended exclusively for the use of the person to whom it has been delivered by the author,
  and it is not to be reproduced or redistributed to any other person.
  Dedicated to Rory Byrne,
  in memoriam
  Acknowledgments
  I have been a student of expected asset returns for over 20 years while wearing many
  diﬀerent hats: buy-side bond portfolio manager in the Finnish central bank, Ph.D.
  scholar at the University of Chicago (UofC), bond research analyst at Salomon
  Brothers, sell-side strategist and prop trader at Salomon/Citigroup, and hedge fund
  trader and strategist at Brevan Howard. I have also advised various institutional
  investors on their long-term investment strategies—most regularly for Norway’s
  sovereign wealth fund in semiannual expert panel meetings. It is mainly this last
  experience that has inspired this book.
  OK, that was too mildly put. I confess: I have been obsessed with expected returns.
  The passion for the topic arose in as diﬀerent places as the Bank of Finland in Helsinki
  and the UofC campus in Hyde Park.
  I earned my ﬁnance doctorate at the University of Chicago Business School (now the
  Booth School of Business) in the early 1990s, with Professors Eugene Fama and
  Kenneth French as my dissertation chairmen. In many minds this background puts
  me squarely in the eﬃcient markets’ camp. However, we Chicago ﬁnance students were
  not taught a dogma. Instead, we were given a lifelong desire to learn more about
  ﬁnancial markets with the emphasis on an empirical approach: let ideas compete freely
  and let data be the judge. The EMH paradigm gave a very useful framework for
  understanding and analyzing markets, but few of us became EMH purists. Indeed,
  many of the anomalies that challenged the EMH were uncovered by Chicago professors
  and students. I hope that readers will ﬁnd my treatment of risk-based and behavioral
  explanations for expected returns surprisingly balanced.
  Fama and French are also among my leading lights when I tackle that perennial
  question ‘‘if your ideas have any investment value, why would you share them?’’
  Evidence abounds that business gains accrue to perceived thought-leaders. Yet, many
  serious writers publish for less selﬁsh reasons as well. They want to enhance the general
  investor experience and improve the marketplace.
  Chicago also had other superb ﬁnance and economics professors and besides faculty
  we got great guest speakers in the ﬁnance workshops. Naturally, I had more active
  dialogue with fellow students, many of whom became excellent talking-partners and
  friends over the years. Cliﬀ Asness is of course the best known. I humbly thank him for
  the characteristically witty and insightful foreword and for making it clear to the reader
  in the ﬁrst lines of his foreword that I am insane in a good way.
  xviii
  Acknowledgments
  I have been lucky with bosses: my managers at the Bank of Finland taught me the
  ropes and assigned me the role of a bridge between academia and practitioners much
  before I had any expertise to fulﬁll this role. After my Chicago years, my bosses at
  Salomon Brothers’ storied Bond Portfolio Analysis Group let me balance research and
  market roles, always stressing the value of conveying complex ideas as intuitively as
  possible. At Brevan Howard, the co-CEOs allowed me to take diﬀerent roles, some
  outside the core hedge fund business, and recognized the value of this book for institu
  tional investors. It helps that the book’s themes have little to do with Brevan Howard’s
  core approach of tactical rates trading based on fundamental macro-views with a focus
  on trade construction and risk management, so I will not be revealing any proprietary
  trade secrets.
  This book has been hugely inﬂuenced by my regular meetings in Oslo discussing the
  long-run investment strategy for Norway’s sovereign wealth fund. One outgrowth of
  those meetings has been even more inspirational—our trialogue with Knut Kjaer and
  Andrew Ang about diverse long-horizon investor topics.
  I have beneﬁted from the thinking of fellow students, colleagues, customers, and
  research peers in academia and business. Some of the best sources I have yet to meet
  personally, but I am a voracious reader—to which this book’s lengthy reference list
  attests. There are too many people to thank by name, but I make an exception for
  Rory Byrne to whom this book is dedicated. For several years Rory was my main
  partner in developing and implementing systematic trading models and always a sensible
  sounding board. Sadly, Rory succumbed last year to a persistent tumor at the age of 35.
  A most emphatic thank-you goes to Laurence Siegel, Knut Kjaer, Matti Ilmanen,
  and Victor Haghani who carefully read the manuscript (or evolving versions of it)
  and greatly improved the book. I am also grateful to Andrew Ang, Cliﬀ Asness,
  William Bernstein, Francis Breedon, Alistair Byrne, Adrian Eterovic, Kenneth French,
  Pal Haugerud, Susan Hudson-Wilson, Doug Huggins, Ray Iwanowski, Matthew James,
  Robert Kosowski, John Liew, Thomas Maloney, Mikko Niskanen, Lasse Heje Pedersen,
  Jonas Rinné, Rudi Schadt, Matti Suominen, Etienne Varloot, and Gerlof de Vrij, for
  their helpful comments on parts of my manuscript. I also thank my editors Pete Baker,
  Aimee Dibbens, Vivienne Wickham and their colleagues at Wiley for all their help,
  as well as Neil Shuttlewood, whose company OPS Ltd managed the project. Of
  course, the responsibility for any errors is mine. In a work of this size, some errors
  are bound to creep in. I welcome any comments on them as well as other feedback
  (antti.ilmanen@gmail.com). I credit my data sources separately in Appendix B.
  Finally, I thank my family, the source of the most precious expected and realized
  returns. The family in Finland: My mother and siblings as well as my late father who
  taught me the love of reading through example and who urged me to read in a way that
  advances my knowledge systematically (‘‘try to position each new piece of knowledge in
  its correct place in the star sky’’). My Nordic background and values likely helped
  counterbalance any free market ideology picked up at UofC or material interests in a
  banking and hedge fund career. And the family in Bad Homburg: My rocks, dear
  Annette as well as Kukka and Akseli, I am hugely grateful for your understanding
  during this long project. I just hope I can be as supportive when it is your turn.
  Antti Ilmanen
  Bad Homburg, November 2010
  Abbreviations and acronyms
  AM
  ATM
  AUM
  BEI
  BF
  B/P
  BRP
  B-S
  C-P BRP
  CAPM
  CAY
  CB
  CCW
  CDO
  CDS
  CF
  CFNAI
  CFO
  CMD
  CPIyoy
  CRB
  CRP
  CRRA
  CTA
  DDM
  DJ CS
  DMS
  D/P
  DR
  Eð Þ
  EMH
  E/P
  EPS
  Arithmetic Mean
  At The Money (option)
  Assets Under Management
  Break-Even Inﬂation
  Behavioral Finance
  Book/Price, book-to-market ratio
  Bond Risk Premium, term premium
  Black–Scholes
  Cochrane–Piazzesi Bond Risk Premium
  Capital Asset Pricing Model
  Consumption wealth ratio
  Central Bank
  Covered Call Writing
  Collateralized Debt Obligation
  Credit Default Swap
  Cash Flow
  Chicago Fed National Activity Index
  Chief Financial Oﬃcer
  Commodity (futures)
  Consumer Price Inﬂation year on year
  Commodity Research Bureau
  Credit Risk Premium (over Treasury bond)
  Constant Relative Risk Aversion
  Commodity Trading Advisor
  Dividend Discount Model
  Dow Jones Credit Suisse
  Dimson–Marsh–Staunton
  Dividend/Price (ratio), dividend yield
  Diversiﬁcation Return
  Expected (conditional expectation)
  Eﬃcient Markets Hypothesis
  Earnings/Price ratio, earnings yield
  Earnings Per Share
  xx
  Abbreviations and acronyms
  ERP
  ERPB
  ERPC
  F
  FF
  FI
  FoF
  FX
  G
  GARCH
  GC
  GDP
  GM
  GP
  GSCI
  H
  HF
  HFR
  HML
  HNWI
  HPA
  HY
  IG
  ILLIQ
  IPO
  IR
  IRP
  ISM
  ITM
  JGB
  K-W BRP
  LIBOR
  LP
  LSV
  LtA
  LTCM
  MA
  MBS
  MIT-CRE
  MOM
  MSCI
  MU
  NBER
  NCREIF
  OAS
  OTM
  Equity Risk Premium
  Equity Risk Premium over Bond (Treasury)
  Equity Risk Premium over Cash (Treasury bill)
  Forward price or futures price
  Fama–French
  Fixed Income
  Fund of Funds
  Foreign eXchange
  Growth rate
  Generalized AutoRegressive Conditional Heteroskedasticity
  General Collateral repo rate (money market interest rate)
  Gross Domestic Product
  Geometric Mean, also compound annual return
  General Partner
  Goldman Sachs Commodity Index
  Holding-period return
  Hedge Fund
  Hedge Fund Research
  High Minus Low, a value measure, also VMG
  High Net Worth Individual
  House Price Appreciation (rate)
  High Yield, speculative-rated debt
  Investment Grade (rated debt)
  Measure of a stock’s illiquidity: average absolute daily return
  over a month divided by dollar volume
  Initial Public Oﬀering
  Information Ratio
  Inﬂation Risk Premium
  Business conﬁdence index
  In The Money (option)
  Japanese Government Bond
  Kim–Wright Bond Risk Premium
  London InterBank Oﬀered Rate, a popular bank deposit rate
  Limited Partner
  Lakonishok–Shleifer–Vishny
  Limits to Arbitrage
  Long-Term Capital Management
  Moving Average
  (ﬁxed rate, residential) Mortgage-Backed Securities
  MIT Center for Real Estate
  Equity MOMentum proxy
  Morgan Stanley Capital International
  Marginal Utility
  National Bureau of Economic Research
  National Council of Real Estate Investment Fiduciaries
  Option-Adjusted (credit) Spread
  Out of The Money (option)
  Abbreviations and acronyms
  P
  P/B
  P/E
  PE
  PEH
  PT
  r
  R
  RE
  REITs
  RWH
  S
  SBRP
  SDF
  SMB
  SR
  SWF
  TED
  TIPS
  UIP
  VaR
  VC
  VIX
  VMG
  WDRA
  X
  Y
  YC
  YTM
  YTW
  xxi
  Price
  Price/Book (valuation ratio)
  Price/Earnings (valuation ratio)
  Private Equity
  Pure Expectations Hypothesis
  Prospect Theory
  Excess return
  Real (rate)
  Real Estate
  Real Estate Investment Trusts
  Random Walk Hypothesis
  Spot price, spot rate
  Survey-based Bond Risk Premium
  Stochastic Discount Factor
  Small Minus Big, size premium proxy
  Sharpe Ratio
  Sovereign Wealth Fund
  Treasury–Eurodollar (deposit) rate spread in money markets
  Treasury Inﬂation-Protected Securities, real bonds
  Uncovered Interest Parity (hypothesis)
  Value at Risk
  Venture Capital
  A popular measure of the implied volatility of S&P 500 index
  options
  Value Minus Growth, equity value premium proxy
  Wealth-Dependent Risk Aversion
  Cash ﬂow
  Yield
  Yield Curve (steepness), term spread
  Yield To Maturity
  Yield To Worst
  Disclaimer
  Antti Ilmanen is a Senior Portfolio Manager at Brevan Howard, one of Europe’s largest
  hedge fund managers.
  The views expressed in this book are the author’s own views and are not the views of any of
  the Brevan Howard group of aﬃliated companies.
  The information and opinions contained in this document are for information and
  discussion purposes only, do not constitute a ﬁnancial promotion and do not purport
  to be full or complete. Whilst the author has used his best eﬀorts to ensure the accuracy
  or completeness of any information contained herein, no reliance may be placed for any
  purpose on the information or opinions contained in this book or their accuracy or
  completeness. No representation, warranty or undertaking, express or implied, is given
  as to the accuracy or completeness of the information or opinions contained in this book
  and no liability is accepted for the accuracy or completeness of any such information or
  opinions.
  This book does not constitute or form part of any oﬀer to issue or sell, or any
  solicitation of any oﬀer to subscribe or purchase, any shares or any other interests
  nor shall it or the fact of its distribution form the basis of, or be relied on in connection
  with, any contract thereof. This book is not intended to constitute, and should not be
  construed as, investment advice.
  Part I
  Overview, historical returns, and
  academic theories
  1.
  2.
  3.
  4.
  5.
  6.
  7.
  Introduction
  Whetting the appetite: Historical averages and forward-looking returns
  The historical record: The past 20 years in a longer perspective
  Road map to terminology
  Rational theories on expected return determination
  Behavioral ﬁnance
  Alternative interpretations for return predictability
  1
  Introduction
  . This book covers the general topic of expected returns on investments. The
  traditional paradigm among institutional investors focuses too much on his
  torical performance and too narrowly on asset class allocation. This book argues
  that investment decision making should be broadened beyond the asset class
  perspective and a wider set of inputs should be used for assessing expected
  returns.
  . The book considers in detail a wide range of return sources: major asset classes
  (stocks, bonds, and alternative investments) and strategy styles (value, carry,
  momentum, and so forth) as well as risk factors (such as growth, inﬂation,
  and liquidity).
  . The main inputs—beyond discretionary views—for investors to judge expected
  returns are (1) historical performance, (2) theories, and (3) forward-looking
  indicators. A better understanding of these inputs and a better balance among
  them is needed.
  . Well-known evidence of historical asset returns include the signiﬁcant long-run
  outperformance of stocks over bonds (less so in the 19th and 21st century than in
  the 20th century) as well as more moderate rewards for bearing interest rate risk
  and credit risk.
  . Less familiar historical ﬁndings include the pervasive success of value, carry, and
  momentum strategy styles in several markets as well as the tenuous relation
  between volatility and average returns. This book highlights the low long-run
  returns of the most volatile assets within each asset class, a ﬁnding that may
  reﬂect risk-seeking (‘‘lottery-playing)’’ behavior by investors, or that may be
  explained by leverage constraints.
  . Finance theories have changed dramatically over the past 30 years, away from
  the restrictive theories of the single-factor CAPM, eﬃcient markets, and constant
  expected returns. Current academic views are more diverse, less tidy, and more
  realistic. Expected returns are now commonly seen as driven by multiple factors.
  Some determinants are rational (risk and liquidity premia), others irrational
  (psychological biases such as extrapolation and overconﬁdence). Expected
  returns on all factors may vary over time.
  . A central insight from academic ﬁnance theories is that required asset returns
  have little to do with an asset’s standalone volatility and more to do with when
  losses can be expected to occur. Investors should require high-risk premia for
  assets that fare poorly in bad times, whereas safe haven assets (that fare well in
  bad times and less well in good times) can justify low or even negative risk
  premia. Strategies that resemble selling ﬁnancial catastrophe insurance—steady
  small gains punctuated by infrequent but large losses—warrant especially
  4
  Overview, historical returns, and academic theories
  .
  .
  .
  .
  .
  high risk premia because their losses are so highly concentrated in the worst
  times.
  Forward-looking indicators such as valuation ratios have a better track record in
  forecasting future asset class returns than rearview mirror measures. The practice
  of using historical average returns as best estimates of future returns is dangerous
  when expected returns vary over time. Recall stock markets in 1999–2000.
  Long-run expected returns for any investment tend to be especially high follow
  ing adverse events. For example, equity markets tend to have predictably higher
  returns after recessions, and nominal bonds after high inﬂations.
  Investors can try to boost expected returns by taking risks that produce attractive
  rewards for all market participants (beta risks) and/or by skillful active manage
  ment (alpha) which may involve exploiting regularities and market ineﬃciencies.
  This book oﬀers a comprehensive guide for smart harvesting of beta risk premia,
  covering both long-run exposures to traditional and alternative betas as well as
  tactical beta timing. However, I concede from the outset that the magic of view
  based alpha generation cannot be conveyed in a book.
  Two visual aids—an elephant and a cube—help the reader keep ‘‘the big picture’’
  in mind through the book.
  Although I present large amounts of empirical evidence about historical returns
  and forward-looking indicators, as well as numerous theories in an attempt to
  make sense of the data, I believe it is important to stress humility. Hindsight bias
  makes us forget how diﬃcult forecasting is, especially in highly competitive
  ﬁnancial markets. Expected returns are unobservable and our understanding
  of them is limited. Even the best experts’ forecasts are noisy estimates of
  prospective returns.
  It was six men of Hindostan,
  To learning much inclined,
  Who went to see the elephant
  (Though all of them were blind);
  That each by observation
  Might satisfy his mind.
  —J.G. Saxe (to be continued )
  The traumatic housing and credit crisis that began in 2007 challenged many beliefs
  about investing and ﬁnancial markets. The aftershocks of the crisis are still felt in many
  markets and economies (not least in public ﬁnances), but it is no longer necessary or
  advisable to view the future solely through the prism of this crisis. Instead, this book
  surveys the landscape of expected returns and long-term investment prospects based on
  lessons learned over decades.
  The traditional paradigm of institutional investing focuses on relatively static asset
  class allocations that are largely determined by historical performance. We must go back
  to basics and broaden the traditional paradigm in two ways. The inputs used for
  assessing expected returns should be better balanced and the idea of what constitutes
  investments should be challenged beyond the asset class perspective.
  Introduction and overview
  5
  Figure 1.1. The elephant: Shining light on expected returns from diﬀerent directions.
  The foremost need for multi-dimensional thinking is on inputs. When investors make
  judgments about the expected returns of various investments, they should guard against
  being blinded by past performance and must ensure that they take all or most of the
  following considerations into account:
  .
  .
  .
  .
  historical average returns;
  ﬁnancial and behavioral theories;
  forward-looking market indicators such as bond yields; and
  discretionary views.
  Figure 1.1 recalls the parable about several blind men and an elephant, as told by the
  American poet John Godfrey Saxe (1816–1887), each man describing one part of the
  elephant from his narrow vantage point. One man is feeling the leg and calling it a tree,
  another touching the ear and naming it a fan, a third mistaking the tail for a rope, and so
  on. Each man misses the big picture—and so will investors who study expected returns
  from a single vantage point.
  The ﬁrst approached the elephant,
  And happening to fall
  Against his broad and sturdy side,
  At once began to bawl,
  ‘‘Bless me, it seems the elephant
  Is very like a wall.’’
  So the challenge is to reﬁne the art of investment decision making in a way that exploits
  all our knowledge about historical experience, theories, and current market conditions,
  without being overly dependent on any one of these. This book will summarize the state
  of knowledge on all these aspects, but it focuses on the ﬁrst three inputs since these are
  systematic. I have less to say about discretionary views since these are inherently
  investor speciﬁc. However, the approaches described in this book will help readers form
  such views. Stated diﬀerently, investing involves both art and science; a solid back
  ground in the science can improve the artist.
  6
  Overview, historical returns, and academic theories
  Figure 1.2. The cube: Three perspectives on investments and their expected returns.
  Before turning to these inputs, I address the reasonable question ‘‘Expected returns on
  what?’’ The traditional paradigm has been to break the complex world of investments
  into simpliﬁed groupings called asset classes. Analyzing, and allocating to, asset classes
  has been the dominant approach but I argue that studying investments from perspec
  tives other than asset classes can enhance our understanding of return sources and our
  ability to diversify eﬀectively. This book will add to the asset class perspective the
  complementary viewpoints of strategy styles and risk factors, as in the three-dimensional
  ‘‘cube’’ in Figure 1.2:
  . Starting with the asset class perspective, I will cover all traditional asset classes
  (equities, government bonds, credits) plus many alternative ones (including real
  estate, commodities, hedge funds, and private equity). I focus on long-run returns
  but also review tactical market-timing approaches. A broader mindset naturally leads
  to questioning the traditional 60/40 portfolio which relies excessively on one source of
  excess returns (the equity premium) and which therefore has highly concentrated risk
  (more than 90% of portfolio volatility is due to equities).
  . The strategy style perspective is especially important for understanding the proﬁt
  potential of popular active-trading approaches. Value, carry, momentum, and
  volatility styles have outperformed buy-and-hold investments in many asset classes.
  Styles can also oﬀer better diversiﬁcation opportunities than asset classes.
  . Sophisticated investors are increasingly trying to look beyond asset classes and
  strategies in order to identify the underlying factors driving their portfolio returns.
  A factor-based approach is also useful for thinking about the primary function of
  each asset class in a portfolio (stocks for harvesting growth-related premia, certain
  alternatives for illiquidity premia, Treasuries for deﬂation hedging, and so on) as well
  as for diversifying across economic scenarios. Among underlying risk factors, I opt to
  focus on growth, inﬂation, illiquidity, and tail risks (volatility, correlation, return
  asymmetries).
  Introduction and overview
  7
  The second, feeling of his tusk,
  Cried, ‘‘Ho! What have we here
  So very round and smooth and sharp?
  To me, ’tis mighty clear
  This wonder of an elephant
  Is very like a spear.’’
  How can investors deal with the complexity of multiple inputs and perspectives, let alone
  with the even more bewildering assortment of novel investment products on oﬀer? This
  book provides a map to investors, giving a bird’s eye view over a rugged terrain and
  occasionally zooming in to interesting locations (12 case studies), not unlike Google
  Earth TM . I hope my two visual aids—the elephant and the cube—will help readers keep
  the forest in sight among the many trees along the way.
  Next, Sections 1.1–1.4 give an overview on the four perspectives on ‘‘feeling the
  elephant’’ (i.e., on considerations for judging expected returns). These themes will be
  expanded on through the book.
  1.1
  HISTORICAL PERFORMANCE
  Historical average returns are a common starting point for judging expected returns.
  The idea is that if expected returns are constant over time, long-run average realized
  return is a good estimate of expected future return. Unexpected news dominates returns
  in the short run but the eﬀects of such news tend to cancel out in the long run.
  Why should you think twice before using historical returns as forecasts of future
  returns?
  . Any sample period may be biased—in the sense of not being representative of market
  expectations—so that unexpected returns do not neatly cancel out, especially if the
  sample starts or ends at times of exceptionally high or low market valuations. Wind
  fall capital gains during a benign sample can boost average returns meaningfully even
  over multiple decades. Bond indices are a prime example, given the downtrend in
  bond yields since the 1970s and 1980s when a number of the widely used bond index
  histories start.
  . In principle, longer historical windows reduce sample speciﬁcity and enable more
  accurate estimates of average returns. However, distant historical data may be
  irrelevant due to structural changes, apart from lower data quality. Would we really
  want to include data from the 1600s even if good-quality returns were available to us?
  . Expected returns may vary over time in a cyclical fashion, which makes extrapolation
  of multi-year performance particularly dangerous. Periods of high realized returns
  and rising asset valuations—think stock markets in the 1990s—are often associated
  with falling forward-looking returns.
  . For speciﬁc funds and strategies, the historical performance data that investors get to
  see are often upward biased. This bias is due to the voluntary nature of performance
  reporting and survivorship bias (so that poor performers are left out of databases or
  are not marketed by the fund manager). A similar caveat applies to simulated ‘‘paper’’
  portfolios because backtests may be overﬁtted and trading costs ignored or
  understated.
  8
  Overview, historical returns, and academic theories
  These concerns notwithstanding, this book presents extensive evidence of long-run
  realized returns, when possible covering 50-to-100-year histories. Several main ﬁndings
  are familiar to most readers:
  . Stock markets have outperformed ﬁxed income markets during the past century in all
  countries studied. The compound average real return for global equities between 1900
  and 2009 is 5.4%, which is 3.7% (4.4%) higher than that of long-term government
  bonds (short-dated Treasury bills). Stocks’ outperformance over bonds is 0.5% to
  0.8% higher for the U.S. than globally and was even more pronounced before the
  negative returns in 2000s. The experience of the current investor generation has buried
  the myth that stocks always beat bonds over 20-year or 30-year horizons. (This myth
  was never true. Many exceptions to it occurred outside the U.S. in the 20th century
  and inside the U.S. during the 19th century.)
  . Among ﬁxed income markets, long-term bonds have outperformed short-dated bonds
  by 0.5% to 1% and credit-risky corporate bonds have outperformed comparable
  government bonds by 0.3% to 1% (low end for investment-grade bonds, high end
  for high-yield bonds). More surprisingly, the reward for bearing interest rate risk or
  credit risk is most consistent at short maturities. At the back end of the yield curve and
  at the low end of the credit spectrum there has been scant long-run beneﬁt for
  additional risk taking.
  . Illiquid assets have tended to oﬀer moderately higher long-run returns than their
  liquid peers. Part of corporate bonds’ excess returns over Treasuries reﬂects the
  liquidity disadvantage of corporates, and the same appears true for small-cap stocks
  over large-cap stocks. Evidence across asset classes is more ambiguous because
  various reporting biases may overstate published private equity and hedge fund
  returns. Moreover, average return diﬀerences can reﬂect premia for various risks
  and not just for illiquidity; disentangling the determinants is quite hard.
  Other ﬁndings are less widely known:
  . Certain active strategy styles have proved proﬁtable in several asset classes, adding
  several percentage points to annual average returns. The most prominent styles are
  value (overweighting assets that appear cheap based on some valuation metrics, while
  underweighting richly valued peers), carry (overweighting high-yielding assets while
  underweighting low-yielding assets), and momentum (overweighting assets that have
  outperformed over multiple months while underweighting recent laggards). The
  rewards from simulated active strategies are often overstated due to overﬁtting or
  selection biases. Yet the value, carry, and momentum proﬁts have been so prevalent
  that there is little doubt that these opportunities really existed in the past. The
  pertinent question is whether these strategies will remain proﬁtable now that they
  are so well known. If their proﬁts represent (at least in part) risk premia rather than
  market ineﬃciencies, it is less likely that future excess returns will be fully competed
  away.
  e A ﬂipside of the value eﬀect is that ‘‘growth assets’’—stocks of ﬁrms or countries
  with high past and expected growth rates—often deliver poor long-run returns that
  can be traced back to their high valuation ratios. One behavioral explanation is that
  investors over-extrapolate past growth rates and thus overpay for growth assets.
  No investment is attractive at any price, however fast growing it has been.
  Introduction and overview
  9
  Yield seeking has been proﬁtable in many contexts but more so in cross-country
  trades than in within-country trades. The worst results are for complex carry
  products that may contain hidden costs and risks.
  e Chasing returns sounds very naive but favoring past winners has not been a bad
  strategy historically—as long as history lengths to measure past returns are
  judiciously selected. Details diﬀer across asset classes but most investments exhibit
  momentum (continuation) tendency over multi-month horizons and a mild reversal
  tendency over multi-year horizons.
  . The empirical relation between volatility and expected returns is tenuous. Volatility
  and long-term average returns are positively related across asset classes. Moreover, a
  strategy of writing equity index options earns positive long-run returns, a justiﬁable
  reward given the inherent riskiness of eﬀectively selling ﬁnancial catastrophe insur
  ance. However, the most volatile assets within each asset class—high-volatility stocks,
  30-year Treasuries, and CCC-rated corporates—tend to oﬀer low long-run returns
  and even worse risk-adjusted returns. This surprising pattern may reﬂect investors’
  lottery-seeking bias (overpaying for the hope of jackpot returns) as well as leverage
  constraints (overpaying for inherently volatile assets that give high bang for the buck
  for naive return seekers). Avoiding the inherently volatile pockets of each market
  (lottery tickets) and leveraging up inherently stable assets have boosted returns in the
  past, even before the leverage restrictions were tightened in the aftermath of the 2008
  crisis.
  e
  1.2
  FINANCIAL AND BEHAVIORAL THEORIES: A BRIEF
  HISTORY OF IDEAS
  The third approached the animal
  And happening to take
  The squirming trunk within his hands
  Then boldly up and spake:
  ‘‘I see,’’ quoth he, ‘‘the elephant
  Is very like a snake.’’
  Finance is a ﬁeld in which academics and investment practitioners have had a huge
  inﬂuence on each other, as highlighted in Peter Bernstein’s books Capital Ideas and its
  sequel Capital Ideas Evolving. The theory of ﬁnance evolved dramatically during the last
  half-century, contemporaneously with the period during which investing grew into a big
  professional business. Until the 1950s ﬁnance theory hardly existed: the focus was on
  predicting cash ﬂows, not on risk or required returns. Then, three decades of pioneering
  research brought about an academic consensus view that relatively simple theories
  employing highly restrictive assumptions—the single-factor CAPM, the eﬃcient market
  hypothesis, constant risk premia—could explain asset prices and expected returns:
  . A starting point in ﬁnance is that investors set prices so that an asset’s cost equals its
  expected beneﬁts. Aggregating across investors, each asset’s market price equals the
  expected sum of its future cash ﬂows discounted to the present value (i.e., expected
  cash ﬂows are divided by 1 þ Discount rate).
  10
  Overview, historical returns, and academic theories
  . Asset-pricing theory focuses on the determinants of discount rates or required returns.
  In market equilibrium, an asset’s expected return equals the required return that
  rational investors together demand. Risk-averse investors do not use the riskless
  rate for discounting, unless the cash ﬂow being discounted is itself riskless; the
  discount rate also reﬂects the required compensation for the riskiness of an asset’s
  expected future cash ﬂows. This compensation in turn reﬂects both the amount of risk
  and the intensity of investor aversion toward risk.
  . According to the Capital Asset Pricing Model (CAPM), an asset’s amount of risk is
  fully captured by its (equity) market beta, while general investor risk aversion deter
  mines the size of the market risk premium. Each asset’s expected return in excess of a
  common riskless rate equals the product of the asset’s beta (sensitivity to market
  movements) and the common market risk premium. The diﬀerence in expected
  returns across assets reﬂects only diﬀerences in the betas of the assets. Investors
  can boost long-run returns by bearing more beta risk: by holding higher beta stocks
  and by shifting allocations from ﬁxed income (with beta near zero) to equities (with
  beta near one).
  . Given the assumption of constant expected returns, the long-run average of realized
  returns is a good estimate of expected return, even if realized and expected returns can
  diﬀer sharply over any short time window. Attempts to time the market were deemed
  a particularly wasteful form of active trading because moving from equities to cash
  implies forfeiting the large and presumably constant equity premium.
  Such restrictive theories did not prove suﬃcient to explain real market behavior. As new
  evidence accumulated, both academic and investor opinions evolved:
  . In recent decades, high-beta stocks and high-volatility stocks gave no return
  advantage, perhaps the reverse. Value and momentum tilts were more consistent
  return enhancers among equities, while related carry and trend strategies fared well
  in other asset markets.
  . The realized premium of equities over bonds turned out to be slim compared with
  earlier histories, and views on the future equity premium were trimmed down.
  . Several very large boom–bust cycles made the idea of constant risk premia less
  credible and that of market timing more acceptable.
  . After the cult of equity busted around the year 2000, alternative assets, carry trades,
  and harvesting illiquidity premia became the preferred ways to boost returns. All
  these approaches resulted in dramatic losses in 2008.
  . Just when investors learned to value conservatism, junk bonds and speculative stocks
  rallied by at least 100% in the year ensuing the crash bottom in March 2009.
  So where are we now? Current academic views are more diverse, less tidy, and more
  realistic than they used to be. Between 1980 and 2010, empirical and theoretical work
  added ﬂesh to the core models by incorporating multiple risk factors, time-varying
  expected returns, liquidity eﬀects and other market frictions, as well as investor
  irrationality. The ﬁeld is increasingly seeking help from outside ﬁnance, economics,
  and statistics by turning to psychology, biology, physics, and even philosophy.
  Greater realism is welcome but is no panacea. Theories can only enhance our
  understanding if they simplify the messy real world. In that spirit, I highlight some core
  ideas that apply to all investments.
  Introduction and overview
  11
  Complex reality with multiple return drivers, both rational and irrational
  If investors want to earn expected returns higher than the riskless rate, the most reliable
  way is to bear risks that markets reward with a premium. A less reliable way is to pursue
  active management, in which successful investors (skillful or lucky) reap gains at the
  expense of their less successful peers.
  The simple story of a single risk factor, constant expected returns, and fully rational
  investors is outdated. Even in a more complex world with several drivers of required
  returns, equity market beta—or more generally sensitivity to economic growth—
  remains the most important risk source. Beyond equity market beta, exposures to
  inﬂation, illiquidity, and tail risks (such as volatility) inﬂuence many assets and are
  rewarded.
  The interrelations between factors matter. Portfolio diversiﬁcation is more eﬀective
  with independent or, even better, with negatively correlated return sources. However,
  many return sources tend to be positively correlated—and especially so during a
  systemic crisis such as that of 2008. I will present return analysis separately for numer
  ous factors or return sources but I already note that these can overlap with each other or
  be empirically correlated (I show some evidence at the beginning of Chapter 16).
  The rewards may have rational or irrational origins. Numerous behavioral stories
  explain the high returns of certain asset types or trading strategies as being due to
  mispricing rather than fair compensation for risk. I present many examples of irration
  ality, emphasizing investors’ extrapolation as well as over- and underreaction tendencies
  as drivers behind the long-run outperformance of value and momentum strategies.
  Expected return diﬀerentials across assets depend less on volatility . . .
  Many investors view the risk–reward tradeoﬀ as being determined through an asset’s
  standalone risk. Stocks are more volatile than bonds and thus deserve higher long-run
  returns. Likewise, long bonds are more volatile than short bonds and thus deserve higher
  long-run returns. This idea points in the right direction—that risk inﬂuences expected
  returns—but misses the fact that all volatility is not equal.
  Each asset reﬂects a bundle of underlying risk factors and some idiosyncratic risk.
  Diversiﬁable (idiosyncratic) risks should not earn any reward; only systematic risks
  (those that cannot be eliminated through diversiﬁcation) can be expected to be rewarded
  with a premium. The reward for volatility can diﬀer depending on which of several
  systematic factors is the source of the volatility. Overall, the theoretical relation between
  volatility and expected return is quite ambiguous (and, as already noted, the empirical
  relation is tenuous).
  . . . and more on the typical timing of losses
  Although there are a number of diﬀerent risk factors, one key rational theme explains
  what drives ﬁnancial risk premia. Assets or factors that perform poorly in ‘‘bad times’’—
  think of recessions and ﬁnancial crises—warrant high required returns. Conversely, safe
  haven assets (such as long-term government bonds, at least since the late 1990s) that
  smooth portfolio returns in bad times deserve a low risk premium. This central insight in
  modern academic ﬁnance about asset risk premia implies that certain assets and/or
  12
  Overview, historical returns, and academic theories
  Figure 1.3. Asset class performance in the long run vs. in bad times.
  Sources: Bloomberg, Ken French’s website, Citigroup, Barclays Capital, S&P GSCI, MIT-CRE.
  strategies deserve high long-term returns (and oﬀer especially juicy returns in good
  times) exactly because they tend to give a terrible performance just when it hurts
  investors most. Many practitioners and policymakers had to wait until 2008 to learn
  this lesson, the hard way.
  For illustration, Figure 1.3 scatterplots 50-year average real returns of various U.S.
  asset classes on a simple proxy of ‘‘bad times performance’’—average losses in arguably
  the three worst years (1974, 1981, 2008) for ﬁnancial markets and the global economy
  during this half-century. The empirical relation is hardly linear but the assets with the
  best long-run performance—small-cap stocks—also gave the worst losses in bad times.
  At the other end, Treasury bills and bonds with low long-run returns were the best safe
  haven assets in bad times (more so in deﬂationary 2008 than in inﬂationary years).
  Traditional equity and bond investments have well-understood risks and premia, but
  the same cannot be said for investments with asymmetric risk proﬁles (‘‘picking up
  pennies in front of a steamroller’’). Investors should be especially wary of strategies that
  amount to selling tail insurance or ‘‘lottery tickets’’ that pay oﬀ in bad times—writing
  options on equity indices, carry trading, and harvesting illiquidity premia. These
  strategies combine the dangers of (i) asymmetric returns and (ii) the coincidence of large
  losses with bad times. The long-run returns of such strategies are justiﬁably high, but
  these returns are concentrated in good times and tend to persist only until a bad event
  materializes. I do not have 50-year histories for such strategies but I will document
  below strong long-run returns for selling volatility, seeking carry, and harvesting
  illiquidity premia—as well as dramatic losses for each in 2008. In contrast, trend
  following strategies have a surprisingly consistent record as safe havens during bad
  times.
  Investors should not be misled by the apparently attractive reward–risk ratios of
  illiquid assets. These assets warrant an extra premium because of their illiquidity and
  poor performance in liquidity droughts, while infrequent price moves artiﬁcially under
  state their measured riskiness. Illiquid assets naturally suit long-horizon investors with
  Introduction and overview
  13
  limited liquidity needs, but even such investors should not assume that illiquidity is
  always amply rewarded.
  Expected rewards on all return sources can vary over time
  It may now seem quaint to talk about constant expected returns but for long this was
  one of the classic assumptions in ﬁnance. While many practitioners questioned this
  assumption, market timing was generally avoided. The reasons were manifold: timing
  was not easy (being right too early often equals being wrong, with substantial career
  risk); the directional bet is highly concentrated (unlike security selection that at least
  beneﬁts from diversiﬁed exposures); and cash holdings miss out the equity premium
  (which was seen to be especially high before the 2000s’ experience).
  The boom–bust cycles of the past decade shifted the consensus to embrace the idea
  that expected returns vary over time. Market timing no longer had such a bad name.
  Investors began to pay attention to forward-looking valuation ratios.
  1.3
  FORWARD-LOOKING INDICATORS
  The fourth stretched out his eager hand
  And felt about the knee,
  ‘‘What most this mighty beast is like
  Is mighty plain,’’ quoth he;
  ‘‘ ’Tis clear enough the elephant
  Is very like a tree.’’
  Forward-looking indicators such as earnings yields and bond yields are often better than
  historical average returns at forecasting long-term returns. Time-varying expected
  returns can make historical average returns very misleading as forecasts of future
  returns. For example, because stock prices were unusually high, the prospective returns
  on equities were especially low in 2000 after nearly two decades of outstanding realized
  returns. Conversely, the halving of global equity values between October 2007 and
  October 2008 surely did not hurt the prospects for subsequent long-term equity returns.
  Empirical evidence suggests that near-term returns of risky assets are relatively high
  around business cycle troughs and relatively low around business cycle peaks. The
  two main explanations for the apparent countercyclic pattern in ex ante returns are
  (1) rationally time-varying risk premia and (2) irrational market mispricing. Time-varying
  risk premia may reﬂect variation in the amount of risk and/or market risk aversion.
  One compelling rational reason for boom–bust cycles is that risk aversion is wealth
  dependent and thus ampliﬁes the gyrations in stock market valuations over time. Many
  people are more risk averse during recessions, which can create a feedback loop that
  pushes asset prices lower. (A similar feedback loop pushes already high prices higher,
  causing bubbles.) An alternative interpretation suggests that irrational fear or gloomy
  cash ﬂow forecasts cause low market valuations during recessions. Market data cannot
  distinguish between rational and irrational stories, and both may have contributed to
  the observed return predictability.
  It is not just the equity premium that varies predictably over time—most premia do.
  Such time variation is most obvious in the ﬂuctuations of credit spreads, but I will review
  14
  Overview, historical returns, and academic theories
  many other examples. The inﬂation risk premium in nominal bonds was clearly higher in
  the 1980s than in the 2000s, while the illiquidity premium in many assets shifted from
  negligible in 2006–2007 to record high levels in 2008–2009. When salient adverse events
  for any risk factor materialize, the ex ante premium tends to widen and then only
  gradually decay from elevated levels, with the pace of the decay perhaps related to
  lingering investor memories.
  Endogenous sources of return and risk—sources arising from within the market
  place—are a recent topic of interest and may aﬀect any investment. The persistent
  success of any asset class or trading strategy leads to a ‘‘virtuous’’ cycle of growing
  popularity and further success, resulting in eventual overcrowding and subsequent
  disappointments. The more persistent the success and the more asymmetric the payoﬀ,
  the more likely that this virtuous cycle turns vicious, ending with a rush to exit by return
  chasers and leveraged traders. Sharp liquidations tend to occur amidst tightening
  ﬁnancial conditions, and these in turn reinforce price and liquidity declines. These forces
  contribute to the short-term momentum and long-term reversal patterns observed for
  many investments.
  Let us not move from the extreme of no market timing to the other extreme of
  thinking it is easy. It is only easy with hindsight. The market’s required returns and
  cash ﬂow expectations are not directly observable. We only estimate them with the help
  of simple valuation ratios, or more complex theoretical models and statistical analyses,
  or survey data [1].
  All forward-looking indicators have their shortcomings and must be used with care.
  A few illustrations:
  . Many stock-market-timers use the dividend discount model to assess prospective
  equity returns. Even when two investors agree that long-term market returns reﬂect
  the sum of starting yield and growth prospect, their estimates can diverge widely. One
  debate is whether to use dividend yields or broader payout yields that include stock
  buybacks and issuance. The disagreement on growth prospects is even worse. Anyone
  using analysts’ earnings growth forecasts inherits the extreme optimism typical of
  analysts who often predict double-digit real growth over long horizons. Historical
  experience has been much more modest. Many investors can hardly believe that long
  run real growth rates for earnings per share and dividends per share are between 0%
  and 2%, clearly lagging the trend growth rate for real GDP.
  . Yield curve steepness is often used as a proxy for the reward for bearing interest rate
  risk. How on earth could the yield curve be inverted in the early 1980s when inﬂation
  was at a record high? To resolve the puzzle, recall that the yield curve reﬂects both risk
  premia and the market’s rate expectations. When short-term rates are exceptionally
  high (1981) or low (2010), many investors expect mean reversion to more normal rate
  levels. This eﬀect makes the curve exceptionally ﬂat (1981) or steep (2010) when short
  rates are extreme and thereby contaminate the curve’s information about the prevail
  ing bond risk premium. Survey-based bond risk premia have given a better picture of
  the market’s required reward for interest rate risk than has curve steepness; survey
  based premia have trended up and down together with the inﬂation level.
  . The credit spread of investment-grade corporates over Treasuries has averaged over
  100 basis points in recent decades. Yet, index investors in corporate credits earned
  only about a quarter of this spread as realized excess return. Where did the rest of the
  Introduction and overview
  15
  yield advantage disappear? It turns out that the obvious culprit, default losses, made
  only a small dent on returns. The worst leakage was due to index investors’ tendency
  to sell assets that leave the index and that tend to subsequently perform well, such as
  the BB-rated ‘‘fallen angels’’.
  1.4
  VIEW-BASED EXPECTED RETURNS
  He ﬁfth who chanced to touch the ear
  Said, ‘‘Even the blindest man
  Can tell what this resembles most;
  Deny the fact who can,
  This marvel of an elephant
  Is very like a fan.’’
  This book focuses on systematic sources of expected returns—reaping rewards for
  bearing risks that the market dislikes or exploiting common errors in investor judg
  ments. Thus, it has little to say on view-based expected returns that are discretionary and
  inherently investor speciﬁc. Views on secular changes are especially important because
  such changes can trip contrarian investors. Even forward-looking value indicators are
  anchored to history; shifting anchors can thus cause persistent investment mistakes.
  Many books try to understand the sources behind the value-added of superstar active
  managers. Unfortunately the skills of truly superior investors are hardly replicable. In
  the less rareﬁed world of ordinary active managers, nearly every view-taking investor
  subjectively expects the trade to be proﬁtable. Yet we know that in the aggregate, active
  trading proﬁts must amount to zero—and this is before subtracting costs and fees. Some
  investors are consistently successful, most are not. Realized value-added is easier to
  measure than prospective value-added.
  If this book can help discretionary view taking only indirectly (by educating readers),
  can it perhaps help more in identifying superior investor subsets, investment approaches, or
  individual managers? To a limited degree, yes. I will quantify the past performance of
  some active investor categories and some systematic strategies but I stress the dangers
  in simply extrapolating past returns. Among investor subsets, the long-run performance
  of individual investor activity appears worst. Mutual fund managers as a group cannot
  cover their fees and the majority tend to lag passive indices. Hedge fund managers have
  a reasonably attractive track record even collectively but critics argue that returns
  may be overstated and reﬂect poorly understood risks. When it comes to individual
  managers, superior investors surely exist but identifying them in advance is a challenge.
  Performance persistence is limited, albeit stronger among alternative managers.
  Evidence on the impact of fund age and size on performance is mixed but more
  distinctive managers with relatively large active risks appear to outperform the index
  hugging types [2].
  Is this book relevant for designing long-term investment benchmarks or for active
  managers trying to beat them? Both. In a typical investment process, benchmark asset
  class allocations and portfolios are designed to reﬂect the investor’s strategic (long-term)
  goals and constraints. The benchmark gives the ex ante ‘‘viewless’’ portfolio, or the
  natural place to stay, for investors who do not have tactical (short-term) views or who
  do not believe they can add value through active management. For active investors who
  16
  Overview, historical returns, and academic theories
  try to outperform the benchmark, benchmark portfolio return is a neutral yardstick for
  ex post performance evaluation. This book’s material is naturally relevant for making
  strategic decisions that could be coded in a benchmark but it also discusses tactical
  ‘‘beta-timing’’ tools. There are plenty of gray areas and fuzzy boundaries (see Section
  11.4) [3].
  1.5
  GENERAL COMMENTS ABOUT THE BOOK
  I have been a student of expected asset returns for over 20 years while wearing many
  diﬀerent hats—in the buyside and in the sellside, in research and in trading. I have also
  advised institutional investors on their long-term investment strategies, and it is mainly
  this last experience that has inspired this book.
  I aim to be broad and comprehensive, going well beyond equities which are the focus
  of most books:
  . The book reviews a lot of historical evidence. Despite the book’s empirical bent, it
  also provides a theoretical and practitioner perspective for interpreting and using the
  data. As usual, U.S. capital markets have the most comprehensive and often longest
  return histories, but I also present evidence from non-U.S. markets.
  . The book focuses on long-term expected returns, although it also discusses tactical
  return forecasting of major asset classes and many active trading styles. Many books
  exist on short-term trading, portfolio construction, and risk management, but few on
  long-term expected returns. The most comparable existing works are Triumph of the
  Optimists by Dimson–Marsh–Staunton (2002) (DMS) and ‘‘Stocks, bonds, bills and
  inﬂation’’ by Ibbotson–Sinqueﬁeld (1976), as updated by Ibbotson Associates and
  Morningstar (2008) [4].
  . Unlike many recent books, this one avoids a focus on the recent crisis—even though
  the crisis will undoubtedly cast a long shadow over markets. I hope that this book can
  be relevant for investors for years to come.
  Given the diverse perspectives taken and asset classes covered, this book does not have
  just one key theme. Rather, it is a mosaic, reﬂecting the complexity of the real world.
  I will brieﬂy discuss many theories and stories that together portray the ways that
  expected returns are determined, but I cannot give one coherent story. I am open
  minded regarding the roles of rational and irrational inﬂuences on expected returns;
  indeed, both surely matter. Among the many theories and stories available, I emphasize
  the ones I ﬁnd the most relevant, but my broader goal is to provide enough material and
  references to help a thoughtful reader make his or her own judgments [5].
  The sixth no sooner had begun
  About the beast to grope
  Then, seizing on the swinging tail
  That fell within his scope,
  ‘‘I see,’’ cried he, ‘‘the elephant
  Is very like a rope.’’
  Introduction and overview
  17
  Health warning: We should humbly recognize the limits of our understanding. Realized
  returns are dominated by randomness, structural uncertainty, and rare events. Expected
  returns are unobservable, at best estimated with noise. We should resist hindsight biases
  wired in us—the outcomes that materialized seem more inevitable or predictable than
  they truly were [6]. It is worth recalling that experts can only explain a fraction of
  realized return variation afterwards, and this is an inherently easier task than predict
  ing. Any observed return predictability is mild, possibly spurious, and rarely robust.
  Therefore I stress humility in interpreting empirical results and even more in making
  predictions and in trading based on them.
  My hope is that this book improves the reader’s understanding of expected returns
  while not adding to overconﬁdence. With better understanding comes a healthy respect
  for investment risks. I do not denounce risk taking, since it is the main way to enhance
  long-run returns, but investors should choose carefully which risks to take and how
  much of each, accepting them mainly when they are well rewarded.
  I review key investment takeaways in Chapters 28 and 29, but here is a one-paragraph
  summary: there are many ways to enhance long-run returns; several can be pursued in
  parallel. Investors should collect risk premia from diverse sources, not just equity premia
  but also illiquidity premia and value, carry, and momentum style tilts. Investors can
  further try to exploit leverage, contrarian timing, and view-driven active management—
  all of which can help when used with moderation. For various caveats and much more
  detail, see Chapters 28 and 29.
  One contribution of this book is to take return measurement seriously. Estimating
  prospective returns is hard enough without misinterpreting available data. We need to
  evaluate critically the published historical returns of any asset class or strategy (chapters
  on equity premium, alternatives, and dynamic strategies focus on various biases and
  data problems). And when ex ante measures are available, we need to recognize their
  pitfalls (bond chapters stress the shortcomings of yields and spreads).
  This book is long enough dealing with expected returns without venturing into the
  art and science of portfolio construction and risk management. Volatility and corre
  lations are traditional building blocks in those endeavors. I touch on these topics
  insofar as they inﬂuence expected returns. Intriguingly, they do, through the monetized
  beneﬁts of diversiﬁcation and rebalancing (see Chapter 28). Leverage can improve
  eﬀective diversiﬁcation, besides helping investors avoid overpriced high-volatility
  assets. Diversiﬁcation can also be enhanced by using the complementary perspectives
  of strategy styles and risk factors. For example, as value and momentum strategies
  tend to be negatively correlated, combining them gives much smoother returns than
  either style alone. Negatively correlated return sources are such powerful diversiﬁers
  that their usefulness should not be wasted. It is much harder to diversify away the
  directional equity market risk, as safe haven assets tend to be either costly or
  unstable.
  Striving to build a bridge between academic and practitioner worlds, this book
  focuses on intuition and contains almost no equations and only very basic statistics
  [7]. For many academics the book will thus seem insuﬃciently rigorous, while for some
  practitioners it may be too intense. My target audience, unsurprisingly, is in the middle:
  experienced professional investors still hungry to learn, including top-down asset
  allocators and fund trustees—as well as advanced ﬁnance students in CFA or MBA
  programs.
  18
  Overview, historical returns, and academic theories
  Outline
  When designing the book’s structure, I needed to ﬁnd a compromise between discussing
  broad issues common to many asset classes and providing evidence on speciﬁc asset
  classes, strategies, or factors. I decided to do both, while trying to avoid repetition. Parts
  I and III are broad while Part II focuses on speciﬁc cases. As the book’s structure is
  complex, the elephant and the cube may help as visual aids.
  In Part I, the Introduction is followed by an empirical appetizer focusing on historical
  average returns (Chapters 2 and 3). Thereafter I present various key concepts as well
  as the theory of expected return determinants—both rational and irrational stories
  (Chapters 4 through 7).
  In Part II, the main meat of this book (Chapters 8 through 19), I drill into the expected
  returns of 12 ‘‘cases’’: four asset classes, four popular active strategies, and four under
  lying risk factors. Figure 1.4 redraws the cube (from Figure 1.2, of three perspectives to
  investments: asset classes, strategy styles, and risk factors) with each side split into four
  parts according to the dozen cases. Besides the traditional asset class premia—equity,
  bond duration, and credit—I discuss a variety of alternative asset premia. The four
  active styles—equity value, currency carry, commodity momentum or trend, and
  volatility selling—have been popular because they have been among the most successful
  trading strategies in recent decades. There are many nominees for underlying factors; my
  subjective picks are growth, inﬂation, liquidity, and tail risks (volatility, correlation, and
  return asymmetry). I will show that all 12 investment approaches have enhanced long
  run returns in the past. I believe that all of them will continue to deliver excess returns,
  albeit in a time-varying fashion.
  While Part II discusses expected returns in the context of each distinct case, Parts I
  and III cover topics common to all or most cases. Recalling the analogy to the elephant
  parable, investors who study expected returns from a single vantage point can miss the
  big picture. To remedy this problem, Parts I and III try to shine light on expected returns
  Figure 1.4. The cube in detail: Asset classes, strategy styles, and underlying risk factors.
  Introduction and overview
  19
  Figure 1.5. The elephant in detail: Structure of this book’s broader chapters.
  from diﬀerent directions (as visualized in Figure 1.5). As emphasized above, historical
  performance, theories, and forward-looking indicators are the most important
  systematic inputs.
  Chapter topics in Part III include endogenous return eﬀects; forward-looking value
  and carry measures; usefulness of survey data; tactical forecasting models; as well as
  seasonal, cyclical, and secular return patterns. The book closes with main investment
  lessons and two appendices: a section on world wealth (size of main asset classes) and a
  description of data series and data sources [8].
  Given the book’s ambitious scope, it may be too much to absorb in one reading. To
  allay this problem, each chapter is reasonably self-contained and the reader can cherry
  pick the topics of interest.
  Now, let us turn to Poet Saxe and this chapter’s concluding reﬂections:
  And so these men of Hindostan
  Disputed loud and long,
  Each of his own opinion
  Exceeding stiﬀ and strong,
  Though each was partly in the right,
  And all were in the wrong!
  In an afterword, often omitted from recitations of his poem, Saxe reveals his hidden
  agenda: he is lampooning those (and there were many in his time) who engage in
  meaningless disputes about theology:
  Moral:
  So oft in theologic wars,
  The disputants, I ween,
  Rail on in utter ignorance
  Of what each other mean,
  And prate about an Elephant
  Not one of them has seen!
  20
  Overview, historical returns, and academic theories
  There are enough theological disputes about ﬁnance and investing. Like many writers,
  I too have a preacher’s passion, but I preach in an ecumenical church. This book stands
  against narrow-mindedness, inﬂexibility, and overconﬁdence in investing, and for
  humility, pragmatism, and diverse perspectives.
  Despite such lofty goals, I hope you enjoy the read, learn a lot, and eventually ﬁnd
  that the insights in this book make you a better investor.
  1.6
  NOTES
  [1] I endorse greater use of survey data to help interpret market pricing. High stock market
  valuations could reﬂect optimistic cash ﬂow growth forecasts or low discount rates while
  steep yield curves could reﬂect the market’s view of rising short rates or a high required bond
  risk premium. Survey data can help make these decompositions if consensus forecasts are
  deemed representative of market views. Survey-based analyses of stock, bond, and currency
  prices often support irrational explanations for asset return predictability instead of time
  varying risk premia.
  [2] When discussing hedge funds (Section 11.4) I review the debates about alpha, (traditional)
  beta, and alternative beta as return sources. The boundaries are blurred. One deﬁnition of
  alpha is ‘‘the average return that cannot be explained by common risk factors.’’ As more and
  more factors are added to models that explain fund returns, ever less scope is left for
  measured alpha. Yet, active managers argue that they are simply taking views against the
  market; if they are right they make money which should be deemed as alpha. Tensions
  naturally arise between these two mindsets. Investors into hedge funds are especially con
  cerned about asymmetric strategies that involve selling various forms of tail risk insurance
  whose payoﬀs can look deceivingly alpha like. If the fund manager’s ‘‘view’’ is that the stock
  market will not fall by more than 10% in any month (or that the real estate market will not
  fall in nominal terms or that yet another rare event will not materialize), even a manager
  without any forecasting skill can be proﬁtable and collect fees for years before the tail event
  with large losses occurs.
  [3] Every investing institution can debate (i) whether dynamic investment approaches—such as
  market timing, value tilt, or factor-based investing—are appropriate for it and (ii) whether
  these approaches should be coded in the benchmark or left for the active manager in the quest
  for outperformance. These questions are not so diﬀerent from asking whether emerging
  market stocks, commodity futures, or hedge funds should be included in their allowable
  investment universe and even into the benchmark. The answers will certainly vary across
  institutions, depending on prior beliefs, resources, costs, and other considerations.
  [4] These masterworks belong on every serious investor’s bookshelf. Books by DMS and
  Ibbotson (including work with various coauthors) provide more underlying data than mine
  does; indeed, I use their data in some of my analyses. Both focus rather exclusively on
  historical average and period-to-period (say, annual) returns on traditional asset classes,
  though the authors have elsewhere expanded empirical analysis to other asset classes and
  investment strategies. My book distinguishes itself by its comprehensive coverage of asset
  classes and strategies as well as by its many perspectives to tackling expected returns. I also
  embrace ‘‘new’’ ideas, such as time-varying expected returns and investor irrationality, more
  than these other books do.
  [5] Selectivity cannot be avoided. I emphasize some of my pet themes that are not yet part of the
  academic consensus, such as the impact of wealth-dependent risk aversion and lottery-type
  preferences on asset prices, the promise in market and/or factor timing, or the usefulness of
  survey data to assess real-time investor expectations. If any personal bias shines through more
  than the others, it is my preference for simple and liquid assets. Such assets are more
  Introduction and overview
  21
  transparent, often leading to better outcomes for end-investors. Sunlight is the best disin
  fectant, protecting investors against abuse.
  [6] In competitive markets, realized returns reﬂect much more variability than expected returns.
  Yet, humans have a tendency to attribute any good past performance to skill or other
  persistent edge. We repeatedly get ‘‘fooled by randomness’’ when we equate ex post success
  with ex ante skills and underestimate the role of chance. This is true in many realms of life but
  especially with investing.
  [7] Frustratingly for academic readers, I rarely show standard errors, t-statistics, or the statistical
  signiﬁcance of my ﬁndings. This partly reﬂects my target audience, and partly my view that
  the time-varying nature of expected returns and various biases make standard statistical
  inferences inappropriate. I prefer to assess the consistency of a return series ‘‘in investment
  language’’ by reporting the Sharpe ratio (which is closely related to statistical signiﬁcance)
  and by displaying cumulative performance graphs that I ﬁnd particularly informative for
  experienced users.
  [8] Personally, I love footnotes. I would also prefer to give too many credits and literature
  references in the text, explaining the intellectual history of each key idea. Finally, I was
  brought up to carefully document my data series construction. I have been advised that I
  am in a minority on all three counts. Thus, I try to shorten the book and improve its
  readability by minimizing notes (now ‘‘only’’ about 100 left), placing them at the end of
  each chapter. I make some references in the main text on the sources of ideas or empirical
  ﬁndings, but a longer list of references can be found at the end of the book. My data sources
  are only brieﬂy listed under each exhibit, but Appendix B describes my data sources and data
  series construction in detail.
  Source notes. Although I make some references in the main text, I leave most of them for
  the ‘‘Source notes’ ’section at the end of each chapter. The reference section proper can
  be found at the end of the book. Given the wide-ranging topic of this book, even these
  source notes must be selective. On many topics, I refer to important recent works rather
  than to seminal works. Even if the new working papers are often specialized and have
  not been tested by time, interested readers can ﬁnd in them references to both other
  recent works and the intellectual heritage of the idea.
  Books closest to this work are Ibbotson–Brinson (1993), Siegel (1994), and Dimson–
  Marsh–Staunton (2002). This book is intended for professional investors and assumes
  much prior knowledge. For professionals wanting to learn about institutions, products,
  and analytical tools in diverse investment markets, I recommend the various handbooks
  edited or written by Frank Fabozzi. For retail investors, I recommend William Bernstein
  (2002, 2009), John Kay (2008), and Malkiel–Ellis (2010). Among ﬁnance textbooks,
  I recommend Bodie–Kane–Marcus (2008) for MBA level and Cochrane (2005a) for
  Ph.D. level, while the history of the interaction between academic and practitioner
  ﬁnance is best covered in Peter Bernstein’s books Capital Ideas and Capital Ideas
  Evolving.
  2
  Whetting the appetite: Historical averages
  and forward-looking returns
  . I present some historical performance statistics for major asset classes and
  investment strategies, but I also highlight the pitfalls in using such data.
  . Average returns across asset classes seem positively related to volatility and
  illiquidity. Bearing duration risk and emerging market risk were exceptionally
  well rewarded during the past 20 years, equity risk not.
  . The results for 1990–2009 may be sample speciﬁc, reﬂecting an abnormally
  benign environment for certain asset classes. This problem can be mitigated
  by adjusting average returns for any windfall gains and by studying subperiod
  results and longer return histories.
  . Historical average returns are particularly misleading measures of prospective
  long-term returns if expected returns vary over time and the past sample period
  includes a signiﬁcant repricing. Forward-looking value indicators have their own
  limitations but are often superior proxies for expected returns.
  Before delving into the terminology and theories of expected return determination in the
  next chapters, I provide some empirical appetizers. Chapters 2 and 3 focus on historical
  average returns over a 20-year window and over even longer windows. I emphasize the
  pitfalls in interpreting historical data. If you do study historical returns, as most
  investors do, this chapter reminds you of several skeptical questions you should ask.
  I ﬁrst summarize the performance of all major (and some minor) asset classes and a
  few exceptionally successful active strategies over the past two decades.
  . The choice of my starting point (1990) is rather arbitrary, largely driven by data
  availability for certain strategies and factors. (Data for the principal asset classes go
  back much further.) Any such historical analysis is inherently sample speciﬁc, a
  problem for which I will suggest some remedies.
  . One 20-year window gives only one historical data point to assess the prospects for the
  next 20 years. For any serious statistical analysis, hundreds of years of data would be
  needed. Chapter 3 turns to evidence over longer time spans, but data availability and
  quality deteriorate the further back we look, and structural changes may make older
  data irrelevant.
  . Historical average returns can be especially poor proxies of future expected returns in
  a world with time-varying expected returns. I prefer ex ante measures of long-run
  expected returns, such as bond yields or earnings yields, and this point, indeed, is one
  of the key themes of this book.
  24
  Overview, historical returns, and academic theories
  . The reported returns may not have been achievable due to trading costs (which are
  especially signiﬁcant for illiquid assets and for strategies with high turnover). Total
  nominal returns also ignore the detrimental impact of taxes and inﬂation.
  Nonetheless, historical returns are a natural starting point of investment analysis, partly
  because humans are hardwired from prehistoric times to imitate successful actions and
  to learn from past experiences. Such hardwiring helped our ancestors survive and
  develop but it may work poorly or even be harmful in the domain of competitive modern
  ﬁnancial markets. The disclaimer ‘‘past performance is no indication or guarantee
  of future results’’ seems overused but bears repeating because it goes against key
  evolutionary traits.
  2.1
  HISTORICAL PERFORMANCE SINCE 1990
  Table 2.1 documents raw annualized compound average returns (nominal geometric
  means) and risk-adjusted returns (Sharpe ratios), as well as some risk statistics, for
  various investments over the period 1990–2009. The Sharpe ratio (henceforth SR) is the
  annualized arithmetic mean excess return over cash, divided by its annualized volatility;
  cash can be represented by the deposit rate (here) or by the Treasury bill rate (Chapter
  3). Illiquidity estimates are subjective assessments of each asset’s liquidity on a scale
  from 1 (liquid) to 5 (illiquid).
  Commenting on results for 1990–2009
  . It barely paid to move from government bonds to either equities or to corporate
  bonds (i.e., the realized equity risk premium and credit risk premium were very low
  over this exceptional sample period).
  . Global equities (the developed market index) even underperformed government
  bonds, dragged down by Japanese stocks whose bubble peaked just before our sample
  period started. Both U.S. and European stocks earned an annualized return over 8%,
  but Japanese stocks averaged �2% returns each year.
  . Among U.S. equity styles, small-cap value stocks fared best, while small-cap growth
  stocks fared worst.
  . Emerging market equities and debt earned much higher returns than developed
  market assets.
  . Duration risk was abundantly well rewarded, thanks to the persistent decline in yields.
  Global government bonds also beneﬁted from diversiﬁcation and earned the highest
  SR among traditional assets: 0.8.
  . Corporate credit risk bearing was poorly rewarded. I will later return to one key
  exception, which is that buying short-dated (1-to-3-year) top-rated (AAA/AA) credits
  while shorting duration-matched Treasuries earned a high Sharpe ratio.
  . Real estate markets ended up earning returns similar to those of stocks and bonds.
  Among other real assets, commodities and art underperformed while timber fared
  especially well.
  . Actively managed venture capital, private equity, and hedge funds earned doubledigit net returns, according to well-known indices (which may tend to capture the
  better performing funds and thus overstate industry returns).
  Whetting the appetite: Historical averages and forward-looking returns
  25
  Table 2.1. Summary statistics of asset classes and strategies, 1990–2009
  Asset/Strategy
  Geometric Sharpe Annual Illiquidity Equity
  mean
  ratio volatility estimate correlation
  (%)
  (%)
  Equities and U.S. equity styles
  Global developed equity (developed markets) 5.9
  Emerging equity (emerging market stocks)
  10.6
  U.S. equity market
  8.5
  Small growth
  5.0
  Small value
  14.0
  Big growth
  8.8
  Big value
  9.1
  0.18
  0.39
  0.34
  0.15
  0.62
  0.36
  0.37
  15.4
  24.3
  15.5
  24.6
  18.8
  15.8
  16.7
  2
  3
  2
  3
  3
  1
  1
  1.00
  0.75
  0.90
  0.69
  0.70
  0.85
  0.77
  1
  2
  3
  1
  1
  NA
  1
  3
  3
  �0.03
  0.16
  0.58
  -0.03
  0.00
  �0.07
  0.04
  0.54
  0.73
  Fixed income and related
  U.S. Treasuries
  U.S. FI (U.S. investment-grade debt)
  HY (U.S. high-yield debt)
  Depo (U.S. 1-month deposit rate)
  TBill (U.S. 1-month Treasury rate)
  CPI (U.S. inﬂation)
  Global governments (hedged debt)
  Emerging FI (emerging market debt)
  ConvB (convertible bonds)
  6.8
  7.0
  8.7
  4.5
  3.8
  2.8
  6.9
  11.5
  9.0
  0.53
  0.67
  0.49
  0.00
  �1.17
  0.79
  0.58
  0.43
  4.7
  3.9
  9.6
  0.6
  0.6
  0.9
  3.2
  14.2
  12.6
  Alternatives including real assets
  CMD (commodity futures)
  U.S. real estate (quarterly)
  U.S. REITs
  Global property stocks
  Global infrastructure stocks
  Timber (quarterly)
  Art
  HF (hedge funds)
  FoF (fund of funds)
  PE (private equity) (quarterly)
  VC (venture capital) (quarterly)
  4.5
  7.7
  9.1
  5.4
  8.2
  11.8
  2.2
  12.3
  8.2
  13.4
  16.2
  0.11
  0.40
  0.35
  0.14
  0.36
  0.96
  �0.20
  1.14
  0.65
  0.92
  0.57
  21.7
  9.2
  18.7
  16.4
  12.8
  7.9
  9.2
  7.1
  6.0
  10.4
  25.5
  2
  4
  3
  3
  3
  5
  5
  4
  4
  5
  5
  0.15
  0.19
  0.52
  0.77
  0.14
  0.14
  �0.08
  0.27
  0.25
  0.59
  0.41
  Active strategies (simulated)
  Value (global equity selection)
  Carry (currency G10 selection)
  Momentum (commodity trend)
  Volatility selling (equity index)
  7.6
  10.3
  13.1
  8.0
  0.51
  0.76
  0.88
  0.35
  7.6
  8.9
  11.2
  15.4
  NA
  NA
  NA
  NA
  �0.15
  0.27
  �0.24
  0.49
  Sources: Bloomberg, MSCI Barra, Ken French’s website, Citigroup, Barclays Capital, J.P. Morgan, Band of America Merrill
  Lynch, S&P GSCI, MIT-CRE, FTSE, Global Property Research, UBS, NCREIF, Art Market Research, Hedge Fund
  Research, Cambridge Associates, own calculations.
  Notes: Data-series descriptions and data sources are in Appendix B). All annualized total returns are shown in dollar
  (i.e., unhedged) terms, thus combining local currency asset returns with foreign exchange gains and losses. As one exception
  to unhedged returns, global government bond returns are currency-hedged into dollars (consistent with many institutional
  bond investors’ habit of hedging the currency risk, in contrast to equity investors’ practice of leaving the currency exposure
  unhedged). The returns of the quarterly sampled series are based on statistical estimates, appraisal values, or internal rates of
  return. The returns of active managers are net of fees but may still be overstated due to voluntary reporting and survivorship
  bias. The active strategies are brieﬂy described in Section B.2 ‘‘Strategy style returns’’ and in m