Talking Your Book About Value (Part 2)

“Holy rusted metal, Batman!  The ground… it’s all metal… it’s full of holes, you know… Hole-y”

- Batman & Robin 1997


The pressure is on as sequels must be better than the original.  Hopefully, this is The Dark Knight and not Batman & Robin.  But the facts are clear – theories of “Value” and the “Value of Value” are full of holes.  So now we must answer the second question from our series:

2)  Do we have a working explanation for why “Value” works, and are there implications?

As discussed in Part 1, the historical evidence for the HML factor is robust, and even the recent unprecedented underperformance is not enough to statistically reject it.  Numerous academic papers have been introduced that suggest underperformance, and the consequent contraction of the value premium, are a function of declining relevance of Book Value as a fundamental measure of value.  The recent Arnott et al. paper (7) introduces this concept with the idea of “iHML” which adjusts B/M via the inclusion of expensed intangibles.  This is not a novel introduction as similar “add backs” were introduced in the literature as early as the mid-1990s with the work of Joel Stern and Bennett Stewart (of EVATM fame) and Bart Madden (of Credit Suisse Holt with his CFROI metric.)  For those with enough gray in their hair, there are memories of the AOL marketing scandal where assumptions surrounding the depreciation of marketing “investment” tied to compact disc mailings underpinned much of the debatable earnings generated by that company (2).  In many ways, the remarkable success of plain vanilla “value” post-2000 seems to have delayed adoption of many of these innovations that might have helped value investors more efficiently deploy capital and unfortunately reinforced the value investing mindset that, “If I just wait long enough, the factor will come back.”

Book Value is an Increasingly Flawed Metric

As is hopefully clear from the prior paragraph, we are sympathetic to these arguments.  Two key dynamics changed post-2000 – the adoption of FASB 142 (3) and the proliferation of corporate share buybacks. The adoption of FASB 142 eliminated the amortization of goodwill, subjecting it instead to a qualitative impairment test.  While adopted with positive intentions to reduce the type of manipulation that led to consistent EPS beats by acquisitive companies like GE and Worldcom, this ruling has substantively changed the character of book value within US public companies by allowing continual accumulation of intangibles via acquisitions.  Under this approach, a company can quickly become a “value” stock by acquiring lots of overpriced assets.  A cozy relationship with an auditor (perhaps by hiring them for consulting work as well) might easily reduce impairment charges that could adversely affect executive compensation.  A quick glance at the composition of book value for the S&P 500 is instructive.  Since the adoption of FASB 142, intangibles have grown from 44% of S&P book value to 71%.

Unfortunately, this is the wrong type of intangibles.  In contrast, the proposal by Arnott et al. to capitalize expenses like R&D (innovation capital) and marketing (brand capital) is sound and helps to reorient “value” away from an accounting identity and closer to its intent – identifying firms trading near/below their replacement value.  From a practical standpoint, the introduction of capitalized expenses shifts the composition of the Value quintile of the S&P500 away from Financials and Energy and noticeably increases the Technology weighting.


This dynamic is further exacerbated by the shift away from tax inefficient dividends and towards share buybacks as a return of capital.  As the following simple example illustrates, buying back shares versus paying dividends makes Company B cheaper than Company A even though shareholder’s (ex-tax) should be ambivalent per Modigliani-Miller.

To dispense with any further question, we agree that Book Value is a flawed metric, and growing more flawed; improving this metric is absolutely one method for improving the performance of a systematic value strategy.  Unfortunately, this does not answer the question “Why does Value work?”  Instead it simply says, “Value works if you use a better measure of value,” which is a bit tautological.  To get to the answer “Why?” we need to dig deeper.

Why Value Works

There are basically two camps on “Why?”  The first camp falls into the behavioral errors camp.  This camp is led by Josef Lakonishok, Ph.D whose iconic paper in 1994 led to the founding of LSV and launched the implementation of behavioral finance.  Cliff Asness sums up the underpinnings of the behavioral camp well, “No matter what the situation, it simply needs investors to net overreact. Companies that are cheap need to tend to be a bit too cheap for whatever set of facts exists at that time, and expensive companies need to tend to be a bit too expensive.”  It is under this camp that systematic strategies were supposed to shine.  Even if the programmer is known for smashing computer screens, the program itself will not overreact.  It is the perfect implementation of a system that relies on human fallibility to generate returns.

So now we are going to commit heresy.  Behavioral finance as framed by Asness , while interesting philosophically, tells us nothing meaningful in being equally guilty of tautology.  Stocks go down because we tend to push them down “too” much. It is seductive to sit at your desk and believe everyone else is prone to framing errors and that your unique insights as to the behavior of financial instruments over time are correct, but all readers should get to the December 2019 Nature publication of “The Ergodicity Problem in Economics” by Ole Peters (4).  It is extraordinarily readable, and the implications are Galileic in scope for our industry.  Behavioral finance under this rubric presumes that the Efficient Market Hypothesis (EMH) is true, at least in weak form, and that deviations from theory represent errors.  Peters demolishes these foundations by demonstrating that the mathematics that sit at the heart of the assumptions behind EMH, expected value theory, is itself the error.  By presuming that “ensemble average” and “time average” are identical, expected value theory ignores our path along the arrow of time.  My lucky number seven must come up on the roulette wheel (this is true in aggregate, but not necessarily for me) and value managers waiting for the return of their factor will eventually be proven right even after all their investors have departed.  Seductive, but untrue.

There is a second dimension to behavioral finance that does have substance.  This is well illustrated by Darrell Duffie in his 2010 address to the American Finance Association and subsequently published in The Journal of Finance (5).  Under Duffie’s model of “Slow-Moving Capital”, the mechanism is market frictions to arbitrage, most notably the inability to quickly deploy large sums of capital.  Unfortunately, this model offers us limited utility in explaining the behavior of Value; if anything, the Job-ian patience of investors to the eventual return of systematic value can explain the recent accelerating underperformance as it gives way and creates the crescendo of value unwinds.  The vigorous defense of the systematic value approach, and the perplexing interest in this defense, suggests this end game has not yet occurred.

The second camp on “Why?” represents the “priced risk” view.  Under this theory, the argument is that the securities in the Value portfolio have higher levels of risk than their growth counterparts and that this higher risk must be “priced” in order to generate higher return.  While I’ll spoil the surprise and suggest that this too is not quite the root of the Value premium as documented by Fama-French, if we adopt the theory that volatility of returns represents risk, the evidence here is stronger.  If we graph the components of the S&P 1500 by size and style using the Invesco “Pure” Value and Growth ETFs (6), we get a relationship that looks quite a bit like a security market line with “risk” negatively correlated with size and positively correlated with Value vs Growth.

While the single stock volatility differentials suggest some explanatory power, when combined in portfolio form the relationship largely breaks down.  The diversification benefits leave the portfolios themselves with inadequate volatility differentials to explain the return differentials.  This cannot be the answer.

All hope is not lost, however, as Ken French and Eugene Fama gave us another important clue in 2006 with the publication of “Migration” (8).  This paper, one of many works that followed their initial 1992 paper that introduced the HML factor, is largely ignored.  To put it into context, the original 1992 paper has 4,336 citations according to Wiley.  The 2006 paper has eight.  Despite its poor readership, the abstract offers tantalizing clues as to the source of the Value premium:

We study how migration of stocks across size and value portfolios contributes to the size and value premiums in average stock returns. The size premium is almost entirely due to the small stocks that earn extreme positive returns and as a result become big stocks. The value premium has three sources: (i) value stocks that improve in type either because they are acquired by other firms or because they earn high returns and so migrate to a neutral or growth portfolio; (ii) growth stocks that earn low returns and as a result move to a neutral or value portfolio; and (iii) slightly higher returns on value stocks that remain in the same portfolio compared to growth stocks that do not migrate.

                Fama-French 2007

This theme is echoed in the recent piece by Arnott (note of thanks to co-author Dr. Campbell Harvey, Ph.D for sending us the latest version after reading Part 1 [7]). 

“The migration and profitability components are at the core of the value premium—combined, they form what we call the structural component of the value premium.”

                Arnott, Harvey et al., 2020

The Migration Phenomenon

The migration phenomenon explains virtually all the returns to the size and value factors, and yet these dynamics are rarely explored.  Arnott provides a useful illustration of the phenomenon where we can see that in any given year, on average, 69% of Small Growth stocks stayed in the small growth bucket, 23% migrated to Small Neutral, 4% migrated to Small Value, and 4% migrated to Large Growth.  In contrast, 77% of Small Value did not migrate rightward.

The contribution of migration to return is high despite relatively low frequency, because the impact is large.  On average, when a stock moves from Small Value to Small Growth (only occurs 3% of the time), it rises in price by 92% (9) (see below table.)  So, 3% x 92% = 2.76% or roughly 30% of the aggregate excess return from Small Value is generated from this one, low frequency migration.  Most of the outperformance of Small Value comes from the migration from Small Value to Small Neutral, and another component comes from migrations to Large Value and Large Neutral.  Notice something important – every surviving company that migrates from Small Value is a positive outcome (10).  Likewise, every migration from Large Growth is negative.  Totaling the migrations yields the source of the outperformance associated with Style Migration.

Now we have a clue as to the question of “Why?” Value outperforms (and likewise why Size works) – because the migrations are net more positive than negative.  By comparing Big Value to Big Growth [8.35% -(7.25%)], we see that HML factor should offer positive returns; the same is true for Small Value vs Small Growth.  The sources of returns to Value are not tied to the individual securities or simply luck, but rather to the rules of portfolio construction and the subsequent probabilities that emerge.  Is it possible that these probabilities changed?  Again, Fama-French offers us a clue:

when stocks are allocated to portfolios in June of year t, one does not know where they will fall with respect to the possible outcomes (Same, Plus, Minus, dSize) to be observed in June of t+1. If prices are rational, however, the prices set at t reflect the best possible forecasts of (i) transition probabilities and (ii) the prices at t+1 that will be observed as a result of transitions

This opens a deeper understanding of the mechanism of the Value factor and how we can “price” it.  Back to our Security Market Line, if we were to look at the average stock in each style box according to the Invesco “Pure” indices and scale their movements by the volatility, we get a good picture of the stochastic outcomes.  These distributions are only along the size vector (x-axis).  A truly accurate description would show a Z-axis capturing valuation in Book/Market terms.

These lognormal distributions of actual data do a reasonably good job of matching up with the observed probability of moving across size boxes.  The probability of Small Cap Value switching to Large Cap Value, for example, is 0.8% versus the observed 1% frequency.

Using Option Theory to Value Value

If we have probability distributions where we can estimate the distribution of outcomes properly, then we open up a tantalizing theory – while any given year will see empirical migrations that drive the excess return, the theoretical return is tied to the probability of these migrations and the pricing of these migrations.  In other words, systematic “style” strategies generate their excess return by agreeing in advance to buy or sell securities that migrate, i.e. they are short or long options respectively.  Small Cap Value investors are short calls to Small Growth, Small Neutral, Big Neutral and Big Value.  They are likewise short put options against these boxes.  Small Growth is short calls to Big Growth and long puts to Small Neutral and Small Value.  The net of these options should give us a picture of the volatility exposure by style. Can we price these options and generate an estimate of theoretical return?

Of course we can!  To do so, we again return to the Invesco Pure ETFs.  For each individual stock, we calculate the value of a one year option using the above lognormal distributions of market value changes for Size and the prospect of style migration (Value to Growth, Growth to Value) determined by the market cap “distance” from the historical ratio of Growth to Value (Arnott’s “Relative Value of Value” -- approximate 5x differential from Part 1 of this series.)  For each style, we sum the value of the options on each stock in the index where the call is struck against the probability of migrating up and out and the put is struck against the probability of migrating down and out.  These totals are then scaled to aggregate market cap of the index.  By calculating in this manner, we arrive at the theoretical return of these style boxes created by selling or buying optionality.  The results match those observed by Fama-French 2006 closely enough that this interpretation of the source of return seems plausible:

There are obvious issues.  The Fama-French datasets do not match perfectly with our Invesco Pure Style ETFs.  Rather than “Neutral” Small and Big, we have “Neutral” (Mid) Value and Growth.  There is also a sampling dynamic as we are utilizing the last 3 years of data for the option value calculation, while the Fama-French data refers to 1963-2006.  Interestingly, the observed return to Small has underperformed expectations; there is little evidence that Large Value should ever have offered significant excess return.  It is likely from this analysis that Small Value is more reliable, while Large Value was simply “lucky” over the observed historical period.

Regardless, our hope is that we have inspired a new avenue of exploration – that looking through the lens of optionality reveals that the source of excess returns to factors are not a function of the securities themselves, but rather the rules of portfolio construction and the embedded optionality these rules create.  If this interpretation is correct, then there is absolutely a source of expected excess return to Value portfolios (biased Small and Mid) and Arnott and Asness are correct that we should expect an eventual return to an environment in which these strategies outperform; but, drumroll… the basis of this excess return is net short volatility positioning, introducing risks we will discuss in Part 3.

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End Notes

  1. Batman & Robin, 1997

  2. AOL SEC Litigation

  3. FASB 142




  7. Arnott, Robert D. and Harvey, Campbell R. and Kalesnik, Vitali and Linnainmaa, Juhani T., Reports of Value’s Death May Be Greatly Exaggerated (May 25, 2020). Available at SSRN: or

  8. Fama, Eugene F. and French, Kenneth R., Migration (February 2007). CRSP Working Paper No. 614. Available at SSRN: or

  9. Note that estimated change on migration is not tied to historical data in Fama French 2007, but rather to the calculated impact of a move from the 95%ile of the beginning style to the 5%ile of the ending style.This decision was made to unify these results with the subsequent analysis.

  10. The issue of survival is ignored for these purposes and per FF 2007 will reduce returns to both Small Value and Small Growth as delisting due to bankruptcy or too small market cap is a negative contributor to returns.The impact of these dynamics is small, however, as market capitalizations are typically reduced to negligible amounts prior to these events affecting index composition.

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