> For the complete documentation index, see [llms.txt](https://laurence-wilse-samson.gitbook.io/textbooks/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://laurence-wilse-samson.gitbook.io/textbooks/financial-economics-claims-prices-holders/part-iv-the-investor-ecology/chapter_17_passive_revolution.md). # Chapter 17: The Passive Revolution *Part IV: The Investor Ecology — Financial Economics: Claims, Prices, and Holders* *** ## Opening Episode: Tesla Joins the Index, December 2020 On the evening of Monday, 16 November 2020, S\&P Dow Jones Indices announced that Tesla would be added to the S\&P 500 before the open on Monday, 21 December. The announcement was unusual only in its timing. The index committee had passed Tesla over in September, when the company first became eligible, and the market had been waiting. What followed was not a debate about whether Tesla was worth what it was worth. It was a logistics problem. Every fund that promises to track the S\&P 500 had to own Tesla by the morning of 21 December, in exactly the weight the index assigned it. There is no discretion in that promise; a tracking fund that failed to buy would have carried a tracking error large enough to end a career. Tesla entered at roughly a 1.5 percent index weight — one of the largest companies ever to join, and the largest ever added in a single step. Estimates circulating at the time put the mechanical demand from S\&P 500 trackers at approximately $70-90 billion of Tesla stock. S\&P itself consulted the market on whether to phase the addition over two dates to spread the trade, and, after feedback, decided to do it all at once. Between the announcement and the inclusion date, Tesla rose by roughly 70 percent. It closed near $408 on the day of the announcement and near $695 on Friday, 18 December, the last session before inclusion. That Friday was a quadruple-witching day, and the closing auctions on 18 December were reported as the largest in US market history, with Tesla alone accounting for a substantial share of a closing cross measured in the tens of billions of dollars. On the first day *inside* the index, Tesla fell. Ask the two questions the chapter is built on. First: who had to buy? Not investors who had formed a view on electric vehicles. The buyers were index funds, exchange-traded funds, and separately managed accounts benchmarked to the S\&P 500 — vehicles whose demand curve for Tesla was, on that date, vertical. Their willingness to pay was whatever the closing auction printed, because the mandate was to hold the index, not to hold it cheaply. Second: who supplied the shares? Some came from active managers happy to sell into forced demand. Some came from investors who had bought in anticipation, which is to say from arbitrage capital positioning against a demand shock it could see coming a month in advance. Some came from other index funds — trackers of total-market and growth benchmarks that already owned Tesla and were rebalancing against it. And roughly $5 billion came from Tesla itself, which announced an at-the-market equity offering on 8 December and sold new shares into the same window. The S\&P 500 trackers also had to sell about $70-90 billion of *everything else in the index*, proportionally, to fund the purchase — a demand shock spread thinly across 500 names, and therefore invisible. Nothing in this sequence involved anyone forming an opinion about Tesla's cash flows. That is the question this chapter asks. When the largest shareholders of nearly every public company buy and sell mechanically — because a payroll deduction arrived, or an index committee met — what is a price? Who is left to make it mean something, and how few of them is too few? *** ## 17.1 The Passive Revolution The most important development in asset management over the past 50 years is the rise of passive investing. Index funds — which simply hold all securities in a benchmark index — have grown from $0 in 1975 to over $15 trillion today across all asset classes and vehicles. Table 17.1 tracks the US equity slice of that total, which is where the ownership consequences of the next several sections are sharpest. **Table 17.1: Growth of Passive Investing (US Equity Funds)** | Year | Active AUM | Passive AUM | Passive Share | | ---- | ---------- | ----------- | ------------- | | 1995 | $1.00T | $0.05T | 5% | | 2005 | $3.42T | $0.72T | 17% | | 2015 | $4.55T | $2.72T | 37% | | 2023 | $6.21T | $9.23T | 60% | *Source: Investment Company Institute, 2026 Investment Company Fact Book, data tables 42 (active and index mutual funds) and 11 (exchange-traded funds), domestic equity only; author's calculations, retrieved 7 September 2026. Passive is index domestic equity mutual funds plus domestic equity ETFs. ICI reports ETF assets by objective and by strategy but not by both, so every domestic equity ETF is counted as index; actively managed ETFs of all objectives were zero before 2008. This is ICI's domestic-equity cut and is narrower than a broad 'US equity' category group, which is why the levels here sit below some published comparisons. Figure 17.1 draws the same construction through 2025.* Passive funds have crossed half of US domestic equity fund assets — a remarkable shift in how markets operate (Figure 17.1). The number worth dwelling on is not the passive share but the active column, and it has to be read against the market rather than against itself. Active domestic equity funds grew from $4.55 trillion in 2015 to $6.21 trillion in 2023, which sounds like growth until it is set against the market: the US total return over those eight years was 2.69 times, so a band that had simply held its 2015 portfolio and taken no flows whatever would stand at $12.2 trillion. The industry ended at half of that. The industry did not shrink in nominal terms so much as stop growing, while every marginal dollar went somewhere else. ![Figure 17.1: The passive share](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-b88165b90d783d125afaac2f4900706ecde99ac0%2Ffig_17_01_passive_share.png?alt=media) **Figure 17.1: The passive share.** Panel (a): US domestic equity fund assets, active and index, at year-end 1993-2025, in trillions of dollars. Panel (b): the index share of that same total, on its own axis rather than a second scale. Built from Fact Book data table 42, "Active and Index Mutual Funds: Total Net Assets", and table 11, "Exchange-Traded Funds: Total Net Assets by Type of Fund", domestic equity only — world equity funds and every non-equity fund are excluded. The point §17.1 makes in prose is the bottom band of panel (a), not the top one. Active domestic equity funds held $4.0 trillion in 2007 and $7.2 trillion in 2025 — but the US market returned 6.69 times over those eighteen years, so a band that had merely held its 2007 dollars and taken no flows would stand at $27.0 trillion. The industry did not shrink; it stopped growing, and every marginal dollar went into the band above, which rose from $1.0 trillion to $14.0 trillion. The index share passed a half in 2020. ICI reports ETF assets by investment objective and by investment strategy but not by both, so every domestic equity ETF is counted as index; the shaded band below the share line in panel (b) is the worst case, which strips out every actively managed ETF of every objective, and on that floor the 2025 share is 59 percent rather than 66. The counterfactual compounds 2007 active assets at the US market total return (Kenneth French, Mkt-RF + RF). *Source: Investment Company Institute, 2026 Fact Book, data tables 42 and 11; Kenneth French's data library; author's calculations.* One clarification before the analysis: "passive" is a claim about a *mandate*, not about trading. An S\&P 500 fund trades constantly — dividends arrive, flows arrive, the index reconstitutes — and what makes it passive is that its portfolio weights are a function of someone else's rule rather than of its own forecast. The boundary blurs in both directions. A smart-beta ETF running a value screen is an active strategy in an index wrapper; a closet-indexing active fund with 20 percent active share is a passive portfolio sold at active prices. *** ## 17.2 Why Index Funds Won The case for index funds rests on three pillars: **1. Fee Advantage:** The average actively managed US equity fund charges \~0.70% annually. Vanguard's S\&P 500 index fund charges 0.03%. Over 30 years, this fee difference compounds dramatically: **Table 17.2: The Compounding of Fees** | Investment | Annual Fee | $100K after 30 years (7% gross return) | | -------------- | ---------- | -------------------------------------- | | Index fund | 0.03% | $754,000 | | Active fund | 0.70% | $625,000 | | **Difference** | | **$129,000** | *Source: Author's calculation; fee levels from ICI, Morningstar* The arithmetic is worth stating in general form, because it is the single most useful calculation in personal finance. An investor who earns gross return $$r$$ and pays fee $$f$$ ends with $$ W\_T = W\_0 (1 + r - f)^T $$ so the fraction of terminal wealth surrendered to fees is $$1 - \left(\frac{1+r-f}{1+r}\right)^T \approx 1 - e^{-fT/(1+r)}$$. The loss is not $$f \times T$$; it is the compounding of $$f$$ against the compounding of $$r$$. At $$f = 0.67$$ percent and $$T = 30$$, roughly a sixth of the terminal portfolio is gone — and it is gone whether or not the manager beat the market. Figure 17.2 draws both halves of that sentence. ![Figure 17.2: What fees compound to](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-993e2536ddeed9baa269bf3a74df012f0f4dcbca%2Ffig_17_02_what_fees_compound_to.png?alt=media) **Figure 17.2: What fees compound to.** Panel (a) is Table 17.2 with the intermediate years filled in, and a third fee level between its two. On a hundred thousand dollars at a 7 percent gross return, thirty years at three basis points ends at 754,849 and thirty years at seventy ends at 625,170 — a gap of 129,679 dollars, which is larger than the initial investment. Nothing in the calculation supposes the active manager did badly; the paths differ only by the fee. Note where the gap opens: the three curves are indistinguishable for the first decade and separate visibly only in the last, which is exactly why a fee looks harmless at the point at which it is agreed. Panel (b) is the fraction of terminal wealth the 67 basis point gap surrenders, as the horizon lengthens. The exact figure and the exponential approximation are the same line to the width of the ink, and at thirty years both give 17.18 percent — roughly a sixth. The dashed line is the calculation most people do in their heads, fee times horizon, and it sits above the truth: 20.1 percent against 17.18. It errs upward because it charges the fee against the terminal balance every year, when in fact each year's fee is levied on a smaller base. It is still the more useful number for a household, because it errs in the conservative direction on a quantity most people put at zero. **2. Zero-Sum Arithmetic:** Before fees, the average actively managed dollar must earn the market return (active managers collectively *are* the market, minus index funds). After fees, the average actively managed dollar must underperform. This is arithmetic, not a hypothesis. Sharpe's original statement of this point is an accounting identity, and French (2008) gives it its empirical teeth: he estimates the aggregate cost society pays for active management — fees, trading costs, and the resources consumed by the search for alpha — and asks what the representative investor gets for it. The answer is that the aggregate active investor pays a large annual toll to hold, in aggregate, the market portfolio. The identity does not say active management is worthless to *anyone*; it says the gains are a transfer among active investors, net of a cost paid to the industry. **3. Tax Efficiency:** Index funds trade infrequently, minimizing capital gains distributions. Active funds that trade frequently generate taxable gains that erode after-tax returns. The tax pillar matters more than its usual one-line treatment suggests, and it interacts with the ETF structure discussed in §17.5: in-kind redemption lets an ETF push low-basis lots out of the fund without realizing a gain, so the tax advantage is partly a wrapper effect rather than a turnover effect. For a holder in a tax-deferred 401(k) — which, as §17.8 argues, is where most passive money actually lives — this pillar is worth nothing at all. *** ## 17.3 Performance Measurement and the Berk-Green Equilibrium The zero-sum argument establishes that active management underperforms *on average*. It says nothing about whether any particular manager has skill. That is a measurement question, and the measurement is much harder than the industry's marketing — or its critics' — usually concede. ### How Noisy Is Alpha? Estimate a fund's alpha from the time-series regression of its excess returns on a benchmark or factor model: $$ r\_{i,t} - r\_{f,t} = \alpha\_i + \sum\_k \beta\_{i,k} f\_{k,t} + \varepsilon\_{i,t} $$ The standard error of $$\hat{\alpha}\_i$$ is approximately $$\sigma \_\varepsilon / \sqrt{T}$$, where $$\sigma \_\varepsilon$$ is the residual (tracking-error) volatility and $$T$$ the number of years. So the $$t$$-statistic on skill grows with the square root of the sample: $$ t(\hat{\alpha}) \approx \frac{\alpha}{\sigma\_\varepsilon}\sqrt{T} $$ The ratio $$\alpha/\sigma\_\varepsilon$$ is the information ratio, and for a diversified equity fund a genuinely good one is around 0.2 to 0.3 per year. Set $$\alpha = 1$$ percent and $$\sigma\_\varepsilon = 5$$ percent: reaching $$t = 2$$ requires $$T = 100$$ years. A more concentrated fund with $$\sigma\_\varepsilon = 10$$ percent and $$\alpha = 2$$ percent needs the same century. Twenty years of monthly data — a manager's entire career, and far more history than most funds have — delivers a $$t$$-statistic under one against a true alpha that would make the manager one of the best of her generation. This is not a technicality. It is the reason the active-versus-passive debate never resolves empirically at the level of the individual fund. The signal-to-noise ratio in fund returns is so low that the data cannot distinguish a skilled manager from a lucky one within any horizon over which either of them is employed. Cross-sectional tests fare better, because thousands of funds provide power the single time series does not, but they answer a different question: whether skill exists in the population, not whether *this* manager has it. Figure 17.3 puts the whole problem on one pair of axes. ![Figure 17.3: How noisy is alpha](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-3cdaa32a6c3b9e9f6620d308b30d87e587138242%2Ffig_17_03_how_noisy_is_alpha.png?alt=media) **Figure 17.3: How noisy is alpha.** Years of data needed to establish a given true alpha at a t of two, on a logarithmic vertical axis because otherwise nothing but the top corner is visible. The three curves are three levels of tracking error, and each falls with the square of alpha: halving the alpha quadruples the horizon. The two markers are the cases §17.3 works — a one percent alpha against a five percent tracking error, and a two percent alpha against ten — and both land at a century. The dashed rule is twenty years, which is a manager's entire career and more history than most funds have; everything above it is a horizon over which no client, no trustee and no manager is available to see the answer. Two things follow. The first is that a fee is observable today and certain, while the alpha that would justify it is unobservable within any horizon a client will live through, and that asymmetry rather than the zero-sum arithmetic is the shape of the real fee debate. The second is that the curves also bound the critic: the same noise that prevents anyone from establishing skill prevents anyone from establishing its absence in a particular fund, which is why the cross-section is where the question actually gets answered. The evidence from those cross-sectional tests, and from the practitioner scorecards built on the same logic — the SPIVA reports are the best known — is consistent and unflattering. Over 10- and 15-year horizons, the large majority of active US equity funds underperform their assigned benchmark after fees, in most categories and most windows. Correct for survivorship, and the picture worsens: funds that close are disproportionately the ones that did badly, so any sample of *surviving* funds overstates the industry's record. ### Flows, Scale, and the Berk-Green Mechanism Now add the second empirical regularity, established in Chapter 16's discussion of delegation and tabulated there as Table 16.5: money chases performance. Investors direct flows toward funds with good recent returns and away from bad ones, and they do so with far more sensitivity than the low informativeness of past returns can justify on forecasting grounds alone. Berk and Green (2004) take these two facts — noisy skill and performance-chasing flows — and show that together they generate an equilibrium that looks nothing like the morality tale the industry debate usually tells. The ingredients are three: 1. **Skill exists and is scarce.** Some managers can generate gross alpha. 2. **There are decreasing returns to scale.** A manager's gross alpha falls as the fund grows, because the good ideas are finite and trading a larger book has larger price impact. 3. **Capital is competitively supplied.** Investors will put money into any fund offering positive expected net alpha. Write gross alpha as a decreasing function of fund size $$A$$ (assets under management), linearly for concreteness: $$ \alpha^{\text{gross}}(A) = a - b A $$ where $$a$$ measures the manager's skill and $$b$$ the speed with which scale erodes it. If the fund charges a proportional fee $$f$$, investors earn $$ \alpha^{\text{net}}(A) = a - b A - f $$ Competitive capital supply drives $$\alpha^{\text{net}}$$ to zero, so the fund settles at $$ A^{\ast} = \frac{a - f}{b} $$ and the manager collects rents of $$f A^{\ast} = f(a-f)/b$$ per year. Skill is real, scarce, and valuable — and *the investor captures none of it*. The skilled manager is paid her marginal product; the marginal investor, who can always buy the index instead, earns the passive return. Fund size, not fund alpha, is the observable signature of skill. This reframing carries sharp predictions, and they are the ones the data show: * **Fund-level performance persistence is weak.** Good performance attracts flows, flows push the fund past the scale at which the manager's edge survives, and measured net alpha reverts toward zero. Persistence in *net* returns is precisely what the model says should not be there. * **Value added at the manager level is real and measurable.** If skill shows up in size rather than in net return, the right statistic is gross alpha times assets — dollars extracted from the market, not percentage points delivered to clients. Berk and van Binsbergen's follow-on work measures exactly that and finds a substantial, persistent, cross-sectionally skewed distribution of manager value added. * **The fee is the price of a scarce input, not a rip-off.** In this model, a high-fee fund is not evidence of exploitation; it is what a scarce factor earns in a competitive market for the capital that hires it. ![Figure 17.4: The Berk-Green equilibrium](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-44ff77677a38ee12e74cb706d2be13b3f0a41ae6%2Ffig_17_04_berk_green_equilibrium.png?alt=media) **Figure 17.4: The Berk-Green equilibrium.** Gross alpha falls linearly in fund size, net alpha is the same line shifted down by the fee, and the fund grows until net alpha reaches zero. The whole content of the model is the vertical position of the two lines at the marker: gross alpha there is exactly the fee, so the manager's edge is real and entirely consumed by what she charges for it. The shaded band between the lines, integrated across the fund's assets, is her annual rent. Three readings the figure makes hard to avoid. Fund size is the observable signature of skill, since a more skilled manager has a higher intercept and therefore a larger equilibrium fund at the same fee — which means that ranking managers by net alpha is ranking them by a quantity the model sets to zero for all of them. Persistence in net returns is what the model says should not be there, so its absence in the data is the theory working rather than failing. And the right measure of a manager's value added is gross alpha times assets, dollars extracted from the market rather than percentage points delivered to clients, which is the statistic Berk and van Binsbergen went on to build. The Berk-Green equilibrium converts "active versus passive" from a question about virtue into a question about who captures a rent. It also belongs squarely in this book's framing, because it is a holders-move-prices story running in reverse: the flow behavior of holders, not the skill of managers, determines the size of the active sector and therefore how much capital is doing the work of price discovery. Section 17.6 picks up the consequence. Two caveats keep the model honest. It assumes competitive, informed capital supply, which sits awkwardly with the evidence that retail flows respond to advertising, distribution channels, and star ratings as much as to expected alpha. And it assumes decreasing returns bind at the fund level; if the binding constraint is instead at the *strategy* level, shared across all managers running the same trade, the aggregate capacity of active management — not any one fund's — is what sets the equilibrium, and Chapter 6 §6.8's discussion of factor crowding is the relevant machinery. *** ## 17.4 Index Construction and Inclusion Effects An index is not a fact about the market. It is a product, built by a firm, according to a rule that firm chooses and can change. The rules come in two families. **Committee-selected** indices — the S\&P 500 is the canonical case — apply published eligibility screens (US domicile, a float-adjusted market-capitalization threshold, adequate liquidity, a minimum public float, and a profitability requirement measured over the most recent quarter and the trailing year) and then leave the final choice to a committee that meets in private and announces after the close. Tesla met the profitability screen in mid-2020 and was still not added until December: the committee has discretion and uses it. **Rules-based** indices — the Russell family, MSCI's country and regional indices, the CRSP indices Vanguard's US funds track — reconstitute mechanically on a published calendar, which makes them predictable and therefore front-runnable, a problem providers have addressed with banding, staggered migration, and multi-day implementation. Both families **float-adjust**: weights are set by shares available to public investors, excluding strategic blocks held by founders, governments, and cross-holding corporates. Float adjustment is why a company's index weight can change with no change in its market capitalization — a lockup expiry, a government privatization tranche, or a founder's secondary sale all move the mechanical demand for the stock. ### The Inclusion Effect and Its Disappearance Index inclusion has long been finance's cleanest natural experiment. Addition to a major index triggers passive buying with no information content whatsoever — the committee is explicit that inclusion is not an endorsement — so any price response measures the slope of the demand curve for a stock, isolated from news. The early evidence found a large one. **Studies estimate 3-7% abnormal returns around index additions** in the 1980s through the early 2000s, with a partial reversal afterward, and the finding became the standard citation against the textbook assumption that individual stocks face flat demand curves. More recent estimates put the S\&P 500 addition effect at or near zero. Three explanations compete, and they have different implications: ![Figure 17.6: The inclusion effect and its disappearance](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-e09e05d18dfc207416714341c7445daa0c712b3d%2Ffig_17_06_the_inclusion_effect.png?alt=media) **Figure 17.6: The inclusion effect and its disappearance.** Two eras and one exception, drawn as ranges because that is the shape of the evidence. Studies of additions from the 1980s through the early 2000s put the abnormal return at three to seven percent — a range rather than a point because the estimates disagree, and the disagreement is part of the finding. Recent additions sit at or near zero. The exhibit deliberately stops there rather than drawing a point estimate per decade: the chapter names no per-decade figures and no studies to attribute them to, and six invented numbers would be worse than two honest ranges. What the effect measures is the slope of the demand curve for a single stock with the information content stripped out, since the committee is explicit that inclusion is not an endorsement. Its disappearance is therefore not evidence that the curve went flat, which is exactly what the third bar shows: Tesla entered at a 1.5 percent weight and ran about seventy percent between announcement and inclusion, in the era when the effect had supposedly vanished, because its size overwhelmed the arbitrage capacity that had been quietly absorbing every ordinary addition. *Source: Published event-study estimates as reported in §17.4; Tesla from the chapter's opening episode.* * **Arbitrage capacity.** The trade is now crowded. Hedge funds and index-transition desks position ahead of announced additions, supplying the shares the trackers need and flattening the effective demand curve. On this reading, the demand curve for an individual stock is still downward-sloping; there is simply more capital standing ready to slide along it. Tesla, whose size overwhelmed that capacity, is the exception that shows the mechanism. * **Anticipation and predictability.** As index rules became more transparent and index-provider behavior more forecastable, the price response migrated from the announcement date to the weeks before it, where event studies do not look. * **Migration rather than entry.** Most modern S\&P 500 additions are promotions from the S\&P MidCap 400 or from broad total-market indices that already held the stock at a similar weight. The *incremental* demand shock is a fraction of the headline index weight, because a large share of the passive complex owned the name already. The disagreement is unresolved, and it matters for more than index arbitrage: if the inclusion effect vanished because arbitrage capital grew, then demand curves are still sloped and the modern market has simply hired more people to lean against flows. If it vanished because the demand shock itself shrank, we have learned nothing about slopes. Chapter 12 §12.9 treats inclusion-as-demand-shock as evidence on the price impact of ownership, with the event-study machinery in Appendix A. > **Box 17.1 — Tesla joins the index, December 2020** > > The opening episode is the case, and it is worth completing with the numbers, because it is the largest clean test the modern market has produced of whether index demand moves prices. > > S\&P announced on 16 November 2020 that Tesla would join the S\&P 500 effective before the open on 21 December. The addition was unusually large: the company entered at a weight of about 1.7 percent, the biggest single addition in the index's history. S\&P consulted the market on whether to phase the entry over two tranches and decided to add it in one. > > The mechanics from there are §17.4's. Every fund managed against the index had to hold roughly 1.7 percent of its assets in a stock it held none of, and index funds do not anticipate — a fund that buys early takes tracking error, which is the one risk its mandate does not permit. The trade therefore had to happen at the close on 18 December, at whatever price cleared. Volume on that closing auction was extraordinary, of the order of a hundred million shares in the single print, and estimates of the index-driven demand ran to tens of billions of dollars. > > The price path is the finding. Tesla rose sharply between announcement and inclusion, roughly by half over the five weeks, then underperformed in the weeks after. No information about the company arrived on 16 November; S\&P announced that Tesla had met criteria that were already public. What moved was the identity of the required holders. > > Section 17.4 records that the average inclusion effect has fallen toward zero over recent decades, and this case does not overturn that. It sharpens it. The average effect is small because the average addition is a promotion from another index that the passive complex already held at a similar weight. Tesla was not that, and the effect returned at full size — which is evidence that the demand curve never flattened, only that the shock usually got smaller. *** ## 17.5 ETFs: The Tradeable Index Exchange-Traded Funds (ETFs) combine index investing with stock-like tradability. Unlike mutual funds, which price once daily at NAV, ETFs trade continuously on exchanges. **Table 17.3: Mutual Funds vs ETFs** | Feature | Mutual Fund | ETF | | ------------------- | ------------------ | --------------------------------- | | Trading | Once daily at NAV | Continuous on exchange | | Minimum investment | Often $1,000+ | 1 share (\~$50-500) | | Creation/redemption | Cash | In-kind (authorized participants) | | Tax efficiency | Lower | Higher (in-kind redemptions) | | Transparency | Quarterly holdings | Daily holdings (most) | | Intraday pricing | No | Yes | *Source: SEC filings; ICI* ### Creation and Redemption in One Page The mechanism in the third row is what makes the rest of the table work, and the reader needs it to follow the rest of the chapter. An ETF's share count is not fixed. A small set of large broker-dealers — **authorized participants (APs)** — hold contractual rights to transact directly with the fund, in blocks called creation units (typically 25,000 to 100,000 ETF shares). Each morning the fund publishes a *creation basket*: the exact list of securities, and any cash residual, that constitutes one unit. * **Creation.** When ETF demand pushes the market price above net asset value, an AP buys the underlying basket in the market, delivers it to the fund, and receives new ETF shares, which it sells. Supply expands; the premium closes. * **Redemption.** When the ETF trades below NAV, an AP buys ETF shares in the market, delivers them to the fund, and receives the underlying basket, which it sells. Supply contracts; the discount closes. Two consequences follow. First, the ETF's price is tethered to the value of its holdings by an arbitrage anyone with an AP agreement can run, so the tether is only as strong as the AP's ability and willingness to trade the basket — a qualification that binds hardest exactly when the underlying is least liquid. Second, redemption *in kind* is not a sale: the fund hands over securities rather than selling them, so it never realizes the capital gain. That is the source of the tax advantage in row four, and it is a feature of the wrapper rather than of indexing. ![Figure 17.5: Creation and redemption](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-7127ac3726df522499c3973ac31d8cbba8d3300e%2Ffig_17_05_creation_and_redemption.png?alt=media) **Figure 17.5: Creation and redemption.** The two circuits, drawn as mirror images because that is what they are. In panel (a) the ETF trades above the value of its holdings, so an authorized participant buys the basket in the market, delivers it to the fund, receives new ETF shares and sells them into the premium; supply expands and the premium closes. In panel (b) the ETF trades below, so the participant buys ETF shares on the exchange, delivers them to the fund, receives the basket in kind and sells it; supply contracts and the discount closes. Read the two panels for what they assume rather than for what they show. The arbitrage requires somebody able and willing to trade the basket at the moment the gap opens, which is a strong assumption precisely when the underlying is illiquid and the gap is largest — the March 2020 bond-ETF discounts are that assumption failing, or the ETF price telling the truth about a stale NAV, and the two readings are hard to separate. And the leg that closes panel (b) is a delivery, not a sale, so the fund never realizes the gain. That is the whole of the tax advantage, and it belongs to the wrapper: an actively managed ETF gets it and an index mutual fund does not. The ETF structure solves a key problem: liquidity transformation. A mutual fund holding illiquid bonds must still honor daily redemptions — creating run risk. An ETF's price can diverge from NAV, allowing the secondary market to absorb liquidity shocks without forcing liquidation. Most ETF trading never touches the underlying market at all: shares change hands between investors on the exchange, and only the residual imbalance reaches an AP. The fixed-income ETF is the sharp case. In March 2020, bond ETFs traded at discounts of several percent to stale NAVs — read by some as an ETF failure, by others as the ETF price telling the truth about a bond market whose quoted marks had stopped clearing. That debate — how ETF arbitrage transmits between fund and underlying, what happens to the tether under stress, and how ETF market structure works across borders — is developed in the companion volume. See *International Finance*, Chapter 14, for ETF arbitrage and market structure and for index-flow dynamics in cross-border portfolios. > **Box 17.2 — Who is an authorized participant** > > Section 17.5 says an ETF's price is kept near its net asset value by arbitrage. That arbitrage is not an anonymous market force. It is a contract, held by a small number of firms, and the terms of the contract are the mechanism. > > An **authorized participant** is a broker-dealer that has signed an AP agreement with the fund's distributor. Only an AP may transact directly with the fund, and it does so in **creation units** — large blocks, typically tens of thousands of shares — delivering the basket of securities the fund publishes each morning and receiving fund shares, or the reverse. Everyone else trades the fund's existing shares with other investors on an exchange. The AP is therefore the only party who can change the number of shares outstanding, and the creation-redemption channel is the only link between the exchange price and the value of the basket. > > Two features of the agreement matter for how well that link holds. First, an AP agreement confers a right, not an obligation. No AP is required to create or redeem, in any quantity, on any day. A market maker who is short liquidity or short balance sheet may simply decline, and the discipline stops for as long as it declines. Second, the number of firms is small. A fund may have a dozen APs on paper, but activity is concentrated in a handful, and those firms are the same dealers whose balance-sheet constraints Chapter 19 §19.3 is about. > > This is why an ETF's discount is informative. In an equity fund holding liquid names, creation and redemption are close to costless and the discount stays inside a few basis points. In a fund holding claims that are themselves hard to trade — corporate bonds, bank loans, municipal debt — the AP must hedge or warehouse a basket he cannot immediately unwind, and the discount widens by exactly the amount that makes the trade worth doing. > > Section 17.5 draws the consequence: the ETF's price is not a promise about the value of the basket. It is a price at which somebody with a balance sheet is willing to intermediate between the two. *** ## 17.6 Passive Ownership and Price Discovery The rise of passive investing has consequences for markets: **1. Increased Correlation:** Index funds buy and sell all stocks in the index together. This mechanically increases the correlation of returns among index members. **2. Price Discovery:** If passive funds don't analyze individual securities, who sets prices? The remaining active managers bear the entire burden of price discovery, even as their share of assets shrinks. **3. Index Inclusion Effects:** Addition to a major index (S\&P 500) triggers passive buying, often pushing prices above fundamental value. Deletion triggers selling. The size of this effect, and its apparent decline, are treated in §17.4. **4. Concentration of Ownership:** The "Big Three" (BlackRock, Vanguard, State Street) collectively hold 20%+ of most large US companies. This concentration raises corporate governance questions, taken up in §17.7. **5. Reduced Liquidity Provision:** Index funds don't provide liquidity — they demand it. When markets fall, they don't buy the dip; they sell proportionally. This may amplify volatility during stress. The fifth point deserves care, because it is the one most often overstated. A pure index fund receiving no flows does nothing at all in a selloff; it is the *flow*, not the indexing, that demands liquidity, and passive vehicles have historically shown lower flow volatility than active funds in the same asset class. What passive ownership removes is not liquidity supply but the *contrarian* component of it: the value manager who buys because the price fell. As the share of assets managed against a rule rises, the share of capital whose demand responds to price falls, and the market's aggregate demand curve steepens. That is the mechanism Chapter 20 formalizes. ### Grossman-Stiglitz, Applied Chapter 7 §7.2 derived the Grossman-Stiglitz result: informationally efficient prices cannot be an equilibrium, because if prices revealed everything, no one would pay the cost of acquiring information, and then prices would reveal nothing. The equilibrium is interior — a positive fraction of investors acquires information, is compensated for it by trading against the uninformed, and in doing so makes prices informative but not perfectly so. Passive ownership is that result playing out at market scale. What the passive revolution does is make the model's central variable — the informed fraction — directly observable and openly contested. Every dollar that moves from an active mandate to an index mandate is a dollar withdrawn from information acquisition. The theory says this cannot go to a corner: as the active share of assets falls, the gross return to information rises, because there are fewer informed traders competing away the same signal and more price-insensitive order flow to trade against. Rising returns to activity should stabilize the active sector before it disappears. The passive share is thus self-limiting in the model, and the interesting question is not whether active management survives but *at what level* it stabilizes, and whether that level delivers prices accurate enough for the real decisions — corporate investment, capital allocation, retirement planning — that lean on them. That question has two parts that are usually run together. **How much active capital is enough?** The Grossman-Stiglitz equilibrium pins down the informed fraction as a function of the cost of information and the amount of noise trading; it says nothing about whether that fraction, in levels, is 1 percent or 30 percent of assets. And there is a strong case that the required fraction has fallen. Price discovery is a technology, and the technology improved enormously: an analyst in 2025 with machine-readable filings, satellite data, and a laptop covers ground that took a research department in 1985. If the *productivity* of active capital rose faster than its share fell, informativeness could be flat or improving while the industry shrinks. The evidence is mixed. Price efficiency metrics (bid-ask spreads, return predictability) have not obviously deteriorated despite passive growth. Perhaps technology allows fewer active managers to process the same information. Or perhaps active managers are becoming more skilled even as their numbers shrink — which is exactly what the Berk-Green mechanism of §17.3 predicts, since capital exits the least skilled managers first. **Enough for *****what*****?** Here the answers diverge. Aggregate market efficiency and firm-level efficiency are different objects, and the growth of index investing plausibly moves them in opposite directions: a market in which everyone trades the S\&P 500 as a block prices the equity premium continuously and prices General Mills versus Kellogg's not at all. The research that finds deterioration tends to find it in *relative* pricing — cross-sectional informativeness, the speed with which firm-specific news gets into individual prices, the co-movement of index members — rather than in the level of the market. That is the version of the concern worth taking seriously, and it is the version with real consequences for capital allocation, because it is relative prices that tell firms where to invest. Note also what Berk-Green implies for the question. If active management is an industry that pays skilled managers their rents and pays investors the index return, then the shift to passive is not a discovery that active management was fraudulent. It is investors' recognition that the *net* product was always the index, purchased at a lower price. Price discovery gets done either way; the question is who pays for it, and the answer has been shifting, decade by decade, toward a smaller and more concentrated set of specialists. *** ## 17.7 Common Ownership, Stewardship, and Index-Provider Power Passive investing concentrates *ownership* even as it disperses *portfolios*. Three asset managers — BlackRock, Vanguard, and State Street — collectively hold upwards of a fifth of the shares of most large US public companies, and vote a still larger share of the ballots actually cast, because index funds vote nearly all their shares while retail holders mostly do not. This is a concentration of formal corporate control without historical precedent, and it arrived as a side effect of a product designed to be indifferent to the companies it owns. Figure 17.7 measures the aggregate directly, from the three managers' own filings. ![Figure 17.7: The Big Three](https://846781005-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F3EupdX99vVBoNySDtmxb%2Fuploads%2Fgit-blob-8d2d1b17bb35a13016bf7754e835416f85f5a76b%2Ffig_17_07_big_three_share.png?alt=media) **Figure 17.7: The Big Three.** Combined BlackRock, Vanguard and State Street US equity holdings, taken from their Form 13F-HR filings for the fourth quarter of each year, as a share of the market value of publicly traded equity issued by US corporations — with the composition of that share in panel (a) and the two levels it is built from in panel (b), on a log scale, where the vertical gap between the lines is the share plotted above. One 13F-HR per franchise per year, fourth quarter, parsed from the filing. Note that the denominator is the whole US public equity market, not the S\&P 500, and that 13F reports at the manager level, long-only, with a 45-day lag and a $100m threshold (Box 20.1): the share is a floor, not a measurement. The series is annual rather than quarterly, and runs 2009-2025 rather than 2000-present, because BlackRock's index business was Barclays Global Investors until December 2009 and no complete BlackRock franchise total can be built from EDGAR before that, while Vanguard filed its last group-level 13F for 2025Q4. Reported values are in thousands of dollars before 2022Q4 and in whole dollars after; the break is normalized rather than smoothed. *Source: SEC EDGAR Form 13F-HR information tables; denominator from the Financial Accounts of the United States (Z.1), table L.223, all domestic sectors' public corporate equities at market value, via its FRED mirror; author's calculations.* ### The Stewardship-Capacity Problem An index fund cannot exit. It holds every company in its benchmark at the benchmark weight regardless of how the company is run, which means the Wall Street Walk — selling the shares of a badly governed firm — is unavailable. In principle this makes index funds ideal stewards: permanent, universal owners with an interest in system-wide governance quality. In practice it makes them stewards with no obvious incentive to invest in the job. The problem is one of shared benefit. Good stewardship at one company raises that company's value, and the index fund captures only its ownership fraction of that gain — while its competitors, who hold the same stock in the same weight, capture theirs for free. Because index funds compete on fee, and stewardship is a cost that shows up in the expense ratio, the private return to serious engagement is small and the competitive penalty is immediate. Bebchuk and Hirst make this argument at length and call the result an agency problem layered on top of the agency problem of delegation: the agents of the agents have systematically weak incentives to monitor. The capacity numbers make the point concrete without any theory. Each of the Big Three runs a stewardship team of a few dozen professionals responsible for voting at tens of thousands of shareholder meetings a year across dozens of markets, on ballots that routinely run to a dozen items. Whatever that process is, it is not company-by-company analysis; it is the application of a policy, published in advance, largely aligned with the recommendations of two proxy advisory firms whose own concentration is a separate concern. The managers' response has been to publish detailed voting guidelines — making the policy explicit and contestable — and, more recently, to experiment with **pass-through voting**, letting underlying fund investors direct how their shares are voted. Whether retail investors will use that machinery, and whether it improves or merely disperses accountability, is an open empirical question. ### The Common-Ownership Hypothesis A sharper claim goes further: that concentrated cross-ownership changes how firms *compete*. If a single investor holds large stakes in every airline on a route, that investor's payoff is maximized not by any one airline winning share but by all of them keeping fares high. Managers who understand whose interests they serve may compete less aggressively than they would under dispersed ownership. This is the common-ownership hypothesis, and its most cited empirical statement is Azar, Schmalz and Tecu (2018), who construct a measure of common ownership across airline routes and report that routes with higher common ownership carry higher fares — with an effect large enough, on their estimates, to matter for antitrust policy. Parallel work has advanced similar claims for retail banking deposit rates, and the argument found a receptive audience among antitrust scholars, some of whom proposed capping institutional investors' holdings in concentrated industries. The pushback has been substantial and comes in three forms. **Measurement.** The concentration measures used (MHHI-delta and its relatives) are constructed from ownership data, and critics have shown the results are sensitive to how ownership is aggregated, how routes and market shares are defined, and how missing or misassigned 13F positions are handled. Reanalyses of the airline data — Dennis, Gerardi and Schenone among them — report that the fare effect does not survive plausible alternative specifications, in particular once the endogeneity of market shares in the concentration measure is addressed. **Identification.** The natural experiments used to establish causality, chiefly the BlackRock-Barclays Global Investors merger of 2009, are single events that coincide with a great deal else, and they change measured common ownership through a mechanical consolidation of two managers' books rather than through any change in how firms are monitored. **Mechanism.** This is the objection with the most force and the least data. For the hypothesis to work, something must transmit the diversified owner's preference into the pricing department of an airline. Index managers do not sit on boards, do not communicate with management about product-market strategy, and would face serious antitrust exposure if they did. Proposed channels — executive compensation tied to industry-relative rather than absolute performance, or simple managerial passivity in the absence of an activist pushing for share gains — are plausible but weakly evidenced, and they predict effects that should be visible in compensation design and in entry behavior, where the evidence is thin. Where this leaves a reader: the *correlation* between common ownership and market power measures is real in several datasets and fragile in several others; the *mechanism* remains unestablished; and the policy proposals built on the finding run well ahead of it. The honest position is that the question is open and that it matters enough to keep testing, not that the case is made. ### Who Decides What "The Market" Is There is a third governance question, less discussed and more concrete. If trillions of dollars track an index, the firm that defines the index exercises real allocative power, and it does so as an unregulated commercial actor selling a licensed product. Country classification is the clearest illustration. When MSCI or FTSE Russell reclassifies a country between its frontier, emerging, and developed universes, every fund benchmarked to the affected indices must buy or sell that country's entire investable equity market on a published date. The reclassifications of the past decade — Pakistan's promotion to emerging-market status and its subsequent demotion to frontier, Argentina's promotion and later removal to standalone status, Kuwait's promotion, and the phased inclusion of China A-shares into the emerging-market indices — each moved capital flows measured in billions and were decided by a consultation process run by a private firm. The same logic applies in fixed income, where the addition of a sovereign's bonds to a major global index generates mechanical foreign demand for that sovereign's debt. The index provider therefore sits at a joint of the system: data vendor, de facto capital-allocation authority, and — through eligibility criteria touching governance standards, share-class structures, and market accessibility — a private regulator that issuers and finance ministries lobby. None of that is illegitimate. But it means "the market portfolio," the object every model in Part II treats as primitive, is in practice a commercial product with an owner and a rulebook. *** ## 17.8 Who Holds the Passive Claim, and What Do Their Constraints Do to Prices? "Passive" names a mandate, not a holder. The pricing consequences depend on *whose* money is in the vehicle, because different holders send flows that respond to different things — and mostly not to price. **Retirement defaults.** The largest single pool of passive equity is the American defined-contribution system, and its dominant vehicle is the target-date fund. Since the Pension Protection Act of 2006 established qualified default investment alternatives, an employee who is automatically enrolled and never makes a choice ends up in a dated fund that holds index funds according to a glide path. Assets in target-date vehicles now run into the trillions. Consider the demand curve this generates. Contributions arrive on payroll dates and are invested regardless of valuation. The glide path sells equities for bonds as a birthday passes. Quarterly rebalancing sells whatever went up and buys whatever went down. Not one of these flows contains a view. The system was designed, deliberately and for good reasons rooted in Chapter 14's evidence on household behavior, to remove price sensitivity from household investing — and it succeeded. The rebalancing rule even makes this holder mildly *contrarian*, which cuts against the reduced-liquidity-provision worry of §17.6, but contrarian on a mechanical schedule rather than on information. **The Fed's absence.** In the US, the central bank is not in this market. The Federal Reserve holds Treasuries and agency MBS; it has never held domestic equities, and its 2020 corporate credit facilities bought bond ETFs in modest size and unwound them. This is a policy choice, not a law of nature: the Bank of Japan spent more than a decade buying domestic equity ETFs and became, by the end, the largest single holder of Japanese equities before halting purchases in 2024. The counterfactual is worth holding in mind when reading §17.7. Every governance question raised by the Big Three's concentrated ownership becomes a different and sharper question when the concentrated owner is a central bank whose price sensitivity is zero by construction and whose voting policy is a matter of state. **Foreign holders.** Roughly a fifth of the US equity market is held from abroad (Financial Accounts, Z.1, approximate), a share that has risen steadily, and much of it arrives through index products benchmarked to global or developed-market indices in which US equities carry a provider-set weight. A European pension fund tracking a world index is a price-insensitive holder of Apple for reasons that have nothing to do with Apple and everything to do with MSCI's float-adjusted arithmetic. **Who is left to be price-sensitive.** Set against these: hedge funds, active mutual funds, dealers, corporate issuers running buybacks — the last of which has become one of the largest sources of genuinely valuation-responsive equity demand in the US market — and households trading directly. This is the residual that must absorb every shock the mandated holders transmit and every mispricing they ignore. It is smaller as a share of assets than at any time in the postwar period, and it is levered, benchmarked, and constrained in the ways Chapters 16 and 19 describe. Before that residual becomes Chapter 20's problem, the line between what this chapter has established and what it has only reported. Three of its claims are settled arithmetic and three are live disputes — graded here on the schema Chapter 6 §6.4 uses for the cross-section and Chapter 20 §20.5 for the demand system, which names §17.7's common-ownership evidence as one of the places the book marks the line. **Table 17.4: The state of the evidence** | Claim | Status | | --------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | | The average actively managed dollar underperforms the index after costs | **Established.** Sharpe's identity is arithmetic rather than a hypothesis, and French's accounting puts a price on the aggregate search for alpha | | Fund-level alpha cannot be measured well enough to identify skill within a career | **Established.** At realistic information ratios a $$t$$-statistic of two takes about a century of data, which is why the debate does not resolve at the level of the fund | | Skill is real and is captured by the manager through size rather than by the investor | **Widely accepted.** Weak net-of-fee persistence and a substantial, skewed distribution of manager-level value added are both in the data | | Addition to a major index once carried a 3-7 percent abnormal return and no longer does | **Established** as a fact about the estimates; *why* it vanished is the contested part, and only one of §17.4's three readings implies that demand curves are flat | | Rising passive ownership has degraded price discovery | **Contested.** Aggregate efficiency measures have not obviously deteriorated; the version worth taking seriously is about firm-level relative pricing, which is what capital allocation runs on | | Common ownership softens product-market competition | **Contested.** The correlation is real in several datasets and fragile in others, the mechanism remains unestablished, and the policy proposals run ahead of the finding | *Source: Author's assessment of the literature discussed in §§17.2-17.7.* Which sets up the question this part ends on. Standard asset pricing assumes that if a stock's price moves away from fundamentals, capital arrives until it moves back — that demand curves for individual securities are, in the limit, flat, and the marginal investor is a price-taking optimizer. This chapter's holders are not that. They buy on payroll dates, on committee announcements, on glide paths, on reconstitution calendars. If a growing share of the market's owners has a vertical demand curve, then aggregate demand for equities is inelastic, flows move prices with a multiplier, and the identity of the marginal investor becomes an empirical object rather than a modeling convenience. That is Chapter 20's question, and the demand-system approach is the machinery built to answer it. *** ## Elsewhere in the Series * **ETF market structure, ETF arbitrage under stress, and index-flow dynamics across borders** — *International Finance*, Chapter 14 (§14.4). This chapter keeps the compact creation/redemption mechanism a reader needs to proceed and points onward for the microstructure. * **Delegation, agency problems of benchmarking, flow-performance fragility, and the institutional balance sheets behind these vehicles** — this book, Chapter 16. * **The Grossman-Stiglitz model, stated and derived** — this book, Chapter 7 §7.2, with the equilibrium informed fraction and price informativeness tabulated there. Section 17.6 applies it; it does not rebuild it. * **Index inclusion as a demand shock, with the event-study evidence** — this book, Chapter 12 §12.9, which takes §17.4's three readings as given and works the size of the shock in its Problem 5; event-study mechanics in Appendix A. * **Demand-system asset pricing and inelastic markets** — this book, Chapter 20. * **What policy-based voting does to corporate control** — this book, Chapter 24 §24.4, which takes §17.7's stewardship-capacity and common-ownership arguments as given and works the voting arithmetic, pass-through voting, and the rise and retreat of mandate-driven voting support. Section 17.7 owns the incentive argument and the common-ownership evidence; Chapter 24 §24.4 owns the governance consequence. *** ## Summary 1. **Passive is now the majority of US equity fund assets.** Index funds grew from nothing in 1975 to more than half of US equity fund assets by 2023 (Table 17.1). Active assets stopped growing rather than collapsing; every marginal dollar went to the index. 2. **The case for indexing rests on fees, arithmetic, and taxes.** Fee differences compound against gross returns, so a 0.67-point annual gap costs roughly a sixth of terminal wealth over thirty years. Sharpe's identity guarantees the average active dollar underperforms after costs, and French's accounting puts a price on the aggregate search for alpha. 3. **Alpha cannot be measured well enough to identify skill in a career.** With realistic information ratios, distinguishing a good manager from a lucky one at conventional significance requires a century of data. The active-versus-passive debate does not resolve at the fund level because the data cannot resolve it. 4. **Berk-Green explains why skill and zero net alpha coexist.** Performance-chasing flows expand a skilled manager's fund until decreasing returns to scale drive net alpha to zero. Skill is real, is captured by the manager as a rent through size, and leaves the investor with the passive return. Weak net persistence and real manager-level value added are the model's signatures, and both appear in the data. 5. **Indices are products, not facts.** Committee and rules-based construction, float adjustment, and eligibility screens all determine who must own what. The large inclusion effects of earlier decades (3-7% abnormal returns) have shrunk toward zero, and whether that reflects deeper arbitrage capacity, better anticipation, or smaller incremental shocks is unsettled. 6. **The ETF wrapper is a creation/redemption mechanism.** Authorized participants exchange baskets for shares, tethering price to NAV and delivering the tax advantage through in-kind redemption. The tether is weakest exactly where the underlying is least liquid, which is why fixed-income ETFs are the interesting case. 7. **Grossman-Stiglitz makes the passive share self-limiting.** As active capital exits, the return to information rises. The open questions are the level at which the active sector stabilizes, and whether firm-level relative pricing degrades even while aggregate market efficiency does not. 8. **Concentrated ownership arrived as a by-product.** The Big Three hold upwards of a fifth of most large US firms with stewardship teams of a few dozen people, and the fee competition that made indexing cheap gives them weak private incentives to invest in monitoring. 9. **The common-ownership hypothesis is contested, not established.** The Azar-Schmalz-Tecu evidence is real; so are the measurement, identification, and mechanism objections to it. Index-provider power over country classification is a smaller literature and a clearer case of private allocative authority. 10. **Passive is not one holder.** Retirement defaults, foreign index trackers, and (elsewhere) central banks hold the passive claim for reasons unrelated to price. As the price-insensitive share of ownership grows, the marginal investor becomes an empirical question — Chapter 20's. *** ## Key Terms * **Passive investing**: Investment strategy that tracks a market index rather than attempting to beat it; a claim about mandate, not about trading frequency * **Active share**: Degree to which a portfolio differs from its benchmark; the measure that separates genuine active management from closet indexing * **Creation/redemption**: The process by which ETF shares are issued and retired in blocks against a published basket of underlying securities, tethering the ETF price to net asset value * **Authorized participant (AP)**: A broker-dealer with a contractual right to transact creation units directly with an ETF; the arbitrageur in the ETF price mechanism * **Inclusion effect**: The abnormal return around a security's addition to (or deletion from) an index, used as evidence on the slope of the demand curve for individual stocks * **Common ownership**: The holding of significant stakes in competing firms by the same institutional investors, and the hypothesis that this softens product-market competition * **Berk-Green equilibrium**: The outcome in which performance-chasing flows expand skilled managers' funds until decreasing returns to scale drive net-of-fee alpha to zero, so managers capture skill rents through size and investors earn the passive return * **Stewardship**: The voting, engagement, and monitoring activity of asset managers on behalf of the funds they run; the governance obligation an index fund cannot discharge by selling * **Float adjustment**: The construction of index weights using only shares available to public investors, excluding strategic and insider blocks *** ## Readings ### Required * Berk, J. and R. Green (2004). "Mutual Fund Flows and Performance in Rational Markets." *Journal of Political Economy* 112(6): 1269-1295. *The equilibrium model of §17.3; read it as a holders-move-markets argument, not a defense of the fund industry.* * French, K. (2008). "Presidential Address: The Cost of Active Investing." *Journal of Finance* 63(4): 1537-1573. *Puts an aggregate price on the search for alpha and turns Sharpe's identity into a measured quantity.* ### Recommended * Grossman, S. and J. Stiglitz (1980). "On the Impossibility of Informationally Efficient Markets." *American Economic Review* 70(3): 393-408. *Derived in Chapter 7 §7.2; §17.6 applies it.* * Azar, J., M. Schmalz and I. Tecu (2018). "Anticompetitive Effects of Common Ownership." *Journal of Finance* 73(4): 1513-1565. *Read alongside the replication and measurement critiques discussed in §17.7.* * Wigglesworth, R. (2021). *Trillions: How a Band of Wall Street Renegades Invented the Index Fund and Changed Finance Forever*. Portfolio/Penguin. *The narrative history — Bogle, Wells Fargo, Dimensional, BlackRock — and the best account of how the product was actually built.* *** ## Discussion Questions 1. **The tipping point.** If passive funds eventually hold 80% of public equities, who sets prices? Is there a "tipping point" beyond which passive investing undermines market efficiency? How would you test this empirically — and would you test it on aggregate market efficiency, on the cross-section, or on something else? Explain why the choice of test changes the answer. 2. **Berk-Green and the fee debate.** In the Berk-Green equilibrium, a skilled manager's fund grows until net alpha is zero, so investors are indifferent between the fund and the index. Does this mean fees are "fair"? Construct a case in which a high-fee fund is exactly what a competitive market should produce, and a case in which the same observed fee reflects a friction (distribution, inattention, advice conflicts) rather than a rent to skill. What data would distinguish them? 3. **Measuring the manager, not the fund.** Berk and van Binsbergen argue that value added — gross alpha times assets — is the right measure of skill, not net alpha. Whose question does each statistic answer? If you were a pension trustee selecting a manager, which would you use, and why is that different from the answer an academic testing market efficiency would give? 4. **Common ownership without a mechanism.** Suppose the empirical correlation between common ownership and product-market prices survives every measurement critique. Design the test that would establish the *channel*: what would you look for in executive compensation contracts, entry decisions, or firm communications? If no channel can be found, what should a regulator conclude? 5. **Price-inelastic defaults.** A target-date fund buys equities on payroll dates and rebalances quarterly regardless of valuation. Is this holder a stabilizing or destabilizing force in a selloff? Work through both the mechanical rebalancing effect and the flow effect, and state what would have to be true of the *other* holders for your answer to flip. *** ## Problems **Problem 1 — The compounding of fees.** An investor puts 100,000 into a fund for 30 years. The gross return is 7 percent a year, and the fee is deducted annually. All figures are in dollars. (a) Using $$W\_T = W\_0(1 + r - f)^T$$, compute terminal wealth at an annual fee of 3 basis points and at 70 basis points, and the difference between them. Compare your three figures with Table 17.2 and state how the table has been rounded. (b) Compute the fraction of terminal wealth surrendered to the 67-basis-point fee gap, first exactly and then with the approximation $$1 - e^{-fT/(1+r)}$$. Compare both with the naive figure $$f \times T$$, and say in which direction the naive figure errs and why it errs in that direction. (c) Solve for the gross alpha the 70-basis-point fund must produce in order to leave the investor exactly where the 3-basis-point fund does. (d) Section 17.3 gives $$t(\hat\alpha) \approx (\alpha/\sigma\_\varepsilon)\sqrt{T}$$. With a tracking-error volatility of 5 percent, how many years of data would be needed to establish the alpha in (c) at $$t = 2$$? Comment on what that does to the fee debate as an empirical question. (e) In a taxable account the active fund also distributes 3 percent of assets a year as short-term gains, taxed at 35 percent. Recompute the required gross alpha and the years needed. Then state what both numbers become for the holder §17.8 says owns most passive money, and which of §17.2's three pillars that holder does not receive. **Problem 2 — Tracking a rule.** A fund tracks a 500-stock index. Holding a sample of 150 names gives an annual tracking-error volatility of 90 basis points; full replication gives 5 basis points but costs an extra 12 basis points a year in trading and custody. The fund's expense ratio is 4 basis points either way. (a) For each approach, report the 95 percent range of the fund's one-year return relative to the index, taking $$\pm 1.96$$ times the tracking-error volatility. (b) Use §17.3's formula with the fund's expected shortfall to the index in place of alpha, and compute how many years of data are needed to establish at $$t = 2$$ that each version lags the index by the amount it actually costs. Which of the two funds can a trustee hold to account, and on what horizon? (c) State the trade-off between the two approaches in one sentence. Then say which version looks better under a mandate written on tracking error and which under a mandate written on net return, and what that implies about how index mandates get written. (d) In December 2020 Tesla entered the S\&P 500 at about a 1.5 percent index weight, with the mechanical demand from trackers put at 70 to 90 billion dollars. Compute the assets tracking the index that those two estimates imply. Compare the range with Table 17.1's 2023 figure for passive US equity fund assets, and give two reasons the two numbers need not agree. (e) Section 17.1 says a fund that failed to buy Tesla "would have carried a tracking error large enough to end a career." Tesla fell on its first day inside the index. If it fell 5 percent that day, compute the one-day tracking error of a fund that had not yet bought, and say in which direction it ran. Explain why the mandate makes the sign of that number irrelevant. **Problem 3 — Tesla joins the index.** Use §17.1's figures. Tesla closed near 408 on 16 November 2020, the day the addition was announced after the close, and near 695 on Friday 18 December, the last session before inclusion. It entered at about a 1.5 percent index weight, mechanical tracker demand was put at 70 to 90 billion dollars, and Tesla itself sold about 5 billion of new stock into the same window. Take the index's float-adjusted capitalization at the time as 33 trillion, a round figure assumed for the arithmetic. All figures are in dollars. (a) Compute the return from the announcement close to 18 December. If the index returned 5 percent over the same window and Tesla's market beta is 1.5, compute the abnormal return under a market model. (b) Write both sides of the trackers' trade in terms of one quantity: the ratio of the assets tracking the index to the index's float-adjusted capitalization. Show that the purchase of Tesla is that ratio itself, expressed as a fraction of Tesla's float, while the proportional sale of the other 499 names is 0.015/0.985 times the ratio, expressed as a fraction of those names' combined value. Compute the ratio of the two, and say what it explains about which side of the trade was reported. (c) Using the 80-billion midpoint of the demand estimate and the 1.5 percent weight, compute the assets tracking the index; then compute the ratio in (b) and hence the purchase as a percentage of Tesla's float. Express the 5 billion the company itself supplied as a fraction of the mechanical demand. (d) Section 17.4 gives three explanations for the disappearance of the inclusion effect. Apply each to your numbers and say which input it says is wrong — the size of the shock, the timing of the window, or the elasticity facing the trackers. Then explain why §17.4 calls Tesla "the exception that shows the mechanism." (e) Tesla fell on its first day inside the index. State what a permanently sloped demand curve and a temporary price-pressure account each predict for the path after inclusion, and say what one day's decline can and cannot settle. Compare your answer with Chapter 12 §12.9 and its Problem 5. **Problem 4 — The Big Three, counted.** A US company has 500 million shares outstanding. The most recent Form 13F-HR filings report BlackRock holding 40 million, Vanguard 45 million, and State Street 25 million. (a) Compute the three managers' combined position as a share of shares outstanding. (b) At the annual meeting 76 percent of outstanding shares are voted, and the three managers vote all of theirs. Compute their combined share of votes cast. Then compute the share of the *remaining* votes cast that a proposal needs in order to carry a simple majority, first if all three support it and then if all three oppose it. (c) Figure 17.7 puts the three managers' combined US equity holdings at 12.3 percent of the market value of US public corporate equity at the end of 2009 and 19.0 percent at the end of 2025, the later figure splitting into 8.3 points for Vanguard, 7.1 for BlackRock, and 3.6 for State Street. Compute the change over the sixteen years, in points and as a ratio. Then reconcile the 19.0 percent aggregate with your answer to (a): if large-capitalization firms are 80 percent of US public equity by value, what share of the remaining fifth do the three hold? (d) Figure 17.7's note calls the share "a floor, not a measurement." Name three features of the 13F regime that make it one and say, for each, in which direction it biases the measured share. Then say what the denominator is, and why that alone puts the aggregate below the figure §17.7's prose quotes for large firms. (e) The same note records that Vanguard filed its last group-level 13F for the fourth quarter of 2025. State what that does to the series and what a researcher would have to do to continue it. Then suppose pass-through voting is adopted and 15 percent of the fund investors behind the position in (a) direct their own votes. Recompute the manager's share of votes cast, first assuming those investors vote and then assuming they abstain, and say which of the two outcomes §17.7 treats as the open question. **Problem 5 ★ — What stewardship is worth to the manager.** An index manager holds 7 percent of a company with a market value of 20 billion. A serious governance engagement would raise the company's value by 2 percent and would cost the manager 200,000 of professional time. The manager charges 3 basis points a year on assets. Two competing index managers hold 6 percent and 5 percent of the same company and would do nothing. All figures are in dollars. (a) Compute the value the engagement creates, the part accruing to the engaging manager's own funds, and the part accruing to the two competitors' funds. (b) Compute the increase in the engaging manager's own annual fee revenue, and the number of years of that revenue needed to repay the 200,000 cost. (c) Compute the fee rate at which the first year's revenue increment alone would cover the cost. Compare it with the 3 basis points index funds charge and with the 70 basis points §17.2 attributes to the average active fund, and state the resulting proposition in one sentence. (d) The manager's stewardship team is 40 professionals covering 12,000 shareholder meetings a year with an average of 12 ballot items each. Compute meetings and items per professional per year, and per working day on a 220-day year. State what that budget makes possible and what it rules out. (e) Section 17.7 says an index fund cannot exit. Explain why the unavailability of the Wall Street Walk is not by itself an argument that index funds will be good stewards. Then name the two responses the industry has made, and say which of them your answers to (a)-(c) suggest will change the incentive and which will not. *** ## Selected Solutions *Solutions to Problems 1 and 2 follow. Solutions to the remainder are in the instructor materials.* **Problem 1.** (a) $$W\_T = 100{,}000(1.0697)^{30} = \mathbf{754{,}849}$$ at three basis points and $$100{,}000(1.063)^{30} = \mathbf{625{,}170}$$ at seventy, a difference of $$\mathbf{129{,}679}$$. Table 17.2 reports 754,000, 625,000 and 129,000, so it has been **rounded down to the nearest thousand** in each row — which is why its difference column is a thousand short of the difference of its own two rounded entries. (b) Exactly, the fraction surrendered is $$1 - 625{,}170/754{,}849 = \mathbf{17.18}$$ **percent**. The approximation gives $$1 - e^{-0.0067 \times 30/1.07} = \mathbf{17.13}$$ **percent**, accurate to five basis points. The naive figure is $$f \times T = 0.0067 \times 30 = \mathbf{20.1}$$ **percent**, which **overstates** the loss. It errs upward because it charges the fee against the *terminal* balance every year; in fact each year's fee is levied on a smaller base than the final one, and the compounding of the fee is slower than the compounding of the portfolio. *The naive figure is nonetheless the more useful one for a household, because it errs in the conservative direction on a quantity most people put at zero.* (c) Terminal wealth is $$W\_0(1 + r + \alpha - f)^T$$, so the two funds are equal when $$r + \alpha - 0.0070 = r - 0.0003$$, giving $$\alpha = \mathbf{67}$$ **basis points a year, every year, before costs**. Note what the horizon did: nothing. A fee difference is a level shift in the compounding rate, so the required alpha does not shrink with a longer holding period — the *loss* compounds, the hurdle does not. (d) $$t = (\alpha/\sigma\_\varepsilon)\sqrt{T} = 2$$ requires $$T = (2 \times 0.05/0.0067)^2 = \mathbf{223}$$ **years**. The active manager must therefore deliver an alpha that could not be distinguished from zero in ten investing lifetimes. *This is the fee debate's real shape and it is rarely stated: the question is not whether the alpha exists but whether anything could ever count as evidence that it does. A fee is observable today and certain; the alpha that would justify it is unobservable within any horizon a client will live through. That asymmetry, not the arithmetic of §17.2's second pillar, is why the flows went where they went.* (e) Short-term gains of three percent of assets taxed at 35 percent are a further drag of 105 basis points a year, so the required gross alpha rises to $$\mathbf{172}$$ **basis points** and the horizon falls to $$(2 \times 0.05/0.0172)^2 = \mathbf{34}$$ **years** — still longer than a career, but no longer absurd. For the holder §17.8 identifies as owning most passive money — the American defined-contribution system, whose assets sit in tax-deferred accounts — the tax drag is zero, so the numbers revert to 67 basis points and 223 years. That holder therefore receives §17.2's first pillar (the fee advantage) and its second (the zero-sum arithmetic), and **not its third**: tax efficiency is worth nothing inside a 401(k). *Two of the three pillars carry the whole case for the vehicle that dominates the market, which is worth knowing before treating the third as evidence of anything.* **Problem 2.** (a) At $$\pm 1.96$$ tracking errors: the sampled fund's relative return lies within $$\pm \mathbf{176}$$ **basis points** and the fully replicated fund's within $$\pm \mathbf{10}$$ **basis points**, nineteen times out of twenty. (b) Each fund's expected shortfall to the index is what it actually costs: 4 basis points for the sampled fund (its expense ratio) and $$4 + 12 = 16$$ basis points for the replicated one. Then $$T = (2\sigma\_\varepsilon/\alpha)^2$$ gives **2,025 years** for the sampled fund and **0.4 years** for the replicated one. A trustee can hold the replicated fund to account inside a **single year**; the sampled fund's shortfall could not be established over the age of the republic, forty times over. (c) The trade-off in one sentence: full replication costs four times as much and is twenty times as accountable. Under a mandate written on **tracking error** the replicated fund wins overwhelmingly — 5 basis points against 90. Under a mandate written on **net return** the sampled fund wins, because it is 12 basis points a year cheaper and the sampling noise has a mean of zero. What that implies is the interesting part: **index mandates are written on tracking error, and they are written that way because tracking error is the quantity a trustee can verify within the term of the trustee's own appointment.** The mandate selects for measurability, not for the beneficiary's return, and §17.4's inclusion effects are the price the market pays for that choice. (d) Assets tracking the index are the demand divided by the weight: $$70/0.015 = \mathbf{4.7}$$ **trillion** and $$90/0.015 = \mathbf{6.0}$$ **trillion**. Table 17.1's 2023 figure for passive US equity fund assets is 8.5 trillion, above the range. Two reasons the numbers need not agree: the estimates are for December **2020** and the table is for **2023**, over which period the passive stock grew substantially; and not all passive US equity money tracks the S\&P 500 — total-market, mid-cap, small-cap and factor indices are all inside Table 17.1's 8.5 trillion and none of them was buying Tesla at a 1.5 percent weight on that date. *A third reason is worth adding: some trackers had bought ahead of the effective date, so the mechanical demand estimate is a flow measure over an unspecified window rather than a stock.* (e) A fund that had not yet bought a 1.5 percent weight that then fell 5 percent **outperformed** its benchmark by $$0.015 \times 0.05 = \mathbf{7.5}$$ **basis points** on the day. The sign is irrelevant because the mandate is written on the *magnitude* of the deviation: a fund whose tracking error is 7.5 basis points in a day is on an annualized path of well over a hundred, against a target of five, and the trustee's question is not "did it help?" but "why were you not holding the index?". **A mandate on tracking error makes being right in the wrong direction a breach.** That is the mechanism by which §17.4's inclusion demand is guaranteed to arrive regardless of what anyone thinks the security is worth. *** ## Data Exercise: The Arithmetic and the Owners **Part A — Fee drag and the market proxy (free data).** Download the monthly market factor and the risk-free rate from Ken French's data library, along with a value-weighted and an equal-weighted market return series. 1. Compute the compounded value of one dollar invested in the value-weighted market over the longest available sample, then recompute it net of an annual fee of 3, 30, and 70 basis points, deducted monthly. Report the fraction of terminal wealth lost at each fee level and compare it to the naive calculation $$f \times T$$. 2. Repeat with the equal-weighted proxy. Equal weighting is an *active* bet relative to the value-weighted market and requires rebalancing. Estimate the annual turnover an equal-weighted portfolio of the same universe would require, and ask at what round-trip trading cost the equal-weighted proxy's historical advantage disappears. 3. Regress the equal-weighted minus value-weighted return difference on the size and value factors. How much of the "outperformance" is a factor tilt you could buy in an index wrapper? **Part B — Who owns this company (free data).** Choose a large US public company. Using SEC EDGAR's full-text and structured 13F data: 1. Retrieve the most recent 13F-HR filings of BlackRock, Vanguard, and State Street and extract their reported positions in your company. Express each as a share of shares outstanding (from the company's most recent 10-Q cover page) and sum them. 2. Repeat for the same quarter ten years earlier. Document the change in combined Big Three ownership, and note the mechanical caveats: 13F covers only reportable US equity positions of managers above the filing threshold, is filed at the manager level rather than the fund level, and reports long positions only. 3. Retrieve the company's most recent proxy statement (DEF 14A) and record the total votes cast on a routine management proposal. What fraction of outstanding shares voted, and how large is the Big Three's combined position relative to *votes cast* rather than to shares outstanding? **Part C ★ (if you have WRDS).** Using CRSP and the Thomson/Refinitiv S12/S34 holdings data, construct an annual time series of the aggregate index-fund ownership share of the S\&P 500 and estimate the cross-sectional relationship between a stock's passive ownership share and (i) its return co-movement with the index and (ii) the speed with which its price incorporates earnings announcements. State clearly which of these estimates can be given a causal reading and what instrument or design would be needed for the other.