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Active and Passive Investing
Nicolae Gˆarleanu and Lasse Heje Pedersen∗
October 1, 2019
Abstract We model how investors allocate between asset managers, managers choose their portfolios of multiple securities, fees are set, and security prices are determined. The optimal passive portfolio is linked to the “expected market portfolio,” while the op- timal active portfolio has elements of value and quality investing. We make precise Samuelson’s Dictum by showing that macro inefficiency is greater than micro ineffi- ciency under realistic conditions — in fact, all inefficiency arises from systematic factors when the number of assets is large. Further, we show how the costs of active and pas- sive investing affect macro and micro efficiency, fees, and assets managed by active and passive managers. Our findings help explain empirical facts about the rise of delegated asset management, the composition of passive indices, and the resulting changes in financial markets.
Keywords: asset pricing, market efficiency, asset management, search, information JEL Codes: D4, D53, D8, G02, G12, G14, G23, L
∗Gˆarleanu is at the Haas School of Business, University of California, Berkeley, and NBER; e-mail: gar- [email protected]. Pedersen is at AQR Capital Management, Copenhagen Business School, New York Uni- versity, and CEPR; www.lhpedersen.com. We are grateful for helpful comments from Antti Ilmanen, Kelvin Lee, and Peter Norman Sørensen as well as from seminar participants at the Berkeley-Columbia Meeting in Engineering and Statistics, Federal Reserve Bank of New York, and Copenhagen Business School. Peder- sen gratefully acknowledges support from the FRIC Center for Financial Frictions (grant no. DNRF102). AQR Capital Management is a global investment management firm, which may or may not apply similar investment techniques or methods of analysis as described herein. The views expressed here are those of the authors and not necessarily those of AQR.
Over the past half century, financial markets have witnessed a continual rise of delegated asset management and, especially over the past decade, a marked rise of passive manage- ment, as seen in Figure 1. This delegation has potentially profound implications for market efficiency (see, e.g., the presidential addresses to the American Finance Association of Gross- man (1995), Stein (2009), and Stambaugh (2014)), investor behavior (presidential address of Gruber (1996)), and asset management fees (e.g., the presidential address of French (2008)). The rise of delegated management raises several questions: What is the optimal portfolio of active (i.e., informed) and passive (i.e., uninformed) managers, respectively? What deter- mines the number of investors choosing active management, passive management, or direct holdings? What are the implications of delegated management on market efficiency at the micro and macro levels? How do macro and micro efficiencies depend on the costs of active and passive management? We address these questions in an asymmetric-information equilibrium model where se- curity prices, asset management fees, portfolio decisions, and investor behavior are jointly determined. Our main findings are: (1) the optimal passive portfolio is the “expected market portfolio,” tilted away from assets with the most supply uncertainty; (2) the optimal active portfolio has elements of value and quality investing; (3) macro inefficiency is greater than micro inefficiency (consistent with Samuelson’s Dictum) when there exists a strong common factor in security fundamentals or when the number of securities is large; (4) when infor- mation costs decline, the number of active managers increases, active fees decrease, market inefficiency decreases, especially macro inefficiency (counter to part of Samuelson’s Dictum); (5) when the cost of passive investing decreases, market inefficiency increases, especially macro inefficiency, the number of active mangers decreases, and active fees drop by less than passive fees; and (6) market inefficiency is linked to the economic value of information and to entropy. These findings help explain a number of empirical findings and give rise to new tests as we discuss below. To understand our results, let us briefly explain the framework. We introduce asset managers into the classic noisy-rational-expectations-equilibrium (REE) model of Grossman
ensure that she is informed) plus an active management fee. Active and passive managers determine which portfolios to choose and, in addition, active managers decide whether or not to acquire information. Market clearing requires that the total demand for securities equals the supply, which is noisy (e.g., because of share issuance, share repurchases, changes in the float, private holdings, etc.). Passive managers seek to choose the best possible portfolio conditional on observed prices (but not conditional on the information that active managers acquire). One may wonder whether they should choose the “market portfolio” (the market-capitalization weighted port- folio of all assets), which is the standard benchmark in the Capital Asset Pricing Model (CAPM). While the market portfolio is the focal point of much of financial economics, it is not discussed in the context of REE models because supply noise renders it unobserv- able (likewise, in the real world no one knows the true market portfolio as emphasized by Roll (1977)); furthermore, much of the REE literature studies a single asset, precluding a meaningful analysis of portfolios. Bridging the REE literature and the CAPM, we show that passive investors choose the closest thing they can get to the market portfolio, namely the “expected market portfolio” based on the distribution of the supply and what can be learned from public signals, under certain conditions (e.g, i.i.d. shocks across securities). This behavior resembles what real-world passive investors do, namely choosing an index that is rebalanced based on public information. However, indices only hold a subset of all securities, typically large and mature firms with sufficient time since their initial public offer- ing. In a similar spirit, we show that passive investors optimally over-weight securities with less supply uncertainty in the more general case when shocks are correlated across securities via a factor structure. Hence, our framework presents a first step toward a theory of optimal security indices. Turning to active managers, we show that they use their information advantage in several ways. First, they naturally tend to overweight securities about which they have favorable information (quality investing). Second, they tend to overweight securities with positive supply shocks, since these securities fall in price (a form of value investing).
Active investors thus exploit market inefficiency across various assets, where inefficiency is defined (following Grossman and Stiglitz (1980)) as the uncertainty about the fundamental value conditional on only knowing the price relative to the uncertainty conditional on also knowing the private information. For example, the market inefficiency is zero (fully efficient market) if the uncertainty about the fundamental value is the same whether one learns from just the price or also the signal. Further, the more information advantage one enjoys from knowing the signal, the more inefficient the market. An interesting question that can be addressed naturally in this framework is whether there are greater inefficiencies at the macro or at the micro level. Indeed, Samuelson fa- mously hypothesized that macro inefficiency is greater than micro inefficiency, a notion known as “Samuelson’s Dictum” (see quote and references in the beginning of Section 3 and the empirical evidence in Jung and Shiller (2005)). We show that Samuelson’s Dictum holds when there exists a strong common factor in security fundamentals. More precisely, we show that the factor-mimicking portfolio is the most inefficient portfolio, while the least inefficient portfolios are long-short relative-value portfolios that eliminate factor risk. Hence, this makes precise what macro and micro efficiency means, and gives precise conditions un- der which Samuelson’s Dictum applies (or does not apply). We further show that, due to diversification, when the number of securities is large, not only does Samuelson’s Dictum always hold, but in fact the combined inefficiency of all micro portfolios becomes negligible — all the inefficiency is in the pricing of systematic factors. This result is related to the Arbitrage Pricing Theory (APT) of Ross (1976). While the APT states that risk premia are driven by systematic factors when the number of assets is large, we show that inefficiencies are also driven by these factors.^2 (^2) Active managers in our model make an all-or-nothing information choice, whereas Veldkamp (2011), Van Nieuwerburgh and Veldkamp (2010), Kacperczyk et al. (2016), Glasserman and Mamaysky (2018), and others study agents’ choice of information, which can affect macro vs. micro efficiency as emphasized by the latter paper. Our assumption captures, for example, the case in which active investors decide whether or not to set up an IT system that captures the main databases, whereas the above papers capture the idea that different investors may focus on different subsets of the available information. See also Breugem and Buss (2018), who consider the effect of benchmarking considerations on information acquisition and efficiency with multiple assets, and Kacperczyk et al. (2018), who consider the effect of large investors’ market power on market efficiency. We complement the literature with regard to macro vs. micro efficiency by providing a general definition of Samuelson’s Dictum, by showing how it arises with many assets (i.e., as the number of
1 Model and Equilibrium
This section lays out our noisy rational expectations equilibrium (REE) model and shows how to solve it.
1.1 REE Model with Multiple Assets and Asset Managers
We model a two-period economy featuring a risk-free security and n risky assets. The return of the risk-free security is normalized to zero while the vector risky asset prices p is determined endogenously. The risky assets deliver final payoffs given by the vector v, which is normally distributed with mean ˉv and variance-covariance matrix Σv, which we write as v ∼ N (ˉv, Σv). Agents can acquire various signals about all the assets at a cost k. We collect all the signals in a vector of dimension n that we denote s = v + ε, where ε ∼ N (0, Σε) is the noise in the signal.^4 The supply of the risky assets is given by q ∼ N (ˉq, Σq) and the shocks to q, ε, and v are independent. The supply is noisy for several reasons (e.g., Pedersen, 2018): New firms are listed in initial public offerings, existing firms issue new shares in seasoned equity offerings, firms repurchase shares (sometimes by buying shares in the market without telling investors), and the number of floating shares changes when control groups buy or sell shares. 5 Further, the de facto supply of publicly traded shares also implicitly changes when correlations vary between public shares and investors’ endowment (e.g., human capital, natural resources, or private equity holdings, where private firms may also issue or repurchase shares). For these declines in his model, the allocation to, and the performance of, active managers both decline. Hence, this model cannot explain the finding of Cremers et al. (2016) discussed above, namely that the size and performance of active management move in opposite directions (but the model can explain a number of other phenomena). 4 If we start with a signal ˆs of any other dimension ˆn, then we can focus on the conditional mean u := E(v|ˆs), which is of dimension n and can be translated into a signal s as modeled above. For example, if ˆn 5 ≥ n, we have s := ˉv + Σv Σ− u 1 (u − ˉv), where Σu = var(u). Many indices use a float adjustment. E.g., S&P Float Adjustment Methodology 2017 states “the share counts used in calculating the indices reflect only those shares available to investors rather than all of a company’s outstanding shares. Float adjustment excludes shares that are closely held by control groups, other publicly traded companies or government agencies.”
and other reasons, no one knows the true market portfolio, the underpinning of the “Roll critique” (Roll, 1977). The economy has Mˉ active asset-management firms and a representative passive manager. The passive manager seeks to deliver the best possible portfolio that can be achieved without acquiring the signal s. The passive manager faces a marginal cost per investor of kp and, since passive investing is assumed to be a competitive industry, this manager charges a fee fp = kp (where the subscript p naturally stands for “passive”). Active managers face a marginal cost of ka (subscript a for “active”) and, in addition, they must decide whether to incur the fixed cost k associated with acquiring the signal s. Specifically, M active managers endogenously decide to pay the cost k to become informed while the remaining Mˉ − M managers seek to collect active asset management fees fa even though they invest without information (e.g., these managers are using “closet indexing”). The economy has Sˉ optimizing investors with initial wealth W and constant absolute risk aversion (CARA) coefficient γ. These investors either search for an active manager, allocate to a passive manager, or invest directly in the financial market. Specifically, Sa investors choose to search for an active manager, Sp investors choose passive, and the remaining Sˉ − Sa − Sp are self-directed. If an investor l makes an uninformed investment (i.e., without using the signal s) directly in the financial market, then he incurs an investor-specific cost dl associated with brokerage fees and time used on portfolio construction. If the investor makes an informed investment, the cost is dl +k, but we show that this behavior is dominated by using an active manager. If the investor uses a passive manager, he incurs the passive management fee fp (as discussed above). Finally, investors can allocate to an informed active manager by paying a search cost c to be sure to find an informed manager and, in addition, pay an asset management fee fa determined via Nash bargaining. The search cost c(M, Sa) is a smooth function of the number of searching investors Sa and the number of informed managers M. For a number of our results, it is helpful that the search cost satisfies the regularity conditions (^) ∂M∂c ≤ 0 and (^) ∂S∂ca ≥ 0, namely that it is easier to find an appropriate manager if there are more managers and harder when there are more
1.2 Efficiency of Assets, Portfolios, and the Market
An important building block of our analysis is the notion of price efficiency. To define this concept, we build on the logic of Grossman and Stiglitz (1980), which considers the inefficiency of a single asset. We wish to define the inefficiency of any set of linearly independent portfolios {ζ 1 , ..., ζl} ⊂ Rn, where the number of portfolios can be anywhere from l = 1, i.e., a single asset, to l = n, that is, the entire market. We collect the portfolio weights in a matrix ζ ∈ Rn×l^ and define their joint inefficiency as follows.
ηζ^ =^12 log
det(var (ζ>v|Fu^ )) det(var (ζ>v|Fi))
where Fi = F(p, s) is the informed information set, consisting of both the price and the signal, and Fu = F(p) is the uninformed information set, consisting only of the price. In words, this definition means that a set of portfolios is considered more inefficient if the uninformed has a larger uncertainty relative to the informed about the fundamental values of these portfolios. For example, the inefficiency of a single asset, say asset 1, is computed by considering the portfolio ζ = (1, 0 , ..., 0)>, which yields
ηasset 1^ =^12 log
(var (v 1 |Fu) var (v 1 |Fi)
= log
var (v 1 |Fu)^1 /^2 var (v 1 |Fi)^1 /^2
This expression is equivalent to that of Grossman and Stiglitz (1980). The expression makes the link between our notion of inefficiency and the amount of information gleaned from signals, respectively only prices, particularly easily to see. The overall market inefficiency plays a special role in the equilibrium of the model. The overall market inefficiency is naturally the inefficiency of the set of all assets. Hence, we consider the largest possible matrix of portfolios, ζ = In, namely the identity matrix in
Rn×n.^8 We denote the overall market inefficiency simply by η:
η = ηoverall market^ = ηIn^ =^12 log
(det(var (v|Fu)) det(var (v|Fi))
This definition of overall market inefficiency is the natural extension of the one-asset definition of Grossman and Stiglitz (1980), since it retains the tight link between market inefficiency and investors’ utility of information as discussed further below and formalized in Proposition 8.^9 Another natural property of our notion of market inefficiency is that it is linked to entropy, which is also stated in Proposition 8. When we analyze macro vs. micro efficiency (in Section 3), we also study the efficiency of individual securities, portfolios, and collections of portfolios; the general definition of efficiency will be very useful.
1.3 Solution: Deriving the Equilibrium
To solve for an equilibrium, one proceeds backwards in time. The first step, therefore, consists of solving for an equilibrium in the asset market, taking as given the masses of investors conditioning on Fi, respectively on Fu. This is done in a standard Grossman- Stiglitz step. We conjecture and verify that prices p are linear in the information s about securities as well as the supply q:
p = θ 0 + θs ((s − vˉ) − θq(q − qˉ)). (4)
The resulting optimal demands are linear, as well. For an investor of type j ∈ {i, u}, where i means that the investor invests through an informed manager and u means that he invests uninformed (passive manager or self-directed), the optimal demand is the portfolio xj that maximizes the investor’s expected utility given the information used. 10 The resulting (^8) The same outcome for the overall market inefficiency obtains for any matrix ζ ∈ Rn×n (^) of full rank. (^9) The link between the value of information and the ratio of determinants of the conditional variances was first derived in Admati and Pfleiderer (1987). 10 When an investor has searched for a manager, confirmed that the manager is informed, and paid the fee, then the manager invests in the investor’s best interest. This lack of agency problems means that there
appears in both terms because it is a cost that is already sunk.^11 The manager’s gain from accepting the investor is her fee revenue fa less his marginal cost ka. Hence, the equilibrium fee is:
fa = arg max f (W − c − f + ui − (W − c − fp + uu)) (f − ka) = arg max f (ui − uu + fp − f ) (f − ka) = ui^ −^ uu^ + 2 fp^ +^ ka = ka^ + 2 kp+ 2 ηγ , (8)
where we use (7) and the equality of the passive management fee and the marginal cost fp = kp. We see that the equilibrium active asset management fee fa equals the average marginal cost of active and passive asset management plus a term that increases in the market ineffi- ciency η. Intuitively, active managers can add more value in a more inefficient market, and hence charge larger fees. The third step involves the ex-ante considerations of managers and investors. Let’s start with the managers. A manager that remains uninformed only attracts a share of the noise allocators, with an expected value of N/ Mˉ. If she acquires the signal instead, and becomes an informed active manager, then she expects Sa/M additional investors, giving rise to an extra income, net of marginal costs, of (fa − ka)Sa/M. Hence, the active manager’s indifference condition for paying the information cost k is
η 2 γ +^
kp − ka 2 =^
M
Sa^ k.^ (9) As for the investors, their optimal allocations are determined as follows. An investor l with a low cost direct investment dl < fp optimally invest directly in the financial market. Investors with higher costs of direct investment dl ≥ fp are indifferent between active and passive management in an interior equilibrium. The indifference condition for these investors (^11) The investor’s outside option can also be seen as searching again for another active manager, which yields the same result in an interior equilibrium.
equalizes the certainty equivalent utility of passive management (W + uu − fp) with that of active management (W + ui − c − fa),
ui − uu = fa − fp + c (10)
which can be rewritten using (7) and (8) as:
η γ =^ ka^ −^ kp^ + 2^ c.^ (11)
The equilibrium condition (10)–(11) is intuitive. It says that the benefit of informed investing (the left-hand side) must equal the net cost of being informed (the right-hand side). The benefit equals the gain from exploiting market inefficiency, η, which we divide by γ to measure in terms of certainty equivalent dollars. The net cost of active investing is the active fee plus the search cost minus the passive fee. This net cost can be reduced to the difference in marginal costs, ka − kp, plus twice the search cost (twice because active investors must both pay the search cost and the active fee, and the latter equals the search cost plus the marginal cost, fa = c + ka, in equilibrium). Figure 2 summarizes the procedure for finding an interior equilibrium by equalizing the cost and benefit of active investing. Starting with the benefit, we first compute the left-hand side of (11) for each number of informed investors, I, generating the solid line in the figure. To do this, we solve for the asset prices (4) using the optimal demand (5) and asset-market clearing (6). This asset-market equilibrium yields the inefficiency η, given by (3), for each I. Turning to the cost of active investing, we compute the right-hand side of (11) for each number of informed investors, I, generating the dashed line in Figure 2. The search cost c (Sa, M ) depends on the number of searching investors Sa and the number of informed managers M they are looking for, so we first derive (Sa, M ) for each I. In particular, we see that (Sa, M ) can be derived uniquely by combining I = Sa + N MM ˉ with the manager indifference condition (9). We can therefore think of this cost as the actual cost that the investor would face, for any I, as long as the managers are in equilibrium for that I.
Assumption 1 Fundamentals have a factor structure:
v = ˉv + βFv + wv (12) ε = βFε + wε (13) q = ˉq + βFq + wq, (14)
where ˉv, qˉ ∈ Rn^ are the average fundamental values, respectively supplies, β ∈ Rn^ is a vector of factor loadings normalized (without loss of generality) such that β>β = n, the common factors Fv, Fε, and Fq are one-dimensional random variables with zero means and variances σ^2 Fv , σ^2 Fε , and σ^2 Fq , respectively, and the idiosyncratic shocks wv, wε, and wq ∈ Rn^ are i.i.d. across assets with variances σ^2 wv , σ w^2 ε , respectively σ w^2 q for each asset.
We will refer to the portfolio proportional to β as the “factor portfolio,” since this port- folio is maximally correlated with the common shocks. It is natural to think of this factor as the average market portfolio — that is, under Assumption 1 it is natural to also assume that the average supply ˉq is proportional to β and we will occasionally make this additional assumption. We also make use of the following assumption, which captures the idea that may underlie Samuelson’s hypothesis, namely that the common factor-component of the risk is especially important for future security prices.
Assumption 1′^ Assumption 1 holds and the common factor of v is non-zero, σ^2 Fv > 0 , and at least as important as that of ε, i.e., σ^2 Fv /σ^2 wv ≥ σ F^2 ε /σ^2 wε.
Finally, we also consider the following assumption.
Assumption 2 There exist scalars zε and zq such that Σε = zεΣv and Σ− q 1 = zqΣv.
The first part of Assumption 2 simply says that fundamentals and signal noise have the same risk structure (which can also hold under Assumption 1). The second part, which is
more unusual, says that the inverse of the variance-covariance matrix of the supply noise also shares this structure.^12 Assumptions 1 and 2 are both satisfied if all shocks are i.i.d. across assets, but otherwise they are different. We focus on Assumption 1, as it is the more standard and more realistic assumption. Assumption 2 is to be thought of as a generalization of the i.i.d.-shock case. In particular, the results that require narrowing Assumption 1 down to the case of i.i.d. shocks also hold under Assumption 2, and we therefore state them in this greater generality.
2 Optimal Passive and Active Portfolios
We wish to understand how active and passive investors construct their portfolios. Specif- ically, we are interested in the optimal informed portfolio xi and uninformed portfolio xu, defined in Equation (5). Given that real-world uninformed investors tend to hold indices, the optimal uninformed portfolio provides a foundation for the economics of indices. A standard benchmark portfolio in financial economics is the “market portfolio,” that is, the portfolio of all assets (cf. the CAPM). However, as emphasized by Roll (1977), the market portfolio is not known in the real world. Likewise, uninformed investors do not know the market portfolio q in our noisy REE economy. While the market portfolio is central in the CAPM, it has not played a role in the REE literature (because this portfolio is public knowledge and because this literature is focused on a single asset). Nevertheless, we can bridge these literatures by introducing the concepts of the “conditional expected market portfolio,” E(q|p), and the “average market portfolio,” q ˉ. The conditional expected market portfolio is the uninformed investors’ best estimate of the true market portfolio, q, based on public information. We first show how the optimal (^12) To understand Assumption, consider what happens if any security j undergoes a two-for-onw stock split, meaning that all shareholders receive two new shares for each old share. In this case, the number of shares outstanding doubles and the value of each share drops by half. This means that, if Assumption 2 was satisfied before the stock split, then it remains satisfied after the stock split. Indeed, the split means that the volatility of the value of shares drops by half, the volatility of the information noise drops by the same ratio, and the volatility of the supply noise doubles. A less natural implication of Assumption 2 is that securities with more correlated fundamentals have less correlated supply shocks (except in the special case, which overlaps with Assumption 1, when all securities are i.i.d.).
c. If v, , and q are i.i.d. across assets, except that the supply uncertainty (Σq)jj varies across assets indexed by j, then passive investors hold larger average posi- tions E(xu,j ) in assets with lower supply uncertainty. It is interesting to compare the conclusions of this proposition to the actual portfolios of real-world passive investors. Passive investors typically hold a combination of (global) stock and bond index funds or ETFs. These indices are typically weighted by the total market-capitalization of each constituent security’s floating shares outstanding. The indices are regularly re-weighted to account for changes in the index constitution, share repurchases, new issuance, and changes in the insider holdings (i.e., shares not part of the float). Hence, consistent with part 1.a of Proposition 1, passive indices seek to use public information to proxy for the expected market portfolio as an input to the portfolio construction. Further, part 1.b states that, under certain conditions, the optimal passive portfolio is literally just that, namely the conditional expected market portfolio. Part 1.c shows that, under the more realistic Assumption 1, the optimal passive portfolio is similar to the conditional expected market portfolio, but tilted away from risky securities. This tilt arises because uninformed investors face an extra risk (relative to informed investors) due to supply uncertainty. Part 2.a shows further that, when the average market portfolio is proportional to the factor portfolio, β ∼ qˉ, then the average passive portfolio is also proportional to the average market portfolio. Part 2.b shows that, in the more general situation in which β and ˉq are not proportional, the optimal passive portfolio tends to downweight risky securities. Part 2.c conveys a similar intuition (under different assumptions), again showing that passive investors optimally down- weight securities with more supply uncertainty. This intuition may help explain why real- world passive indices only include a subset of listed securities, which may be interpreted as a binary version the result of parts 2.b and 2.c of the proposition. While the proposition states that passive investors will hold more of securities with less supply uncertainty, real-world passive investors may exclusively hold these securities. Indeed, indices typically exclude
securities with too low price, too low market capitalization, too low liquidity, too recent IPO, or involved in certain corporate actions.^13 Finally, we note that portfolio holdings scale with the degree of risk aversion. The results therefore only depend on the actual risk aversion of any given investor through a (positive) constant of proportionality. We next turn to the portfolio holdings of the informed investors.
Proposition 2 (Optimal active portfolio: value and quality) Under Assumption 1 or Assumption 2, an informed investor’s position in any asset j is more sensitive than that of an uninformed agent to
(a) supply shocks for asset j, ∂E[ ∂qxi,jj |q]> ∂E[ ∂qxu,jj |q] (value investing); (b) the signal sj about asset j, ∂E[ ∂sxi,jj |s]> 0 > ∂E[ ∂sxu,jj |s] (quality investing).
The first part of the proposition states that informed investors buy more when the supply increases. For example, when there is an initial public offering, informed investors likely buy a disproportional fraction of the shares during book-building process. Likewise, if the supply of an existing company increases (for a given value of the signal), this extra supply will tend to lower the price, creating buying opportunity for informed investors (who realize that the price drop is not due to bad information). Buying securities at depressed prices can be viewed as a form of “value investing.” The second part of the proposition states that, when the signal for a given security improves, informed investors tend to increase their position in this security while uninformed investors tend to lower their position. Clearly, when informed investors receive favorable information about a security, they are more inclined to buy it. This extra demand tends to increase the price, leading the uninformed to reduce their position (markets must always clear) since uninformed investors cannot know whether the price increase due to favorable information or a drop in supply. Buying securities with strong fundamentals, even if their price has increased, is called “quality investing.” (^13) See, e.g., and “Russell U.S. Equity Indexes 2017” and “S&P U.S. Indices Methodology 2017.”
