**Main Results and Relevance to the Q Group Mission**

A central question in asset management is how to correctly measure risk. Fifty years ago Jack Treynor, along with Bill Sharpe and others, developed the Capital Asset Pricing Model (CAPM). However, in the intervening years the validity of the CAPM as a measure of risk has been questioned. In response, researchers have developed extensions to the original model that better explain the cross sectional distribution of expected returns.

The implicit assumption in this research agenda is that a model that better explains cross sectional variation in returns necessarily better explains risk differences. But this assumption is problematic. To see why, consider the following analogy. Rather than look for an alternative theory, early astronomers reacted to the inability of the Ptolemaic theory to explain the motion of the planets by fixing” each observational inconsistency by adding an additional epicycle to the theory. By the time Copernicus proposed the correct theory that the Earth revolved around the Sun, the Ptolemaic theory had been fixed so many times it better explained the motion of the planets than the Copernican system. (Copernicus wrongly assumed that the planets followed circular orbits when in fact their orbits are ellipses.) Similarly, although the extensions to the CAPM better explain the cross section of asset returns, it is hard to know, using traditional tests, whether these extensions represent true progress towards measuring risk or simply the asset pricing equivalent of an epicycle. To determine whether any extention to the CAPM better explains risk, one needs to confront the models with facts they were not designed to explain.

In this paper we design a new test of asset pricing models by starting with the obser- vation at all asset pricing models assume that investors compete fiercely with each other tofind positive net present value investment opportunities, and in doing so, eliminate them. As a consequence of this competition, equilibrium prices are set so that the ex- pected return of every asset is solely a function of its risk. When a positive net present value (NPV) investment opportunity presents itself in capital markets (that is, an asset is mispriced relative to the model investors are using) investors react by submitting buy or sell orders until the opportunity no longer exists (the mispricing is removed). These buy and sell orders reveal the preferences of investors and therefore they reveal which asset pricing model investors are using. That is, by observing these orders one can infer which asset pricing model investors use to price risk. xedWe demonstrate that we can implement this test using mutual fund data. We derive a simple test statistic that allows us to infer, from a set of candidate models, the model that is closest to the asset pricing model investors are actually using. We find that the CAPM is the closest model. That is, none of the extensions to the original model better explains investor behavior. Importantly, the CAPM better explains investor decisions than no model at all, indicating that investors do price risk. Most surprisingly, the CAPM also outperforms a naive model in which investors ignore beta and simply chase any outperformance relative to the market portfolio. Investors’ capital allocation decisions reveal that they measure risk using the CAPM beta

##### Assessing Asset Pricing Models

using Revealed Preference

^{*}

**Jonathan B. Berk
Stanford University and NBER**

Jules H. van Binsbergen

University of Pennsylvania and NBER

**September 2013
This draft: August 11, 2015**

##### Abstract

We propose a new method of testing asset pricing models that relies on using quantities rather than simply prices or returns. We use the capital ows into and out of mutual funds to infer which risk model investors use. We derive a simple test statistic that allows us to infer, from a set of candidate models, the model that is closest to the model that investors use in making their capital allocation decisions. Using our method, we assess the performance of the most commonly used asset pricing models in the literature.

^{*} We are grateful to John Cochrane, George Constantinides, Peter DeMarzo, Wayne Ferson, Ravi Ja-gannathan, Valentine Haddad, Lars Hansen, John Heaton, Binying Lui, Tim McQuade, Lubos Pastor,Paul Peiderer, Monika Piazzesi, Anamaria Pieschacon, Martin Schneider, Ken Singleton, Rob Stam-baugh, and seminar participants at the 2015 AFA meetings, Harvard, the Kellogg Junior Finance Confer-ence, Notre Dame, Princeton University, Stanford GSB, the Stanford Institute for Theoretical Economics (SITE), the University of Chicago, University of Washington Summer Finance Conference and Washing-ton University in St. Louis for their comments and suggestions.

All neoclassical capital asset pricing models assume that investors competefiercely with each other to find positive net present value investment opportunities, and in doing so, eliminate them. As a consequence of this competition, equilibrium prices are set so that the expected return of every asset is solely a function of its risk. When a positive net present value (NPV) investment opportunity presents itself in capital markets (that is, an asset is mispriced relative to the model investors are using) investors react by submitting buy or sell orders until the opportunity no longer exists (the mispricing is removed). These buy and sell orders reveal the preferences of investors and therefore they reveal which asset pricing model investors are using. By observing whether or not buy and sell orders occur in reaction to the existence of positive net present value investment opportunities as defined by a particular asset pricing model, one can infer whether investors price risk using that asset pricing model.

There are two criteria that are required to implement this method. First, one needs a mechanism that identifies positive net present value investment opportunities. Second, one needs to be able to observe investor reactions to these opportunities. We demonstrate that we can satisfy both criteria if we implement the method using mutual fund data. Under the assumption that a particular asset pricing model holds, we use the main insight from Berk and Green (2004) to show that positive (negative) abnormal return realizations in a mutual fund investment must be associated with positive net present value buying (selling) opportunities. We then measure investor reactions to these opportunities by observing the subsequent capital ow into (out of) mutual funds.

Using this method, we derive a simple test statistic that allows us to infer, from a set of candidate models, the model that is closest to the asset pricing model investors are actually using. Our test can be implemented by running a simple univariate ordinary least squares regression using the t -statistic to assess statistical significance. We illustrate our method by testing the following models: the Capital Asset Pricing Model (CAPM), originally derived by Sharpe (1964), Lintner (1965), Mossin (1966) and Treynor (1961), the reduced form factor models specified by Fama and French (1993) and Carhart (1997) (that are motivated by Ross (1976)) and the dynamic equilibrium models derived by Merton (1973), Breeden (1979), Campbell and Cochrane (1999), Kreps and Porteus (1978), Epstein and Zin (1991) and Bansal and Yaron (2004).

We find that the CAPM is the closest model to the model that investors use to make their capital allocation decisions. Importantly, the CAPM better explains ows than no model at all, indicating that investors do price risk. Most surprisingly, the CAPM also outperforms a naive model in which investors ignore beta and simply chase any outperformance relative to the market portfolio. Investors’ capital allocation decisions reveal that they measure risk using the CAPM beta.

Our result, that investors appear to be using the CAPM to make their investment decisions, is very surprising in light of the well documented failure of the CAPM to adequately explain the cross-sectional variation in expected stock returns. Although, ultimately, we leave this as a puzzle to be explained by future research, we do note that much of the ows in and out of mutual funds remain unexplained. To that end the paper leaves as an unanswered question whether the unexplained part of ows results because investors use a superior, yet undiscovered, risk model, or whether investors use other, non-risk based, criteria to make investment decisions.

It is important to emphasize that implementing our test requires accurate measure- ment of the variables that determine the Stochastic Discount Factor (SDF). In the case of the CAPM, the SDF is measured using market prices which contain little or no mea- surement error, and more importantly, can be observed by investors as accurately as by empiricists. Testing the dynamic equilibrium models relies on observing variables such as consumption, which investors can measure precisely (they presumably know their own consumption) but empiricists cannot, particularly over short horizons. Consequently our tests cannot differentiate whether these models underperform because they rely on vari- ables that are diffcult to measure, or because the underlying assumptions of these models are awed.

Because we implement our method using mutual fund data, one might be tempted to conclude that our tests only reveal the preferences of mutual fund investors, rather than all investors. But this is not the case. When an asset pricing model correctly prices risk, it rules out positive net present value investment opportunities in all markets. Even if no investor in the market with a positive net present value opportunity uses the asset pricing model under consideration, so long as there are investors in other markets that use the asset pricing model, those investors will recognize the positive net present value opportunity and will act to eliminate it. That is, if our test rejects a particular asset pricing model, we are not simply rejecting the hypothesis that mutual fund investors use the model, but rather, we are rejecting the hypothesis that any investor who could invest in mutual funds uses the model.

Of course, the possibility exists that investors are not using a risk model to price assets. In that case our tests only reveal the preferences of mutual fund investors because it is possible, in this world, for investors in other markets to be uninterested in exploiting positive net present value investment opportunities in the mutual fund market. However, mutual fund investors actually represent a very large fraction of all investors. In 2013, 46% percent of households invested in mutual funds. More importantly, this number rises to 81% for households with income that exceeds $100,000. ^{1}

The first paper to use mutual fund ows to infer investor preferences is Guercio and Tkac (2002). Although the primary focus of their paper is on contrasting the inferred behavior of retail and institutional investors, that paper documents ows respond to outperformance relative to the CAPM. The paper does not consider other risk models. Clifford, Fulkerson, Jordan, and Waldman (2013) study the effect of increases in idiosyn- cratic risk on in ows and out ows separately (rather than the net ow) and show that both in ows and out ows increase when funds take on more idiosyncratic risk (as defined by the Fama-French-Carhart factor specification). In work subsequent to ours, Barber, Huang, and Odean (2014) use fund ows to infer investor risk preferences and also find (using a different method) that the investors use the CAPM rather than the other reduced form factor models that have been proposed.

##### 1 A New Asset Pricing Test

The core idea that underlies every neoclassical asset pricing model in economics is that prices are set by agents chasing positive net present value investment opportunities. Whenfinancial markets are perfectly competitive, these opportunities are competed away so that, in equilibrium, prices are set to ensure that no positive net present value opportuni- ties exist. Prices respond to the arrival of new information by instantaneously adjusting to eliminate any positive net present value opportunities that arise. It is important to appreciate that this price adjustment process is part of all asset pricing models, either explicitly (if the model is dynamic) or implicitly (if the model is static). The output of all these models { a prediction about expected returns { relies on the assumption that this price adjustment process occurs.

The importance of this price adjustment process has long been recognized byfinancial economists and forms the basis of the event study literature. In that literature, the asset pricing model is assumed to be correctly identified. In that case, because there are no positive net present value opportunities, the price change that results from new information (i.e., the part of the change not explained by the asset pricing model) measures the value of the new information.

Because prices always adjust to eliminate positive net present value investment oppor- tunities, under the correct asset pricing model, expected returns are determined by risk

^{1} As reported in the 2014 Investment Company Fact Book, Chapter Six, Figures 6.1 and 6.5 (see http://www.icifactbook.org ).

alone. Modern tests of asset pricing theories test this powerful insight using return data. Rejection of an asset pricing theory occurs if positive net present value opportunities are detected, or, equivalently, if investment opportunities can be found that consistently yield returns in excess of the expected return predicted by the asset pricing model. The most important shortcoming in interpreting the results of these tests is that the empiricist is never sure that a positive net present value investment opportunity that is identified ex post was actually available ex ante . ^{2}

An alternative testing approach, that does not have this shortcoming, is to identify positive net present value investment opportunities ex ante and test for the existence of an investor response. That is, do investors react to the existence of positive net present value opportunities that result from the revelation of new information? Unfortunately, for mostfinancial assets, investor responses to positive net present value opportunities are diffcult to observe. As Milgrom and Stokey (1982) show, the price adjustment process can occur with no transaction volume whatsoever, that is, competition is sofierce that no investor benefits from the opportunity. Consequently, for mostfinancial assets the only observable evidence of this competition is the price change itself. Thus testing for investor response is equivalent to standard tests of asset pricing theory that use return data to look for the elimination of positive net present value investment opportunities.

The key to designing a test to directly detect investor responses to positive net present value opportunities is to find an asset for which the price is fixed. In this case the market equilibration must occur through volume (quantities). A mutual fund is just such an asset. The price of a mutual fund is always fixed at the price of its underlying assets, or the net asset value (NAV). In addition, fee changes are rare. Consequently, if, as a result of new information, an investment in a mutual fund represents a positive net present value investment opportunity, the only way for investors to eliminate the opportunity is by trading the asset. Because this trade is observable, it can be used to infer investments investors believe to be positive net present value opportunities. One can then compare those investments to the ones the asset pricing model under consideration identifies to be positive net present value and thereby infer whether investors are using the asset pricing model. That is, by observing investors’ revealed preferences in their mutual fund investments, we are able to infer information about what (if any) asset pricing model they are using.

^{2} For an extensive analysis of this issue, see Harvey, Liu, and Zhu (2014).

##### 1.1 The Mutual Fund Industry

Mutual fund investment represents a large and important sector in U.S.financial markets. In the last 50 years there has been a secular trend away from direct investing. Individual investors used to make up more than 50% of the market, today they are responsible for barely 20% of the total capital investment in U.S. markets. During that time, there has been a concomitant rise in indirect investment, principally in mutual funds. Mutual funds used to make up less than 5% of the market, today they make up 1/3 of total investment. ^{3} Today, the number of mutual funds that trade in the U.S. outnumber the number of stocks that trade.

Berk and Green (2004) derive a model of how the market for mutual fund investment equilibrates that is consistent with the observed facts. ^{4} They start with the observation that the mutual fund industry is like any industry in the economy | at some point it displays decreasing returns to scale. ^{5} Given the assumption under which all asset pricing models are derived (perfectly competitivefinancial markets), this observation immediately implies that all mutual funds must have enough assets under management so that they face decreasing returns to scale. When new information arrives that convinces investors that a particular mutual fund represents a positive net present value investment, investors react by investing more capital in the mutual fund. This process continues until enough new capital is invested to eliminate the opportunity. As a consequence, the model is able to explain two robust empirical facts in the mutual fund literature: that mutual fund ows react to past performance while future performance is largely unpredictable. ^{6} Investors \chase” past performance because it is informative: mutual fund managers that do well (poorly) have too little (much) capital under management. By competing to take advantage of this information, investors eliminate the opportunity to predict future performance.

A key assumption of the Berk and Green (2004) model is that mutual fund managers are skilled and that this skill varies across managers. Berk and van Binsbergen (2013) verify this fact. They demonstrate that such skill exists and is highly persistent. More importantly, for our purposes, they demonstrate that mutual fund ows contain useful information. Not only do investors systematically direct ows to higher skilled managers,

^{3} See French (2008).

^{4} Stambaugh (2014) derives a general equilibrium version of this model based on the model in Pastor and Stambaugh (2012).

^{5} Pastor, Stambaugh, and Taylor (2015) provide empirical evidence supporting this assumption.

^{6} An extensive literature has documented that capital ows are responsive to past returns (see Chevalier and Ellison (1997) and Sirri and Tufano (1998)) and future investor returns are largely unpredictable (see Carhart (1997)).

but managerial compensation, which is primarily determined by these ows, predicts future performance as far out as 10 years. Investors know who the skilled managers are and compensate them accordingly. It is this observation that provides the starting point for our analysis. Because the capital ows into mutual funds are informative, they reveal the asset pricing model investors are using.

##### 1.2 Private Information

Most asset pricing models are derived under the assumption that all investors are sym- metrically informed. Hence, if one investor faces a positive NPV investment opportunity, all investors face the same opportunity and so it is instantaneously removed by competi- tion. The reality is somewhat different. The evidence in Berk and van Binsbergen (2013) of skill in mutual fund management implies that at least some investors have access to different information or have different abilities to process information. As a result, under the information set of this small set of informed investors, not all positive net present value investment opportunities are instantaneously competed away.

As Grossman (1976) argued, in a world where there are gains to collecting information and information gathering is costly, not everybody can be equally informed in equilibrium. If everybody chooses to collect information, competition between investors ensures that prices reveal the information and so information gathering is unprofitable. Similarly, if nobody collects information, prices are uninformative and so there are large profits to be made collecting information. Thus, in equilibrium, investors must be differentially informed (see, e.g., Grossman and Stiglitz (1980)). Investors with the lowest information gathering costs collect information so that, on the margin , what they spend on information gathering, they make back in trading profits. Presumably these investors are few in number so that the competition between them is limited, allowing for the existence of prices that do not fully reveal their information. As a result, information gathering is a positive net present value endeavor for a limited number of investors.

The existence of asymmetrically informed investors poses a challenge for empiricists wishing to test asset pricing models derived under the assumption of symmetrically in- formed investors. Clearly, the empiricist’s information set matters. For example, asset pricing models fail under the information set of the most informed investor, because the key assumption that asset markets are competitive is false under that information set. Consequently, the standard in the literature is to assume that the information set of the uninformed investors only contains publicly available information all of which is already impounded in all past and present prices, and to conduct the test under that information set. For now, we will adopt the same strategy but will revisit this assumption in Section 5.2, where we will explicitly consider the possibility that the majority of investors’ infor- mation sets includes more information than just what is already impounded in past and present prices.

##### 3 Results

We use the mutual fund data set in Berk and van Binsbergen (2013). The data set spans the period from January 1977 to March 2011. We remove all funds with less than 5 years of data leaving 4275 funds.^{11} Berk and van Binsbergen (2013) undertook an extensive data project to address several shortcomings in the CRSP database by combining it with Morningstar data, and we refer the reader to the data appendix of that paper for the details.

To implement the tests derived in Propositions 2 and 5 it is necessary to pick an observation horizon. For most of the sample, funds report their AUMs monthly, however in the early part of the sample many funds report their AUMs only quarterly. In order not to introduce a selection bias by dropping these funds, the shortest horizon we will consider is three months. Furthermore, as pointed out above, we need a horizon length of more than a month to compute the outperformance measure for the dynamic equilibrium models. If investors react to new information immediately, then ows should immediately respond to performance and the appropriate horizon to measure the effect would be the shortest horizon possible. But in reality there is evidence that investors do not respond

^{11} We chose to remove these funds to ensure that incubation ows do not in uence our results. Changing the criterion to 2 years does not change our results. These results are available on request.

immediately. Mamaysky, Spiegel, and Zhang (2008) show that the net alpha of mutual funds is predictably non-zero for horizons shorter than a year, suggesting that capital does not move instantaneously. There is also evidence of investor heterogeneity because some investors appear to update faster than others. ^{12} For these reasons, we also consider longer horizons (up to four years). The downside of using longer horizons is that longer horizons tend to put less weight on investors who update immediately, and these investors are also the investors more likely to be marginal in setting prices. To ensure that we do not inadvertently introduce autocorrelation in the horizon returns across funds, we drop all observations before the first January observation for a fund, that is, we thereby insure that the first observation for all funds occurs in January.

The ow of funds is important in our empirical specification because it affects the alpha generating technology as specified by h(.). Consequently, we need to be careful to ensure that we only use the part of capital ows that affects this technology. For example, it does not make sense to include as an in ow of funds, increases in fund sizes that result from in ation because such increases are unlikely to affect the alpha generating process. Similarly, the fund’s alpha generating process is unlikely to be affected by changes in size that result from changes in the price level of the market as a whole. Consequently, we will measure the ow of funds over a horizon of length T as

**Table 4: Tests of Statistical Significance:** The first two columns in the table provides the coefficient estimate and double-clustered t -statistic (see Thompson (2011) and the discussion in Petersen (2009)) of the univariate regression of signed ows on signed out- performance. The rest of the columns provide the statistical significance of the pairwise test, derived in Proposition 5, of whether the models are better approximations of the true asset pricing model. For each model in a column, the table displays the double-clustered t-statistic of the test that the model in the row is a better approximation of the true asset pricing model, that is, that ß_{F row}>ß_{F column}.The rows (and columns) are ordered by ß_{Fe}, with the best performing model on top. The number following the long run risk models denotes the percentage of the wealth portfolio invested in bonds.

we can reject the hypothesis that investors just react to past returns. The next possibility is that investors are risk neutral. In an economy with risk neutral investors we would find that the excess return best explains ows, so the performance of this model can be assessed by looking at the columns labeled \Ex. Ret.” Notice that all the risk models nest this model, so to conclude that a risk model better approximates the true model, the risk model must statistically outperform this model. The factor models all satisfy this criterion, allowing us to conclude that investors are not risk neutral. Unfortunately, none of the dynamic asset pricing model satisfy this criterion. Finally, one might hypothesize that investors benchmark their investments relative to the market portfolio alone, that is, they do not adjust for any risk differences (beta) between their investment and the market. The performance of this model is reported in the column labeled \Ex. Mkt.” Again, all the factor models statistically significantly outperform this model | investors actions reveal that they adjust for risk using beta. We view this result as the most surprising result in the paper.

Our results also allow us to discriminate between the factor models. Recall that both the FF and FFC factor specifications nest the CAPM, so to conclude that either factor model better approximates the true model, it must statistically significantly outperform the CAPM. The test of this hypothesis is in the columns labeled \CAPM.” Neither factor model statistically outperforms the CAPM at any horizon. Indeed, at all horizons the CAPM actually outperforms both factor models implying that the additional factors add no more explanatory power for ows.

The relative performance of the dynamic equilibrium models is poor. We can confidently reject the hypothesis that any of these models is a better approximation of the true model than the CAPM. But this result should be interpreted with caution. These models rely on variables like consumption which are notoriously difficult for empiricists to measure, but are observed perfectly by investors themselves.

It is also informative to compare the tests of statistical significance across horizons. The ability to statistically discriminate between the models deteriorates as the horizon increases. This is what one would expect to observe if investors instantaneously moved capital in response to the information in realized returns. Thus, this evidence is consistent with the idea that capital does in fact move quickly to eliminate positive net present value investment opportunities.

The evidence that investors appear to be using the CAPM is puzzling given the inabil- ity of the CAPM to correctly account for cross-sectional differences in average returns. Although providing a complete explanation of this puzzling finding is beyond the scope of this paper, in the next section we will consider a few possible explanations. We will leave the question of which, if any, explanation resolves this puzzle to future research.

##### 4 Implications

The empirical finding that the CAPM does a poor job explaining cross-sectional variation in expected returns raises a number of possibilities about the relation between risk and return. The first possibility, and the one most often considered in the existing literature, is that this finding does not invalidate the neoclassical paradigm that requires expected returns to be a function solely of risk. Instead, it merely indicates that the CAPM is not the correct model of risk, and, more importantly, a better model of risk exists. As a consequence researchers have proposed more general risk models that better explain the cross section of expected returns.

The second possibility is that the poor performance of the CAPM is a consequence of the fact that there is no relation between risk and return. That is, that expected returns are determined by non-risk based effects. The final possibility is that risk only partially explains expected returns, and that other, non-risk based factors, also explain expected returns. The results in this paper shed new light on the relative likelihood of these possibilities.

The fact that we find that the factor models all statistically significantly outperform our \no model” benchmarks implies that the second possibility is unlikely. If there was no relation between risk and expected return, there would be no reason for the CAPM to best explain investors’ capital allocation decisions. The fact that it does, indicates that at least some investors do trade off risk and return. That leaves the question of whether the failure of the CAPM to explain the cross section of expected stock returns results because a better model of risk exists, or because factors other than risk also explain expected returns.

Based on the evidence using return data, one might be tempted to conclude (after properly taking into account the data mining bias discussed in Harvey, Liu, and Zhu (2014)) that if multi-factor models do a superior job explaining the cross-section, they necessarily explain risk better. But this conclusion is premature. To see why, consider the following analogy. Rather than look for an alternative theory, early astronomers reacted to the inability of the Ptolemaic theory to explain the motion of the planets by “fixing” each observational inconsistency by adding an additional epicycle to the theory. By the time Copernicus proposed the correct theory that the Earth revolved around the Sun, the Ptolemaic theory had been fixed so many times it better explained the motion of the planets than the Copernican system.^{15} Similarly, although the extensions to the CAPM better explain the cross section of asset returns, it is hard to know, using traditional tests, whether these extensions represent true progress towards measuring risk

or simply the asset pricing equivalent of an epicycle.

Our results shed light on this question. By our measures, factor models do no better explaining investor behavior than the CAPM even though they nest the CAPM. This fact reduces the likelihood that the reason these models better explain the cross section of expected returns is because they are better risk models. This is a key advantage of our testing method. It can difierentiate between whether current extensions to the CAPM just improve the model’s it to existing data or whether they represent progress towards a better model of risk. The extensions of the CAPM model were proposed to better it returns, not ows. As such, ows provide a new set of moments that those models can be confronted with. Consequently, if the extension of the original model better explains mutual fund ows, this suggests that the extension does indeed represent progress towards a superior risk model. Conversely, if the extended model cannot better explain ows, then we should worry that the extension is the modern equivalent of an epicycle, an arbitrary fix designed simply to ensure that the model better explains the cross section of returns.

Our method can also shed light on the third possibility, that expected returns might be a function of both risk and non-risk based factors. To conclude that a better risk model exists, one has to show that the part of the variation in asset returns not explained by the CAPM can be explained by variation in risk. This is what the ow of funds data allows us to do. If variation in asset returns that is not explained by the CAPM attracts ows, then one can conclude that this variation is not compensation for risk. Thus our method allows us to infer something existing tests of factor models cannot do. It allows us to determine whether or not a new factor that explains returns measures risk. What our results imply is that the factors that have been proposed do not measure additional risk not measured by the CAPM. What these factors actually do measure is clearly an important question for future research.

##### 5 Tests of the Robustness of our Results

In this section we consider other possible alternative explanations for our results. first we look at the possibility that mutual fund fee changes might be part of the market equilibrating mechanism. Then we test the hypothesis that investors’ information sets

^{15} Copernicus wrongly assumed that the planets followed circular orbits when in fact their orbits are ellipses. contain more than what is in past and present prices. Finally, we cut the data sample along two dimensions and examine whether our results change in the subsamples. Specifically, we examine whether our results change if we start the analysis in 1995 rather than 1978 and if we restrict attention to large return observations. In both cases we show that our results are unchanged in these subsamples.

##### 5.1 Fee Changes

As argued in the introduction, capital ows are not the only mechanism that could equili- brate the mutual fund market. An alternative mechanism is for fund managers to adjust their fees to ensure that the fund’s alpha is zero. In fact, fee changes are rare, occurring in less than 4% of our observations, making it unlikely that fee changes play any role in equi- librating the mutual fund market. Nevertheless, in this section we will run a robustness check to make sure that fee changes do not play a role in explaining our results.

The fees mutual funds charge are stable because they are specified in the fund’s prospectus, so theoretically, a change to the fund’s fee requires a change to the fund’s prospectus, a relatively costly endeavor. However, the fee in the prospectus actually specifies the maximum fee the fund is allowed to charge because funds are allowed to (and do) rebate some of their fees to investors. Thus, funds can change their fees by giving or discontinuing rebates. To rule out these rebates as a possible explanation of our results, we repeat the above analysis by assuming that fee changes are the primary way mutual fund markets equilibrate

forward by these readers, once the factors were discovered, people started using them, and so the appropriate time period to compare the CAPM to these factor models is the post 1995 period. Of course, such a view raises interesting questions about the role of economic research. Rather than just trying to discover what asset pricing model people use, under this view, economic researchers also have a role teaching people what model they should be using. To see if there is any support for this hypothesis in the data, we rerun our tests in the sample that excludes data prior to 1995.

Because the time series of this subsample covers just 16 years, we repeat the analysis using horizons of a year or less.^{18} Tables 7 and 8 report the results. They are quantita- tively very similar to the full sample, and qualitatively the same. At every horizon the performance of the factor models and the CAPM are statistically indistinguishable. At the 3 and 6 month horizon the CAPM actually outperforms both factor models. All 3 models all still significantly outperform the \no model” benchmarks. In addition, the dy- namic equilibrium models continue to perform poorly. In summary, there is no detectable evidence that the discovery of the value, size and momentum factors had any in uence on how investors measure risk.

##### 5.4 Restricting the Sample to Large Returns

One important advantage of our method, which uses only the signs of ows and returns, is that it is robust to outliers. However, this also comes with the important potential lim- itation that we ignore the information contained in the magnitude of the outperformance and the ow of fund response. It is conceivable that investors might react differently to large and small return outperformance. For example, a small abnormal return might lead investors to update their priors of managerial performance only marginally. Assuming that investors face some cost to transact, it might not be profitable for investors to react to this information by adjusting their investment in the mutual fund. To examine the importance of this hypothesis, we rerun our tests in a subsample that does not include small return realizations.

We focus on deviations from the market return, and begin by dropping all return observations that deviate from the market return by less than 0.1 standard deviation (of the panel of deviations from the market return). The first column of Table 9 reports the results of our earlier tests at the 3 month horizon in this subsample. ^{19}The performance

^{18} Because of the loss in data, at longer horizons the double clustered standard errors are so large that there is little power to differentiate between models.

^{19} Results for the one year horizon are reported in the internet appendix to this paper. We choose to report the short horizon results because as before, the results for longer horizons have little statistica

of all models increases relative to the full sample, but only marginally. The other columns in the table increase the window of dropped observations: 0.25, 0.5, 0.75 and 1 standard deviation. What is clear is that increasing the window substantially improves the ability of all models to explain ows. Table 10 reports the statistical significance in these subsamples of the test derived in Proposition 5. The results are again quantitatively similar to the main sample and qualitatively identical. The CAPM is statistically significantly better at explaining ows than the \no model” benchmarks, and none of the factor models statistically outperform the CAPM.

It might seem reasonable to infer from the results in Table 9 that transaction costs do explain the overall poor performance of all the models in explaining ows. But caution is in order here. Although the CAPM does explain 75% of ow observations at the 1 standard deviation window, in this sample almost 80% of the data is discarded. It seems hard to believe that transaction costs are so high that only the 20% most extreme observations contain enough information to be worth transacting on.

##### 6 Conclusion

The field of asset pricing is primarily concerned with the question of how to compute the cost of capital for investment opportunities. Because the net present value of a long-dated investment opportunity is very sensitive to assumptions regarding the cost of capital, computing this cost of capital correctly is of first order importance. Since the initial development of the Capital Asset Pricing Model, a large number of potential return anomalies relative to that model have been uncovered. These anomalies have motivated researchers to develop improved models that \explain” each anomaly as a risk factor. As a consequence, in many (if not most) research studies these factors and their exposures are included as part of the cost of capital calculation. In this paper we examine the validity of this approach to calculating the cost of capital.

The main contribution of this paper is a new way of testing the validity of an asset pricing model. Instead of following the common practice in the literature which relies on moment conditions related to returns, we use mutual fund capital ow data. Our study is motivated by revealed preference theory: if the asset pricing model under consideration correctly prices risk, then investors must be using it, and must be allocating their money based on that risk model. Consistent with this theory, we find that investors’ capital ows in and out of mutual funds does reliably distinguish between asset pricing models. We find that the CAPM outperforms all extensions to the original model, which implies,

given our current level of knowledge, that it is still the best method to use to compute the cost of capital of an investment opportunity. This observation is consistent with actual experience. Despite the empirical shortcomings of the CAPM, Graham and Harvey (2001) find that it is the dominant model used by corporations to make investment decisions.

The results in the paper raise a number of puzzles. First, and foremost, there is the apparent inconsistency that the CAPM does a poor job explaining cross sectional variation in expected returns even though investors appear use the CAPM beta to measure risk. Explaining this puzzling fact is an important area for future research.

A second puzzle that bears investigating is the growth in the last 20 years of value and growth mutual funds. If, indeed, investors measure risk using the CAPM beta, it is unclear why they would find investing in such funds attractive. There are a number of possibilities. First, investors might see these funds as a convenient way to characterize CAPM beta risk. Why investors would use these criteria rather than beta itself is unclear. If this explanation is correct, the answer is most likely related to the same reason the CAPM does such a poor job in the cross-section. Another possibility is that value and growth funds are not riskier and so offer investors a convenient way to invest in positive net present value strategies. But this explanation begs the question of why the competition between these funds has not eliminated such opportunities. It is quite likely that by separately investigating what drives ows into and out of these funds, new light can be shed on what motivates investors to invest in these funds.

Finally, there is the question of what drives the fraction of ows that are unrelated to CAPM beta risk. A thorough investigation of what exactly drives these ows is likely to be highly informative about how risk is incorporated into asset prices.

Perhaps the most important implication of our paper is that it highlights the use- fulness and power of mutual fund data when addressing general asset pricing questions. Mutual fund data provides insights into questions that stock market data cannot. Be- cause the market for mutual funds equilibrates through capital ows instead of prices, we can directly observe investors’ investment decisions. That allows us to infer their risk preferences from their actions. The observability of these choices and what this implies for investor preferences has remained largely unexplored in the literature.

##### Appendix

##### A Proofs

##### A.1 Proof of Proposition 2

The denominator of (6) is positive so we need to show that the numerator is positive as well. Conditioning on the information set at each point in time gives the following expression for the numerator:

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