Disagreement and asset prices

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Journal of Financial Economics

Journal of Financial Economics 114 (2014) 226–238

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journal homepage: www.elsevier.com/locate/jfec

Disagreement and asset prices$

Bruce I. Carlin n, Francis A. Longstaff, Kyle MatobaAnderson Graduate School of Management, University of California, Los Angeles, 110 Westwood Plaza, Los Angeles, CA 90095, USA

a r t i c l e i n f o

Article history:Received 16 January 2013Received in revised form31 July 2013Accepted 10 January 2014Available online 5 July 2014

JEL classification:G12G17C11

Keywords:DisagreementAsset pricesReturn volatilityTrading volume

x.doi.org/10.1016/j.jfineco.2014.06.0075X/& 2014 Published by Elsevier B.V.

would like to thank Daniel Andrei, Snehaaren Chaltikian, Hui Chen, Anna Cieslak,, Xavier Gabaix, Stuart Gabriel, Mark Grinblardlicka, Scott Joslin, Ron Kaniel, Bryan KKumar, Hanno Lustig, Toby Moskowitz, Tern, Jeff Pontiff, Mike Rierson, Nick Roussanovmit Seru, Jules van Binsbergen, Andrea Vedond Jailin Yu, as well as seminar participants, University of California at Los Angeles, And the 2013 Spring National Bureau of EconMeeting for their helpful insights and suggeonsibility.esponding author. Tel.: þ1 310 825 2508.ail address: bruce.carlin@anderson.ucla.edu

a b s t r a c t

How do differences of opinion affect asset prices? Do investors earn a risk premium whendisagreement arises in the market? Despite their fundamental importance, these ques-tions are among the most controversial issues in finance. In this paper, we use a novel dataset that allows us to directly measure the level of disagreement among Wall Streetmortgage dealers about prepayment speeds. We examine how disagreement evolves overtime and study its effects on expected returns, return volatility, and trading volume in themortgage-backed security market. We find that increased disagreement is associated withhigher expected returns, higher return volatility, and larger trading volume. These resultsimply that there is a positive risk premium for disagreement in asset prices. We also showthat volatility in and of itself does not lead to higher trading volume. Instead, only whendisagreement arises in the market is higher uncertainty associated with more trading.Finally, we are able to distinguish empirically between two competing hypothesesregarding how information in markets gets incorporated into asset prices. We find thatsophisticated investors appear to update their beliefs through a rational expectationsmechanism when disagreement arises.

& 2014 Published by Elsevier B.V.

1. Introduction

Understanding how disagreement affects securityprices in financial markets is one of the most importantissues in finance. When participants in a market disagreewith each other, an investor who goes out on a limb and

l Banerjee, JonathanBrett Dunn, Andreatt, David Hirshleifer,elly, Shimon Kogan,ry Nercessian, Lasse, Avindhar Subrama-lin, Ivo Welch, Amirat the University ofQR Capital Manage-omic Research Assetstions. All errors are

(B.I. Carlin).

takes a position based on his unique expectations couldface a greater risk of being wrong. Such trading risk oradverse-selection risk differs fundamentally from thetraditional types of market risks that are priced in assetvalues. This means that investors who trade when dis-agreement exists could require additional compensationfor bearing this risk. Despite the fundamental nature ofthis issue, though, significant controversy in the literaturestill remains about how disagreement risk affects expectedreturns and asset prices.

On one hand, an extensive theoretical literature impliesthat divergence in beliefs or opinions should lead to apositive risk premium. For example, Varian (1985, 1989),Abel (1989), David (2008), and many others argue that theequity premium puzzle could be explained in terms of arisk premium for heterogeneous beliefs or differences ofopinion, or both. As such, it appears that investors shouldbe compensated for bearing trading risk or the risk due toadverse selection when disagreement arises.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238 227

On the other hand, Miller (1977) argues that differencesof opinion in the market can lead to lower expectedreturns (higher prices) when short-sale constraints arepresent. This occurs because pessimists sit out of themarket and asset prices reflect only the valuation ofoptimists. Chen, Hong, and Stein (2002) and Diether,Malloy, and Scherbina (2002) find compelling support forthe Miller hypothesis in several markets in which there arebinding short-sale constraints. However, Boehme,Danielsen, Kumar, and Sorescu (2009) and Avramov,Chordia, Jostova, and Philipov (2009) find evidence to thecontrary. Either way, this still leaves open the morefundamental issue of how disagreement is priced ingeneral markets without significant short-sale constraints,illiquidity, or other trading frictions.

To best resolve the controversy, we would ideally wantto study a market with several key characteristics. First,the market should be highly liquid and essentially freefrom short-sale constraints. Second, the key drivers of anasset's value should be easily defined and common knowl-edge. Finally, disagreement about these key drivers amongthe institutions that actually trade the assets should bedirectly observable. This last condition bypasses the mea-surement uncertainty that results when an indirect proxyfor disagreement is used.

In this paper, we analyze a time series of prepaymentspeed (PSA) forecasts issued by major Wall Street mort-gage dealers and then consider how disagreement affectsexpected returns, return volatility, and trading volume inthe agency mortgage-backed security (MBS) market.1 Thismarket provides unique advantages. First, because the PSAforecasts are given for various interest rate scenarios andthe mortgage-backed securities are guaranteed by the USgovernment, credit risk and interest rate risk do not affectthe dealers' PSA estimates. Thus, the only cash flowuncertainty associated with a mortgage-backed securityis the timing of prepayments. In turn, the timing of cashflows is a key factor affecting how investors valuemortgage-backed securities. This allows us to preciselycorrelate disagreement with the return characteristics ofmortgage-backed securities. Second, the PSA forecasts aremade by members of the trading desks at the sameinstitutions that intermediate the trade of mortgage-backed securities. Therefore, we know directly what thedealers' best estimate is for the key input to valuing theassets under consideration, which allows us to best studythe relation between disagreement and asset prices.

Using PSA estimates from July 1993 to January 2012, weconstruct a disagreement index and find a surprisinglyhigh level of disagreement among the participants in thesurvey. We show that disagreement is time-varying, cor-related with financial and macroeconomic variables, andmagnified when major events occur in financial markets

1 Providers of PSA estimates included Barclays, Bank of America, BearStearns, Credit Suisse, Deutsche Bank, Donaldson, Lufin, and Jenrette,Goldman Sachs, HSBC, JP Morgan Chase, Lehman Brothers, Merrill Lynch,Morgan Stanley, Nations Bank, Prudential, Greenwich Capital, SalomonBrothers, Smith Barney, and UBS Warburg. These dealers intermediatedthe majority of trade in MBS markets during the period that we analyzein this paper.

(e.g., the failure of Long-Term Capital Management, theSeptember 11 attacks, and Lehman Brothers default).

Following this, we study whether disagreement ispriced in the market. To examine whether disagreementabout prepayment rates affects the expected returns ofmortgage-backed securities, we use the standard approachof regressing ex post realized returns on the ex antemeasures of disagreement and other proxies for riskpremia. For disagreement to be priced in expected returns,the disagreement index should have predictive power forsubsequent returns on mortgage-backed securities evenafter controlling for the other ex ante risk premiumproxies. Using a proprietary data set of daily returns onthe Fannie Mae To Be Announced (TBA) security closest tothe current coupon mortgage rate, we construct a measureof monthly returns.2 Including the disagreement index inthe regression significantly increases the predictive power,and the coefficient on the disagreement variable is positiveand highly significant. Based on this, we can conclude thatincreased disagreement is associated with higher expectedreturns, which supports the thesis that disagreement isassociated with a positive risk premium, as posited byVarian (1985, 1989) and Abel (1989). Further, because wecontrol for several measures of market risk in our empiri-cal specification (e.g., interest rate risk, the S&P 500volatility index (VIX), the monthly excess return on theCRSP value weighted index, and the effective duration ofthe Lehman/Barclays US MBS index), this implies thatdisagreement risk is likely to be a form of trading risk orrisk due to adverse selection.

Finally, we analyze the relation between disagreement,return volatility, and trading volume. We use a simplevector autoregression (VAR) framework in which weinclude all three variables with lags and controls. We findthat increasing disagreement is followed by periods ofhigher volatility and trading volume. This is consistentwith Shalen (1993) and Zapatero (1998), who posit thatdisagreement and price volatility should be positivelycorrelated. More strikingly, though, we find that volatilityin and of itself does not lead to higher trading volume.Instead, it is only when more disagreement exists thattrading volume increases. Our findings lend support to thepredictions of Harris and Raviv (1993), that differences inopinion is the primary channel through which uncertaintyleads to higher trading volume. To our knowledge, ourstudy is the first to empirically show the importance ofthis channel. Our results are also consistent with theempirical findings of Kandel and Pearson (1995), who findthat dispersion in analyst forecasts affects trading volume,particularly around anticipated earnings announcements.Interestingly, we find that higher trading volume is asso-ciated with lower subsequent disagreement. We view thisas intuitive: As investors learn through trade, they haveopportunities to update their beliefs about the drivers ofasset value.

2 The To Be Announced market is a highly liquid market in whichbuyers and sellers agree on the future sale prices of mortgage-backedsecurities but do not specify which particular assets will be delivered.Details about this market are in Section 3.2.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238228

Besides providing evidence that disagreement is asso-ciated with a positive risk premium, we are able todistinguish between two competing hypotheses regardinghow information in markets gets incorporated into assetprices. As Banerjee (2011) highlights, investors can updatetheir beliefs via a rational expectations mechanism or theycan agree to disagree, which results in persistent differ-ences in opinion. According to Banerjee (2011), these twomechanisms can be distinguished empirically by compar-ing how return-volume characteristics vary with disagree-ment in the market. We find that higher disagreement isassociated with higher expected returns, higher subse-quent return volatility, and higher trading volume. Theseresults directly support the rational expectations channel.Especially given our finding that higher trading volume isassociated with lower subsequent disagreement, rationalinvestors are more likely to learn from prices and opinionsin the market, updating their beliefs using Bayes' rule via arational expectations channel.

The rest of the paper is organized as follows. In Section2, we review the literature in this area to highlight ourcontribution. In Section 3, we review the data that wecollect and some important institutional details regardingthe estimation of prepayment speeds, the agencymortgage-backed security markets, and the TBA market.In Section 4, we construct a measure of disagreement anddescribe its empirical properties. In Section 5, we char-acterize the relation between disagreement and expectedreturns, return volatility, and trading volume. Section 6provides some concluding remarks.

2. Literature review

2.1. Disagreement and learning

At any time, disagreement could arise due to hetero-geneous beliefs or persistent differences of opinion. Muchattention has been devoted to whether the former even-tually leads to asymptotic agreement when learningoccurs. Starting with Blackwell and Dubins (1962),Aumann (1976), and Geanakoplos and Polemarchakis(1982), investigators have focused on conditions that makedisagreement impossible in a rational setting. As Aumann(1976) shows in a remarkably clear way, if agents share acommon prior and have common knowledge of eachother's posterior beliefs, they cannot agree to disagree.Geanakoplos and Polemarchakis (1982) extend this analy-sis showing that communication, either direct or indirect,results in an equilibrium with common posterior beliefs.In their words, “we can't disagree forever”.

Later work, however, shows that permanent disagree-ment can arise even when agents have common priorsand observe the same time series of public information. AsAcemoglu, Chernozhukov, and Yildiz (2006) point out,many empirical settings exist where such permanentdisagreement arises. As such, they study a setting in whichindividuals are uncertain about the interpretation of thesignals they receive, which implies they have non-degenerate probability distributions over the conditionaldistribution of signals given the underlying parameter ofinterest. In such case, Acemoglu, Chernozhukov, and Yildiz

(2006) show that agreement could be impossible, despitethe fact that all agents update their beliefs as Bayesians.

Given this, at any time there could be several mechan-isms whereby disagreement in a financial market couldarise. First, investors could update according to Blackwelland Dubins (1962), but at the time of observation inves-tors' beliefs have yet to fully converge. Second, investorsupdate their beliefs rationally, but because they are uncer-tain about the quality of their signal, their beliefs could failto converge. Last, market participants can simply “agree todisagree” in that they observe the same public informationbut adhere to different models. This etiology can have anadded behavioral component, but has been used by Varian(1985), Harris and Raviv (1993), and David (2008).

Given this, the evolution of beliefs can occur via twolearning mechanisms. Investors could learn over time via arational expectations channel in which heterogeneousbeliefs are more likely to converge. Alternatively, disagree-ment could persist as differences of opinion lead todispersion in forecasts. As pointed out by Banerjee (2011)in a theoretical model, these two channels can be distin-guished empirically. With the rational expectations chan-nel, Banerjee (2011) predicts that increased disagreementshould induce higher expected returns, higher volatility,higher market betas, and higher covariance betweenvolume and absolute returns, but lower return autocorre-lation. When investors agree to disagree (i.e., differences inopinion persist), the opposite trends should be present. Inboth channels, disagreement is positively correlated withtrading volume.

2.2. Disagreement and risk premia

Much of the extant theoretical work posits that apositive risk premium should be associated with disagree-ment in the market. Following the seminal work of Mehraand Prescott (1985), several authors rationalize the equitypremium puzzle by considering that investors could haveheterogeneous beliefs or differences of opinion. Varian(1985) considers an Arrow-Debreu economy with agentswho have different subjective probabilities. In equilibrium,an increase in the range of probability beliefs typicallydecreases asset values, as long as risk aversion is notabnormally high. As such, disagreement is associated witha positive risk premium under reasonable preferences.Varian (1989) provides an elegant summary of theseresults.

Likewise, Abel (1989) investigates an equilibrium assetpricing model in which investors' demands for risky stocksand riskless bonds depend on their subjective beliefs aboutpayoffs to the risky capital. When beliefs are more hetero-geneous, this reduces the stock's price, and can dramati-cally increase the equity premium relative to bonds. Abel(1989) concludes that the equity premium under homo-genous beliefs understates the premium that would ariseunder heterogeneous beliefs.

Subsequent theoretical work has confirmed these find-ings. Basak (2005) provides a good survey. More recently,David (2008) studies a general equilibrium exchangeeconomy in which two types of agents have heterogeneousbeliefs. The agents have a difference of opinion and agree

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238 229

to disagree, in that they update their beliefs differentlyabout the state of the economy even though they observethe same signals. Agents trade and can speculate on therelative accuracy of their respective models. David (2008)shows that less risk-averse agents speculate more, but theydemand higher risk premia. Chen, Joslin, and Tran (2010)study an equilibrium model with affine disagreementabout fundamentals, which allows them to consider sto-chastic disagreement about growth rates, volatilitydynamics, and the likelihood and size of jumps. Theyshow that the risk premium depends on whether disastersstrike. In normal times, optimistic agents accumulatewealth and there is a decline in the risk premium. Whendisasters strike, pessimistic agents become wealthier,which causes the risk premium to increase.

One important exception in this literature is Miller(1977), who posits that short-sale constraints should causedisagreement to have a positive effect on stock prices. Theintuition is that when pessimists are forced to sit out of themarket, stock prices reflect the demand from optimistsonly, which causes prices (returns) to increase (decrease).This intuition is supported in Liu and Seasholes (2011),who study dual-listed shares in China and Hong Kong.They show that when there is a short-sale ban in China,the prices of Chinese stocks are 1.8 times higher comparedwith those in Hong Kong.

Miller (1977) has been tested in several empiricalstudies and has been shown to be plausible. Chen, Hong,and Stein (2002) develop a stock market model in whichan increase in divergence of opinion results in a decreasein the breadth of stock market ownership, causing a highstock price and a lower expected return. Then, they showempirically that reducing the breadth of mutual fundownership of stocks forecasts a lower stock return.Diether, Malloy, and Scherbina (2002) analyze the role ofdispersion in analysts' earnings forecasts in predicting thecross section of future stock returns. They find that stockswith higher dispersion in analysts' earnings forecasts earnsignificantly lower future returns than otherwise similarstocks. Park (2005) extends this work by testing whetherthe aggregate stock market also becomes overpriced whendifferences in expectations are high. According to Park(2005), the dispersion in expectations among marketanalysts has predictive power for future stock returns:Higher dispersion predicts lower stock returns. Similarly,Yu (2011) uses the Institutional Brokers' Estimate System(I/B/E/S) database on analyst forecast and finds that the expost market return is negatively related to the bottom-updisagreement.

These findings have led others to study disagreementand expected returns in other settings where short-saleconstraints exist. Moeller, Schlingemann, and Stulz (2007)study the impact of divergence of opinion on acquirerreturns in mergers and acquisitions. They find thatincreasing diversity of opinion about an acquirer's valuecauses the acquirer's return in stock payment acquisitionsto decrease but has no effect in cash transactions.Chatterjee, John, and Yan (2012) show that the totaltakeover premium, pre-announcement target stock pricerun-up, and post-announcement target stock price run-upare all higher when investors have a higher divergence of

opinion. They use analysts forecasts, change of breadth ofmutual fund ownership, and idiosyncratic volatility asthree proxies for divergence of analyst opinions.

In contrast, Avramov, Chordia, Jostova, and Philipov(2009) show that the negative relation between dispersionin analysts' forecasts and stock returns could be simplyexplained by financial distress risk. Specifically, they showthat the profitability of dispersion-based trading is onlyhigh when credit conditions deteriorate and is concen-trated in a small number of firms with the worst creditratings. However, the authors find that when their disper-sion measure is adjusted by credit risk, even for this smallgroup of firms, the negative dispersion-return relationdisappears. Likewise, Boehme, Danielsen, Kumar, andSorescu (2009) demonstrate a positive relation betweendispersion of beliefs and expected returns, after control-ling for short interest and investor recognition as proxiedby institutional ownership.

Given this, the support for Miller (1977) is mixed.However, the more fundamental issue is left open ofhow disagreement is priced in general markets withoutshort-sale constraints, illiquidity, or other trade frictions.As described by Fama and French (2007), disagreement ordifferences in tastes can rationalize empirical deviationsfrom the capital asset pricing model (CAPM) in eitherdirection. In their framework, sophisticated investorschoose the correct tangency portfolio, whereas unsophis-ticated investors choose portfolios that deviate. Unless theunsophisticated investors choose the right portfolio inaggregate on average, the observed market portfolio devi-ates from optimal. Fama and French (2007) posit thatempirical deviation from the CAPM, either to portfolioswith higher expected returns or lower, can be explained bythe disagreement by unsophisticated investors. As such,it remains an unresolved issue whether disagreement isassociated with a risk premium empirically.

2.3. Disagreement, trading volume, and price volatility

The earlier literature, both theoretical and empirical,shows a positive relation between disagreement, tradingvolume, and price volatility. Harris and Raviv (1993) studythe effect of news announcements on trading prices andvolume. They assume that traders receive the same com-mon information but differ in the way they interpret theinformation. In addition, each trader believes absolutely inthe validity of his own interpretation, so there is differencein opinion. Some of their key findings are that absoluteprice changes and volume are positively correlated andthat absolute changes in the mean forecast of the finalpayoff and volume are positively correlated.

Shalen (1993) examines a two-period noisy rationalexpectations model of a futures market and studies theeffect that dispersion in expectations has on price volatilityand trading volume. Higher dispersion causes higher pricevolatility, has higher expected trade volume, and increasesthe correlation between absolute price changes and bothcontemporaneous and lagged trading volume.

Kandel and Pearson (1995) study how dispersion inanalyst forecasts affects trading volume and asset prices. Theyanalyze trading activity around anticipated announcements

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238230

and show increases in trading volume, even when there areno changes in price. The authors posit that this occurs becausetraders are using different likelihood functions when theyBayesian update.

Zapatero (1998) considers a model with two logarith-mic utility maximizers that observe aggregate consump-tion but disagree about its expected rate of change.Additional information, which induces heterogeneousbeliefs, causes higher volatility of interest rates in theeconomy.

Finally, Banerjee and Kremer (2010) study the relationbetween disagreement and the dynamics of trade in atheoretical model in which investors differ about theinterpretation of public signals. They show that disagree-ment exacerbates volatility and leads to higher tradingvolume and that a positive correlation exists betweenvolatility and trading volume.

3. The data

In this paper, we focus on generic agency MBS in whichthe monthly principal and interest payments are pooled ina pass-through and distributed to investors on a pro-ratabasis.3 The speed at which homeowners prepay theirmortgages is a key driver of value for these securities. Inwhat follows, we describe PSA estimates that were madeby major MBS dealers for GNMA mortgage-backed secu-rities. We then describe how we construct a return seriesof FNMA forward contracts that are traded in the TBAmarket.

4 Although slight differences could exist in the characteristics of themortgage-backed securities for which the dealers provide forecasts, thesedifferences have a negligible effect on prepayment speeds. This is becauseany mortgage-backed security that does not have a generic prepayment

3.1. Prepayment speed forecasts

In the MBS market, prepayments speeds are typicallyquoted according to the PSA convention in which anannualized constant prepayment rate (CPR) is adjustedfor the age of the underlying mortgages. New mortgagestend to have very low prepayment speeds and the rate ofprepayment rises with age until the mortgages becomeseasoned, at which point the rate of prepayment remainsconstant. The PSA benchmark curve was introduced in the1980s and is often referred to as the 100% curve. At 100%,the prepayment rate starts at 0% for new mortgages, risesby 0.2% per month until month 30, after which theprepayment speed remains constant at 6%. PSA estimatesare quoted relative to this benchmark. For example, aGNMA MBS with a PSA of 200% would experience prepay-ments at a rate twice that of the usual benchmark rate and aGNMA MBS with a PSA of 50% would experience prepay-ments at a rate that is half the usual benchmark rate.

The expected rate of mortgage prepayment is a key driverof value for valuing MBS but is challenging to forecast. Manyfactors affect prepayments: home sales, refinancings,defaults, and curtailments. In turn, these are driven bychanges in housing supply, mobility, inflation, interest rates,income, employment, and consumer confidence. Estimating

3 For in-depth discussions of pass-through securities and the MBSmarket, see Hayre (2001) and Fabozzi, Bhattacharya, and Berliner (2007).

prepayment speeds requires sophisticated modeling and,given the degree of complexity involved, could be a sig-nificant source of heterogeneous beliefs about the value of ageneric MBS.

Major Wall Street dealers in the MBS market participatein a monthly survey, in which they provide Bloombergwith their best estimate of what the PSA would be fora generic GNMA MBS with a given coupon rate.4 PSAestimates are given for several interest rate scenarios,ranging from 300 basis points below the current rate to300 basis points above. As such, the forecasts not onlyreflect the dealers' expectations of current prepaymentspeeds, but also how those speeds would change inresponse to interest rate shocks. This has importantramifications to our analysis. Because the PSA estimatesoffered by the dealers vary with interest rate changes, anydifference of opinion or beliefs that they exhibit is only afunction of their calculation of prepayment risk, not ofexpected interest rate dynamics. As such, the dealers'opinions regarding the prepayment speeds are the onlysource of variation driving returns of the MBS. This allowsus to study the relation between disagreement and assetprices (Section 5).

Table 1 provides an illustration of the prepaymentforecasts provided by survey participants for a genericGNMA I 4.0% pass-through security as of January 31, 2012.Fig. 1 plots the forecasts. Not surprisingly, forecastedprepayment speeds are very sensitive to changes in inter-est rates. As interest rates decline, PSA forecasts increaseand vice versa. More interestingly, however, considerablecross-sectional variation exists in the pattern of PSAforecasts across dealers. In particular, these PSA forecastsdiffer by a factor of roughly two at current and lower ratelevels, but they tend to converge for rate levels substan-tially above the current rate level.

Another way to compare prepayment forecasts is toconsider measures based on normalized values. For eachdate and each MBS, we normalize the PSA forecastsprovided by a participant in the survey by their PSAforecast for the current rate level. As such, the normalizedvalue represents the relative change or slope in the PSAforecast for a given change in the level of rates. Fig. 2 plotsthe normalized version of the data in Table 1. Even withthis normalization, Fig. 2 shows that significant cross-sectional variation remains across the various dealers interms of their estimates of the sensitivity of prepaymentspeeds to changes in the level of mortgage rates.

Fig. 3 provides three more snapshots of disagreementduring extreme market events: the failure of Askin CapitalManagement in 1994, the attacks of September 11, 2001,and the failure of Lehman Brothers in 2008. In the topthree plots, substantial cross-sectional variation exists in

speed behavior is excluded from the pool of mortgages that are traded inthe TBA markets and for which dealers have provide forecasts. Instead,mortgage-backed securities with non-generic prepayment behavior aretraded in the separate specified pool market (Hayre, 2001).

Table 1An example of the Public Security Association (PSA) forecasts provided by survey participants.

This table shows the PSA forecasts provided by the survey participants on January 31, 2012 for a 4% Government National Mortgage Association (GinnieMae; GNMA) mortgage-backed security. The PSA forecasts are given for term structure scenarios ranging from a downward shift of 300 basis points to anupward shift of 300 basis points. The PSA forecasts for the current term structure are given in the column denoted by zero. Maturity denotes the weighted-average maturity of the mortgages underlying the GNMA mortgage-backed security. Coupon denotes the weighted-average coupon or mortgage rate of themortgages underlying the GNMA mortgage-backed security.

Dealer Maturity Coupon Term structure shift in basis points

�300 -200 �100 �50 0 50 100 200 300

Barclays 348 4.00 819 728 391 241 172 144 127 111 107Bank of America 358 4.00 909 881 533 333 226 185 153 126 117Credit Suisse 357 4.00 969 969 789 598 357 201 144 118 101Deutsche Bank 359 4.00 1,230 1,045 578 373 255 192 154 118 110JP Morgan Chase 354 4.00 844 761 579 402 205 149 131 105 90Morgan Stanley 356 4.00 1,456 1,497 1,283 875 496 314 232 115 81UBS Warburg 355 4.00 751 736 417 387 244 195 169 115 110

-300 -200 -100 0 100 200 300

200

400

600

800

1000

1200

1400

Change in interest rates (basis points)

PS

AFo

reca

st

Fig. 1. Prepayment speed forecasts. This figure plots the Public SecuritiesAssociation (PSA) forecasts from seven mortgage dealers for a Govern-ment National Mortgage Association (Ginnie Mae; GNMA) mortgagesecurity with a 4% coupon on January 31, 2012. Each dealer providedforecasts for nine term structure scenarios ranging from an upward shiftof 300 basis points to a downward shift of 300 basis points.

-300 -200 -100 0 100 200 3000

1

2

3

4

5

Changein interestrates (basis points)

Nor

mal

ized

PS

AFo

reca

st

Fig. 2. Normalized prepayment speed forecasts. This figure plots theprepayment forecasts described in Fig. 1, scaling each dealer's forecast byits forecast for no change in interest rates. PSA¼Public SecuritiesAssociation.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238 231

dealer prepayment forecasts for nine interest rate scenar-ios ranging from 300 basis points above the current rate to300 basis points below. The three bottom plots usenormalized prepayment forecasts for the same nine inter-est rate scenarios. As is evident, disagreement is presentduring the three distinct time periods and its magnitude istime-varying.

We collect monthly survey data from Bloomberg duringJuly 1993 to January 2012. In total, 18 dealers participate inthe survey at some time during the sample period. The

participants are listed in Table 2. On average, in eachmonth the survey contains forecasts from 8.42 dealers,with the actual number ranging from 3 to 14. Table 2 alsoreports the average ratio of each dealer's forecast relativeto the cross-sectional average across all dealers for a givendate and coupon rate. As shown, the average ratios are allin the range from 0.90 to 1.10, suggesting that none of thedealers is producing forecasts that are, on average, funda-mentally different from the others on average. This lastpoint highlights the fact that disagreement about prepay-ment speeds is not likely due to asymmetric access topublic or private information.

The very nature of the mortgage pass-through marketinherently makes it unlikely that differences in access topublic information drives variation in PSA estimates. All ofthe dealers in the survey are large financial institutions thathave devoted extensive resources to the mortgage market,and each has the ability to obtain all publicly availableinformation about the term structure of interest rates, inter-est rate forecasts, volatility, fixed income markets, mortgageprepayment rates, market liquidity, funding availability, andmacroeconomic fundamentals. As such, the inputs to mostPSA models are readily available to the dealers.

Variation in estimates is unlikely to rest on access toprivate information. This is simply because very little privateinformation is available to anyone about the mortgage poolsunderlying the MBS or TBA markets. For example, the genericpools traded on a forward basis in the TBA market tend to bebased on recently originated mortgages for which there islittle prepayment history. In addition, the dealers generallydo not hold or service the mortgage pass-through securitiesfor which they provide forecasts. Thus, they are likely to havelittle or no private information about the performance of theunderlying mortgages. Finally, all of the data about thecharacteristics of individual mortgage borrowers (such asincome, FICO score, appraisals, etc.) are readily available to allmarket participants.

Taken together, these considerations suggest that asym-metric information is unlikely to drive disagreement aboutprepayment speeds. Instead, a more likely explanation is thatvariation in PSA estimates is driven by differences in inter-pretation and beliefs about the common set of informationavailable to them. These differences in interpretation and

-300 -200 -100 0 100 200 300

200

400

600

800

April 1994

Change in interest rates (basis points)

PS

AFo

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-300 -200 -100 0 100 200 300

200400600800

100012001400

September 2001

Change in interest rates (basis points)

PS

AFo

reca

sts

-300 -200 -100 0 100 200 300

200400600800

100012001400

September 2008

Change in interest rates (basis points)

PS

AFo

reca

sts

-300 -200 -100 0 100 200 300

1

2

3

4

Change in interest rates (basis points)

Nor

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ized

PS

AFo

reca

sts

-300 -200 -100 0 100 200 30002468

10

Change in interest rates (basis points)

Nor

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ized

PS

AFo

reca

sts

-300 -200 -100 0 100 200 300

0.5

1.0

1.5

2.0

2.5

Change in interest rates (basis points)

Nor

mal

ized

PS

AFo

reca

sts

Fig. 3. Prepayment speed forecasts. This figure plots Public Securities Association (PSA) prepayment forecasts and normalized forecasts for three distinctperiods: the failure of Askin Capital Management in 1994, the attacks of September 11, 2001, and the failure of Lehman Brothers in 2008. As in Fig. 1, the topthree plots show the cross section of dealer prepayment forecasts to nine interest rate scenarios ranging from 300 basis points above the current rate to300 basis points below. As in Fig. 2, the bottom row shows normalized prepayment forecasts for the same nine interest rate scenarios.

Table 2Summary statistics for Public Securities Association (PSA) forecasts provided by survey participants.

This table provides reports summary statistics for the PSA forecasts provided by each of the participants in the survey. Number of months denotes thenumber of months that the participant provided forecasts. Total observations denote the total number of forecasts provided by the participant. Averagenumber of observations denotes the average number of forecasts provided by the participant during months in which the participant provided forecasts.Average ratio denotes the average ratio of the PSA forecast provided by the participant to the average PSA forecast provided by the other participants forthe same mortgage-backed security that month. Standard deviation of ratio is the standard deviation of the average ratio.

Dealer Number ofmonths

Totalobservations

Average number ofobservations

Averageratio

Standard deviation ofratio

Barclays 66 679 10.29 0.967 0.262Bank of America 129 1,157 8.97 1.091 0.269Bear Stearns 181 1,228 6.78 0.993 0.161Credit Suisse 223 2,145 9.62 0.985 0.227Deutsche Bank 95 801 8.43 0.903 0.271Donaldson, Lufkin, andJenrette

56 504 9.00 1.011 0.212

Goldman Sachs 116 1,009 8.70 1.025 0.295Greenwich Capital 84 762 9.07 1.059 0.271HSBC 14 70 5.00 1.072 0.119JP Morgan Chase 107 1,022 9.55 1.069 0.258Lehman Brothers 144 826 5.74 0.919 0.167Merrill Lynch 188 2,009 10.69 0.999 0.174Morgan Stanley 133 1,212 9.11 1.089 0.322Nations Bank 20 140 7.00 0.901 0.223Prudential 92 671 7.29 0.948 0.130Salomon Brothers 182 1,524 8.37 0.978 0.245Smith Barney 44 286 6.50 1.026 0.186UBS Warburg 223 1,617 7.25 0.977 0.232Number/Total 223 17,662 8.42 1.002 0.242

5 For example, during the period 2007–2013, brokers and dealersheld only between 1.37% and 3.92% of the total agency- and GSE-backedsecurities (Federal Reserve Statistics Release, 2013).

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238232

beliefs could manifest themselves as differences in theassumptions or the structure of the models that each dealeruses to estimate mortgage prepayments, or both.

Finally, one concern that could arise is whether thedealers have an incentive to disclose their best estimateof prepayment speed truthfully. We believe that they do.First, as Table 2 suggests, none of the dealers system-atically provides different forecasts from their contempor-aries. Second, based on a time series of disagreement thatwe present in Section 4, times of larger variation inestimates correspond to large economic events in which

uncertainty is present in the market. Last, the dealers inour study generate substantial revenue from intermediat-ing MBS trade, but they hold little inventory for proprie-tary trading.5 Because the PSA estimates are observable topotential clients of the dealers and provide a signal of

6 As a robustness check, we also computed an alternative disagree-ment index by first computing the cross-sectional variance across dealersof their normalized PSAs for the �100, �50, þ50, and þ100 basis pointscenarios and then averaging the variances across the four scenarios andcomputing the overall standard deviation. The empirical results obtainedusing this alternative measure of the disagreement index, which areavailable in the online Appendix, are virtually the same as those wereport here.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238 233

technical expertise, the dealers have a strong incentive todemonstrate their skills as they compete for order flow.

3.2. Returns on TBA securities

The TBA market is an attractive setting to study returnson MBS, as it is such a highly liquid market. In a TBA trade,the buyer and seller agree on a future sale price, but theydo not specify which particular securities will be delivered.Instead, only five additional parameters are promised: thesettlement date, issuer, maturity, coupon, and par amount.According to Vickery and Wright (2010), this conventionsimplifies trade, as well as ameliorates asymmetric infor-mation conflicts in the MBS market, leading to higheragency MBS liquidity. In the context of our analysis,though, this makes our study of the relation betweendisagreement and returns more precise. That is, becausethe TBA market is so liquid, we can be confident that theasset pricing results we find are not merely due to time-varying transaction costs or other trading frictions.

To measure the returns on mortgage-backed securities,we make use of a proprietary data set provided to us by amajor fixed-income asset management firm. This data setconsists of daily returns on Fannie Mae TBA's closest to thecurrent coupon mortgage rate. Because TBAs are forwardcontracts, the return series consists of the return fromgoing long a one-month TBA, investing the TBA price in ariskless margin account, and then rolling the portfolio overevery month on the monthly TBA settlement date. Con-structing it this way provides continuity over the monthlyroll date in the TBA settlement. We then compute monthlyreturns by aggregating the daily returns during the month.

4. Measuring disagreement

Our extensive data set of PSA forecasts provides us witha unique opportunity to measure the amount of disagree-ment in the market directly. Not only does the data setcover a broad cross section of dealers over nearly 20 years,but a number of key features of the data also allow us toobtain more accurate measures of disagreement. First,each PSA forecast is conditional on a specific term struc-ture scenario. Thus, we can compare forecasts acrossdealers while holding fixed assumptions about the evolu-tion of the term structure. Second, because all of theforecasts are visible in the Bloomberg system, dealers areaware of the extent to which they disagree with otherdealers. Finally, and most important, because dealersprovide multiple forecasts for each pass-through security,we can normalize each dealer's forecasts before estimatingcross-sectional variation among dealers. This allows us tocontrol for the possibility that the levels of PSA forecastsvary across dealers because of model calibration issuesinstead of actual disagreement. The mortgage prepaymentmodels used by the Wall Street dealers all require exten-sive calibration, and each firm likely has a differentapproach from the others. For example, some dealerscalibrate their models using the Treasury yield curve fordiscounting purposes and to project interest rates forward,whereas others use the swap curve for the same purpose.These differences could easily result in dealers having

different calibrations even if the current yield curve isheld fixed. Normalization allows us to eliminate the fixedeffects among different dealers when we construct adisagreement index.

We construct a monthly disagreement index based onthe cross-sectional dispersion among dealers in theirnormalized PSA forecasts. Specifically, we first identifythe GNMA coupon that is closest to the current yield ofpar mortgage-backed securities (the current coupon) andfor which three or more dealer forecasts are available.Generally, the GNMAs closest to the current coupon tendto have the greatest homogeneity across dealers in termsof their maturity, pricing, and information availability.Then, for each dealer providing forecasts for the GNMAwith the closest coupon, we take the ratio of the PSAforecast for the �100 basis point scenario to the PSA forthe þ100 basis point scenario. Thus, this ratio is a measureof the relative (normalized) change in prepayment forecastas rates move from 100 basis points above the currentlevel of interest rates to 100 basis points below. Alterna-tively, this ratio can be viewed as a measure of the slope orsensitivity (duration) of prepayments to changes in inter-est rates, in the spirit of a difference-in-differences mea-sure. Finally, we compute the simple standard deviation ofthe ratios across dealers providing forecasts for thatmonth. We repeat the same process for all 223 monthsin the study period to form the index.

The top panel of Table 3 presents summary statisticsfor the disagreement index, and Fig. 4 plots its time series.The index has a number of interesting features that couldprovide some insight into the nature of disagreement infinancial markets. First, a surprisingly high level of dis-agreement exists among the participants in the survey.The average value of the index is 40.29%, and the medianvalue is 35.43%. Thus, even after normalizing the data,wide dispersion is evident among the dealers in theirviews about changes in prepayment rates. Second, con-siderable time series variation exists in the amount ofdisagreement among dealers. In particular, the indexvaries from a low of 1.96%, reflecting almost perfectagreement among dealers, to a high of 138.60%, represent-ing extreme diversity among dealers in terms of theirforecasts. The standard deviation of the index is 24.80%.Thus, disagreement is a dynamic phenomenon. Finally,disagreement among the dealers tends to be persistent innature: The first-order serial correlation coefficient for theindex is 0.6298. Meanwhile, the disagreement index is alsostrongly mean reverting as evidenced by the serial corre-lation of monthly changes in the index (�0.455). Intui-tively, this suggests that the persistence of a period ofhigher (or lower) disagreement can be measured in termsof months, rather than years.6

Table 3Descriptive statistics for the disagreement index, mortgage returns, mortgage return volatility, and mortgage trading volume.

This table reports the indicated summary statistics for the disagreement index and for monthly Federal National Mortgage Association (Fannie Mae;FNMA) mortgage-backed security returns, monthly mortgage return volatility (calculated as the standard deviation of daily mortgage returns for eachmonth in the study period), and total monthly mortgage trading volume (in billions of dollars) by US primary government bond dealers as reported by theNew York Federal Reserve Bank. Mortgage returns and volatility are expressed as percentages.

Variable Mean Standard deviation Minimum Maximum Serial correlation N

Disagreement index 0.4029 0.2480 0.0196 1.3860 0.6198 223Mortgage returns 0.2069 0.8715 �4.2850 1.9926 0.1077 165Mortgage return volatility 0.1781 0.0922 0.0441 0.5331 0.6715 165Mortgage trading volume 938.65 444.94 212.56 1917.80 0.8959 165

1995 2000 2005 2010

Dis

agre

emen

tin

dex

MBScrisis

LTCMcrisis 9/11 attack

Fed funds rate ≤ 3.5%refinancing wave

Resumptionof Fed MBS

purchases

Fed begins MBS purchases under QE1

Lehman bankruptcy

0

0.5

1

1.5

Fig. 4. The time series of disagreement: July 1993 through January 2012. The disagreement measure is the cross-sectional standard deviation of a dealer'snormalized prepayment duration forecast, which is the ratio between the normalized forecast prepayment forecasts conditional upon a �100 and a þ100basis point shift in the term structure. We use the forecast on the instrument having a coupon closest to the current pay yield, which generally has the bestcoverage and the most uniform terms. MBS¼Mortgage-backed security; LTCM¼Long-Term Capital Management; QE1¼An abbreviation for the first roundof quantitative easing launched by the Federal Reserve following the 2008 financial crisis.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238234

Fig. 4 also shows that there is a strong episodic natureto periods of higher disagreement. In particular, the graphillustrates that peaks in the level of disagreement tend tocoincide with major events in the mortgage and financialmarkets. Important examples include the mortgage crisisin early 1994 during which the prominent mortgage hedgefund Askin Capital Management failed. Similarly, the high-est level of disagreement during the study period occurredin August 1998 during the Long Term Capital Managementcrisis in the financial markets. Other major events asso-ciated with high levels of disagreement include the attacksof September 11, 2001 and the Lehman Brothers default ofSeptember 2008. Clearly, disagreement increases duringtimes of extreme uncertainty in the financial markets.

To explore this in more depth, we examine the relationbetween the disagreement index and a number of keyfinancial and macroeconomic variables that could affectaggregate prepayment behavior. It is important to stressthat in estimating this regression, we are not implyingcausality in the relation between the level of disagreementand these financial and macroeconomic variables. In fact,the level of disagreement and the financial variables arelikely all endogenously determined. Instead, our objectiveis simply to describe the contemporaneous relationbetween the disagreement index and the other variables.

Table 4 reports the results from the regression and liststhe independent variables that we include. As shown, anumber of the variables are significantly related to thedisagreement index. For example, the mortgage refinan-cing index is positively related to the level of disagree-ment. This is intuitive because an increase in prepaymentsis likely to result in greater dispersion among dealers intheir estimates of subsequent prepayments. Similarly, bothof the volatility measures are significantly related to thedisagreement index. Interestingly, however, the sign of thetwo volatility measures differ. An increase in stock marketvolatility results in higher disagreement, while the oppo-site is true for Treasury yield volatility. An increase in theslope of the term structure is associated with an increasein disagreement. Stock returns are negatively related todisagreement. Finally, an increase in unemployment isassociated with a decline in disagreement.

5. Is disagreement priced?

5.1. Disagreement and expected returns

To examine whether disagreement about prepaymentrates affects the expected returns of mortgage-backedsecurities, we use the standard approach of regressing ex

Table 4Results from the regression of the disagreement index on contempora-neous variables.

This table reports the results from the regression of the disagreementindex on its first two lags and on the indicated contemporaneousfinancial and economic variables. Refinancing denotes the refinancingindex reported by the Mortgage Bankers Association. Mortgage ratedenotes the current coupon rate for Government National MortgageAssociation (Ginnie Mae; GNMA) I mortgages as reported by Bloomberg.VIX denotes the Standard & Poor's 500 volatility index as reported byBloomberg. Treasury volatility denotes the Merrill Lynch Option VolatilityEstimate (MOVE) Index of Treasury volatility as reported by Bloomberg.Slope is the difference between the constant maturity 10-year and two-year Treasury rates as reported by the Federal Reserve Board. Stock returndenotes the monthly excess return on the Center for Research in SecurityPrices value-weighted index. Inflation is computed from the CPI-U index(Consumer Price Index for All Urban Consumers, nonseasonally adjusted)reported by the Bureau of Labor Statistics. Unemployment is theunemployment rate reported by the Bureau of Labor Statistics. Themonthly sample period is from July 1993 to January 2012. The reportedt-statistics are based on the Newey and West estimate of the covariancematrix (with four lags). ** denotes significance at the 5% level; * denotessignificance at the 10% level.

Variable Coefficient t-Statistic

Intercept 0.26806 1.94*Indext�1 0.28294 2.71**Indext�2 0.29352 4.27**Refinancing 0.02140 2.13**Mortgage rate 0.01088 0.88VIX 0.00446 2.01**Treasury volatility �0.00210 �2.81**Slope 0.08068 3.04**Stock return �0.00979 �2.03**Inflation 2.93231 1.51Unemployment �0.02856 �2.25**Adjusted R2 0.5188N 223

7 Although not shown in Table 5, we also estimate the regression byincluding a number of additional control variables including changes inthe 10-year interest rate cap volatility, one year into one-year swaptionvolatility, five years into five-year swaption volatility, the spread on10-year A-rated financial bonds, the 10-year swap rate, and the change inthe slope of the swap spread curve (i.e., the 10-year spread minus thetwo-year spread). None of these additional control variables is significant,and the disagreement index variable remains highly significant whenthese additional variables are included.

8 We also consider a trading strategy in which an investor holds aposition in MBS when the change in the disagreement index during theprior month is larger than the Nth percentile of all changes in the indexand otherwise holds a position in Treasury bills. The online Appendixshows that this strategy can result in an increase in the Sharpe ratio from0.2371 in the buy-and-hold case (i.e., N¼0), to values ranging from 0.29to 0.33 for N¼10% and 20%. We are grateful for the referee for suggestingthis analysis.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238 235

post realized returns on the ex ante measures of disagree-ment and other proxies for risk premia. If disagreement ispriced in expected returns, then the disagreement indexshould have predictive power for the subsequent returnson mortgage backed securities even after controlling forthe other ex ante risk premium proxies.

As discussed in Section 3, we make use of a proprietarydata set provided to us by a major fixed-income assetmanagement firm to construct a monthly return series onmortgage-backed securities. The lower panel of Table 3provides summary statistics for the FNMA TBA returns.

Table 5 reports the results from the regression ofthe monthly mortgage returns on the risk premium anddisagreement proxies. The first specification in the tablereports the results when only the risk premium proxies areincluded. The second specification reports the resultswhen the change in the disagreement index is added tothe regression. To control for other factors besidesdisagreement that could drive the expected returns ofmortgage-backed securities, we include a number ofex ante financial and macroeconomic variables in theregression. In forecasting the mortgage-backed securityreturn for month tþ1, we use only the ex ante values ofthese variables measured from the end of month t�1 tothe end of month t. By including the change in the currentcoupon mortgage rate and the change in the effectiveduration of the Lehman/Barclays US MBS index for fixed

rate mortgages, we can control for mortgage marketspecific risks. By including the lagged mortgage return,we control for the possibility of persistence in the returns.The various fixed income variables control for any termpremia, credit risk premia, or liquidity premia that couldbe present in expected returns. The stock return andvolatility variables potentially capture any equity risk orvolatility risk premia in mortgage returns. The refinancingindex, inflation, and unemployment variables are includedto control for any macroeconomic related risk premia notcaptured by the other variables.

As shown in the first specification, the risk premiumproxies collectively have a significant amount of predictivepower for the mortgage returns. The coefficients for thelagged mortgage return, the change in the mortgage rate,the stock return, and the inflation rate are significant ateither the 5% or 10% level. The adjusted R2 for theregression is 12.46%. Thus, variation in expected mortgagereturns is clearly predictable on the basis of these riskpremium proxies.

The second specification, however, shows that thepredictive power of the regression increases significantlyto 18.34% when the disagreement variable is included.The coefficient is positive and highly significant witha t-statistic of 2.86. Thus, the expected return onmortgage-backed securities increases when disagreementincreases. This is consistent with the existence of a riskpremium for disagreement (i.e., Varian, 1985, 1989; Abel,1989; David, 2008). Finally, the same risk premium proxiesthat are significant in the first panel remain significantwhen the change in disagreement is added to the regres-sion specification.7

To provide some perspective on the economic signifi-cance of our results, note that the slope coefficient for thechange in the disagreement index in Table 5 is 0.00932.This implies that a one standard deviation increase in thedisagreement index (i.e., 0.2480 from Table 3) translatesinto a 23.11 basis point increase in the subsequent month'sexpected return. This annualizes to a risk premium of2.77%.8

5.2. Disagreement, volatility, and trading volume

To explore the effects of disagreement on volatility andtrading activity we use a simple vector autoregression

Table 5Results from the regression of monthly mortgage returns on ex ante mortgage disagreement, financial, and economic variables

This table reports the results from the regression of the monthly mortgage return on the indicated ex ante variables, all of which are observed as of theend of the prior month. Riskless rate denotes the yield on one-month Treasury bills. Mortgage rate denotes the current coupon rate for GovernmentNational Mortgage Association (Ginnie Mae; GNMA) I mortgages as reported by Bloomberg. Mortgage duration is the Lehman/Barclays US MBS effectiveduration index for fixed rate mortgages reported by Bloomberg. Refinancing denotes the refinancing index reported by the Mortgage Bankers Association.Slope is the difference between the constant maturity ten-year and two-year Treasury rates as reported by the Federal Reserve Board. Corporate creditspread is the difference in the yield of Baa-rated bonds and the ten-year Treasury rate as reported by the Federal Reserve Board. Ten-year swap spread isthe difference between ten-year swap rates and the ten-year constant maturity Treasury rate as reported by Bloomberg. Stock return denotes the monthlyexcess return of the Center for Research in Security Prices value-weighted index. VIX denotes the Standard & Poor's 500 volatility index as reported byBloomberg. Treasury Volatility denotes the Merrill Lynch Option Volatility Estimate (MOVE) Index of Treasury volatility as reported by Bloomberg. Inflationis computed from the CPI-U index (Consumer Price Index for All Urban Consumers, nonseasonally adjusted) reported by the Bureau of Labor Statistics.Unemployment is the unemployment rate reported by the Bureau of Labor Statistics. The monthly sample period is April 1998 to January 2012. Thereported t-statistics are based on the Newey and West estimate of the covariance matrix (with four lags).

Variable Without Disagreement With Disagreement

Coefficient t-statistic Coefficient t-statistic

Intercept 0.00404 2.75nn 0.00392 2.73nn

Lagged mortgage return 0.73874 3.38nn 0.81355 4.09nn

Change in riskless rate −0.00173 −0.63 −0.00085 −0.31Change in mortgage rate 0.00741 1.07 0.00961 1.41Change in mortgage duration 0.00928 4.17nn 0.00934 4.48nn

Refinancing −0.00113 −1.80n −0.00110 −1.83*

Change in slope −0.00334 −0.96 −0.00318 −0.95Change in corporate credit spread 0.00113 0.32 0.00292 0.7200Change in ten-year swap spread −0.00007 −0.01 0.00311 0.3500Stock return −0.00058 −3.44nn −0.00055 −3.00nn

Change in the VIX index −0.00036 −1.48 −0.00047 −1.96n

Change in the Treasury volatility 0.00002 0.51 0.00003 0.72Inflation −0.21927 −2.53nn −0.24833 −2.82nn

Change in Unemployment −0.00432 −1.08 −0.00465 −1.25Change in disagreement index 0.00932 2.86nn

Adjusted R2 0.1246 0.1834N 165 165

n denotes significance at the 10% level.nn denotes significance at the 5% level.

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238236

(VAR) framework in which we include measures of allthree of these variables. To measure mortgage returnvolatility, we use the daily return data described pre-viously to calculate the standard deviation of returns foreach month in the sample period. As the measure oftrading volume, we use the total agency mortgage tradingvolume of primary government bond dealers reported bythe Federal Reserve Bank of New York. This series isaggregated to the monthly level and includes both tradingactivity among primary government bond dealers andtrading activity among customers of these bond dealers.An important advantage of this series is that it covers thetrading activity of virtually every major dealer included inthe PSA surveys. Summary statistics for the mortgagereturn volatility and trading volume measures are alsopresented in the lower panel of Table 3. We estimate theVAR using a specification that has three lags of themonthly change in the disagreement index, mortgagereturn volatility, and trading volume.

Table 6 reports the results from the estimation of theVAR system. Focusing first on the regression for disagree-ment, the table again shows that disagreement is stronglymean reverting because two of the three lagged changes indisagreement are negative and significant. Thus, anincrease in disagreement this month tends to be followedby a decrease in disagreement in the next two months. Nosignificant relation appears to exist between volatility and

subsequent changes in disagreement. The results indicatethat there is a relation between trading activity andsubsequent changes in disagreement. In particular,changes in trading activity are significantly related todisagreement. The negative sign of the coefficient indi-cates that an increase in trading volume is associated withlower disagreement in the second subsequent month. Thisresult is intuitive: As investors learn through trade, whichgives them opportunities to update their beliefs about thedrivers of asset value.

Turning next to the second regression for volatility, wealso see that volatility is strongly mean reverting, with allthree lagged values of changes in volatility significantlynegative. This is not surprising given the well-knownproperties of return volatility. What is interesting, how-ever, is that a strong positive relation exists betweendisagreement and subsequent volatility. In particular, thesecond lagged change in disagreement is positive andhighly significant, indicating that an increase in disagree-ment tends to be followed by higher levels of mortgagereturn volatility. This effect can be viewed as providingsupport for Shalen (1993) and Zapatero (1998), who positthat a positive correlation exists between disagreementand price volatility. The results also show that increases intrading activity tend to be followed by higher levels ofreturn volatility. All three lagged values of the change intrading volume are positive and significant.

Table 6Vector autoregression (VAR) estimation of monthly changes in disagreement, mortgage return volatility, and mortgage trading volume.

This table reports the results from VAR estimation of the three indicated equations, where the dependent variable in each specification is shown in thecolumn heading. Disagreement denotes the disagreement index. Volatility denotes the standard deviation of mortgage returns computed using dailyreturns each month. Trading volume denotes the total trading volume of mortgage-backed securities by primary government bond dealers as reported bythe Federal Reserve Bank of New York. The VAR is estimated using monthly data for the April 1998 to January 2012 period. The reported t-statistics arebased on the Newey and West estimate of the covariance matrix (with four lags). ** denotes significance at the 5% level; * denotes significance at the10% level.

Variable Change in disagreement Change in volatility Change in trading volume

Coefficient t-Statistic Coefficient t-Statistic Coefficient t-Statistic

Intercept �0.00161 �0.12 �0.00009 �0.14 0.00971 0.77Change in disagreement, t-1 �0.59158 �4.58** 0.00052 0.16 0.13705 2.49**Change in disagreement, t-2 �0.27546 �2.24** 0.01746 3.38** 0.12737 2.58**Change in disagreement, t-3 �0.19971 �2.46** 0.00317 0.77 0.04341 0.69Change in volatility, t-1 1.21180 1.08 �0.29826 �4.27** �0.04704 �0.03Change in volatility, t-2 �0.57288 �0.53 �0.27740 �3.71** �1.74449 �1.65Change in volatility, t-3 �0.02100 �0.02 �0.19749 �2.82** �1.01908 �0.95Change in trading volume, t-1 �0.04493 �0.54 0.00837 1.67* �0.63393 �5.79**Change in trading volume, t-2 �0.21791 �2.03** 0.01619 2.17** �0.22545 �2.20**Change in trading volume, t-3 �0.17262 �1.86* 0.01690 2.49** 0.14746 1.65Adjusted R2 0.3174 0.2380 0.3169N 165 165 165

B.I. Carlin et al. / Journal of Financial Economics 114 (2014) 226–238 237

Finally, turning to the third VAR equation in whichchanges in trading volume are the dependent variable,Table 6 shows that there is a strong relation betweendisagreement and trading activity. Both the first andsecond lagged changes in disagreement are significantlypositively related to changes in trading volume. This effectcan be viewed as providing support for Harris and Raviv(1993) and consistent with the empirical findings inKandel and Pearson (1995). The results also show thatincreases in volatility are not significantly related tosubsequent changes in trading volume, after controllingfor disagreement. This provides evidence that uncertaintyincreases trading volume only when disagreement arises.Alternatively, disagreement is the mechanism by whichuncertainty increases trading in the market. To our knowl-edge, this is the first paper to identify this relation. Finally,we again find that trading volume has a mean-revertingtendency as both the first and second lagged changes intrading volume are significant and negative in sign.

6. Concluding remarks

Understanding how information gets incorporated intoasset prices could be one of the most fundamental issuesin finance. This paper contributes by helping to showwhether and how heterogeneous beliefs and differencesin opinions are priced in the market. It also clarifies howinvestors take disagreement into consideration and whateffect that has on the time series of asset prices.

Previous theoretical work tends to support a positive riskpremium that is associated with disagreement. The equityrisk premium as identified by Mehra and Prescott (1985)can be rationalized by introducing heterogeneous beliefs ordifferences of opinion (Varian, 1985, 1989; Abel, 1989). To ourknowledge, this paper is the first academic study to show thisfact empirically in a setting in which there are essentially noshort-sale constraints or other trade frictions.

Disagreement is also associated with higher volatilityand trading volume. This relation has been studied intheoretical work (Harris and Raviv, 1993; Shalen, 1993;Zapatero, 1998) and shown empirically by Kandel andPearson (1995). In our paper, we find that disagreementis the primary channel through which uncertainty leads tohigher trading volume. That is, volatility in and of itselfdoes not lead to higher trading volume. Instead, it is onlywhen there exists more disagreement that trading volumeincreases with uncertainty. This distinction has not beenidentified empirically in previous work.

Finally, disagreement could become incorporated intoasset prices via two different mechanisms. As Banerjee(2011) highlights, investors can update their beliefs via arational expectations mechanism or can agree to disagree,which results in persistent differences in opinion. By studyinghow return-volume characteristics vary with disagreement inthe market, we find support for the rational expectationschannel. We find that higher disagreement is associated withhigher expected returns, higher subsequent return volatility,and higher trading volume. Especially given our finding thathigher trading volume is associated with lower subsequentdisagreement, rational investors are more likely to learn fromprices and opinions in the market, updating their beliefs usingBayes' rule.

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