mutual funds, part ii: fund flows and security returns

Peter Fortune

Senior Economist and Advisor to theDirector of Research, Federal ReserveBank of Boston. The author thanksRichard Kopcke and Lynn Browne forconstructive comments, and KathrynCosgrove for her able research assistance.

Mutual Funds, Part II:Fund Flows andSecurity Returns

This study is the second in a two-part analysis of the mutual fundindustry. The first part (Fortune 1997, referred to here as “Part I”)examined the basic structure of the industry and discussed the

historical relationship between mutual fund flows and returns on bothshort-term and long-term financial instruments. That study ended with adiscussion of the role that momentum investing by mutual fund share-holders—buying in rising markets, selling in declines—might play indestabilizing financial markets. This study begins where Part I ended.The goal is to assess the historical evidence to see whether the interactionsbetween mutual fund inflows, redemptions, and security prices arepotentially destabilizing.

Any analysis of the effect of mutual funds on financial stabilityshould, in principle, be a comparative analysis in which performance ofa financial system with mutual funds is compared to performance of asystem with only direct ownership of securities. If we knew the structureof financial markets and the behavior of economic agents in each world,we could examine the effects of shocks on asset prices and financial flows,allowing us to determine whether specific asset markets are more or lessdisturbed by specific shocks in the “mutual fund” and “sans mutualfund” worlds.

While some physicists subscribe to the “many universes” view ofquantum theory, we do not have access to data from any universe otherthan our own. Our data come from a history in which mutual fundsevolved in response to pressures inducing the decline of traditionalfinancial institutions. Mutual funds played a very small role until the1970s, before which ownership of financial instruments was dominatedby commercial banks, thrift institutions, insurance companies, and pen-sion funds. A comparison of financial market performance in that earlierworld with performance in the modern financial system might shed somelight on our fundamental question: Do mutual funds add to or reducefinancial market volatility? But the results will not be definitive, for the

financial system of the 1990s is not simply the systemof the 1970s with more mutual funds. Much else haschanged. Evolution in financial laws and regulations,increasing global interactions, the rise of new financialinstruments, major shifts in the structure and natureof financial institutions, and a change in the locus ofrisk-bearing from institutions to individuals have alsoshaped investors’ decisions. Because we have no wayto compare a world with direct investments withone having pooled investment opportunities, we mustresort to analysis of the world as it is, using historicalinformation to make inferences about the connectionbetween financial stability and mutual funds.

The first section of this study addresses someissues of shareholder behavior. Generalizations, or“stylized facts,” about the sources of variation of flowsinto mutual funds are examined; factors relevant toshareholder redemption are reviewed; and differencesbetween direct ownership and pooled ownership ofsecurities are discussed. The second section reportsthe results of our econometric assessment of the inter-actions between security returns and mutual fundflows. The third section simulates our model to traceout the effect of shocks to security returns and fundflows over a 24-month period. The final section sum-marizes the paper.

I. Some Issues of Mutual FundShareholder Behavior

Historical Evidence

The analysis of mutual fund flows in Part Iargued that the historical record supports severalpropositions about redemptions. Figures 1 through 4provide support for two of these propositions. Thesefigures, based on monthly Investment Company Insti-tute data using the mutual fund classification reportedin Box 1, show gross new money, net new money, andredemptions (all measured as percentages of net as-sets) for money market, bond, equity, and bond &equity funds.

First, the primary source of cyclical variation innet new money flowing into mutual funds is notshareholder redemptions. Rather, it is changes in grossnew money—new shares sold plus net exchanges intoa fund. This suggests that discussions of mutual fundexposure to fund outflows have placed too muchemphasis on redemptions, and too little emphasis onthe sources of variation in gross new money. Except inthe case of money market mutual funds, redemptions

are a small and stable share of net assets, punctuatedwith brief spikes.

Second, the mutual fund industry has rarely facedperiods of net outflows of money that would forcesales of financial assets. At bond funds, net newmoney was negative in 1987 and throughout 1994,both periods of rising interest rates and decliningbond prices. At bond & equity funds, the period fromthe October ’87 crash through late 1988 shows netoutflows, but at other times only small and verytemporary net outflows occurred. Equity funds expe-rienced net outflows in a number of months prior to

The primary source of cyclicalvariation in net new moneyflowing into mutual funds

is shares sold plus netexchanges into a fund, and

not shareholder redemptions.

1991, October ’87 through 1988 being the most serious,but no net outflows after 1991. The infrequency of netoutflows in the 1984–97 period is consistent with thelonger-term perspective in Rea and Marcis (1996):From 1942 to 1995, they report, equity mutual fundsshowed significant net losses of funds only during the1970s, when stocks performed poorly, and in the late1987 to early 1989 period.

A third proposition demonstrated in Part I is thatflows into both bond and equity funds are positivelycorrelated with the contemporaneous price apprecia-tion in those funds: When stock or bond prices arerising, flows into the respective funds increase; whensecurity prices are falling, inflows decline or outflowsoccur. This is consistent with positive feedback, ormomentum investing, a behavior that might exagger-ate market movements. It is also consistent with otherhypotheses, for example, the hypothesis that fundflows are directly related to the rate of return on thesecurities they hold, or the hypothesis that fund in-flows directly affect rates of return. We will addressthe momentum investing argument in some detail. Itshould be noted that momentum investing, should itoccur, is not limited to mutual funds; direct investorsmight also behave this way, although less evidence isavailable to demonstrate it.

January/February 1998 New England Economic Review4

Shareholder Profile

As discussed in detail in Part I, much attentionhas been given in the press and in the industry to the“shareholder profile” as a factor affecting mutual fundflows. One school of thought argues that the largerecent inflows to mutual funds have come from inves-tors who are less sensitive to market conditions thanearlier shareholders. Particular emphasis is placed onthe increased use of mutual funds for retirement

purposes, through Individual Retirement Accounts(IRAs), defined contribution pension accounts like401(k) and 403(b) accounts, and variable annuities.According to Reid and Crumrine (1997, Table 7), atyear end 1996 about 35 percent of all net assets ofmutual funds were held for retirement accounts. Dur-ing 1996 retirement’s share of net new money atmutual funds (excluding price appreciation) wasabout 26 percent for all mutual funds, but it wasconsiderably higher for the Investment Company In-

January/February 1998 New England Economic Review 5

stitute’s “bond and income” funds (83 percent) than forequity funds (25 percent) or money market funds (22percent). The long-term perspective of retirement inves-tors is often cited as a reason to believe that shares inmutual funds have become more stable over time. If so,this stability should be most pronounced at our “bond &equity” funds.1 Figure 3 does, in fact, show greaterstability of net new money at those funds since 1990.

However, there are counter arguments. Almost

all observers agree that institutional money—heldby fiduciaries, insurance companies, and pensionfunds—is insensitive to short-term market fluctua-tions. This shift toward individually managed retire-ment funds has been at the expense of traditional

1 The Investment Company Institute’s “bond and income”group is our “bond & equity” group excluding global bond funds,which the Institute places in its “equity” fund group.

Box 1: Types of Mutual Funds

The Investment Company Institute identifies 22 groups of open-end mutual funds, according to theobjectives outlined in the prospectus. This box describes those groups and shows how they have beenaggregated for this study into five groups: equity, bond & equity, bond, money market, and excluded. Thelatter group is excluded from this study because its assets are unique. The ICI data exclude closed-end funds,unit investment trusts, and hedge funds.

Equity Funds

Aggressive GrowthGrowthGrowth and IncomeEquity-InternationalEquity-Global

Investing primarily in common stocks with the goal of long-term growth

Maximum appreciation with no concern for current incomeCapital appreciation with some concern for current incomeCapital appreciation and steady current incomeCapital appreciation from non-U.S common stocksCapital appreciation from both U.S. and non-U.S. common stocks

Bond & Equity Funds

Equity-IncomeFlexible PortfolioBalancedIncome-Mixed

Investing in a mix of common stocks and long-term debt with the goal ofachieving both long-term growth and income

High income from common stocks with history of continuous dividendsStocks, bonds, and liquid assets varying with market conditionsCapital appreciation, current income, and stability of principalHigh current income from both stocks and bonds

Bond Funds

National MunicipalState MunicipalIncome-BondGovernmentGNMAGlobal BondCorporate BondHigh-Yield Bond

Investing in long-term bonds with the primary goal of income

Municipal bonds issued by any or all statesMunicipal bonds issued by specific statesMixture of corporate and government bondsU.S. Treasury securitiesMortgage securities backed by Government National Mortgage AssociationBonds of both U.S. and non-U.S. issuersDiversified portfolio of corporate bondsMaintain at least 2⁄3 of assets in non-investment-grade corporate bonds

Money Market Funds

Tax-Exempt, NationalTax-Exempt, StateTaxable

Investing in short-term, highly liquid securities

Short-term obligations of state and local governmentsShort-term obligations of state and local governments within specific statesShort-term obligations of U.S. government and corporations

Excluded

Precious MetalsOption/Income

Reported by ICI but excluded from this study

Securities of firms engaged in producing and distributing precious metalsThese were redesignated as income-equity funds in January of 1992.


pension funds, as defined-benefit pension plans ad-ministered by institutions have given way to defined-contribution plans in which the employee has thepower to reallocate his retirement portfolio. The dein-stitutionalization of retirement money managementmight make the average retirement dollar less stableeven while increasing the stability of the average mutualfund dollar. In short, even if mutual funds have becomemore stable, financial markets might have become lessstable with the growth of mutual funds.

The long-term perspective ofretirement investors is often citedas a reason to believe that shares

in mutual funds have becomemore stable over time.

If so, this stability should bemost pronounced at our “bond

& equity” funds.

The hypothesis that the stability of the averageretirement dollar has increased is also undermined bythe access employees have to information about theirretirement money and by factors that make it lesscostly to reallocate retirement portfolios. For example,the ability to exchange funds within a defined-contri-bution plan, with no transactions charges or capitalgains tax liability, has made defined-contributionplans an even easier way to carry out portfolio shiftsthan either direct investment or mutual funds held fornon-retirement purposes.

Almost no empirical evidence is available on assetswitching by employees in defined-contribution plans.One report by Hewitt Associates, a defined-contri-bution pension plan manager, indicated that duringthe very brief decline in the stock market in July of1996 active switching out of equity funds occurred atits 401(k) plans between July 11 and 17. The magni-tude of the switching—about 0.6 percent of net as-sets—was slightly more than the magnitude reportedfor all equity funds during the same period.2 This

report suggests that 401(k) money in equity funds isless stable than the average equity fund dollar.

Can Mutual Funds Mimic Direct Investments?

Is security ownership through mutual fundssomehow different from direct ownership? Should weexpect the sensitivity of trading by direct investors tomarket conditions to be different from the sensitivityof mutual fund shareholders? In this section we showthat any direct investor’s portfolio can be replicated bya mutual fund investor if both can invest in the sameinstruments. In the next section we present somereasons why direct and mutual fund investors mightbehave differently.

Consider two investors, each with the same assetallocation and with $100,000 in assets. Investor Dholds assets directly, placing 10 percent in cash, 40percent in bonds, and 50 percent in stocks. Investor Mholds 10,000 shares, or 1 percent of the 1 millionoutstanding shares of a mutual fund. The mutualfund’s net assets are $10 million, so the net asset valueis $10 per share. Investor M’s asset allocation mimicsInvestor D’s, with 10 percent in cash, 40 percent inbonds, and 50 percent in stock.

Now suppose that, in response to new informa-tion, each investor decides to reduce the share instocks by 10 percentage points, investing the proceedsin cash. Investor D sells 10 percent of his holdings ofstocks ($5,000) and holds the proceeds in cash. Hisnew portfolio is $15,000 in cash, $40,000 in bonds, and$45,000 in stocks, an asset allocation of 15 percentcash, 40 percent bonds, and 45 percent stocks.

Investor M is easily able to replicate Investor D’sreallocation. Recalling that each of Investor M’s orig-inal 10,000 shares is a claim to $1 cash plus $4 bondsplus $5 stocks, he must sell 1,000 mutual fund sharesif he is to reduce his holdings of stock from $50,000 to$45,000. He will receive redemption proceeds of$10,000, of which he will reinvest $4,000 in directlyheld bonds and the remaining $6,000 in cash. Hisnew portfolio has $15,000 in cash ($6,000 direct,$9,000 via the fund), $40,000 in bonds ($4,000 direct,$36,000 in the fund) and $45,000 in stocks (allthrough the fund). After the reallocation both inves-tors hold 15 percent in cash, 40 percent in bonds and45 percent in stocks.3

2 See Wall Street Journal, “Market Bumps Rattle Nerves at401(k)s,” August 23, 1996, and Wall Street Journal, “Mutual FundWithdrawals Up Sharply,” July 20, 1996.

3 The assumption of an across-the-board sale of securities tofinance redemptions is reasonable because, in the long run, portfoliomanagers will set asset allocation goals that are not altered by


Why Should Mutual FundShareholders Be Different?

Investors in mutual funds might be different fromdirect investors for several reasons. First, direct inves-tors have more investment alternatives than mutualfund investors because direct investors are typicallywealthier and face lower transactions costs. Mutualfunds allow investors to hold a broad range of assetsin a diversified portfolio and to reap the benefits ofprofessional management while enjoying economiesof scale. The investors to whom mutual funds are mostadvantageous are those with relatively small financialnet worth and with less confidence in their financialacumen. Direct investors, on the other hand, are morelikely to be able to achieve the benefits of economies ofscale, professional management, and diversificationon their own.

Redemptions might move theportfolio of a mutual fund towardgreater leverage and toward lessmarketable securities, giving all

mutual fund investors anincentive to redeem in largeramounts than simple assetallocation would require.

Second, current orthodoxy appears to attributemore farsightedness and a better understanding ofshort-term security price cycles to more sophisticatedinvestors. This would suggest that the mutual fundinvestors might respond to short-term market condi-tions and therefore trade more frequently, and thatthey might be more subject to swings in “animalspirits” that encourage them to overreact to newinformation.

A third factor affecting the behavior of mutualfund investors is that mutual funds might face afinancial analog of the classic “Problem of the Com-

mons,” a problem arising from each shareholder’sawareness that other shareholders have incentives tobehave in ways that harm him. The Problem of theCommons is that when numerous economic agentshave access to a limited resource, each knows thatother agents will use too much of the resource in theshort run, leaving too little available to him for futureuse. The result is that every agent uses too much in theshort run. This has been applied to water supply useand to the extraction of depletable natural resources todemonstrate how common ownership without indi-vidual limits results in a too-rapid extraction of thenatural resource. It also helps to explain bank runsand runs on commodities during periods of shortage.A potentially important, but hitherto untested, hy-pothesis is that each mutual fund shareholder has anincentive to redeem quickly if the volume of redemp-tions affects the quality of the fund. Delay means thatother shareholders might redeem, forcing the slowredeemer to accept a loss in quality. We call this the“rapid redeemer incentive.”

Again consider investors D and M, holding iden-tical portfolios, one directly and the other through amutual fund. Once again, each holds 10 percent incash, 40 percent in bonds, and 50 percent in stocks. Ageneral decline in stock prices has induced bothinvestors to shift from stocks to cash. Investor M willredeem shares to achieve his new asset allocation, asdescribed above. However, as mutual funds experi-ence redemptions they are unlikely, at least in theshort run, to pay the redeemer by selling an equalproportion of all securities. Rather, they might followa financial pecking order, first drawing down theircash assets, then drawing on their lines of credit withbanks, and finally selling securities. If they sell secu-rities, they might “cherry pick,” selling the mostmarketable securities first.

The implication of this pecking order is thatredemptions might change the characteristics of themutual fund, moving the portfolio toward greaterleverage and toward less marketable securities havingwider confidence intervals for prices and higher bid-ask spreads. Investor M, anticipating the declinein quality resulting from redemptions by others, hasan incentive to redeem shares, not because he isunhappy with the asset allocation but because he doesnot want to hold a portfolio with more leverage andless quality.

All mutual fund investors have an incentive toredeem in larger amounts than simple asset reallo-cation would require, just as each farmer has anincentive to use more water than the long-term inter-

temporary cash flows. Thus, even if, in the short run, the managerpays for redemptions by drawing down his cash position, he willeventually sell securities to replenish his cash and to restore theoriginal portfolio shares.


ests of all farmers drawing on a water aquifer woulddictate. By doing so, rapid redeemers exit from thefund with cash, leaving the remaining shareholderswith more leverage, less liquidity, and, perhaps, lessmarketability.

II. Review of the Literature

A short academic literature can be found on thedynamic interaction between security returns andmutual fund flows. This literature focuses on ques-tions important to this study: Is “momentum trading,”either direct or indirect via mutual funds, rational?Do mutual fund flows respond to either contempora-neous or lagged security returns? Do security returnsrespond to contemporaneous or lagged mutual fundflows, and, if they do, is there a positive feedbackeffect in which a shock to security returns can affectflows, which then affect returns, and so on?

Momentum Trading

The hypothesis of momentum trading by mutualfund shareholders has received considerable attentionin recent years. A recent best-selling book for amateurinvestors, The Motley Fool Investment Guide (Gardnerand Gardner 1994), proposes that investors shouldselect stocks according to a number of criteria, amongwhich is “relative strength,” defined as the stock’sposition in the distribution of price increases duringthe previous year. A relative strength of 95 (the 95thpercentile) or better is necessary to meet the MotleyFool test.

Momentum investing is predicated on an up-ward-sloping demand curve, typically attributed to“elastic” expectations. If momentum trading is notrational, it will soon die out as those who use itdiscover that they are buying high and selling low.But if momentum trading is rational, it can be chronicand might destabilize security prices, as demand forstocks will increase when an upward shock to stockprices occurs. Several studies bear on the rationality ofmomentum investing.

An axiom of basic finance theory is that stockprices are based on information about the firm’sfuture. If so, the demand curve for stock should behorizontal—an increase in one investor’s demand forreasons unrelated to the firm’s prospects will leadother investors to sell at the prevailing price becausetheir assessment of the value of the firm’s stock hasnot changed. Schleifer (1986) examined movements in

prices of stocks that were newly included in the S&P500 Index, arguing that Standard & Poor’s reasons forincluding a firm in the Index are independent of thefirm’s performance, so inclusion carried no informa-tion about the firm’s prospects. Schleifer finds that theprice of a firm’s shares increases at the time of theannouncement that they will be included in the S&P500, and that this increase lasts for about 10 days. Theconclusion is that the demand curve for stocks isdownward-sloping, not horizontal, because any inves-tor buying as a result of the inclusion must pay ahigher price to induce sellers to hold fewer shares.This provides a basis for momentum investing evenwhen there is no new information about the firm.For example, a “noise trader,” who buys on whimrather than on information, can push a stock’s priceup, leading momentum investors to see a buyingopportunity.

A motive for momentum investing can also arisefrom incomplete reaction to new information. David-son and Dutia (1989) analyzed all AMEX and NYSEfirms from 1963 to 1985 in an effort to determinewhether investors overreact or underreact to newinformation. Overreaction should induce a negativeserial correlation among stock returns: Investors whorespond to good information by driving the price uptoo much should experience a subsequent decline inprices as fundamental relationships are restored. Un-derreaction should induce a positive serial correlation,encouraging investors to buy during days followingprice increases and sell after price decreases. Davidsonand Dutia found a positive serial correlation usingannual data; that is, unusually good (poor) returns inone year are followed by unusually good (poor)returns in the next year. This indicates a significantpersistence in rates of return, supporting investorunderreaction to new information and providing along-term rationale for including momentum as acriterion in stock selection.

The Davidson-Dutia study applied to stockprices, hence it was relevant for both direct andmutual fund investors. A well-known study of relativepersistence in mutual fund returns reaches the sameconclusion for mutual fund investors. Hendricks, Pa-tel, and Zeckhauser (1993) analyzed the quarterlyperformance of over 150 growth-oriented, no-load,open-end equity funds between 1974 and 1988, find-ing a statistically significant and positive serial corre-lation in mutual fund returns over a four-quarterhorizon: Unusually good (poor) performance in thepast four quarters was followed by unusually good(poor) performance in the subsequent four quarters.


Once again, performance shows a strong persistence,a persistence that is both statistically and economi-cally significant. A shareholder who assessed hisportfolio quarterly and selected randomly amongthose mutual funds in the top octile (top 12.5 per-cent) of recent performance would have earned anannual return about 1 percent per year greater thanthe median mutual fund with the same level ofsystematic risk.4

Warther (1995), in a widely cited study using theInvestment Company Institute’s monthly data forJanuary 1984 to June 1993, with slightly different fundgroupings than we employ, decomposed net newmoney inflows into expected and unexpected compo-nents. Expected fund flows are defined as a functionof past flows into the same fund group, and unex-pected fund flows are defined as the residual from theexpected flow regression. Warther finds that unex-pected money inflows to equity funds are positivelycorrelated with current-month returns on commonstocks, that unexpected money inflows to bond fundsare positively correlated with current-month bondreturns, and that both correlations are statisticallysignificant. This result is consistent with three alter-native hypotheses. The first is that momentum invest-ing is present in the short run, with investors buyingmore of a mutual fund in a month when the prices ofthe securities it holds rise. The second hypothesis isthat a feedback is present in which a rise in demandfor mutual fund shares induces an increase in theprices of the securities the fund holds; that is, fundflows “cause” changes in security prices. The thirdhypothesis is that both fund flows and security returnsrespond directly to a third factor. For example, ifinvestors become more optimistic about stocks, theywill bid up stock prices through direct investmentsand also increase their purchases of mutual fundshares.

Momentum investing can be a relatively short-lived phenomenon, for example, a rule of “buy nowif stocks are rising,” or it can be longer-lived, lookingto performance in past periods as a guide to the future.In the first case there should be a direct correlationbetween fund inflows and returns on the securitiesowned by the fund (“own-returns”), as found byWarther. In the second case, there should be a persis-tence in returns, as found by Davidson and Dutia, andby Hendricks et al. We return to the question ofpersistence later.

The “Causal” Connection betweenFund Flows and Security Returns

This study is concerned with the implications ofsecurity returns for mutual fund flows, and with thepossibility of a reverse transmission from mutual fundflows to security returns. In short, we would like toknow whether security price changes “cause” fundflow changes, fund flow changes “cause” securityprice changes, or causality works in both directions.The notion of causation is inherently slippery, andeconomists often use a particular definition called“Granger causation,” in which the direction of causa-tion is synonymous with the existence of a lead or lagrelationship (see Box 2). Variable A is said to“Granger-cause” variable B if past values of A containinformation useful in forecasting B. Variable B is saidto Granger-cause variable A if past values of B containinformation useful in forecasting A.

We would like to know whethersecurity price changes “cause”fund flow changes, fund flow

changes “cause” security pricechanges, or causality works

in both directions.

Granger causation is, therefore, determined bywhether a variable is useful in predicting anothervariable, and not necessarily by whether a variable“causes” another in a philosophical sense. In fact,variable A might well Granger-cause variable B eventhough B philosophically causes A. For example, sig-nificant wage increases often precede inflation, so thatwage rate changes Granger-cause inflation. But ifeconomic agents are forward-looking, they will formexpectations of future prices and the wage rate in-crease achieved now might reflect the correct an-ticipation of future price increases. Future inflation“causes” current wage increases but wage increasesGranger-cause future inflation!

In spite of its limited use of the notion “causa-tion,” Granger causation has become a widely usedconcept. The fundamental reason is that any definitionof “causation” is subject to criticism, and the definitionchosen should be determined by the uses to which the

4 Transaction costs were not considered, but the sample offunds included only no-load funds.


concept will be put. Granger causation is an appropri-ate definition for our purposes because we are con-cerned primarily with whether a change in securityreturns appears to be correlated with future mutualfund flows, and vice versa. It is in such leads and lagsthat signs of destabilizing behavior of economic agentsmay be found. However, the reader should be awarethat this study uses “cause” as a code word for “leadsand lags,” not in the deeper sense.

Warther’s 1995 study, cited above, investigatedthe relationship between mutual fund flows and pastreturns as well as the contemporaneous relationshipbetween mutual fund flows and current returns, dis-cussed above. He found no evidence that past own-returns influence new money flows into a group offunds: Bond fund flows were not affected by past bond

returns; stock fund flows were not affected by paststock returns. Many economists, especially those whobelieve that security markets adjust rapidly to newinformation, will not be surprised by this, for ifsecurity market equilibrium is reached quickly, thenall the action ensuing from a shock to markets mighthappen within a short period, certainly within amonth, creating contemporaneous correlations but nocorrelations with past values. But Warther’s resultdoes support the hypothesis that mutual fund flowsare not affected by security returns.

Warther also reports that he finds no statisticallysignificant effect of past mutual fund inflows on cur-rent stock returns. In short, he rejects both sides of afeedback trading model, arguing that security returnsneither lag nor lead mutual fund flows.

Box 2: Granger Causation

Economists are very interested in determiningdirections of causation: Does A cause B, does Bcause A, or is there a mutual two-way causation?One concept of causation is “Granger Causation,”proposed by the statistician Clive Granger in 1969.According to Granger, event A is said to causeevent B if predictions of event B can be improvedby using information on past occurrence of event A.

Suppose, for example, that one is interested inpotential causation between the Treasury bill rateand the unemployment rate. The bill rate is said toGranger-cause the unemployment rate if, in anautoregression of the unemployment rate on itspast values and the past values of the bill rate, thepast values of the bill rate are statistically signifi-cant. The Granger test is simple. First, estimate thefollowing regression:

(2.1) Ut 5 a0 1 a1Ut21 1 . . . 1 apUt2p

1 b1Rt21 1 . . . 1 bpRt2p 1 et

in which U is the unemployment rate, R is the billrate, and p is the lag length (determined by priortests, the Schwartz criterion in this study). Thenestimate the same equation without the bill rate.Finally, using the residuals from both regressions,test the hypothesis that b1 5 b2 5 . . . bp 5 0. Thisis the hypothesis that the bill rate does not provideinformation useful in predicting the unemploymentrate, that is, that the bill rate does not Granger-cause the unemployment rate. That test can be done

using the F-statistic or, as we do, the Chi-squarestatistic.

The same test can be applied to the reversecausation by regressing the bill rate on laggedvalues of itself and of the unemployment rate. Onceagain, the hypothesis that the unemployment ratedoes not Granger-cause the bill rate is equivalent toall coefficients on past unemployment rates in (2.1)being zero.

Granger causation is a very limited view ofcausation in several ways. First, it focuses on lead-lag relationships, which do not necessarily corre-spond with common notions of causation. For ex-ample, event A could be found to Granger-causeevent B even if the true relationship is that B causesA. A case in point is the relationship between wagerate changes and inflation. The historical record indi-cates that wage increases precede (thereby Granger-causing) inflation. However, wage increases dependon forecasts of inflation, and the true relationshipmight be that an increase in future inflation (cor-rectly forecasted) causes current wage increases.

A second criticism of Granger-causation tests isthat they are based on linear forecasting models. Ifthe true economic model is nonlinear, Granger testswill be based on incorrect forecasts and will bemisleading. Yet another criticism, one that appliesto most econometric models, is that Granger testsassume that the parameters of the model—thecoefficients and the elements of the covariancematrix of residuals—are constant.


Remelona, Kleiman, and Gruenstein (1997) used amethod similar to Warther’s, involving decompositionof mutual fund flows into expected and unexpectedcomponents. However, they included returns on othersecurities not held by the fund (“other-returns”) aswell as own-returns as determinants of unexpectedfund flows. Their regressions of unexpected flows intoa mutual fund group on the own-returns and other-returns was estimated using Instrumental Variablesmethods rather than Ordinary Least Squares in aneffort to correct for possible feedback from fund flowsto security returns. They found that unexpected equityfund flows were not affected by either contemporane-ous or lagged stock returns, and that bond fund flows(specifically, government, corporate, and municipalbond fund flows) were affected by contemporaneousbond returns but not by lagged bond returns. Thecoefficient measuring the effect of bond returns onbond fund flows was higher in Remolona et al. than inWarther’s study, a result they attribute to the ability ofInstrumental Variables estimation to eliminate biasesdue to reverse feedbacks.

Potter (1996), explicitly employing the conceptof “Granger causation,” examined the lead-lag rela-tionship between returns and fund flows for severalcategories of equity funds. He reported evidence thatsecurity returns are useful in predicting flows intoaggressive growth funds and growth funds, but notinto growth and income funds or equity funds. LikeWarther, he firmly rejects, for all four fund groups,the hypothesis that equity fund flows lead securityreturns.

None of the studies cited find evidence thatmutual fund flows are affected by past security re-turns, or that security returns are affected by pastmutual fund flows. In short, they find no evidencesupporting a feedback in which a shock to securityreturns or to fund flows is associated with subsequentchanges in flows or returns. However, they do findevidence that fund flows are positively correlated withcontemporaneous returns on the same type of securi-ties held by the fund, a relationship consistent withshort-run momentum trading, but also consistent withother hypotheses.

III. The Interaction between SecurityReturns and Mutual Fund Flows

In this section we extend the notion of Grangercausation discussed above to a multivariate contextby estimating an unrestricted Vector Autoregression

model (see Box 3). We avoid placing arbitrary restric-tions on the dynamics of the model because restric-tions, like those used by Warther (1995) and byRemolona, Kleiman, and Gruenstein (1997), limit therange of outcomes that a dynamic model can gener-ate.5 Our model is used to test hypotheses about theleads and lags between mutual fund flows and secu-rity returns.

Economic models of portfolio choice assume thatinvestors will consider the returns on all assets whenthey determine their optimal portfolios. This will betrue of both direct investors and mutual fund inves-tors. Thus, we should expect that relative rates ofreturn on securities will have value in predicting flowsof money into alternative assets—a result rejected insome of the studies cited above.

Economic models of portfoliochoice assume that investors willconsider the returns on all assets

when they determine their optimalportfolios. Thus, we should expect

that relative rates of return onsecurities will have value in

predicting flows of money intoalternative assets.

The explosive growth of mutual funds has ledsome observers to reverse this order, attributing thehigh returns on common stocks in the United Statesto high inflows into equity mutual funds. One encoun-ters this view in the financial press when money fundflow data are cited as a predictor of stock prices(“because lots of cash is available”) or equity fundsales are used to predict stock prices (“because theyhave to invest it in stocks”). If valid, this dynamicinteraction could result in a feedback in which a shockto security returns leads to a change in mutual fundinflows, which leads, in turn, to a further change insecurity returns. If feedbacks are especially strong, a

5 The restrictions imposed by Warther and Remolona et al.were designed to decompose cash flows into expected and unex-pected components.


snowball might result, with cycles in returns andflows getting larger over time.

The reasons for a possible feedback from fundflows to security prices are not clear. One story,probably in the mind of financial journalists, is a“price pressure” story: A rise (say) in equity fundinflows means that portfolio managers will be buyingstocks, a fall in flows means that they will reducepurchases. This, of course, ignores the possibility thatinvestors are switching from direct investment in

equities to investment through mutual funds. Anotherpossible explanation is that mutual fund investorshave information that they reveal to the market whenthey buy fund shares, thereby inducing other inves-tors to buy or sell securities. For example, if mutualfund investors are unsophisticated and frequentlywrong, their purchases of equity funds might be asignal to sell stocks, or if they are particularly wellinformed, the signal might be a buy signal.

In order to investigate the potential for a snow-

Box 3: Vector Autoregressions

Suppose that an endogenous variable is af-fected by current and past values of all endogenousvariables in an economic system. If there are Nendogenous variables, each labeled yit to representthe ith variable (i 5 1, . . . , N) at time t, and if thelength of the lags describing the evolution of eachvariable is p periods, the system can be expressedas

(3.1) Yt 5 A0Yt 1 A1Yt21 1 . . . 1 ApYt2p 1 et

where Yt is the vector of values of endogenousvariables at time t, et is the vector of “surprises” inthe endogenous variables, and Ak (k 5 0, 1, . . . , p)is the matrix of coefficients for the effects of Yt2k onYt. The surprise vector, et, is assumed to be jointlynormally distributed with zero mean and covari-ance matrix (. The contemporaneous covariancematrix, A0, will have zeros where the right-sidevariable is the same as the left-side variable; that is,the element aii 5 0.

The system described above can be rewritten asa Vector Autoregression (VAR) by solving for theleft-side variable, expressing the vector of currentvalues of endogenous variables as a linear functionof the lagged values. The result is

(3.2) Yt 5 B1Yt21 1 . . . 1 BpYt2p 1 et

where Bk 5 (I 2 A0)21Ak and et 5 (I 2 A0)21et. Thisexpresses the vector of endogenous variables as alinear function of the past values of endogenousvariables. The new surprise vector will have zeromean and covariance matrix (*. Note that even ifthe elements of et are independently distributed,the elements of et will not be. Thus, going from thestructural form in (3.1) to the VAR form in (3.2)introduces a contemporaneous correlation betweenresiduals in different equations.

The VAR system can be easily estimated usingOrdinary Least Squares, in which case each right-side variable is included in all regressions. Becausethis is equivalent to Seemingly Unrelated Regres-sion, the contemporaneous correlation between re-siduals will be incorporated in the estimation andthe estimates of the B matrices will be both unbi-ased and efficient. Unless certain conditions aremet, the original A matrices cannot be recoveredfrom estimates of the B matrix elements, but that isnot necessary for our purposes.

Granger tests can also be applied to VectorAutoregression models. The hypothesis that onegroup of variables does not Granger-cause anothergroup is simply a test that the appropriate elementsin the matrices of coefficients are all zero, that is,that the “causing” variables have no value in pre-dicting the “caused” variables. Suppose that wewish to test the hypothesis that three endogenousvariables (variables 3, 4, and 5) in equation system(3.2) “Granger cause” the first two variables. Thisis equivalent to a test of the hypothesis that theelements in the first two rows and the third tofifth columns of each B matrix are all zero. Thenull hypothesis is that there is no “Granger cau-sation.” This hypothesis is tested by estimatingthe first two equations in the unrestricted VARsystem (3.2), then re-estimating those equationswith the third, fourth, and fifth variables re-moved from the right-hand side. The residualsfrom the restricted and unrestricted regressionsare then used to form a likelihood ratio test: Ifthe Chi-square test statistic is sufficiently high,the hypothesis of no Granger causation is re-jected in favor of the conclusion that the third tofifth variables “Granger-cause” the first two vari-ables.


ball, we have estimated a small Vector Autoregression(VAR) model with seven variables: new money in-flows for each of four types of mutual funds, eachexpressed as a percentage of the previous month’sassets, and three rates of return. The four types ofmutual funds are money market funds, bond funds,bond & equity funds, and equity funds, aggregationsdescribed in Box 1. These data, provided by theInvestment Company Institute, are monthly valuesfrom January 1984 through December 1996. The threerates of return are the realized returns on the S&P 500,on long-term U.S. Treasury bonds, and on one-yearU.S. Treasury bills, all provided by Ibbotson Associ-ates. These realized returns, available through Decem-ber 1996, are the actual rates of return experiencedduring the month, including both cash income (divi-dends or coupons) and capital value changes. It isimportant to note that realized returns will moveinversely to the required returns on securities, a resultthat affects the interpretations of our results. Forexample, if investors require a lower return on stocks,the first effect will be to raise the price of commonstocks, thereby increasing the realized return onstocks. In the long run, realized returns should matchrequired returns, but during a transition they willmove in opposite directions.

Each of the seven variables (four fund inflows andthree security returns) was regressed on a constant, on11 seasonal dummy variables, on a dummy variablefor the October ’87 crash (with a value of one inOctober-November 1987, zero otherwise), and on eachof the five prior months’ values for all seven vari-ables.6 The sample period was July 1985 throughDecember 1996. This provides the basic unrestrictedVAR model, with the same 48 variables in eachequation. This model was then restricted in a varietyof ways to allow tests of “block exogeneity,” that is,tests of hypotheses that one subset of variables doesnot have value in predicting the remaining vari-ables. Block exogeneity tests are a multivariateversion of the “Granger causation” tests (see aboveand Box 2). If, for example, it was found thatexcluding lagged returns on both Treasury bondsand the S&P 500 from the equations explainingflows into bond and equity funds did not signifi-cantly affect predictions of bond and equity fundflows, then we would conclude bond and stockreturns do not Granger-cause bond and stock fund

flows. An equivalent statement is that fund flowsare exogenous with respect to security returns.

We believe that this VAR method is superior tothe methods used in the studies cited above. Theestimation methods used by Warther and by Re-molona et al. are equivalent to a restricted VAR, whichis encompassed by our unrestricted VAR but withsome variables arbitrarily excluded in some equations.If those exclusions are not valid, the results will bebiased in favor of rejecting past returns as variablesexplaining mutual fund flows. Warther’s paper showsthis most clearly. He estimates a regression of currentfund flows on lagged fund flows in the past threemonths, interpreting the resulting series as measuringexpected fund flows. He then examines the correlationbetween unexpected fund flows (the residual in the firstregression) and both current and past security returns,concluding that current returns are important but pastreturns are not. This method arbitrarily excludes pastsecurity returns from having any effect on expectedfund flows, putting any influence of past returns intothe residual. If current fund flows are positivelycorrelated with current returns, as Warther finds, thiswill bias his results in favor of finding no effect of pastreturns on current fund flows.7

6 The VAR was estimated for increasing lag lengths from 1 to 12months. Both the Akaike and Schwartz criteria indicated a five-month lag for the VAR.

7 Suppose the “true” model is Nt 5 a 1 bNt21 1 cRt21 1 «t,where N is new money at mutual funds and R is the return onthe fund’s securities. The parameter b is the effect of a change in thelagged fund flow holding the lagged security return constant; theparameter c is the effect of a change in the lagged security returnholding the lagged fund flow constant. We would like to know the valueof c, that is, how sensitive are fund flows to lagged security returns.

If one estimates this model using OLS, the parameter estimateswill be unbiased and efficient. But suppose that a two-stage ap-proach like Warther’s is used. First, the equation Nt 5 a 1 bNt21 1 htis estimated; Rt21 becomes an excluded variable whose effect isplaced into the residual, which has the “true” value ht 5 cRt21 1 «t.Second, the estimated residual from this first regression (call it vt)is regressed on Rt21 to determine whether current fund flowsare sensitive to lagged security returns; denote this regression asvt 5 c9Rt21 1 et.

The question is, how is the estimate of c9 in the second stage ofthis two-stage approach related to the estimate of c in the single“true” equation? If Nt and Rt are uncorrelated, c9 is an unbiasedestimate of c and the two approaches are equivalent. But if Nt andRt are correlated, this is no longer true and the two approachesdiffer. Suppose that, as Warther argues, Nt and Rt are positivelycorrelated. Then it is easy to show that the estimator of b in thefirst-stage regression is biased upward. The reason is that thepositive correlation between Nt21 and the excluded variable, Rt21,will be partially attributed to the influence of Nt21 on Nt, creating anupward bias in the estimate of b. This upward bias in b in the first-stage regression will create a downward bias in the estimate of cin the second-stage regression, so the estimator of c9 will be adownward-biased estimator of c.

In short, if fund flows and security returns are contemporane-ously correlated, Warther’s two-stage estimation will be biasedtoward the conclusion that fund flows are not sensitive to laggedsecurity returns.


Persistence in Security Returns

As noted above, there is considerable evidencethat purchases of mutual fund shares are positivelycorrelated with returns on the securities held (see PartI). This is consistent with, but not proof of, a short-lived (within a month) role for momentum in share-holder investment in mutual funds. However, mo-mentum investing is more likely to pose a seriousproblem for market stability when security returns arepersistent; that is, when it is rational for investors toextrapolate current performance into future periods.

We have used our VAR model to examine persis-tence in security returns. All three security returnequations were estimated with five lagged months ofeach of the three security returns included as indepen-dent variables. Then the three equations were re-estimated with the five lagged months of one securityreturn excluded. Finally, a likelihood ratio test wasused to determine whether the security return thathad been excluded Granger-causes the three returns.This was done for each of the security returns beingexcluded.

The results are reported in Table 1, whose col-umns designate the dependent, or “caused,” variablesand whose rows define the independent, or “causing”variables. Each cell reports the value of the Chi-square

statistic for the likelihood ratio test that the “causing”variable Granger-causes the “caused” variable. This is,of course, the test of the joint hypothesis that allcoefficients on the causing variables (rows) in regres-sions with the caused variables (columns) as depen-dent variables are zero. The significance level associ-ated with each Chi-square statistic is shown inparentheses; this is the probability that a value ofChi-square equal to or greater than the observedsample value would occur by chance. A significancelevel of 0.05 or less indicates that Granger-causationexists; if the significance level exceeds 0.05, anyeffect of the causing variable observed in the data isattributed to chance. Cell entries in bold text arestatistically significant by that standard. For exam-ple, the Chi-square statistic for the Rsp500 row andRus column in Table 1 is 4.64, a result that is notstatistically significant because the significance levelin parentheses is a very weak 0.46. We conclude thatthe five lagged values of the return on stocks do nothave a statistically significant effect on the return onbonds.

The results in Table 1 soundly reject the notion ofpersistence in the realized returns on stocks or bonds.In no case is the history of either stock or bond returnsstatistically significant in explaining current returnson long-term securities. For example, the Chi-squarevalue for the hypothesis that the history of stockreturns is relevant to the current stock return (Rsp500)is 8.33, which, at a significance level of 0.14, is notstatistically significant. This suggests that it is notrational for investors to project current performance ofstock returns into the future, a fundamental require-ment of destabilizing momentum investing. The sameconclusion applies to bond returns.8

However, significant persistence is evident in thereturn on one-year Treasury bills. Indeed, the resultssuggest that the history of both bill and bond returnsis relevant in explaining bill returns. Persistence in thismarket is interesting, as it indicates that the long-termsecurities market provides information to short-terminvestors, but not the reverse. However, persistence inthe bill market is not a foundation for momentuminvesting in stocks and bonds.

8 Note that this result applies to the broad indices of securityreturns used in this study, not to returns on individual equities oron specific mutual funds. As noted above, there is evidencesupporting persistence at the micro level of individual firms andfunds.

Table 1Granger Causality Tests for Persistence inSecurity ReturnsJuly 1985 to December 1996

Independent (Causing)Variables

Dependent (Caused)Variables

Rsp500 Rus Rbills

Returns on the S&P 500(Rsp500)

8.33 4.64 6.34(.14) (.46) (.27)

Returns on Long-TermU.S. Treasury Bonds (Rus)

6.52 4.34 13.70(.26) (.50) (.02)

Returns on One-YearU.S. Treasury Bills (Rbills)

6.94 2.49 256.64(.22) (.78) (.00)

Test statistics are derived from a 7-equation VAR for net new money andsecurity returns, with a 5-month lag structure. Monthly dummy variablesand a dummy variable for September–November 1987 were included.The sample period was July 1985 to December 1996. The numbers ineach cell are Chi-square statistics for the null hypothesis that the causalvariable(s) in each row do not Granger-cause the “caused” variables ineach column. A high Chi-square statistic leads to rejection of that hypoth-esis in favor of the alternative hypothesis, that there is a causal effect. Thenumbers in parentheses are significance levels for the Chi-square statis-tic; a level less than 0.05 indicates statistical significance. Bold-facednumbers indicate statistical significance.


Are Mutual Fund Flows Affected byReturns on Stocks and Bonds?

Table 2 reports the results of our Granger testsfor net new money and realized returns on the S&P500, long-term U.S. government bonds, and one-year Treasury bills. The cells at the bottom left ofTable 2 indicate that the history of each return, andof other returns as well, is relevant in explainingmutual fund flows. For example, the test of thehypothesis that changes in Rsp500 do not Granger-cause fund flows is sharply rejected for each of thefour types of funds. The Treasury bond return, Rus,Granger-causes flows into money market, bond, andbond & equity funds, but not into equity funds. Billreturns Granger-cause flows into money market andbond & equity funds. The results provide strongsupport for the basic portfolio choice assumptionthat realized security returns affect subsequent se-curity purchases, and are in strong contrast with theconclusions of Warther, Remolona et al., and Potter,that flows do not appear to be affected by pastsecurity returns.

Table 3 reports the results of Granger tests for

redemptions instead of net new money. The resultsare consistent with those for net new money, provid-ing strong evidence that rates of return affect redemp-tions, even after lags of several months. There is alsoevidence that bond and bond & equity fund redemp-tions “cause” returns on bonds and on stocks, al-though no support is shown for the view that equityfund redemptions affect subsequent stock or bondreturns.

Do Fund Flows Influence Security Returns?

As noted above, previous studies have found noevidence that mutual fund flows play a role in deter-mining security returns. However, the cells in theupper right-hand section of Table 2 suggest somesupport for the “reverse causation” view: Moneymarket fund flows are significant predictors of Trea-sury bill returns, bond fund flows play a statisticallysignificant role in predicting returns on all threesecurities, and bond & equity fund flows Granger-cause returns on equities and on Treasury bills (but notTreasury bonds).

While net new money flows into debt-type funds

Table 2Granger Causality Tests for Net New Money and Rates of ReturnJuly 1985 to December 1996

Independent (Causing) Variables

Dependent (Caused) Variables

Net New Money at Mutual Funds Rates of Return

MMF Bonds Bond & Equity Equity Rsp500 Rus Rbills

Net New Money at Mutual FundsMMF 9.00 2.19 1272.05

(.11) (.82) (.00)

Bond 10.75 11.57 13.46(.05) (.04) (.02)

Bond & Equity 12.31 5.03 10.74(.03) (.41) (.05)

Equity 7.87 1.76 30.99(.16) (.88) (.00)

Rates of ReturnRsp500 30.71 19.64 17.21 12.72

(.00) (.00) (.00) (.03)

Rus 37.03 16.94 13.46 7.28(.00) (.00) (.02) (.20)

Rbills 22.49 8.12 18.86 7.06(.00) (.15) (.00) (.22)

Note: See note to Table 1. A 5-month lag length was used for the net new money-security returns relationship. This was selected by the Schwartz criterionfor lag-length selection.


appear to Granger-cause returns on debt securities,equity fund flows do not Granger-cause returns oneither equities or bonds. The reverse-causation storyfails only in the case of equity funds, a result consis-tent with the work both of Potter and of Remolona,Kleiman, and Gruenstein. It is worth noting (see Table3) that redemptions show a stronger case for reversecausation from redemptions to stock and bond re-turns, but there is still no evidence of reverse causa-tion for equity fund redemptions.

Why Are This Study’s Results Different?

We find very strong evidence for forward causa-tion, from security returns to fund flows, as well asstrong evidence, especially at debt-type funds, forreverse causation, from fund flows to security re-turns. These results are very different from thosereported by Warther and by Remolona et al. Allthree studies use the Investment Company Insti-tute’s monthly data, but with different sample peri-ods and with different aggregations of mutualfunds. If these are the reasons for disagreement, wemust conclude that relatively small changes in data

definitions might have a large impact on the conclu-sions.

Other differences are, perhaps, more important.First, as noted above, we estimate an unrestrictedVAR, while the other two studies use a restricted VARin which arbitrary restrictions are placed on someparameters of the model, restrictions that might sig-nificantly alter the conclusions. Second, we includereturns on several different securities as predictors ofmutual fund flows, so our hypothesis tests are tests ofthe effect of relative rates of return on flows. Economictheory suggests that relative rates of return determinethe allocation of financial flows, but Warther uses onlyown-returns, and Remolona et al. use own-security re-turns and only one other-return, as predictors of flows.

Finally, we use realized returns rather than ameasure of expected returns (yield to maturity). Thismeans that we are not attempting to decompose ob-served returns into their expected or unexpected com-ponents. While investors do make an effort to estimateexpected returns, the available data do not tell ushow that is done, and attempts to model the forecast-ing process will necessarily introduce errors in ourestimates.

Table 3Granger Causality Tests for Redemptions and Rates of ReturnJuly 1985 to December 1996

Independent (Causing) Variables

Dependent (Caused) Variables

Redemptions at Mutual Funds Rates of Return

MMF Bonds Bond & Equity Equity Rsp500 Rus Rbills

Redemptions at Mutual FundsMMF 12.53 11.63 1255.32

(.08) (.11) (.00)

Bond 27.30 14.79 16.10(.00) (.04) (.02)

Bond & Equity 14.79 14.72 9.65(.04) (.04) (.21)

Equity 6.68 5.05 8.73(.46) (.65) (.27)

Rates of ReturnRsp500 18.10 25.16 9.55 23.80

(.01) (.00) (.22) (.01)

Rus 13.51 14.36 6.47 12.14(.06) (.05) (.49) (.10)

Rbills 7.87 25.88 6.54 21.95(.34) (.00) (.49) (.00)

Note: See note to Table 1. A 7-month lag length was used for the redemptions-security returns relationship. This was selected by the Schwartz criterion forlag-length selection.


IV. How Important Is the SecurityReturn–Fund Flow Interaction?

We have found evidence that security returnshave statistically significant subsequent effects on netnew money and redemptions at each type of mutualfund, and that some fund flows, particularly at bondand bond & equity funds, have statistically significantsubsequent effects on some security returns. Thistwo-way causation with lags defines a feedback mech-anism. But is the feedback of economic as well as ofstatistical significance? Does it magnify a temporarydeparture of variables from a long-run equilibriuminto a prolonged period of financial market volatility?

In order to assess that question we have estimatedthe dynamic multipliers associated with our seven-equation model. These multipliers are embedded inthe VAR’s “impulse response functions” (see Box 4),each showing the effect of a temporary shock to one of

the seven variables on the values of each of the sevenvariables. In order to adjust for differences in measure-ment units, each shock is measured as a temporaryincrease in the variable by one standard deviation,maintained for only one month. The impulse responsefunction shows the subsequent effects on each of theseven variables, each measured relative to the standarddeviation of that variable.9 Thus, the impulse responsefunction shows the number of standard deviations bywhich a variable changes following a temporary one-standard-deviation shock to a driving variable.

9 The VAR system has been transformed so that shocks areorthogonal. The standard deviations of the orthogonalized shocksare used to standardize the values of responses in each variable. Thestandard deviations of these shocks are as follows: one-year Trea-sury bill rate, 0.38 percent; long-term Treasury bond rate, 25.97percent; S&P 500 return, 38.04 percent; MMF flows, 10.23 percent;BOND flows, 5.38 percent; EQUITY flows, 4.14 percent. All returnsand flows are measured at annual rates.

Box 4: Impulse Response Functions

The response of each endogenous variable to aone-time shock in any variable can be evaluated byrewriting the Vector Autoregression model (equa-tion 3.2 in Box 3) in its Moving Average Represen-tation. When Y is covariance stationary, the VARmodel (equation 3.2 in Box 3), after repeated sub-stitution to solve for Yt as a linear function of pastvalues of the surprise, et, gives the following con-vergent series of infinite length:

(4.1) Yt 5 et 1 C1et21 1 C2et22 1 . . . 1 Cpet2p 1 . . . ,

with E(e) 5 0 and E(ee’) 5 (

in which the matrices Cj (j 5 1, . . . , `) are formedfrom the matrices Bi (i 5 1, . . . , p). The impulseresponse function traces out the values of Yt1s/et(s 5 1, . . . , `); that is, of the effect of a one-time shockto Y at time t on the future values of Y. Thus, aone-time shock of De to the elements of Y will changeY by DYt 5 De in the same period, by DYt11 5 C1Dein the next period, by DYt12 5 C2De in the secondperiod, and so on. Estimates of the parameters in theB matrices can be obtained by Ordinary Least Squaresestimation of the VAR in equation 3.2 of Box 3, andthe matrices Cj can be formed from those estimates.

It is often convenient to express the shocks andresponses in units of standard deviations ratherthan in raw values. If each element in DYt1k is

divided by the respective standard deviation of thatendogenous variable, and the shock vector De isalso divided by the standard error of the respectivesurprises, a standardized impulse response functioncan be traced out. This shows the number of stan-dard deviations by which each endogenous vari-able changes when there is a one-standard-devia-tion shock in an element of e.

Some researchers are concerned that the shocksto the endogenous variables, measured as the errorvector et, are correlated. For example, if GrossDomestic Product and an interest rate are two of theendogenous variables, one should expect that ashock affecting one will also affect the other. Thisshows up as ( being a nondiagonal matrix, mean-ing that a shock to one equation affects otherequations. To correct for this, these researchers willtransform the original VAR model so that all equa-tion errors are orthogonal, then compute the or-thogonalized impulse response function. To do this,they estimate the VAR, and compute its errorcovariance matrix (. Using sophisticated methods,they transform the system so that the new errorvector, call it ut, has a diagonal covariance matrix, thatis, each transformed equation’s error is independentof every other transformed equations error. They thencalculate the values of Yt1s/ut (s 5 1, . . . , `); theseform the orthogonalized impulse response function.


There are 49 different impulse response functionsfor our seven-equation VAR, seven for each variable.Rather than stupefy the reader with a tedious reporton each of those 49 dynamic responses, we focus onthose central to the concerns about stock marketvolatility and fund flows. We assume a shock in theform of an absolute decrease of Rsp500 by 2.70 stan-dard deviations, about the size of the October 1987stock market break. Because the standard deviation ofRsp500 is 38.04 percent, this translates to a value ofabout 2103 percent.10

Figures 5a and 5b show the responses of securityreturns and mutual fund flows to this shock over thesubsequent 24 months. In the months following thestock break, returns on long-term securities (bondsand stocks) are slightly above normal. This reflects anabove-normal increase in security prices following astock market break. The return on Treasury bills isreduced during the six months after the break. Notethat our persistence tests (see Table 1) indicate that thesubsequent deviations of bill, bond, and stock returnsfrom their normal values are not statistically different

from zero. Thus, after a sharp stock market break, bill,bond, and stock returns rapidly go back to normallevels.

Figure 5b shows that a stock market break has along-lived effect on mutual fund flows, particularly onnet new money flowing into bond funds. The imme-diate effect of the decline in stock prices is to inducenet outflows at equity funds and net inflows at bothmoney market funds and bond funds—a sign of aflight to quality. While bond fund inflows remainabove normal throughout most of the 24 months,slowly returning to normal, equity fund flows remainslightly below normal for almost a year, and moneymarket funds rapidly return to normal flows.

While our VAR model does indicate that an initialdisturbance to stock prices sets off a cycle in fundflows and, perhaps, in security returns, there is noindication of a destabilizing feedback. Both returnsand flows eventually return to normal levels, returnsmore quickly than flows. We find no evidence thateven an October 1987-size shock initiates a protractedperiod of strong cyclical responses.

The effect of shocks to equity and bond fundflows on security returns are shown in Figures 6 and 7.Each of these shocks is a one-standard-deviation in-crease in the net new money flowing into the mutual

10 The return data are monthly values expressed at annualrates, so a 10 percent decline in one month is a 2120 percent returnat an annual rate.


fund. In both cases, a temporary increase in fundinflows has no long-term effects on bond or stockreturns, but it does reduce Treasury bill returns in thelong run. A shock to equity fund flows raises the billrate in the short run, presumably because the fundsare being transferred from money market mutualfunds, but a shock to bond funds reduces bill rates inthe short run as well as in the long run.

The impulse response functions charted in Figure6 suggest that the subsequent responses of stockreturns to a shock in equity fund flows is that aone-standard-deviation increase in equity flowschanges stock returns by the largest amount (about 0.1standard deviation) in the first and fourth subsequentmonths. If we compute the responses using actualrather than standardized values, a rise in equity fundinflows by an annual rate of about 4 percent of netassets will have the maximum effect of changing stockreturns by an annual rate of about 3.8 percent, roughlya 1-to-1 effect. This is a short-term effect of someeconomic significance (although, as we have seen, ofdubious statistical significance). It is interesting to notethat a shock to bond fund flows has as large an effecton stock returns as does a shock to equity fund flows:The largest change in stock returns after a 5.4 percent

bond fund flow shock is about 5.7 percent. Once again,the maximum response is about 1-to-1.

V. Summary and Conclusions

Prior to this study, the evidence on the interactionof mutual fund flows and rates of return suggestedlittle connection. While strong evidence had beenfound for a positive contemporaneous correlation be-tween fund flows and own-security returns, there wasno evidence of a persistence in the relationship overtime; that is, flows into mutual funds did not appear tobe influenced by past values of the return on own-securities. Neither did returns on securities appear tobe related to past values of flows into the mutualfunds holding that type of security. In short, anydisturbance to financial market equilibrium that af-fected security returns and mutual fund flows ap-peared to create a new equilibrium quickly, leaving nodynamic effects for subsequent periods.

The contemporaneous correlation between secu-rity returns and mutual fund flows is consistent withseveral hypotheses. The first is that a fundamentalassumption of financial theory is valid: The demand


for a security is a decreasing function of the returnrequired by investors. According to this postulate, adecline in required returns on, say, common stock willstimulate demand, driving stock prices and equityfund flows up, and raising the realized return on thesecurity.

A second hypothesis consistent with a contempo-raneous correlation between fund flows and own-returns is that investors include momentum amongtheir criteria for selecting asset allocations. Good per-formance is expected to be followed quickly by goodperformance, bad performance by bad, so that whensecurity prices (and realized returns) rise, investorsbuy in anticipation of further increases, driving pricesup further. The momentum hypothesis implies a de-stabilizing behavior by investors.

A third hypothesis is that increases in flows into amutual fund will drive up prices of its securities. Thismight be explained as the result of price pressure—ifequity funds have more money to invest, they mustinvest it and doing so will push stock prices up. Itmight also be explained by information transmis-sion—if equity fund investors are particularly savvy,increased purchases of equity funds reveal to otherinvestors that common stocks are a good buy, induc-ing that result.

Previous studies have also investigated the pos-sibility of a feedback mechanism in the dynamics ofthe interaction between mutual fund flows and secu-rity returns. Recently, concerns have been raised aboutthe role mutual funds might play in transmitting, andperhaps aggravating, financial shocks. The snowballscenario is that a shock to stock prices, say a break inthe market on the order of the October 1987 experi-ence, might induce redemption of shares at equitymutual funds. This, in turn, might lead equity fundmanagers to sell shares, driving prices down furtherand inducing more redemptions, ad infinitum. Thisfeedback mechanism might lead to an exaggeration inthe fluctuations of prices and flows following a shock,with eventual return to an equilibrium, or it mightinduce an instability in which prices decline for aprolonged period.

Previous studies have found scant support forthis scenario. First, several studies have failed to findevidence that mutual fund flows are affected bylagged security prices, so the first step of the feedbackis lost—a decline in stock prices affects this month’sfund inflows (the contemporaneous effect citedabove), but it does not affect fund inflows in futuremonths. Furthermore, no evidence has been foundthat security prices in one period are affected by

mutual fund flows in previous periods, so the secondstep of the feedback is lost. In short, the currentorthodoxy is that when financial market shocks occur,they quickly get resolved through changes in pricesand flows, with no persistent subsequent effects onprices and flows.

Clearly, security returns have acontemporaneous and direct effect

on fund flows, so momentumtrading might be a short-runphenomenon, but we find no

persistence in security returns,so the rationale for momentum

trading over a longer periodfinds no support.

This study reaches a less comforting conclusion,but it does not refute the ultimate conclusions of theprevious studies. We find that a feedback exists—security returns do affect future fund flows, and somefund flows do affect future security returns. In partic-ular, we find that returns on long-term Treasurybonds and on the S&P 500 are statistically significantpredictors of flows of net new money into bond funds,bond & equity funds, and equity funds. In each casethe own-security return is statistically significant, andin most cases the other-security return is also statisti-cally significant. In short, disturbances to securityreturns do have repercussions on future fund flows aswell as on current flows.

We also find evidence supporting a reversecausation, though it is less strong. Past flows intobond funds are statistically significant predictors ofthe returns on long-term bonds and on stocks, andflows into bond & equity funds are significantpredictors of equity returns. However, like previousstudies, we find no evidence that past flows intoequity funds shape current returns on either stocksor bonds. Thus, we find no direct effect of equityfund flows on future common stock returns. Thisdoes not mean that there are no effects of equityflows on stock returns; these effects might be indi-rect, operating through a disturbance in equity


flows on (say) Treasury bill returns, thence on toother returns and flows and, finally, on to commonstock returns.

Our conclusions with regard to momentum in-vesting are agnostic. Clearly, security returns have acontemporaneous and direct effect on fund flows, somomentum trading might be a short-run phenome-

non. But we find no persistence in security returns—shocks to, say, stock returns do not imply furtherchanges in stock returns, so the rationale for mo-mentum trading over a longer period finds nosupport. Thus, if momentum trading does exist, itappears to be ephemeral and not the source ofsnowball effects.

References

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Hamilton, James D. 1994. Time Series Analysis. Princeton, NJ: Prince-ton University Press.

Hendricks, Daryll, Jayendu Patel, and Richard Zeckhauser. 1993.“Hot Hands in Mutual Funds: Short-Run Persistence of RelativePerformance, 1974–88.” Journal of Finance, vol. XLVIII, no. 1,March, pp. 93–130.

Investment Company Institute. 1996a. Mutual Fund Fact Book. Wash-ington, DC.

———. 1996b. Mutual Fund Shareholders: The People Behind theGrowth. Washington, DC.

Marcis, Richard et al. 1995. “Mutual Fund Shareholder Response toMarket Disruptions,” Perspective, Investment Company Institute,Washington, DC, July.

Potter, Mark. 1996. “The Dynamic Relationship Between SecurityReturns and Mutual Fund Flows.” University of Massachu-setts-Amherst Ph.D. Dissertation chapter, mimeo, October.

Rea, John and Richard Marcis. 1996. “Mutual Fund ShareholderActivity During U.S. Stock Market Cycles.” Perspective, Invest-ment Company Institute, Washington, DC, March.

Reid, Brian and Jean Crumrine. 1997. “Retirement Plan Holdings ofMutual Funds, 1996.” Investment Company Institute, Washing-ton, DC.

Remolona, Eli, Paul Kleiman, and Debbie Gruenstein. 1997. “MarketReturns and Mutual Fund Flows.” FRBNY Economic Policy Review,Federal Reserve Bank of New York, July, pp. 33–52.

Schleifer, Andre. 1986. “Do Demand Curves for Stocks SlopeDown?” Journal of Finance, vol. XLI, no. 3, pp. 579–90.

Warther, Vincent A. 1995. “Aggregate Mutual Fund Flows andSecurity Returns.” Journal of Financial Economics, vol. 39, pp.209 –35.


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