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Market Timing, Selectivity, and Mutual Fund Performance: An Empirical InvestigationAuthor(s): Cheng-Few Lee and Shafiqur RahmanReviewed work(s):Source: The Journal of Business, Vol. 63, No. 2 (Apr., 1990), pp. 261-278Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/2353219.

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Cheng-few LeeRutgers University

Shafiqur RahmanPortland State University

Market Timing, Selectivity, andMutual Fund Performance: AnEmpirical Investigation*I. IntroductionThe investment performance of mutual fundmanagershas been extensively examinedin thefinance literature. Most of these studies em-ployed a method developed by Jensen (1968,1969) and later refined by Black, Jensen, andScholes (1972) and Blume and Friend (1973).Such a methodcomparesa particularmanager'sperformancewith that of a benchmark indexfund. Such investigations assume that the risklevel of the portfoliounderconsideration s sta-tionarythroughtime, and they exclusively con-centrateon a fund manager'ssecurity selectionskills or lackthereof. Oneweakness of the aboveapproachis that it fails to separatethe aggres-siveness of a fund manager from the qualityof the informationhe possesses. It is apparentthat superiorperformanceof a mutual undman-ager occurs because of his abilityto time themarket(market iming)and/orhis abilityto fore-cast the returns on individualassets (selectionability).Indeed,portfoliomanagersoftencharac-

This article empiricallyexamines market tim-ing and selectivity per-formance of a sampleof mutual funds. Ituses a very simple re-gression technique toseparate stock selec-tion ability from timingability. This technique,first suggested by Trey-nor and Mazuy andlater refined by Bhat-tacharya andPfleiderer, uses amodified security-mar-ket line approach toproduce individualmeasures of timing andstock selection ability.The inputs to themodel are only the re-turns earned on thefund and those earnedon the market port-folio. The empirical re-sults indicate that atthe individual fundlevel there is some evi-dence of superior mi-cro- and macrofore-casting ability on thepart of the fund man-ager.

* We appreciate an anonymous reviewer's helpful com-ments and valuable suggestions, which have added signifi-cantly to the clarity of presentation in this article. We alsoappreciate editor Albert Madansky's encouragement whilewe were revising the article. We thank Michael Gibbons forproviding us with the mutual funds data base and JanetHamilton and John Settle for helpful discussions and com-ments.(Journal of Business, 1990, vol. 63, no. 2)? 1990 by The University of Chicago. All rights reserved.0021-9398/90/6302-0006$01.50

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262 Journal of Businessterizethemselves as market imersand/or stock pickers.Jensen(1968)acknowledged he ability of the fundmanagers o changethe risklevelof theirportfolios.Indeed, the portfoliomanagersmayshift the overallrisk composition of their portfolios in anticipationof broad market-price movements. Fama(1972) andJensen (1972) addressedthis issueand suggesteda somewhatfinerbreakdownof performance.The purpose of this article is to examine empirically the markettimingand selectivity performanceof a sample of mutualfunds. Sec-tion II discusses two components of investmentperformance.SectionIII discusses various attempts to model these two components andrelevant empirical works to date. Section IV reports results of ourempiricalwork. Section V concludes the article.II. Identifying Timing and Selection AbilityFama(1972)suggestedthatportfoliomanagers' orecastingskillscouldbe partitioned into two distinct components: (1) forecasts of pricemovements of selected individualstocks (i.e., microforecasting); nd(2) forecasts of pricemovements of the generalstockmarketas a whole(i.e., macroforecasting).The formeris knownas security analysiswhile the latter s called market iming. Thispartitioning f forecast-ingskills is also evident in TreynorandBlack(1973),who have shownthatportfoliomanagerscaneffectivelyseparateactions related o secu-rity analysis from those related to markettiming.Microforecasting,or security analysis, involves the identificationofindividualstocks that are under- or overvaluedrelative to equities ingeneral. Within the specification of the capital asset pricing model(CAPM),a microforecasterattemptsto identify securities whose ex-pected returns ie significantlyoff the security market ine. Specifically,the microforecasterwouldonly forecastthe nonsystematicor security-specificcomponentof securityreturn.FollowingJensen(1972, p. 132),the excess returnon a portfolio can be writtenas

RP= f3P Rm + et, (1)whereRPPs the excess (net of risk-freerate) returnon pth portfolio,Rmis the excess (net of risk-freerate) returnon the marketportfolio, P3measuresthe sensitivity of the portfolioreturn o the marketreturnandetP is a random error, which has expected value of zero. Within thisframework, microforecastaboutpth portfoliowould involve concen-tratingon et. If the portfolio manager s a superior orecaster(perhapsbecause of special knowledgenot available to others) he will tend toselect securities thatrealizeJP > 0. Hence his portfoliowill earnmorethan the normal risk premiumfor its level of risk. Allowance forsuch forecasting ability can be made by simply not constraining heestimatingregression to pass through he origin. Thatis, we allow for



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Market Timing 263the possible existence of a nonzero constant in equation(1) as follows:

RP = otP + P Rm + 0P (2)The new errorterm, tv', will now have expected value of zero. Thus ifthe portfolio manager has an ability to forecast security prices, theinterceptoWn equation (2) will be positive. On the one hand, a passivestrategy(randombuy-and-holdpolicy) can be expected to yield a zerointercept. On the other hand, if the manager s not doing as well as arandom election buy-and-holdpolicy, &' will be negative. Such resultsmay very well be due to the generationof too many expenses in unsuc-cessful forecastingattempts. Macroforecasting r market imingrefersto forecasts of future realizations of the market portfolio. A mac-roforecasterwill attemptto capitalize on any expectation he may haveregarding he behavior of the market return n the next period. If themanagerbelieves he can make better than averageforecasts of marketreturns, he will adjust his portfolio risk level in anticipationof marketmovements.If successful, he will earn abnormalreturnsrelativeto anappropriate enchmark.For example, if, on the one hand,the manager(correctly)perceivesthatthere is a high probability hat marketreturnswill be up next period, he will be able to increase the return on hisportfolioby increasing ts risk. On the other hand, if the marketreturnis expected to be down next period, he can reduce the losses on theportfolioby reducing he risk level of the portfolio. Indeed,the markettimerswitches from more risky to less risky securities(or vice versa)inan attemptto outguess the movementof the market.We can allowforthe existence of timingability in equation(2) by permitting he sensitiv-ity coefficient(3P) to be stochastic. Market-timing bilitywill be pres-ent where 3 and R, are positively correlated.III. A Model of Market Timing and SelectivityIt is important hat fund managersbe evaluated by both selection abil-ity and market-timingkill. Accordingly,it is necessary to model tim-ing and selectivity simultaneously.Jensen (1968)demonstrated hat, inthe presenceof market-timing bility,the estimatedriskparameter3P)inequation (2)willbe biased downwardand theestimatedperformancemeasure(&x)will be biasedupward.Grant(1977) explainedhow mar-ket-timingactions will affect the results of empiricaltests that focusonly on microforecasting kills. He showed that market-timing bilitywill cause the regressionestimate of of'in equation(2) to be downwardbiased.'

1. Grant (1977) showed that, given Jensen's (1968) assumptions, the least-squaresestimator of PPis an upward-biased estimate of the expected value of PP, and thereforehis performance measure represents downward-biased, not upward-biased, estimates ofperformance. See Grant (1977, p. 843) for details.



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264 Journal of Business

Treynorand Mazuy (1966)added a quadratic ermto equation(2) totest for market-timing bility. In the standardCAPMregressionequa-tion, a portfolio's return is a linear function of the market return.However, the authors argue that if the managercan forecast marketreturns,he will hold a greaterproportionof the marketportfoliowhenthe return on the market is high and a smaller proportionwhen thereturnon the market s low. Thus, the portfolioreturnwill be a convexfunction of the market return. Using annualreturnsfor 57 open-endmutual unds, they find that the hypothesis of no market-timing bilitycan be rejectedwith 95% confidence for only one of the funds.Jensen (1972) developed theoretical structures or the evaluation ofmicro- andmacroforecastingperformanceof fundmanagerswhere thebasis for evaluationis a comparisonof the ex post performanceof themanager's und with the returnson the market.Jensen defined r, to beR- - E(Rm),where E(R' ) s the expected value of RA nconditionalupon any special informationand fr* is the expected valueof rr, ondi-tional upon t,, the information set available to the managerat thebeginningof the period. Assume that the portfoliois managed n theinterest of a group of investors who have constantabsoluteriskaver-sion of anunknowndegree.Given the objectiveof the managerandtheassumptionthat the conditional distributionof ftt is normal,Jensenshowed that

Pt _3 ft*, (3)wheref3Ps the targetbeta of the fund and 0 measures he manager'response to his information.Above, and in the sequel, we place a timesubscriptupon PPas the value is assumed to changeover time. If theinvestors in whose interestthe fund is being managedhave a coefficientof absolute risk aversion equal to a, 0 will equal 1/[a var(f,/rt/)] and PTwill equal 0 E(Rm) see Bhattacharyaand Pfleiderer1983, p. 8). In theJensen analysis, the market timer is assumed to forecast the actualreturnon the market,and the forecasted returnand the actualreturnonthe marketare assumed to have a joint normal distribution.Jensenshows that, underthese assumptions,a market imer'sforecastingabil-ity can be measured by the correlation between the market timer'sforecast and the realized return on the market(see Jensen 1972, pp.317-18; Treynorand Black 1973).Jensen writes for anoptimal orecast

,t =- t + v, (4)and assumes thatii, is normallydistributedand independentof frt.He then writes equation (2) as

RP== otP + [P3P + O(fTt + V )][E(Rm) + ftt] + UP. (5)



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Market Timing 265Considerthe regression of RP7 n a constant, fTt, and iTt:

RP = no + lt + t+U (6)Jensen (1972) claims thatplim ' = oP + Pr-E(Rm) + O(p2_ 1)U2, (7)plim p = p2 OE(Rm) + m39 (8)andplim = 0 (9)

where p is the correlationbetween the predictionand the realizationofftt and a2 is the variance of frt. This system has more unknowns thannumberof equations. Jensen concludedthat, under the above struc-ture, separatecontributionsof micro-and macroforecasting an not beidentifiedunless, for eachperiod,the market iming orecastandE(Rm)are known.Merton(1981)and Henrikssonand Merton(1981)have attempted oovercomesome of the problemscausedby lackof a preciseestimateofE(Rm).Their model differs from the Jensen (1972)formulation n thattheir forecastersfollow a more qualitativeapproach o market iming.Namely, the market timer forecasts either that stocks outperformbonds or vice versa. The forecasters in this model are less sophis-ticated than those of Jensen (1972),where they do forecasthow muchbetter the superiorinvestment will perform.They assume that man-agers have a coarse informationstructure n which dichotomoussig-nals are only predictiveof the sign of the excess returnof the marketrelativeto the risk-freerate.In theirmodel, theprobabilityof receivingan up or a down signal in no way depends upon how far themarketwill be up or down. Changand Lewellen(1984)and Hen-riksson (1984) employed the Merton-Henrikssonmodel in evaluatingmutualfund performanceandfound no evidence of markettiming byfundmanagers.Bhattacharyaand Pfleiderer(1983) extended the work of Jensen(1972).By correctingan error made in Jensen (1972),they show thatone can use a simpleregressiontechniqueto obtainaccuratemeasuresof timingand selection ability.2The authorsassume that the manager

2. In deriving the probability limits of i0, I, and i2, Jensen implicitly assumed inde-pendence between fr, and i,. This is not true. Since frt*and fr, are jointly normallydistributed, it is possible to write=do* + d*** + i,*

where v,* is normally distributed and independent of frT*.f -ft* s the optimal forecast,do*= 0 and dt = 1. However, if we write= do + dlf, + v,,

we cannot have doand d, equaling zero and unity, respectively, and v3, ndependent of fr,.



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observes at the beginningof period t a signal, ftt + it, where it is amean-zeronormaldeviate that is independentof ftt. It is easy to showthat the optimal forecast iS3= 1i= frt + t) (10)

where= 2/ + , (11)

and u2 iS the varianceof t. Using equation(10) and the relationshipsmentionedearlier,that rP = 0 E(Rm) and ftt = R - E(Rm), we canrewriteequation (2) asRP = o&P+ 0{E(Rm) + it,[R7m E(Rm) + it]}(R7m)+ O. (12)Rearranging,we get

RP = oxP + OE(Rm)(1 - iJ,)R7m+ 40(R7)2 + OitR7m + a, (13)and

t= no + TjRR + mR7)2 + Co' (14)The relationship n equation(14)is similar o one suggestedby TreynorandMazuy(1966)andis in terms of observablevariables.If we run the

3. We want to set ij to minimize he varianceof the forecast error:minE[iTt (4fTt+ it)]2

orminE[VT2 2*tt4(*, + it) + %i2(iTt it)2],

or minE(-fr2 2IfT2i - 2*titt + qp2rT2+ 22,fTt,t + p2i2).'pSince E(tr,) = E(i,) = E(frttt) = 0, we have

minE(*2 - 2ft2q + t2ft2 + 4 20,or

minE[(1 - )2-2 + q2],or

min (1 - 4t,)2Ur2 + p2(f2The first-order ondition s

-2(1 - 't0f + 24iu2 = 0,' = =2/(cr + oE).



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Market Timing 267quadraticregression given by equation (14), the large-samplecoef-ficientestimates are

plim o14 (15)plim OOE(Rm)(I- i), (16)

andplim i2 = 04u. (17)

The above regressionallows us to detect the existence of stock selec-tion ability as revealed by o&P.Now consider the disturbance erminequation (14):

co, = Og,tRt + atP* (18)The first term in Co' ontains the informationneeded to quantifythemanager's imingability.We can extractthis informationby regressing((),t)2 o Rm)2:t) on

(.),)2 = 024v2a2 (Rtm)2 + Zt, (19)where

02=2(R)2(i2 _ U2) + (atp)2 + 20R,miteUP (20)The proposed regression produces a consistent estimatorof O22EA2.Using the consistent estimatorof 04u,whichwe recoverfromequation(14),we obtaino2 . This, coupledwith knowledgeabouto2, allowsus toestimate a2 /(I(2 + or) = p2. Finally, we calculatep, whichtrulymeasuresthe qualityof the manager'stiminginformation.4

4. We will ignore the negative correlation. Bhattacharya and Pfleiderer (1983) arguedthat negative correlation between the prediction and the realization of fr,would implythat the fund manager possessed timing information that had positive value but that themanager was misguided by its application. Another manager would do well to takepositions opposite of those taken by the misguided manager. We rule out the possibilitythat there exist managers who are both well informed and foolish. Admati et al. (1986)extended the work of Bhattacharya and Pfleiderer (1983). They offer two basic modelingapproaches to identify timing and selectivity-the factor approach and the portfolioapproach. The portfolio approach is simply a generalization of the Bhattacharya andPfleiderer (1983) model. In the factor approach, a factor-generating process is postulatedfor asset returns, and timing and selectivity information are interpreted in terms of theirstatistical relation to the factors and to the idiosyncratic terms in the generating process,respectively. It is possible to recover the appropriate measures of the quality of both thetiming and selectivity information. In this approach, it is not necessary to assume anyparticular asset-pricing model to identify the information quality of a manager. However,because of the larger number of interactions between information signals and assetreturns, this approach requires an extremely large number of regressors in the estimationequation and, most likely, this exceeds the number of time-series observations obtain-able for any fund. For this reason, estimation of the quality parameters of the timing andselectivity information seems to be possible only when the number of time-series obser-



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268 Journal of BusinessIt should be noted that the procedure discussed above does notproduce the most efficient estimates of the parameters since the distur-

bance term in equations (14) and (19) are heteroscedastic. Moreefficient estimates can be obtained by taking into account the hetero-scedasticity of the disturbance terms.IV. Empirical ResultsTo detect selection ability and market-timing ability of a mutual fundmanager, monthly returns for 87 months (January 1977-March 1984)for a sample of 93 mutual funds were used. A list of funds in thesample, including the objective of the individual funds, is presented inthe Appendix. The monthly rate of return on the Center for Research inSecurity Prices (CRSP) value-weighted index (including dividends)was used for market return. Monthly observations of the 91-day Trea-sury bill rate was used as a proxy for the risk-free rate. All returns aremeasured as continuously compounded rates of return. To detect thequality of the manager's timing information, we need an estimate of thevariance of *,. Merton (1980) presented a simple technique of estimat-ing the variance of ft, from the available time series of realized returnon the market under the assumption that ft, follows a stationary Wienerprocess. The advantage of this estimator is that the variance can beestimated without knowing, or even having an estimate of, the mean. Italso, of course, saves one degree of freedom. A reasonable estimate ofr92 was derived as follows: n

Um= [ln(1 + R )]2j/n. (21)Because the estimator for o2 is not taken around the sample mean, &r2will be biased. However, for large n, the difference between the secondvationsis impracticallyarge.Although he factorapproachhas conceptualadvantagesover the portfolioapproach,identificationof informationquality is easier undertheportfolioapproach hanit is underthe factorapproach.The work of Bhattacharya ndPfleiderer 1983)has been conducted n the context of a modelwithprivate nformationwhere equilibrium s determinedaccordingto the CAPM that assumes homogeneousbeliefs. Suchanalysis mplicitlyassumes thatfundmanagers,whomightnot sharethesehomogeneousbeliefs, do not effect equilibrium.Admatiand Ross (1985)argued hat thisis somewhatdisturbing ince there is no reason to believe either that the bulk of themarkethasthe same beliefs or thatthecombinedeffectof managedportfolioson equilib-rium is zero. In contrast, they developed a model that includes many agents withheterogeneous and asymmetricinformation.These agents are perfectlyrationalandoptimallyuse all the informationavailableto them, includingprices. Their model is anoisy rational-expectationsquilibrium apital asset pricingmodel. Undersome condi-tions, theBhattacharya ndPfleiderer1983)modelcanbe treatedas a specialcase of theAdmatiand Ross (1985)specification.However, the Admatiand Ross (1985)analysis sstillpreliminary.To developa completestatisticalmodelthat s consistentwith observa-tionof a time series, a multiperiodmodelis required, rom whichthe propertiesof suchtime series can be derived. This is a difficult ask, especiallyin the contextof rational-expectationsequilibriummodels.



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Market Timing 269'2centralandnoncentralmoments is trivial. In our case, U7r s estimatedin equation (21) was .0018633, while the sample variance of frt was

.0018444.In order to obtain efficient estimates of parameters,a generalizedleast squares (GLS) procedure, with correction or heteroscedasticity,is used. The correctionfor heteroscedasticity s of the following form.We first derive the variance of the error terms in equations (14) and(19). These are2= 2qj2 2u(R m)2 + o2 (22)

andr2 = 204q]4(Rm)4cr4+ 2cr4+ 402qJ2ur2(Rj)2ur2 (23)

where cr2, cr, and cr2are variances of Co , p, and Zt, respectively.5 Topredictor2 anduo2,we need estimates of uo2andc2 . An estimateof o2 iSobtainedby using equations (14) and (19) in the mannerdescribedinSection III, while an estimate of o2 is obtainedby using equation (2).The variables in equations (14) and (19) are divided by U2 and o2,respectively, and an ordinary east squares (OLS) procedure s appliedto the transformed bservations to obtain the most efficient estimates.Table 1 presents regression results. These results show some evi-dence of selectivity and market imingat the individual undlevel. Outof 93 funds,24 funds(25.81%)have aPsignificantlydifferent romzeroat the .05 level. Fourteen of these funds (15.05%)have positive OtP.Sixteenfunds (17.2%)have p significantlydifferent romzero at the .05level. The correlationbetween otPand p is .47. This implies that thefunds do not exhibit a considerable degree of specializationin oneforecastingskill. Ten funds have both significantselection and timingskills. Four funds have significantselection skill with no timingskill

while five funds have significant timing skill with no selection skill.Table 2 presents summaryresults. For comparison,it also presentsresults obtainedwithoutcorrectionfor heteroscedasticityand resultsobtainedby usingJensen's (1968)originalspecification,which ignoresmarkettiming. Apparently, hereis some difference n the resultswithand without correctionfor heteroscedasticity.Correctionfor hetero-5. Equation(23) is derived as follows:

a [O22(R,7)2]2var(, - _3 + var[(tP)2] + (204R7')2var(i,O)= 0444(R1&)4var(2) + var[(ap)2] + 4024i2(R7&)2(o2(= 204+4 R -)4(T4 + 2T4, + 40242(R7&)2(T2(T2

Here var(i2), var[(ap)2], andvar(i,uO)have been derivedfollowingStevens(1971).Theauthor showed that the variance of the product of two random variables (x and y) is2rar(1 + p + I2(3-2 + y2(r2 +2xy PxVTVrTN

where x and y are expected values and p, is the correlation coefficient between x and y.



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270 Journal of BusinessTABLE 1 Estimated Parameters for Individual Mutual Funds

Selectivity Timing Risk ToleranceFund No. (otP) (p) (1/a)1 .000478 .020132 .4752682 .006653 .335453* .0815013 .003639* .066912 .1369404 -.001667 .022494 .3514665 -.002925 .067333 .3307546 -.001884* .169254 .0312187 .001113 .063949 .4279388 .001426 .038000 .7569429 -.003167 .170767 .05766310 -.000007 .081222 .09867911 -.002307 .095340 .27688212 -.001732 .102088 .16527413 - .003723 .074079 .29935414 .006082* .237678* .06742015 .000281 .168343 .10197016 .000320 .007486 2.78061917 - .002209 .190182 .03248618 .005322* .400737* .01915219 .002481 .274264* .03720120 .000224 .080037 .09575721 .004423* .219963* .05837322 - .003189 .123008 .08994223 .000776 .075288 .16969324 .001709 .125399 .16644125 - .007199* .147792 .06888026 .003517 .065447 .19094227 .000816 .041892 .28209128 - .006435* .026715 .54728829 .026101* .140325 .45673530 .000359 .071318 .17598731 - .005553* .226560* .05316332 .000320 .079312 .54052533 .001068 .099352 .14979234 - .004555 .104514 .14453635 - .001128 .086810 .21063536 - .001417 .049843 .41053137 - .001768 .030302 .49829738 - .004186 .164544 .10322739 - .005178 .037160 .37838540 .001900 .163631 .25196141 .001681 .097798 .30304742 .002433 .300712* .04040443 .003828 .161170 .12004644 -.000574 .059656 .31344645 .009882 .156354 .22522146 .013015* .460663* .02426547 -.000676 .040750 .18732848 - .006713* .197276 .06752249 .003260 .132463 .08309450 .001701 .075589 .15498551 - .001283 .032803 .58011252 - .001220 .024250 .48131153 - .002234 .029640 .59182154 - .004298 .044560 .34973655 - .003708 .047015 .42681956 - .002843 .016250 1.164849



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Market Timing 271

TABLE 1 (Continued)Selectivity Timing Risk ToleranceFund No. (OLP) (p) (1/a)

57 .001262 .050319 .19600258 .001998 .270515* .05664259 .011764* .227052* .06911360 - .000793 .058885 .18389461 .001997 .047408 .32191062 - .003425 .041408 .26396863 .003324 .199712 .04890964 - .006290* .158683 .06672265 - .001598 .096472 .12984366 .002601* .083389 .09124367 .007745* .271983* .07237468 - .010029* .048784 .31737869 .002687 .293644* .03017870 - .002058 .057089 .27196071 -.004360 .014077 1.35522772 .009806* .310578* .07412173 - .000085 .110481 .05427774 - .003531 .135722 .10229475 - .001547 .143489 .05544276 .000112 .151980 .05665977 - .000801 .030183 .39527078 - .007927* .019138 .60653679 - .005650* .062168 .31320380 - .001381 .037569 .49610281 - .001951 .080268 .16395882 .007862* .322760* .03814783 .013417 .156453 .48289584 - .001073 .036027 .28964385 .022220 .102765 .81011186 .008511* .255405* .08473687 .005592* .195902* .08212488 .013559* .346244* .05940289 - .004381* .196457 .02748590 - .002031 .095676 .11730691 .001323 .024031 .51718992 - .001994 .039311 .37532193 - .000512 .058520 .145089

NOTE.-Funds are identified by number in the Appendix.* Significant at the .05 level.

scedasticity significantlyaffects the conclusions. Our results are con-sistentwithBreen,Jagannathan, ndOffer(1986).The authorsshowedthat the test of market iming hat ignores heteroscedasticityrejectsthenull hypothesis of no markettimingtoo often, when, in fact, the nullhypothesis is true. Table 2 has other interestingevidence.Theestimateof cfPtends to be slightlylower when timing s ignored.This is consis-tentwith Grant's(1977)contentionthat Jensen'sperformancemeasurewill be downwardbiasedwhen timing s ignored.A similarconclusionwas drawnby Changand Lewellen (1984)and Henriksson(1984).We computed each fund's risk-tolerancecoefficient, which is the



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TABLE 2 Summary Statistics for Mutual Fund PerformanceSelectivity (oxP) Timing (p)

Model Mean Positive Negative Mean PositiveMarket timing ignored - .0005 4* 9* ... ...Market timing considered:Without correction forheteroscedasticity .0011 15* 9* .1696 28*With correction for het-eroscedasticity .0008 14* 10* .1231 16*

* Significantly ifferent rom zero at .05 level.reciprocal of the Pratt-Arrowmeasure of absolute risk aversion, a.6Since eachfundis managed or a groupof investorswitha specificrisk-tolerance coefficient, by selecting a fund, the investors provide infor-mation about their risk tolerance. The risk-tolerancecoefficient indi-cates the investor's (or fund manager's)willingnessto accept greaterriskin order to earn a greaterexpected reward.The lower (higher) herisk tolerance, the more conservative (aggressive) he asset mix. Thesecoefficients can be used to rank the funds in order of their aggres-siveness. The estimatedrisk-tolerancecoefficients (1/a) are displayedin the final column of table 1. These coefficients rangefrom .019152 o2.7806 with a sample mean of .27429. The risk-tolerance oefficientforthe individual unds can be used to ascertain the average size of riskyinvestment in the fund, that is, the asset allocation between risklessasset andriskyinvestment(marketportfolio).Theaveragesize of riskyinvestmentin the fund (as a fraction of total net assets of the fund)isgiven by

W = (Ila)[E(Rm)/2Ur2], (24)6. We thank an anonymousreviewer for suggestingthis work. The risk-tolerancecoefficient (1/a) is derived directly from f) as follows: using eq. (17) and the previouslymentioned relationship that 0 = 1a var(*r/l,), we have f l14a varQfrI4,),where a is thecoefficient of absolute risk aversion. From n. 4 above,

var(*r/4,)= (1 - o)2 + qj2 Dj2= -_ 2ij,4 + ku2u2+ q2ur2= U2- 02f + q2(U2 + a3.

Using 2= 4/(Cr2 + a.),var(*/I,) = 'T2 - 2ql'2 + q2W2q

= 'TrT-= 42(1 - Ofu)= 'r4 2/(or 2 + (re)= J(Je2

Now, substituting42for var(wr/4,)n the expressionfor -2, we have Il1a a2. Rear-ranging he termsgive 1/la - .



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Market Timing 273whereua, is the variance of marketreturn.7Table 3 presents the aver-age size of riskyinvestmentgiven by equation(24). It also presents theactual percentage of fund assets invested in risky assets (assets otherthan cash and government securities) as reported by WiesenbergerInvestment CompaniesService. The sample correlationcoefficientbe-tween averagesize and actual size is .26 witha t-statisticof 2.32. Thisis significantat the .05 level.V. ConclusionThis article discusses conceptual and econometric issues associatedwith identifying two components of mutual fund performance. Theempirical results obtained using the technique developed by Bhat-tacharyaandPfleiderer 1983) ndicate that at the individualevel thereis some evidence of superior orecastingabilityon the partof the fundmanager.Thisresult has an important mplication.Fundswithno fore-castingskillmightconsidera totally passive management trategyandjust providea diversification ervice to their shareholders.Ourresultsindicate a substantial mprovementover previous attemptsto evaluatefund managers.Kon (1983) empiricallyexaminedthe performanceofmutual funds. Of those 37 funds, 14 had overall timing estimates thatwere positive, but none was statistically significant.Recently, Connorand Korajczyk (1986) developed a method of portfolio performancemeasurementusing a competitive version of the arbitragepricingthe-ory (APT). However, they ignored any potential market timing bymanagers. Lehmann and Modest (1987) combined the APT perfor-mance evaluation method with the Treynor and Mazuy (1966) qua-

7. This derivation ollows Sharpeand Alexander 1989).The fundmanagernvests Wfractionof fund assets in marketportfolioand (1 - W)fraction n risk-freeasset. Theexpected excess return E(RP)] and varianceof return a,) on the portfolioareE(RP) = WE(h-)(i)

aD2= W2DM. (ii)Solving eq. (i) for W and substituting he resultin eq. (ii) yields

ap2 = [E(RP)E(Rm)]2(M. (iii)Equation iii) describes the functionalrelationshipbetweenthe expectedexcess returnandthe varianceof returnon the portfolio.Its slope,dE(RP)/dap = l/[dap2dE(RP)] = [E(Rm)]212E(RP)o.T, (iv)equals the slope of the indifference urve (betweenmean and variance)of the fund(andeachof its investors).For constantrisk tolerance,the latterslopeis equalto the inverseof the risk-tolerance oefficient. This implies

a = [E(Rm)]212E(RP)U7m. (v)Now, substituting he right-hand ide of eq. (i) forE(RP) in eq. (v) resultsin

a = E(Rm)12 WM. (vi)Next, solving eq. (vi) for W results in eq. (24).



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TABLE 3 Size of Risky Investment in theIndividual FundsFund No. Average (%)* Actual (%)t

1 45 952 79 973 41 854 35 925 61 866 46 927 43 878 45 959 51 9410 35 8711 28 4912 34 9113 44 8814 42 N.A.15 50 8716 49 8317 35 9218 48 9019 28 3820 38 N.A.21 49 8122 49 9423 32 N.A.24 41 7525 51 9826 56 9627 51 9028 56 N.A.29 46 8630 47 8731 52 8832 73 7833 45 7434 13 7335 18 8236 18 9037 26 8738 50 8539 48 9540 58 9541 85 9642 40 N.A.43 63 9244 20 9545 18 N.A.46 38 9647 45 9048 56 9149 41 N.A.50 30 9151 25 N.A.52 34 N.A.53 16 9454 22 9255 17 N.A.56 14 95



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Market Timing 275TABLE 3 (Continued)Fund No. Average (%)* Actual (%)t57 49 8958 65 9659 26 9060 48 9161 53 8362 44 8963 51 9664 53 9365 39 8466 44 7467 40 N.A.68 11 6969 49 9070 52 N.A.71 17 9072 28 8973 45 N.A.74 61 N.A.75 42 9476 28 7677 38 9578 28 8779 49 8680 61 8881 44 N.A.82 45 9283 87 9384 38 8185 52 N.A.86 58 9287 43 8388 73 8889 50 N.A.90 48 9491 43 9692 22 9793 36 93

NOTE.-Funds are identified by number in the Appen-dix; N.A. = not available.* Reflects value given by eq. (24).t Reflects actual fraction of fund assets invested inrisky assets (assets other than cash and government secu-rities).

draticregression technique.Theirfindingsare consistentwith our re-sults. They found statistically significantmeasured abnormaltimingand selectivity performanceby mutual unds. They also examinedtheimpactof alternative CAPMand a varietyof APT)benchmarkson theperformanceof mutualfunds. They found thatperformancemeasuresarequitesensitive to the benchmark hosen. The authors ounda largenumber of negative selectivity measures. Also, Kon (1983)and Hen-riksson (1984)found a negative correlationbetween the measures ofselectivity and timing. Jagannathan nd Korajczyk (1986) arguedthat



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276 Journal of Businesssuch results could arise fromartificialmarkettimingdue to the differ-ential leverage of the firmsin the indices and those invested in by themutual unds. They theoreticallyandempiricallydemonstratedhow tocreate a portfoliothatwould exhibitpositive(negative) imingperform-ance and negative (positive)securityselection when no true timingorselectivity exists. However, unlike the predictions n Jagannathan ndKorajczyk (1986), Lehmannand Modest (1987) found no systematicevidence that funds with large negative quadraticterms have largepositive intercepts. Specifically, they were unable to detect any sub-stantive correlationbetween intercepts and the coefficients on thesquaredterms.

AppendixTABLE Al List of Mutual FundsFund Name Objective

1. AffiliatedFund G, I2. American nvestorsFund MCG3. AmericanMutualFund G, I, S4. Axe-HoughtonFundB S, I, G5. Axe-HoughtonStock Fund G6. Bullock Fund G, I7. CanadianFund G8. CenturyShares Trust G9. ChemicalFund G10. ColonialFund G, I11. Commerce ncome Shares G, I12. CompositeBond and Stock Fund I, S, G13. CompositeFund G, I, S14. ConcordFund MCG15. De Vegh MutualFund G16. DelawareFund G, I17. Dodge and Cox Balanced Fund I, G, S18. DreyfusFund G19. Dreyfus SpecialIncomeFund I, G, S20. EatonVance Investors Fund G, I, S21. EnergyFund G22. FidelityFund G, I23. FidelityPuritanFund I, G24. FinancialIndustrialFund G, I25. FoundersMutualFund G, I26. GrowthIndustryShares G27. GuardianMutualFund G, I28. HamiltonFund G, I29. International nvestors G, I30. InvestmentCompanyof America G, I31. InvestmentTrustof Boston G, I32. Investors ResearchFund G33. Istel fund G, I34. Keystone CustodianFundsB-1 I35. Keystone CustodianFunds B-2 I36. Keystone CustodianFundsB-4 I37. KeystoneCustodianFundsK-1 I38. Keystone CustodianFunds K-2 G



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Market Timing 277

TABLE Al (Continued)FundName Objective39. Keystone CustodianFundsS-1 G, I40. Keystone CustodianFundsS-3 G41. Keystone CustodianFundsS-4 MCG42. Keystone InternationalFund G43. Loomis-SaylesCapitalDevelopmentFund G44. MagnaIncomeTrust I, S, G45. MerrillLynchPacificFund G46. MutualShares MCG47. NationalSecuritiesStock Fund G, I48. National SecuritiesGrowthFund G49. NationalSecuritiesTotalReturnFund I50. National SecuritiesIncomeFund I51. National SecuritiesPreferredFund I, S52. NationalSecuritiesBalancedFund I, S, G53. NationalSecuritiesBondFund I, S54. Newton IncomeFund I55. NicholasIncomeFund I56. NortheastInvestorsTrust I57. One WilliamStreetFund G, I58. OppenheimerFund MCG59. Over-the-Counter ecuritiesFund G60. PennSquareMutualFund G61. PhiladelphiaFund G, I62. Pine StreetFund G, I63. PioneerFund G, I64. PriceT. Rowe GrowthFund G65. PutnamGeorgeFund of Boston G, I, S66. PutnamGrowthFund G67. Putnam nternationalEquities MCG68. Rowe PriceTax Free I69. Safeco EquityFund G, I70. ScudderCommonStock Fund G71. ScudderIncomeFund I, S72. ScudderInternationalFund G73. SeligmanCommonStock Fund G, I74. SeligmanGrowthFund G75. SigmaInvestmentShares I76. SigmaTrustShares G, I, S77. SovereignInvestors G, I78. SteadmanAssociated Fund I, G79. Steadman nvestmentFund G, I80. Stein Roe and FarnhamStock Fund G81. SteinRoe TotalReturnFund I, G82. TempletonGrowthFund G83. Twentieth-CenturyGrowthInvestors MCG84. UnifiedMutualShares G, I85. United Services Gold Shares G, I86. Value Line Fund G87. Value Line IncomeFund I88. Value Line SpecialSituationsFund MCG89. Vanguard ndexTrust G, I90. Wall Street Fund G, I, S91. WashingtonMutualInvestorsFund G, I92. WellesleyIncome Fund I93. WellingtonFund S, I, G

NOTE.-G = growth; I = income; MCG = maximum capital gain; S =stability.



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