The Sensitivity of Individual and Institutional Investors' Expectations to Changing Market Conditions: Evidence from Closed-End Funds

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Review of Quantitative Finance and Accounting, 8 (1997): 245–269© 1997 Kluwer Academic Publishers, Boston. Manufactured in The Netherlands.

The Sensitivity of Individual and InstitutionalInvestors’ Expectations to Changing MarketConditions: Evidence from Closed-End Funds

RICHARD W. SIASAssistant Professor of Finance, Insurance and Real Estate, Washington State University, Department ofFinance, College of Business and Economics, Pullman, WA 99164-4746 (509) 335-2347 [email protected]

Abstract. This study investigates whether individual and institutional investors respond differently to changesin market conditions. Closed-end funds are the medium used to test the hypothesis because closed-end fundshares (held primarily by individual investors) and the underlying assets (held primarily by institutional inves-tors) are claims to the same stream of distributions. The empirical results suggest that individual investors aremore responsive than institutional investors to changes in market conditions. Moreover, although the response ofinstitutional investors differs across stock and bond markets, we cannot reject the hypothesis that the additionalsensitivity of individual investors’ expectations is uniform across stock and bond markets.

Key words: Closed-end funds, institutional investors, individual investors

Closed-end funds are investment companies with a fixed capitalization of shares that tradein the secondary market. Absent market frictions (e.g., transaction costs, short sale re-strictions, finite horizons), arbitrage would ensure that closed-end fund share pricesclosely track the underlying net asset values. However, because such frictions exist,closed-end fund share prices can, and do, differ from the value of the underlying assets.Although the shares of some funds command a premium, closed-end funds typically tradeat discounts from their net asset values. Furthermore, discounts display substantial time-series variation.

One possible explanation for time-series variation in discounts is shifts in shareholders’expectations of management’s ability to garner abnormal returns. That is, because closed-end fund managers pursue active trading strategies, differences in closed-end fund shareprices and the underlying net asset values likely reflect closed-end fund shareholders’expectations of managements’ future portfolio alterations. It seems likely, however, thatvariation in expectations of managements’ ability to garner abnormal returns will becross-sectionally independent, i.e., fund-specific rather than market-wide.1 An alternateexplanation, and the focus of this study, is that time series variation in closed-end funddiscounts reflects shifts in the differences between the expectations of closed-end fundshareholders and holders of the underlying assets of the funds. That is, because the netasset values and the closed-end fund shares are claims to the same stream of distributions,in the absence of heterogeneous expectations between holders of closed-end fund sharesand holders of the underlying assets, share return betas should equal the betas of the

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underlying assets.2 Moreover, because individual investors are the primary closed-endfund shareholders and institutional investors play a more important role in the underlyingportfolios, differences in share and net asset value betas may reflect how variation inmarket conditions influences individual and institutional investors’ expectations.3

In this study, we examine the relationship between common movement in closed-endfund discounts and innovations in variables that may differentially affect individual andinstitutional investors’ expectations.4 We study the difference between the return on theclosed-end fund share and the return on the underlying assets of the fund. If a set ofvariables influences individual investors’ expectations (as reflected in share return betas)differently than institutional investors’ expectations (as reflected in net asset value returnbetas), then time-series variation in the variables will induce changes in closed-end funddiscounts. We examine nine variables that may affect individual and/or institutional in-vestors’ expectations: six economic variables and three measures of “individual investorsentiment.”

For a sample including bond, diversified stock and specialized funds, variation in the sixeconomic factors explains about 13 percent of the monthly time-series variation in theaverage discount. Two of the investor sentiment variables, the ratio of mutual fund salesto redemptions and the ratio of net mutual fund sales to total assets, add little explanatorypower. The final investor sentiment variable, the monthly percentage change in the ratio ofodd lot purchases to odd lot sales, nearly doubles the explanatory power (i.e., R2 5 26percent). The results are consistent with the hypothesis that variation in market conditionsheterogeneously influences institutional and individual investors’ expectations.

Closed-end fund return and its component parts

Methodology

The rate of return garnered by a closed-end fund shareholder can be partitioned into twocomponents: the return on the fund’s assets and an adjustment that arises from thediscount or premium. Specifically, as shown in Appendix A, the continuously com-pounded return on a closed-end fund share can be written as the sum of the continuouslycompounded return on the net assets and an adjustment due to the presence of discountsand premiums:

ln~1 1 Ri! 5 ln~1 1 RN! 1 ln Fkt11Nt11 1 Dt11

ktNt11 1 ktDt11G (1)

where Ri and RN are the discrete single period rates of return from t to t 1 1 on theclosed-end fund’s shares and portfolio, respectively. Nt11 and Dt11 are the net asset valueand dividend per share, respectively, at time t 1 1. kt is the ratio of share price to net assetvalue at time t. Alternatively, kt 2 1 is the percentage discount at time t.

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The last term on the right-hand side of equation (1), the “discount adjustment,” is drivenprimarily by changes in discounts or premiums. For example, the term reflects the gain orloss due to changes in the discount or premium in a period when no distributions aremade. If a fund is selling at a discount (premium), and a distribution is made, the last termwill be positive (negative) if there is no change in discounts. This reflects the advantage(disadvantage) of buying dividend paying securities at a discount (premium).

Data

To perform the analyses, we construct time-series of continuously compounded returns forthe closed-end fund shares (share return), the portfolio of assets held by the fund (net assetvalue return) and their difference (the discount adjustment) for each fund. The necessaryinformation for constructing the return series came from three sources. We obtain closed-end fund share returns from the Center for Research in Security Prices (CRSP) daily files.Data on the net asset values and the corresponding discounts or premiums were collectedfrom the Wall Street Journal or Barron’s for the Friday closest to calendar month-end.5 Ingeneral, the monthly net asset values and discounts were within three days of the calendarmonth-end. We obtained information about the funds’ dividends and the ex-dividend datesfrom Moody’s and the Standard and Poor’s Dividend Record.6

The daily returns on the funds’ shares were converted to “monthly” returns by settingthe beginning and the end of each month to the Friday closest to the calendar month-end.This procedure ensures that the “monthly” share returns are measured contemporaneouslywith the “month-end” net asset values and discounts. We used the information on sharereturns, net asset values, dividends and discounts to calculate the discount adjustment andthe return on the underlying portfolios of the funds.7

A fund had to have a minimum of five years of monthly data to be included in theanalyses. The final data set consists of 54 funds from July 1965 (when the Wall StreetJournal and Barron’s began to publish net asset values and discounts) to December 1990.8

There are 10,381 observations generated from 25 bond funds, 15 diversified stock funds,three non-diversified stock funds and 11 specialized funds. The sample of funds used inthis study appears in Appendix B. Descriptive statistics for each return series are presentedin table 1.

Table 1. Descriptive statistics for monthly returns (in percent per month) (650702-901228, n 5 10,381 fund/months). Presented below are descriptive statistics for monthly closed-end fund share returns and its twocomponent parts: the return on the underlying assets (the NAV return) and the adjustment due to the presenceof discounts.

Variable

Maximum

value

Upper

quartile Median

Lower

quartile

Minimum

value Mean

Share Return 48.84 3.55 0.74 22.07 245.40 0.79NAV Return 61.26 2.70 0.74 21.17 250.90 0.72Discount Adj. 42.06 2.35 0.00 22.25 278.45 0.06

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Factors

We hypothesize that “market conditions” may influence variation in the difference be-tween individual and institutional investors’ expectations. In this section we consider twoclassifications of market conditions—economic conditions and measurements of indi-vidual investor “sentiment.”

Economic factors

Because of data availability and the desire to keep the number of factors at a reasonablelevel, we limit our set of economic factors to those state variables employed by Ferson andHarvey (1991). Ferson and Harvey note two important issues associated with this list ofvariables. First, the list is composed of variables shown to influence asset prices.9 Second,it is unlikely that these factors capture all the economic variables relevant to securityreturns. Similarly, we do not claim that these variables uniquely capture all of the factorsthat may be relevant to institutional and individual investors’ expectations. Nonetheless,variation in these economic factors should influence discounts if innovations in thesefactors influence individual investors’ expectations differently than institutional investors’expectations.

The economic variables include: (1) the excess return on the CRSP value-weightedmonthly index (XVW), (2) monthly real, per capita growth of personal consumptionexpenditures for non-durables, seasonally adjusted (CGNON), (3) monthly return of non-investment grade corporate bonds less the long-term U.S. government bond return(PREM), (4) the change in the difference between the average monthly yield of a ten-yearTreasury bond and a three-month Treasury bill (D SLOPE), (5) the unexpected inflationrate (UI) and (6) the one month Treasury bill return less the monthly rate of inflation(REALTB).10

Although the “market’s” response to changes in economic conditions will be an ag-gregation of institutional and individual investors’ responses, limits to arbitrage may allowus to capture differences between individual investors’ response (as captured by sharereturn betas) and institutional investors’ response (as captured by net asset value betas).Institutional and individual investors may respond differently to innovations in thesevariables for several reasons. First, Lee, Shleifer and Thaler (1991) argue that individualinvestors’ expectations are influenced by their irrational, but systematic, “sentiments.” Ifthese sentiments are a function of economic conditions, individual and institutional in-vestors’ responses to changes in economic conditions will differ. For example, individualinvestor sentiment may be manifested in a simple form of “overreaction” implying sharereturn betas may be greater than net asset value betas.

In addition, Brennan (1995) argues that individual investors’ response to variables mayseem irrational to a well-informed agent. However, such responses may not be irrationalfor individual investors who lack “expert knowledge” or are “less well-informed.” Forexample, Patel, Zeckhauser and Hendricks (1991) present evidence that the fraction ofincome individual investors place in mutual funds is an increasing function of recent

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market performance. Such behavior suggests that recent past price performance influencesindividual investors’ expectations. If such behavior occurs over a short period, the absolutevalue of share betas are likely to exceed the absolute value of net asset value betas.Consider, for example, that on a given day an unexpected decrease in interest rates causesan increase in market prices. In addition, assume that prices adjust to their new fair (i.e.,rational) value by the end of the day. Over the next week, however, some less informedindividual investors may continue to buy shares as a result of the initial change in price,i.e., positive feedback trading. If market frictions keep more rational investors from fullyoffsetting the irrational trades of individual investors, share prices of the securities domi-nated by individual investors will continue to rise. Thus, measured over a monthly period,securities dominated by individual investors will tend to exhibit a greater reaction to thefall in interest rates than securities dominated by institutional investors.

Sentiment factors

Expectations may also be influenced by “noise” that some investors interpret as informa-tion, i.e., “pseudo-signals” that are unrelated to the economic variables described in theprevious section.11 Lee, Shleifer and Thaler’s (1991), for example, propose that individualinvestors’ expectations (and hence, demand for closed-end fund shares), are influenced byirrational sentiment. Irrational sentiment presumably may vary with these “pseudo-signals.” Although it is not clear what “pseudo-signals” may influence individual inves-tors, extant evidence suggests several variables that may be positively correlated withindividual investors’ trading activity. We consider three such variables in this study. Thefirst two variables are the ratio of mutual fund sales to redemptions (S/R) and the ratio ofnet mutual fund sales (sales less redemptions) to total fund assets (NSAL). Lee, Shleiferand Thaler (1991) use two similar variables as dependent variables in a regression on thevalue-weighted market return and changes in closed-end fund discounts. They find that asdiscounts increase, so do net redemptions. Malkiel (1977) likewise found a similar direc-tional relationship with changes in average discounts as the dependent variable and netredemptions as the independent variable, although the relationship was not statisticallysignificant. Additionally, we include a third measure for the trading activity of individualinvestors—odd lot trading.12 Specifically, we measure variation in odd-lot trading as themonthly percentage change in the ten-day average of the ratio of total odd-lot purchasesto total odd-lot sales (DPS). Odd-lot data is collected from Standard and Poor’s DailyStock Price Record for the NYSE.

In addition, it is possible that these proxies of individual investors’ trading may simplycapture the difference between individual and institutional investors’ responsiveness tosome (possibly unknown) omitted economic factors. For simplicity, however, we refer tothese variables as “sentiment factors” for the remainder of this study.



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Factor estimation

To estimate variation in the “factors” that influence investors’ expectations and securityreturns, we employ the time-series mimicking portfolio methodology demonstrated inBreeden, Gibbons and Litzenberger (1989). Specifically, instead of using raw factors, weestimate closed-end fund share, net asset value and discount adjustment betas relative toa portfolio of CRSP-generated size, industry and bond returns that have maximum cor-relation with the factors. The size-based portfolios are decile returns based on NYSEstocks (generated from the monthly CRSP tapes). Similarly, the industry portfolios arebased on NYSE stocks, value-weighted, and grouped according to 2-digit SIC codes(following Sharpe (1982), Breeden, Gibbons and Litzenberger (1989) and others). The 12industry portfolio group classifications are provided in Appendix C. Finally, three bondportfolio returns are computed. Two bond portfolio returns are generated from CRSPdata—a long-term government bond and the Treasury bill that is closest to six months tomaturity. A corporate bond return is estimated as the final asset.13

Following Breeden, Gibbons and Litzenberger (1989), we estimate the maximum cor-relation portfolio for each economic and sentiment variable from the scaled fitted value ofa regression of the factor on the 25 size, industry and bond portfolios. Specifically, theweights for the maximum correlation portfolio are proportional to the regression coeffi-cients of each factor on the 25 size, industry and bond portfolio returns, where the factorof proportionality is the inverse of the sum of the regression weights.

Methodology and empirical results

Methodology

As shown in equation (1), the discount adjustment can be written as the linear differencebetween the continuous return on the closed-end fund share and the continuous return onthe underlying assets held by the fund. It follows that the discount adjustment beta issimply the difference between the share return beta and net asset value return betas.Specifically, assume that the following multi-beta model drives asset returns:

Rit 5 g0t 1 (j51

K

gjtbij 1 eit (2)

where gjt is the factor associated with the jth state variable and bij is the beta for asset iand state variable j. Then the discount adjustment can be written as:

Dt 5 (j51

K

gjt~bsj 2 bnj! 1 udt (3)

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where Dt is the discount adjustment at time t. Equation (3) shows that the discountadjustment beta for factor j is simply the difference between the beta on the closed-endfund share (bsj) and the beta for the underlying portfolio held by the fund (bnj). Ifindividual investors’ expectations are influenced by innovations in the state variablesdifferently than institutional investors’ expectations (i.e., bsj Þ bnj), discount adjustmentbetas will be non-zero and innovations in the state variables will induce changes inclosed-end fund discounts. To investigate how individual and institutional investors’ ex-pectations may be differentially influenced by innovations in the factors, time-series re-gressions of share returns, net asset value returns and discount adjustments on the maxi-mum correlation factor portfolios are estimated:

Rst 5 as 1 (j51

n

R̂jtbsj 1 hst Rnt 5 an 1 (j51

n

R̂jtbnj 1 hnt Dt 5 ad 1 (j51

n

R̂jtbdj 1 hdt

(4)

where, Rst, Rnt and Dt are the cross-sectional average share return, net asset value returnand discount adjustment in period t and R̂jt is the return on the maximum correlationportfolio for factor j in period t. bsj and bnj are the estimated sensitivity of individual andinstitutional investors’ expectations, respectively, to variation in factor j. bdj (5 bsj 2 bnj),then, is the estimated difference in sensitivity between individual and institutional inves-tors’ expectations to innovations in factor j.

Empirical results

Table 2 provides the result of estimating the time-series regressions given in equation (4)for an equal-weighted portfolio of all closed-end funds’ share returns, net asset valuereturns, and discount adjustments. Specifically, four regressions are estimated for eachseries. The first regression limits the independent variables to the economic factors. Thesecond through fourth regressions each include a sentiment factor as an independentvariable.

Results of the regression limited to the economic factors show that closed-end fundshare returns are significantly influenced by the excess market return (XVW), consump-tion growth (CGNON), unanticipated inflation (UI) and the real T-bill rate (REALTB). Incontrast to the share returns, net asset values also load on the default premium (PREM)but fail to load significantly on the real T-bill rate (REALTB). As seen in the first row ofthe last panel in table 2, differences in share and net asset value economic factor betasexplain about 13 percent of the time-series variation in the discount adjustment. Thedifferences are statistically significant (at the 5 percent level or better) for four of theeconomic factors. For two factors, the excess market return (XVW) and the defaultpremium (PREM), the absolute value of the net asset value beta is greater than theabsolute value of the share return beta consistent with the hypothesis that institutionalinvestors are more sensitive than individual investors to these factors. For the other two



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factors, consumption growth (CGNON), and the real T-bill rate (REALTB), share returnbetas are greater than net asset value return betas consistent with the hypothesis thatindividual investors are more sensitive than institutional investors to these factors.

Including the ratio of mutual funds sales to redemptions (S/R) or the ratio of net mutualfund sales to total assets (NSAL) adds little to the share, net asset value or discountadjustment regressions, i.e., the coefficient estimates for S/R and NSAL are never statis-tically significant. We do find, however, that the percentage change in the ratio of odd-lotpurchases to sales (DPS) is related (statistically significant at the 1 percent level) to thetime series variation in share returns but not to the returns on the underlying assets.Moreover, adding DPS to the discount adjustment regression nearly doubles the explana-tory power (i.e., adjusted R2 5 26 percent). Although adding the percentage change in theratio of odd-lot purchases to sales results in a strong increase in explanatory power, it alsoimpacts the significance of the relationship between discount adjustments and the other

Table 2. Betas for Share Returns, Net Asset Value Returns and Discount Adjustments: All Funds (n 5 306months). The coefficient estimates presented below result from a time-series regression of the share return, netasset value return or discount adjustment for an equally-weighted portfolio of closed-end funds on the maxi-mum correlation factor portfolios (t-statistics appear in parenthesis).

Dependent

Var/Adj. R2 XVW CGNON PREM DSLOPE UI REALTB S/R NSAL DPS

Share 0.3937 0.1877 0.0169 0.6800 20.6161 0.24510.6594 (10.20)** (5.23)** (0.87) (1.30) (23.72)** (2.43)*Share 0.3887 0.1830 0.0174 0.6502 20.6047 0.2344 0.03670.6586 (9.81)** (4.96)** (0.89) (1.23) (23.62)** (2.27)* (0.54)Share 0.4131 0.1875 0.0191 0.6868 20.5446 0.3203 20.02360.6591 (9.22)** (5.23)** (0.97) (1.32) (22.93)** (2.39)* (20.85)Share 0.4573 0.1510 0.0054 1.0718 20.7365 0.1411 0.31870.6765 (11.25)** (4.19)** (0.28) (2.07)* (24.49)** (1.39) (4.11)**

NAV 0.4996 0.0845 20.0380 0.2730 20.4223 0.08570.7621 (17.46)** (3.18)** (22.64)** (0.71) (23.44)** (1.14)NAV 0.4931 0.0783 20.0373 0.2329 20.4070 0.0712 0.04940.7621 (16.80)** (2.86) (22.59)* (0.60) (23.29)** (0.93) (0.98)NAV 0.5160 0.0844 20.0362 0.2787 20.3620 0.1492 20.01990.7620 (15.53)** (3.17)** (22.49)* (0.72) (22.63)** (1.50) (20.97)NAV 0.4836 0.0938 20.0351 0.1746 20.3921 0.1118 20.08000.7628 (15.65)** (3.42)** (22.42)* (0.44) (23.14)** (1.44) (21.36)

Discount 20.1059 0.1031 0.0549 0.4070 20.1937 0.15950.1314 (23.65)** (3.82)** (3.76)** (1.04) (21.55) (2.10)*Discount 20.1043 0.1048 0.0548 0.4173 20.1977 0.1632 20.01270.1286 (23.49)** (3.77)** (3.73)** (1.06) (21.57) (2.10)* (20.25)Discount 20.1029 0.1031 0.0553 0.4081 20.1826 0.1712 20.00370.1285 (23.05)** (3.81)** (3.74)** (1.04) (21.30) (1.69) (20.18)Discount 20.0263 0.0573 0.0406 0.8971 20.3445 0.0293 0.39880.2573 (20.91) (2.22)* (2.97)** (2.43)* (22.94)** (0.40) (7.19)**

**denotes statistical significance at the 1 percent level.*at the 5 percent level.

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variables. That is, although the signs of the discount adjustment coefficients for theeconomic factors do not change, two coefficients that were statistically significant (XVW)and (REALTB), are no longer significant (at the 5 percent level or better). In addition, twodiscount adjustment coefficients that were not statistically significant (D SLOPE and UI),become statistically significant when DPS is added to the regression (at the 5 percent levelor better). For both of these coefficients, the absolute value of the share return betasexceed the absolute value of the net asset value betas.14

The results reported in table 2 suggest that variation in both the economic and senti-ment variables influence institutional and individual investors’ expectations. It is possible,however, that investors’ expectations may be market-specific. For example, an increase inthe slope of the yield curve may increase individual investors’ demand for bond funds atthe expense of stock funds. Thus, we next repeat the analysis by fund type.

Table 3 reports the regression results for a sample limited to bond funds.15 In the first

Table 3. Betas for Share Returns, Net Asset Value Returns and Discount Adjustments: Bond Funds (n 5 228months). The coefficient estimates presented below result from a time-series regression of the share return, netasset value return or discount adjustment for an equally-weighted portfolio of closed-end bond funds on themaximum correlation factor portfolios (t-statistics appear in parenthesis).

Dependent


Share 0.1453 0.2016 20.0859 2.0448 0.2752 0.65160.4789 (3.15)** (4.40)** (23.44)** (3.33)** (1.30) (5.16)**Share 0.1473 0.2030 20.0858 2.0569 0.2746 0.6560 20.01190.4766 (3.04)** (4.31)** (23.43)** (3.30)** (1.30) (5.02)** (20.14)Share 0.1873 0.2039 20.0805 2.0497 0.4311 0.8127 20.05050.4816 (3.45)** (4.46)** (23.20)** (3.34)** (1.83) (4.86)** (21.46)Share 0.1989 0.1621 20.0995 2.4297 0.1688 0.5533 0.28700.4978 (4.10)** (3.46)** (24.00)** (3.94)** (0.80) (4.32)** (3.05)**

NAV 0.1664 0.0547 20.1335 1.0027 0.2596 0.37750.5959 (5.77)** (1.91) (28.56)** (2.61)** (1.97) (4.78)**NAV 0.1680 0.0559 20.1335 1.0125 0.2591 0.3811 20.00970.5841 (5.54)** (1.90) (28.54)** (2.60)** (1.96) (4.66)** (20.18)NAV 0.1771 0.0553 20.1322 1.004 0.2993 0.4186 20.01280.5847 (5.20)** (1.92) (28.37)** (2.61)** (2.02)* (3.98)** (20.59)NAV 0.1787 0.0457 20.1366 1.0909 0.2352 0.3550 0.06580.5863 (5.78)** (1.53) (28.62)** (2.78)** (1.76) (4.35)** (1.10)

Discount 20.0211 0.1469 0.0476 1.0422 0.0156 0.27410.2142 (20.62) (4.30)** (2.57)** (2.28)* (0.10) (2.92)**Discount 20.0208 0.1471 0.0477 1.0444 0.0155 0.2749 20.00220.2107 (20.58) (4.20)** (2.56)* (2.25)* (0.10) (2.93)** (20.03)Discount 0.0102 0.1486 0.0516 1.0458 0.1318 0.3942 20.03760.2183 (0.25) (4.36)** (2.76)** (2.29)* (0.75) (3.16)** (21.46)Discount 0.0201 0.1165 0.0371 1.3389 20.0664 0.1983 0.22130.2449 (0.56) (3.34)** (2.01)* (2.92)** (20.43) (2.08)* (3.16)**

**denotes statistical significance at the 1 percent level;*at the 5 percent level.



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regression, share returns load on all of the economic factors except unanticipated inflation(UI). In addition, the underlying assets generally load on the same factors. For four of thesix economic factors, however, share return betas differ significantly from net asset valuereturn betas (i.e., the discount return betas differ from zero at the 5 percent level of better).For three factors (CGNON, DSLOPE, and REALTB), the absolute value of share betas aregreater than the absolute value of net asset value betas. Net asset values, however, aremore sensitive to innovations in the default premium (PREM) than are the shares ofclosed-end bond funds. The six economic factors explain 21 percent of the time-seriesvariation in the mean closed-end bond fund discount adjustment. As with the previousanalysis, inclusion of either mutual fund sentiment factor (S/R or NSAL) in the regres-sions adds little explanatory power and the coefficient estimates are never statisticallysignificant. Also consistent with the previous analysis, the coefficient associated with thepercentage change in the ratio of odd-lot purchases to sales (DPS), is strongly related toshare returns but unrelated to the returns on the underlying assets (and thus, related todiscount adjustments).

Table 4 reports the regression results for a sample limited to diversified stock funds. Inthe first regression (limited to the economic factors) share returns load significantly onfour of the economic factors (XVW, CGNON, PREM and UI). Net asset values load (i.e.,statistically significantly at the 5 percent level or better) on three factors (XVW, UI,REALTB). The first regression in the third panel suggests that institutional investors areinfluenced to a greater degree than individual investors by the value-weighted marketreturn, i.e., the discount adjustment XVW beta is significantly (at the 1 percent level)negative. This particular result is consistent with Lee, Shleifer and Thaler (1991) whodocument a negative relationship between diversified closed-end fund discounts and thelargest capitalization stocks (that dominate XVW). Alternatively, the results are consistentwith the hypothesis that individual investors are more sensitive than institutional investorsto innovations in consumption growth (CGNON) and the default premium (PREM). Thesix economic factors explain about 11 percent of the time-series variation in the meandiscount adjustment of diversified funds.

As before, inclusion of either mutual fund sentiment factor (S/R or NSAL) adds littleto the regressions. Also consistent with the previous analyses, the coefficient associatedwith the percentage change in the ratio of odd-lot purchases to sales (DPS) is positivelyrelated to share returns. Surprisingly, DPS is negatively related to the return on theunderlying net asset values. Adding DPS to the diversified fund discount adjustmentregression nearly doubles the explanatory power (adjusted R2 5 20 percent) but doesreduce the difference between share and net asset values’ sensitivity to consumptiongrowth (CGNON) and increases the difference between share and net asset values’ sen-sitivity to unanticipated inflation (UI).

Table 5 reports results for a sample limited to specialized closed-end funds. In the firstregression, specialized fund share returns load on the same factors as the diversified fundshare returns. The specialized funds’ net asset values load on all of the factors (at the 5percent level or better) except the default premium (PREM). As shown in the last panel,when the factors are limited to the economic variables, share and net asset value betasdiffer significantly for the value-weighted market return (institutional investors are more

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sensitive) and consumption growth (individual investors are more sensitive). The sixeconomic factors explain about 5 percent of the time-series variation in the discountadjustment for the sample of specialized funds.

Again, inclusion of either mutual fund sentiment factor (S/R or NSAL) adds littleexplanatory power to the regressions. Addition of the percentage change in odd-lot pur-chases to sales (DPS), however, influences the share and discount adjustment regressions.In fact, the addition of DPS to the discount adjustment regression more than doubles theexplanatory power (adjusted R2 5 11 percent). Moreover, the addition of DPS reduces thedifference between share and net asset value sensitivities to the value-weighted marketreturn (so that XVW is no longer statistically significant for the discount adjustment) andincreases the difference between share and net asset value sensitivities to unanticipatedinflation (UI).

Table 4. Betas for share returns, net asset value returns and discount adjustments: diversified stock funds (n 5306 months). The coefficient estimates presented below result from a time-series regression of the share return,net asset value return or discount adjustment for an equally-weighted portfolio of closed-end diversified stockfunds on the maximum correlation factor portfolios (t-statistics appear in parenthesis).

Dependent


Share 0.6541 0.1313 0.0841 20.2174 21.1148 20.11880.7146 (14.60)** (3.15)** (3.73)** (20.36) (25.79)** (21.01)Share 0.6522 0.1294 0.00843 20.2296 21.1102 20.1232 0.01500.7137 (14.16)** (3.02)** (3.73)** (20.38) (25.71)** (21.03) (0.19)Share 0.6330 0.1315 0.0817 20.2247 21.1923 20.2004 0.02560.7143 (12.16)** (3.16)** (3.59)** (20.37) (25.53)** (21.29) (0.80)Share 0.7174 0.0948 0.0726 0.1724 21.2347 20.2222 0.31710.7249 (15.08)** (2.25)* (3.25)** (0.29) (26.43)** (21.87) (3.49)**

NAV 0.8646 0.0242 0.0262 20.1528 20.7884 20.21760.8805 (30.74)** (0.93) (1.85) (20.40) (26.52)** (22.95)**NAV 0.8515 0.0114 0.0276 20.2346 20.7573 20.2471 0.04910.8818 (29.66)** (0.43) (1.96) (20.62) (26.25)** (23.31)** (2.05)*NAV 0.8447 0.0245 0.0240 20.1597 20.8615 20.2945 0.02420.8807 (25.87)** (0.94) (1.68) (20.42) (26.37)** (23.02)** (1.20)NAV 0.8362 0.0406 0.0314 20.3281 20.7345 20.1710 20.14270.8825 (27.72)** (1.52) (2.21)* (20.86) (26.03)** (22.27)* (22.48)*

Discount 20.2105 0.1070 0.0578 20.0647 20.3264 0.09880.1057 (25.43)** (2.97)** (2.96)** (20.12) (21.96) (0.97)Discount 20.1994 0.1179 0.0567 0.0049 20.3529 0.1239 20.08560.1074 (25.01)** (3.18)** (2.90)** (0.01) (22.10)* (1.20) (21.26)Discount 20.2117 0.1070 0.0577 20.0651 20.3308 0.0942 0.00150.1027 (24.69)** (2.96)** (2.92)** (20.12) (21.77) (0.70) (0.05)Discount 20.1187 0.0542 0.0413 0.5005 20.5002 20.0513 0.45980.2016 (22.99)** (1.54) (2.21)* (0.99) (23.12)** (20.52) (6.08)**

** denotes statistical significance at the 1 percent level;*at the 5 percent level.



5% 50% 90% 100%


Differences across fund types

The results presented in tables 2 through 5 demonstrate that the signs and/or the statisticalsignificance of the coefficients for share returns, net asset value returns and discountadjustments vary across fund types. To examine the relationship between differences ininstitutional and individual investors’ expectations to innovations in market conditionsacross different (i.e., bond, diversified stock and specialized) markets, we estimateF-statistics for the hypotheses that share betas do not differ between (1) bond and diver-sified funds, (2) bond and specialized funds, and (3) diversified and specialized funds.Since share betas are the sum of the net asset value and discount adjustment betas,differing share betas imply that either net asset value betas differ (institutional investors’expectations are influenced differently across markets) or discount adjustment betas differ

Table 5. Betas for share returns, net asset value returns and discount adjustments: Specialized funds (n 5 306months). The coefficient estimates presented below result from a time-series regression of the share return, netasset value return or discount adjustment for an equally-weighted portfolio of closed-end specialized funds onthe maximum correlation factor portfolios (t-statistics appear in parenthesis).

Dependent


Share 0.5780 0.2629 0.0729 0.5627 20.9297 20.23740.5109 (8.60)** (4.21)** (2.16)* (0.62) (23.22)** (21.35)Share 0.5780 0.2629 0.0729 0.5627 20.9297 20.2374 20.00000.5109 (8.37)** (4.09)** (2.15)* (0.62) (23.19)** (21.32) (20.00)Share 0.5288 0.2635 0.0674 0.5457 21.1101 20.4274 0.05970.5134 (6.78)** (4.22)** (1.98)* (0.60) (23.44)** (21.83) (1.24)Share 0.6834 0.2022 0.0539 1.2119 21.1293 20.4097 0.52820.5346 (9.62)** (3.21)** (1.61) (1.34) (23.94)** (22.31)* (3.90)**

NAV 0.7015 0.0973 0.0418 1.4702 20.5294 20.30730.6888 (16.27)** (2.43)* (1.93) (2.52)* (22.86)** (22.72)**NAV 0.6975 0.0934 0.0422 1.4457 20.5200 20.3162 0.03020.6879 (15.74)** (2.26)* (1.94) (2.46)* (22.78)** (22.74)** (0.40)NAV 0.6856 0.0974 0.0400 1.4648 20.5874 20.3684 0.01920.6882 (13.68)** (2.43)* (1.83) (2.51)** (22.83)** (22.46)* (0.62)NAV 0.7130 0.0906 0.0397 1.5410 20.5511 20.3262 0.05760.6882 (15.27)** (2.19)* (1.81) (2.59)** (22.92)** (22.80)** (0.65)

Discount 20.1235 0.1657 0.0311 20.9075 20.4003 0.06990.0466 (22.38)* (3.43)** (1.19) (21.29) (21.79) (0.51)Discount 20.1195 0.1695 0.0307 20.8830 20.4097 0.0788 20.03020.0437 (22.24)* (3.41)** (1.17) (21.25) (21.82) (0.57) (20.33)Discount 20.1568 0.1661 0.0274 20.9191 20.5227 20.0590 0.04050.0472 (22.60)** (3.44)** (1.04) (21.31) (22.09)* (20.33) (1.09)Discount 20.0295 0.1116 0.0142 20.3292 20.5782 20.0836 0.47060.1050 (20.54) (2.31)* (0.55) (20.48) (22.63)** (20.62) (4.53)**

**denotes statistical significance at the 1 percent level;*at the 5 percent level.

256 RICHARD W. SIAS


5% 50% 90% 100%


(the additional sensitivity of individual investors’ expectations is influenced differentlyacross markets). Therefore, we also estimate F-statistics for the hypotheses that net assetvalue betas (or discount adjustment betas) do not differ across markets.

Table 6 presents the results of analyses (the coefficient estimates are the same as thosereported in tables 3 through 5). As shown in panel A, share returns for all fund types loadsignificantly on the value-weighted market return (XVW). As one may suspect, however,the F-statistics suggest the betas for the diversified and specialized funds are significantlylarger than the share betas for the bond funds. Evaluation of net asset value and discountbetas (panels B and C, respectively) reveals that the behavior of the underlying assetslargely drives the difference.

Share returns for all fund types also tend to be sensitive to innovations in consumptiongrowth (CGNON). In this case, however, the share return sensitivity appears to arise pri-marily from the discount adjustment. Moreover, there is relatively little difference betweenfund types for shares, net asset values or discount adjustments. For the next four economicfactors (the default premium, the changing slope of the yield curve, unanticipated inflationand the real T-bill rate) share returns for bond funds tend to react differently than sharereturns for the specialized or diversified funds. In each case, however, the results presentedin Panels B and C suggest that the difference is primarily driven by differences in theunderlying assets’ sensitivity to changes in economic conditions. We find little evidencethat discount adjustment sensitivities to these economic factors differ significantly acrossfund types. For the final factor, the percentage change in odd-lot purchases to sales (DPS),share return sensitivities are similar across all three markets. Moreover, the sensitivity ofshare return to changes in DPS arises primarily from the sensitivity of the discount ad-justments. In addition, bond fund discounts are somewhat less sensitive to changes in DPSthan diversified or specialized fund discounts. The difference, however, is statistically sig-nificant (at the 5 percent level) only for bond versus diversified funds and is influenced bythe negative sensitivity of diversified fund net asset values to DPS.

The results presented in Table 6 yield interesting implications regarding the uniformityof the impact of changes in economic conditions across fund types. Specifically, theresults suggest that the underlying assets of bond, diversified and specialized funds differin their sensitivity to changes in market conditions. The additional sensitivity of sharereturns to changes in market conditions (i.e., the discount adjustment betas), however, islargely uniform across fund types. That is, the differences in discount adjustment betasacross fund types are generally smaller than the differences in net asset value betas. Theresults are consistent with the hypothesis that changes in market conditions heteroge-neously influences institutional investors’ expectations across markets (i.e., bond versusstocks). In general, however, we cannot reject the hypothesis that changes in marketconditions similarly affect the additional sensitivity of individual investors’ expectationsfor all three markets (diversified stocks, specialized and bond markets).

Non-synchronous net asset values and leverage

Table 7 summarizes the results of the last regression (including the six economic factorsand DPS as explanatory variables) for share, net asset value and discount adjustments by



5% 50% 90% 100%


Table 6. Share return, net asset value return and discount adjustment beta comparisons across fund types. Thecoefficient estimates presented below are generated from performing a time-series regression of the sharereturn, net asset value return or discount adjustment for an equally-weighted portfolio of closed-end funds onthe maximum correlation factor portfolios. F-statistics based on the null hypotheses that betas do not differacross (1) bond and diversified funds, (2) bond and specialized funds and (3) diversified and specialized fundsare also reported.

Var XVW CGNON PREM D SLOPE UI REALTB D PS

Panel A: Share Beta Comparison

Bond 0.1989** 0.1621** 20.0995** 2.4297** 0.1688 0.5533** 0.2870**Diversified 0.7174** 0.0948* 0.0726** 0.1724 21.2347** 20.2222 0.3171**F-statistic 57.41** 1.12 26.00** 6.74** 23.89** 19.40** 0.05

Bond 0.1989** 0.1621** 20.0995** 2.4297** 0.1688 0.5533** 0.2870**Specialized 0.6834** 0.2022** 0.0539 1.2119 21.1293** 20.4097* 0.5282**F-statistic 28.82** 0.23 11.87** 1.13 11.75** 17.19** 1.92

Diversified 0.7174** 0.0948* 0.0726** 0.1724 21.2347** 20.2222 0.3171**Specialized 0.6834** 0.2022** 0.0539 1.2119 21.1293** 20.4097* 0.5282**F-statistic 0.16 2.00 0.22 0.91 0.09 0.77 1.67

Panel B: NAV Beta Comparison

Bond 0.1787** 0.0457 20.1366** 1.0909** 0.2352 0.3550** 0.0658Diversified 0.8361** 0.0406 0.0314* 20.3281 20.7345** 20.1710* 20.1427*F-statistic 228.76** 0.02 61.37** 6.60* 28.26** 22.11** 6.20*

Bond 0.1787** 0.0457 20.1366** 1.0909** 0.2352 0.3550** 0.0658Specialized 0.7130** 0.0906* 0.0397 1.5410** 20.5511** 20.3261** 0.0576F-statistic 82.24** 0.67 36.81** 0.36 10.12** 20.18** 0.01

Diversified 0.8361** 0.0406 0.0314* 20.3281 20.7345** 20.1710* 20.1427*Specialized 0.7130** 0.0906* 0.0397 1.5410** 20.5511** 20.3261** 0.0576F-statistic 4.91* 1.03 0.10 6.99** 0.67 1.25 3.56

Panel C: Discount Adjustment Beta Comparison

Bond 0.0202 0.1165** 0.0371* 1.3389** 20.0664 0.1983* 0.2213**Diversified 20.1187** 0.0542 0.0413* 0.5005 20.5002** 20.0513 0.4598**F-statistic 6.45* 1.50 0.02 1.46 3.58 3.15 5.14*

Bond 0.0202 0.1165** 0.0371* 1.3389** 20.0664 0.1983* 0.2213**Specialized 20.0295 0.1116* 0.0142 20.3292 20.5782** 20.0836 0.4706**F-statistic 0.52 0.01 0.46 3.65 3.15 2.54 3.55

Diversified 20.1187** 0.0542 0.0413* 0.5005 20.5002** 20.0513 0.4598**Specialized 20.0295 0.1116* 0.0142 20.3292 20.5782** 20.0836 0.4706**F-statistic 1.75 0.92 0.73 0.94 0.08 0.04 0.01


258 RICHARD W. SIAS


5% 50% 90% 100%


fund type. For the ratio of odd-lot purchases to sales (DPS), the absolute value of sharereturn betas are greater than the absolute value of net asset value betas for all fund typesand the difference is statistically significant across the three fund types. In addition, theresults suggest that individual investors are more sensitive than institutional investors toseveral economic factors: consumption growth (CGNON) across both bond and special-ized funds, the default premium (PREM) for diversified funds, changes in the slope of theyield curve (DSLOPE) for bond funds, the real T-bill rate (REALTB) for bond funds, andunanticipated inflation (UI) for specialized and diversified stock funds. Moreover, insti-tutional investors are more sensitive than individual investors to changes in the defaultpremium (PREM) for bond funds and the market return (XVW) for diversified stockfunds.

There are, however, several possible reasons for the difference between share and netasset value return sensitivity to changes in market conditions that may be unrelated toinvestors’ expectations. First, leverage may induce differences in share and net asset valuesensitivity to variation in market conditions. Second, closed-end fund share and net assetvalue returns may be non-synchronous.

If the net asset values reported in the Wall Street Journal are stale, for example,contemporaneous share return betas would tend to be greater than contemporaneous netasset value return betas. As noted above, in most cases share return betas exceed the betason the underlying assets consistent with the stale net asset value hypothesis. To examinewhether the tendency for share betas to exceed net asset value betas results from stale netasset values, we repeat the last regressions presented in tables 3 through 5 (i.e., includingthe percentage change in odd-lot purchases to sales) adding a lead and a lag value of eachfactor. If stale net asset values drive the difference between share and net asset value betas,

Table 7. Summary of betas for share returns, net asset value returns and discount adjustments: bond, diversifiedstock and specialized funds.

Dependent Var. XVW CGNON PREM D SLOPE UI REALTB D PS

Share Return

Bond positive** positive** negative** positive** positive positive** positive**Diversified positive** positive* positive** positive negative** negative positive**Specialized positive** positive** positive positive negative** negative* positive**

Net Asset Value Return

Bond positive** positive negative** positive** positive positive positiveDiversified positive** positive positive* positive negative** negative* negative*Specialized positive** positive* positive positive** negative** negative** positive

Discount Adjustment

Bond positive positive** positive* positive** negative positive* positive**Diversified negative** positive positive* positive negative** negative positive**Specialized negative positive* positive negative negative** negative positive**




5% 50% 90% 100%


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260 RICHARD W. SIAS


5% 50% 90% 100%


then the recorded contemporaneous net asset value returns should load on the lag (lead)factor to a greater (lesser) extent than the share return. Moreover, given a positive con-temporaneous beta, the lag net asset value beta should be positive, while the lead net assetvalue beta should be negative if net asset values returns are recorded less frequently thanmarket returns (see Dimson (1979)).

Extant evidence (e.g., Chen (1991)), however, suggests non-zero correlations existbetween lead and lag economic state variables and stock returns. This, of course, impedesthe ability to interpret lead and lag coefficients for the economic variables as strictlyresulting from non-synchronous trading. Because the lead-lag relationship between re-turns and the economic variables may be more complex than the relationship betweenreturns and stock indices, we primarily focus on the relationship between the lead and lagstock index (XVW) and the difference between share and net asset value betas. Considerfirst the relationships between diversified fund share returns, net asset value returns,discount adjustments and the stock index. As shown in table 8, the contemporaneous netasset value beta exceeds the contemporaneous share return beta inconsistent with the stalenet asset value explanation. Similarly, the lag share return beta exceeds the lag net assetvalue beta (i.e., the lag discount adjustment beta is positive) inconsistent with the stale netasset value hypothesis. In fact, if anything, the results suggest that closed-end fund shareprices are more likely to be stale than the underlying assets. Moreover, the results suggestthat the negative relationship between changes in diversified fund discounts and largecapitalization stocks (which dominate XVW) documented in table 4 and in Lee, Shleiferand Thaler (1991) may result from stale share prices. The results, however, are inconsis-tent with the hypothesis that the tendency for share betas to exceed net asset value betasfor the other factors is driven by stale net asset values.

A similar relationship holds for the specialized funds. Specifically, the contemporane-ous net asset value beta exceeds the contemporaneous share beta. Moreover, the lag sharebeta exceeds the lag net asset value beta. Although the differences are not statisticallysignificant, the pattern is inconsistent with the hypothesis that stale net asset values drivethe tendency for share return betas to exceed net asset value betas.

For bond funds, however, the relationship between contemporaneous share and net assetvalue betas is consistent with the stale net asset value hypothesis, i.e., the contempora-neous net asset value beta is less than the contemporaneous share beta for XVW. Simi-larly, the difference between the lag net asset value and share beta is also consistent withthe stale net asset value hypothesis, i.e., the lag net asset value beta exceeds the lag sharereturn beta. Thus, although the differences are not statistically significant, the pattern isconsistent with stale net asset values.

Given the evidence that bond fund net asset values may be stale, we also consider thepossibility that the bond fund discount adjustment coefficients associated with the otherfactors may be driven by stale net asset values. As noted above, the interpretation is morecomplex because these variables may have non-zero correlations at various leads and lagsirrespective of stale net asset values. Examination of the results presented in table 8,however, yields little evidence to support the hypothesis that stale net asset values drivethe contemporaneous relationship between the bond funds’ discount adjustments and theother factors. Consider first the coefficients associated with consumption growth(CGNON) and the percent change in odd-lot purchases to sales (DPS). In both cases,



5% 50% 90% 100%


contemporaneous and lag share betas exceed contemporaneous and lag net asset valuebetas, respectively, inconsistent with the pattern expected if net asset values are stale.Alternatively, for changes in the slope of the yield curve and (DSLOPE) and the real t-billrate (REALTB), the lag net asset value betas are negative (contemporaneous betas arepositive) inconsistent with the pattern predicted if stale net asset values drive the differ-ence between the contemporaneous betas. Finally, for the default premium (PREM), therelative magnitudes of the contemporaneous (and lag) share and net asset value betas areconsistent with stale share prices rather than stale net asset values.

A second possible source for differences in share and net asset value betas is that someclosed-end funds employ leverage. If the debt values subtracted from the gross assetvalues in the calculation of net asset values are smaller than the true market values, thenshare return betas are likely to exceed net asset value betas. Although we have no way ofknowing whether fund estimated debt values are, in general, lower than market values, wedo know which funds employ leverage.16 Fortunately, only about 11 percent of our fund-month observations include leverage. Therefore, we repeated the analyses reported inTable 2 through 5 with the sample limited to those funds not employing leverage. Theresults were essentially identical to those reported here.17

In sum, the results presented in Table 8 do not support the hypothesis that stale net assetvalues drive the tendency for share returns to be more sensitive to changes in marketconditions than the returns on the underlying assets. We do find some evidence, however,that stale share prices drive the relationship between large capitalization securities andchanges in diversified closed-end fund discounts. Moreover, leverage effects do not appearto drive the results.

Summary and conclusions

Although closed-end fund shares are held primarily by individual investors and institu-tional investors play a greater role in the underlying assets of the funds, both the sharesand the net assets are claims on the same stream of distributions. Therefore, in the absenceof differences between revisions in institutional and individual investors’ expectations asa result of changing market conditions, shares and net asset values should have the samebetas. The results of this study provide evidence consistent with the hypothesis thatvariation in market conditions heterogeneously influences individual and institutionalinvestors’ expectations. Six economic factors and odd-lot trading explain over 25 percentof the time-series variation in the cross-sectional mean difference between continuousshare and net asset value returns (i.e., the discount adjustment) for a sample of bond,diversified and specialized funds. Individual investors appear to be more sensitive thaninstitutional investors to several economic factors: consumption growth (CGNON) acrossboth bond and specialized funds, the default premium (PREM) for diversified funds,changes in the slope of the yield curve (DSLOPE) for bond funds, the real T-bill rate(REALTB) for bond funds, and unanticipated inflation (UI) for specialized and diversified

262 RICHARD W. SIAS


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stock funds.18 Moreover, one individual investor sentiment factor, the percentage changein odd-lot purchases to sales (DPS), is strongly related to time-series variation in closed-end fund discounts for diversified, specialized and bond funds.19

The results are consistent with a special case of the investor sentiment hypothesespresented by DeLong Shleifer, Summers and Waldmann (1990) and Zweig (1973) wherethe irrational ebullience of individual investors is manifested as overreaction to changes ineconomic conditions and other factor(s) proxied for by the odd-lot data. Alternatively,Brennan (1995) argues that evidence individual investors respond to variables that mayseem irrational for well-informed agents may not be irrational for individual investorswho lack “expert knowledge” or are “less well-informed.”

In sum, the results are consistent with the hypothesis that individual investors’ expec-tations are more sensitive than institutional investors’ expectations to changes in marketconditions. Thus, a change in market conditions generally results in a larger change inshare prices than the value of the underlying assets. In addition, the common variation inclosed-end fund share prices appears to be tied to other trading activities by individualinvestors (as captured by odd-lot trading). Moreover, although institutional investors’expectations across markets (bond, diversified stock and specialized) are heterogeneouslyinfluenced by changes in market conditions, we cannot reject the hypothesis that theadditional sensitivity of individual investors’ expectations across markets is homoge-neously influenced by changes in market conditions.

Appendix A

The continuously compounded return on closed-end fund shares can be written as the sumof the continuously compounded return on the net asset values and an adjustment due tothe presence of discounts and premiums (i.e., the discount adjustment). Let:

P0 5 price per share of closed-end fund share at time 0P1 5 price per share of closed-end fund share at time 1N0 5 net asset value per share at time 0N1 5 net asset value per share at time 1D1 5 distributions per share between time 0 and time 1k0 5 P0/N0, k0 2 1 5 % discount or premium at time 0k1 5 P1/N1, k1 2 1 5 % discount or premium at time 1

Then the return to the closed-end fund i shareholder is given by:

1 1 Ri 5k1N1 1 D1

k0N0

(A.1)

where Ri is the discrete return from time t 5 0 to t 5 1. Similarly the return on the netasset value of the fund is given by:



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1 1 RN 5N1 1 D1

N0

(A.2)

where RN is the discrete return from time t 5 0 to t 5 1. Equation (A.1) can be rewrittenas:

~1 1 Ri! 5 ~1 1 RN!F k1N1 1 D1

k0N1 1 k0D1G (A.3)

Taking natural logs yields:

ln~1 1 Ri! 5 ln~1 1 RN! 1 lnF k1N1 1 D1

k0N1 1 k0D1G (A.4)

Appendix BSample of closed-end funds

Name1 Type2

The Adams Express Company DiversifiedAmerican Capital Bond Fund

(American General Bond Fund)Bond

American Capital Convertible SpecializedAMEV Securities

(St. Paul Securities)Bond

Baker, Fentress & Co. DiversifiedBancroft Convertible Fund SpecializedBergstrom Capital Corp.

(Claremont Capital Corp.)(Diebold Venture Capital Corp.)

Specialized

Bunker Hill Income Securities BondCarriers & General Corp. DiversifiedCastle Convertible Fund

(C.I. Convertible Fund)Specialized

Central Securities Corp. Non-DiversifiedChase Convertible Fund of Boston SpecializedCircle Income Shares BondCNA Income Shares BondCurrent Income Shares BondThe Dominick Fund, Inc.

(National Bond and Share)Diversified

1838 Bond-Debenture Trading Fund(Drexel Bond-Debenture Trading Fund)

Bond

Energy and Utility Shares Specialized(Drexel Utility Shares)

Excelsior Income Shares BondFederated Income & Private Placement Bond

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table—continued

Name1 Type2

Fort Dearborn Income Securities BondGeneral American Investors DiversifiedJohn Hancock Income Securities BondJohn Hancock Investors BondHatteras Income Securities BondINA Investment Securities BondIndependence Square Income Securities BondIntercapital Income Securities

(Standard and Poor’s Intercapital Income Securities)Bond

International Holdings Corporation DiversifiedInterwest Corporation

(Overseas Securities Co., Inc)Diversified

Lincoln National Income(Lincoln National Direct Placement)

Bond

Madison Fund, Inc. DiversifiedMassMutual Income Investors BondMontgomery Street Income Securities BondMutual of Omaha Interest Shares BondNational Aviation and Technology

(National Aviation Corporation)Specialized

Nautilus DiversifiedNew America Fund

(Fund of Letters, Inc.)Specialized

Niagara Share Corp. DiversifiedPacific American Income Shares BondPetroleum & Resources Corp.

(Petroleum Corp. of America)Specialized

RET Income Fund(The REIT Income Fund)

Specialized

The Salomon Brothers Fund, Inc.(The Lehman Corp.)

Diversified

Source Capital, Inc.(SMC Investment Corp.)

Diversified

Standard Shares, Inc. Non-DiversifiedState Mutual Securities BondSterling Capital Corp.

(The Value Line Development Capital Co.)Specialized

Surveyor Fund(General Public Service)

Diversified

Transamerica Income Shares BondTri-Continental Corp. DiversifiedUnited Corp. Non-DiversifiedU.S. & Foreign Securities Corp. DiversifiedUSLIFE Income Fund, Inc. BondVestaur Securities Fund, Inc. Bond

1. Earlier names appear in parentheses.2. Types are taken from Weisenbergers Investment Companies.



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Appendix C

Acknowledgment

I have benefitted from the helpful suggestions of seminar participants at Purdue Univer-sity, Santa Clara University, Texas A&M University, The University of Texas at Austin,Washington State University and two anonymous referees. I thank Wayne Ferson, MartinFridson, Lori Glickman-Laueano, Ehud Ronn, Merrill Lynch and Salmon Brothers forproviding data.

Notes

1. That is, abnormal returns are market-adjusted. Thus, the interpretation of the results is conditional on theassumption that current expectations of abnormal fund performance are not influenced by systematicexpectations of future portfolio substitutions.

2. Alternative explanations for time-series variation in closed-end fund discounts include changes in agencycosts, changes in the value of future tax liabilities and irrational individual investor sentiment. Extant workhas found little support for the first two explanations (see Rozeff (1993) for an excellent review). Asdiscussed in the paper, the results are consistent with a special case of the investor sentiment hypothesis.

3. See Lee, Shleifer and Thaler (1991) for evidence that individual investors are the predominant owners ofclosed-end fund shares and institutional investors play a larger role in the underlying assets of the funds. Itis possible, of course, that individual and/or institutional investors’ demand for securities may be motivatedby factors other than changes in expectations. One possibility is that the demand for securities may beinfluenced by the characteristics of the security. Falkenstein (1996), for example, suggests that institutionalinvestors will rid their portfolios of low-priced stocks in order to minimize transactions costs. Similarly, itis often hypothesized that stock splits are motivated by individual investors’ reluctance to hold higher pricedstocks (e.g., Baker and Gallagher (1980)).

4. Sias, Starks and Tinic (1995) demonstrate that approximately 90 percent of the month-to-month variance inclosed-end fund discounts is fund-specific. Thus, the current study evaluates the 10 percent that is commonacross funds. It is important to recognize, however, that our goal is to examine the hypothesis that institu-tional and individual investors respond differently to changes in economic conditions. Variation in the meanclosed-end fund discount is the medium used to examine this hypothesis. That is, although the tests examine

Industry Portfolio Groups

Portfolio 2-Digit SIC Codes Industry Name

1 13,29 Petroleum2 60–69 Finance/Real Estate3 25,30,36–37,50,55,57 Consumer Durables4 10,12,14,24,26,28,33 Basic Industries5 1,20,21,54 Food/Tobacco6 15–17,32,52 Construction7 34–35,38 Capital Goods8 40–42,44,45,47 Transportation9 46,48,49 Utilities

10 22–23,31,51,53,56,59 Textiles/Trade11 72–73,75,80,82,89 Services12 27,58,70,78–79 Leisure

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whether changes in economic conditions explain variation in closed-end fund discounts, the results have twoimportant implications for asset pricing in general: (1) evidence that institutional and individual investorsrespond differently to changes in economic conditions and (2) evidence that the difference in responsesappears to influence at least some asset prices.

5. In most cases, the Friday closing price closest to the month-end was chosen to represent end-of-month netasset values. However, in December, the closest Friday to month-end in December was used, to ensure thatmost of the January seasonal was captured in the “quasi-January”. As noted by Roll (1983) and others, theJanuary effect generally begins the last trading day of December. Thus, when December 31 falls on a Friday,Saturday or Sunday, we are likely to not capture the entire turn-of-the-year effect in our “quasi-January”returns.

6. The Center for Research in Security Prices (CRSP), considers dividends to be distributed on the CRSP tapeson the ex-dividend date. Furthermore, AICPA’s Audits of Investment Companies (1987) guide notes thatmost closed-end investment companies record the distribution liability on the ex-dividend date. Therefore,distributions should be impounded into share returns (CRSP data) and net asset values (Wall Street Journaldata) on the same date. In addition, the hand gathered data was checked to ensure its validity. For example,when inputting net asset values and share prices from the Wall Street Journal information, an implieddiscount was calculated automatically that was compared to the Wall Street Journal data. In addition, filterswere run on all the data to check for outliers which were then re-evaluated to ensure validity. Occasionally,a fund would not have data available for a particular week. In such cases, the next Friday closest tomonth-end was used for net asset value and discount information. If that Friday’s information was alsomissing, then the Friday data in the other direction was used as a proxy for quasi-month-end data. Ifinformation was unavailable for a fund within one week from the quasi-month-end, then the observation wascoded as missing.

7. The data were filtered to eliminate the known systematic behavior of closed-end funds around their initialpublic offerings (see, for example, Weiss (1989) and Peavy (1990)). Specifically, no fund is included in theanalysis until it is at least six months old. Dates for initial offerings are taken from Weisenberger’sInvestment Companies, the Wall Street Journal or The Complete Guide to Closed-End Funds.

8. Cyprus Corporation technically met the requirements for inclusion in the sample. However, the fund wasexcluded because of the extremely small (even negative) net asset values which imply very large (infinite)premia.

9. As noted by Ferson and Harvey, see Folger, John and Tipton (1981), Chan, Chen and Hsieh (1985), Chen,Roll and Ross (1986), Sweeney and Warga (1986), Shanken and Weinstein (1987), and Burmeister andMcElroy (1988) for analyses of these variables.

10. XVW, DSLOPE, CGNON, and REALTB are essentially extensions of the Ferson and Harvey data. ThePREM variable was extended from 1987;1 to 1990;12 with Merrill Lynch’s All High Yield Bond returnindex. Expected inflation was estimated with a naive interest rate model (see Fama and Gibbons (1984)).Unexpected inflation was then estimated as the difference between actual and expected inflation.

11. Examples of potential pseudo-signals include patterns in stock prices and volumes, or recommendations ofstock market “experts.”

12. See Lakonishok and Maberly (1990) or Abraham and Ikenberry (1994) for evidence on the relationshipbetween individual investors and odd-lot trading.

13. The corporate bond return is estimated with data from Ferson and Harvey (1991) through 1987 andextended to 1990 using the Salomon Brothers Corporate Bond Index return.

14. One likely interpretation for the impact of DPS on the other variables is that exclusion of a relevant variableresults in biased estimates of other coefficients that are related to the excluded variable, i.e., multicollinear-ity.

15. No bond funds enter our sample until 1972. Therefore the bond fund analysis is based on 228 months versus306 months for the diversified and specialized fund analyses.

16. Specifically, Weisenberger’s Investment Companies annual surveys report which funds employ capitaliza-tion other than common stock.

17. Results are not reported to conserve space. A second possibility is that contingent management claims arenot accurately reflected in the net asset value calculations. Although we have no way of knowing whether



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such fees are accurately calculated, the magnitude of the differences in the coefficients seem improbablylarge compared to management fees. For example, the share return beta associated with unanticipatedinflation is nearly twice as large as the beta for the underling assets, while the mean annual expense ratiofor funds included in this analysis is less than 1 percent.

18. The results presented in table 3 suggest that institutional investors are more responsive than individualinvestors to changes in the default premium (for bond funds). The results reported in table 8, however,suggest that the difference may be attributed to stale share prices. Similarly, the results presented in table4 suggest that institutional investors are more responsive than individual investors to the market return (fordiversified stock funds). Again, however, the results presented in table 8 suggest that such differences mayresult from stale share prices.

19. Other authors suggest that the sentiment of individual investors is likely to show up in the returns of smallcapitalization stocks (e.g., Lee, Shleifer and Thaler (1991)). Given that the mimicking portfolios areestimated from the returns of small stocks (among others), mimicking portfolios for the economic variablesmay contain individual investor sentiment.

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The Sensitivity of Individual and Institutional Investors' Expectations to Changing Market Conditions: Evidence from Closed-End Funds