closed-end fund premia and returns implications for financial market equilibrium

ELSEVIER Journal of Financial Economics 37 (1995) 341-370

Closed-end fund premia and returns Implications for financial market equilibrium

Jeffrey Pontiff lJniversi@ of Washington, Seattle, WA 98195, USA

(Received September 1993; final version received July 1994)

Abstract

This paper examines the relation between closed-end fund premia and returns. Addi- tional evidence is provided on Thompson’s (1978) finding that fund premia are negatively correlated with future returns. Funds with 20% discounts have expected twelve-month returns that are 6% greater than nondiscounted funds. This correlation is attributed to premium mean-reversion, not to anticipated future portfolio performance. Economically motivated explanations do not account for this effect.

Key words: Closed-end fund; Discount; Abnormal return; Book-to-market; Market efficiency JEL class$cation: G12; G29; G14

1. Introduction

Closed-end funds are the simplest of corporations. They hold investments that are managed by the fund’s officers. The size of this industry has grown substantially in recent years. For example, the total value of assets invested in closed-end funds increased from $8 billion in 1985 to $56 billion in 1989. Unlike open-end mutual funds, which trade their shares at the net asset value of their

I am grateful to Michael Barclay, David Chapman, Craig Dunbar, Stephen Fisher, Stacey Kale, Mark Huson, Auke Jongbloed, John Long, Robert Parrino, Neil Pearson, Ed Rice, Jay Shanken, Bill Schwert (the editor), Andy Siegel, Amy Sweeney, Rex Thompson (the referee), Michael Weis- bath, and seminar participants at Arizona State, Clemson, New York Federal Reserve, Penn State, Pitt, Purdue, University of Alberta, and the University of Washington. I also thank Ken French and Charles Lee for generously providing me with data.

0304-405X/95/$09.50 0 1995 Elsevier Science S.A. All rights reserved SSDI 0304405X9400800 G

342 J. PontifSIJournal of Financial Economics 37 (1995) 341-370

portfolio, closed-end fund shares are traded on an exchange. Thus, investors can agree to trade a closed-end fund at prices other than the market value of its assets. If the price of the fund’s shares is greater than the value of its portfolio, the fund is said to sell at a premium. The term ‘discount’ is used to describe a negative premium.

This paper examines an empirical regularity documented by Thompson (1978): Closed-end funds with positive premia accrue negative abnormal returns, while funds with discounts accrue positive abnormal returns. Thompson finds that annual strategies based on this finding yield abnormal risk-adjusted returns of about 4% per year. Although Thompson’s study is similar to other studies that document return predictability inconsistent with the Capital Asset Pricing Model (CAPM), his study is unusual in that there have been no attempts in the finance literature to reconcile his results within the framework of an efficient market. This study fills this gap by positing predictions that are consistent with both market efficiency and Thompson’s results, and systematically tests the validity of these predictions. I estimate that closed-end funds with 20% differences in premia have differences in expected returns of 0.7% per month. Although factors consistent with market efficiency can predict closed-end fund returns, these factors are not the source underlying the ability of premia to forecast future returns. Thus, the premium-return relation remains enigmatic.

The closed-end fund premium-return relation sheds light on the ability of book-to-market to predict returns for firms that are not closed-end funds. The net value of a closed-end fund’s portfolio is called ‘net asset value’ (NAV) or ‘book value of shareholder’s equity’. Since a closed-end fund’s premium is equal to its market value divided by the book value of shareholders’ equity (minus unity), the premiun-return effect can be con- strued as a book-to-market effect. Closed-end funds provide a unique opportunity to examine the ability of book-to-market to predict returns. First, a fund’s book value is a measure of economic value that is undistorted by accounting conventions, such as depreciation. Second, unlike typical firms that report accounting numbers quarterly, closed-end funds report book values weekly or daily. As long as the book-to-market effect is related to book value’s economic content, as opposed to the accounting content, closed-end funds are ideal securities for studying this effect. This paper addresses factors other than size and market beta that may proxy for the ability of book-to-market to forecast returns.

In examining the premium-return relation, this paper also tests general financial theories. One advantage of using closed-end funds is that they represent claims to well-diversified portfolios, reducing risk estimation problems. Also, they frequently announce the market value of their assets, thus avoiding information effects in response to corporate decisions. These peculiarities are used to draw inferences that are applicable to all securities. For the sample of closed-end funds examined in this study:

J. Pontiff/Journal of Financial Economics 37 (1995) 341-370 343

l Expected returns are consistent with a dividend taxation effect. A dollar dividend is associated with 47# of price appreciation.

l Similar to Amihud and Mendelson (1986), larger bid-ask spreads are associated with higher expected returns.

l The cross-sectional pattern of premia is related to exposure to investor sentiment risk. This finding weakly supports an implication of Lee, Shleifer, and Thaler (199 1).

The paper proceeds as follows. Section 2 generates premium-return identities and documents some stylized facts regarding relations between premia and returns. Section 3 presents potential explanations of the ability of premia being correlated with future stock returns. Section 4 motivates a model that incorporates these explanations. Section 5 estimates the model and Section 6 concludes the paper.

2. Preliminary overview of relations between premia and returns

Before embarking on formal tests of the relation of returns and premia, this section documents some stylized facts that are useful in addressing previous explanations of premia.

The sample of closed-end funds used in this paper is identical to that in Lee, Shleifer, and Thaler (1991). It includes 68 funds that were covered in the Wall Street Journal’s publicly traded funds column in the period between July of 1965 and 1985. Funds with six or fewer months of premium data are deleted, yielding a sample of 53 funds. Returns and price data are from the Center for Research in Security Prices (CRSP) database. Net asset value returns were computed using both sets of data.’

2.1. Premium variation at the fund level

The financial press defines a fund’s premium as the difference between unity and the ratio of the fund’s price per share to portfolio NAT/ per share. In this paper, the natural log of price to net asset value is used to represent the

‘The return of a fund’s net asset value can be computed from the premium and stock return information. Specifically,

NR = (I+ SRX) + (SR - SRX)(PREM,- 1 + 1) - 1,

where NR is the net asset value return, SRX is the stock return without dividends, SR is the stock return, and PREM, is the time r premium. In months where no dividend is paid, the second term is zero. If returns are continuous, the first term is the stock return minus the change in premium.

344 J. Pontiff/Journal ofFinancial Economics 37 (1995) 341-370

premium.’ Thus, a fund’s premium can be expressed as

PREM, = ln(P,/N,), (1)

where P, is defined as the closed-end fund’s price per share and N, is defined as the fund’s net asset value per share. Time differencing this identity yields

APREM, = lnP, - lnN, - lnP,- 1 + lnN, _ I ,

where APREM, = PREM, - PREM,- 1.

(2)

If the fund pays no dividends,

APREM, = R: - RF, (3)

where R: is the continuously compounded return of the fund’s shares, and is referred to as the fund’s stock return, and R: is the continuously compounded return accruing to the fund’s net asset value, and is referred to as the fund’s net asset value return.

Next period’s expected change in premium, conditional on this periods premium, can be written as

E(APREM,+, 1 PREM,) = E(R:+, 1 PREM,) - E(R:+, I PREM,). (4)

If this period’s premium can forecast next period’s change in premium, then either the premium forecasts future stock returns, the premium forecasts future net asset value returns, or the premium can forecast both future net asset value returns and future stock returns. Therefore, if future changes in premia are correlated with the current premium, current prices (P,, Nt) contain information regarding future returns (R:, 1, RF+ 1).

To examine the information content of current prices and net asset values, correlations between premium and return measures are calculated for each of the 53 funds. These correlations are used to compute a weighted average, with each fund’s correlation weighted proportional to the inverse of the correlation’s standard error. These average correlations are presented in Fig. 1, which shows a correlogram of fund level premia and returns. As the first plot suggests, premia are persistent, implying that current premium contain information regarding future premia. The average first-order autocorrelation is about 0.85 and decays to about 0.60 after six months. Theoretically, premia are long-run mean-reverting. Brickley and Schallheim (1985) show that when funds announce plans to liquidate or become open-ended, premia move towards zero, and at liquidation, premia are zero.

Although premia can reasonably be expected to remain stationary over long time periods, it is possible that over short intervals premia are nonstationary. An augmented Dickey-Fuller test was conducted on 49 funds with more than 25

*The conclusions of this paper are unaffected if the popular press definition of premium is used.


months of data. For 53% of the funds in this subsample, this test rejects a unit root at the 10% level. These results are similar to those reported by Ammer (1990), who concludes that the aggregate premium of closed-end funds in the United Kingdom is stationary.

For a fund with a premium that is autocorrelated in a manner similar to the average autocorrelations presented in the first plot of Fig. 1, it is possible to infer the amount of premium variation that can be explained by different time-series processes (Nelson, 1976). The average first-order autocorrelation of premia is 0.854, implying that a first-order autoregressive process can explain about 73% (0.8542) of the premium variation for a fund with average autocorrelation. A second-order autoregressive process would explain 74% of premium variation, whereas using six lags would explain 75%. These R2s imply that most of the information about the level of future premia is contained in current premium.

As Eq. (4) demonstrates, the ability of a fund’s premium to predict future changes that a fund’s premium will also have the ability to predict either the net asset value return, the closed-end funds stock return, or both. As the second plot in the first row suggests, lagged closed-end fund returns are positively correlated with current premia, and current premia are negatively correlated with future stock returns. The third plot in the first row uses stock return net of market return as a return measure. The relation is similar to that of the stock return plot. The average correlation between current premium and next months return is about -0.24. The strength of this relation decays to about -0.03 after six months. If we

consider the difference between a closed-end funds return and the market’s return to be an abnormal return measure, this column presents initial evidence that supports Thompson’s finding that premia predict future abnormal returns.

The correlation of premia with NAV returns is illustrated in columns 4 and 5 of row 1. The correlation with the largest magnitude is the contemporaneous correlation of premium and NAV return minus market return, about -0.14. This contemporaneous relation might be attributable to ‘stale’ net asset values. If the securities in the funds portfolio are not actively traded and the fund’s stock is actively traded, then the price of the fund’s stock would reflect the expected NAV of the portfolio when the securities held in the portfolio are traded. Regarding noncontemporaneous correlations, both of these plots are similar; past NAT/ returns appear to be weak and negatively correlated with current premia, and current premia appear unrelated to future NAV returns. Some, such as Malkiel(1977) and Fredman and Scott (1991), have argued that premia may be partially caused by capital gains liabilities. On the surface, this is supported by the inverse relation between past NAV returns and premia. If portfolio performance has been good and capital gains liabilities are large, premia are small. This reasoning is not consistent with the plot in column 5, row 1, which shows that past NAV returns net of the market return are more strongly related to current premia than simple NAT/ returns. This is inconsistent with a capital gains argument since capital gains are based on total return.

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J. PontiffJJournal of Financial Economics 37 (1995) 341-370 341

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348 J. PontiffJJournal of Financial Economics 37 (1995) 341-370

Both academics and practitioners have argued that a possible reason for variation in premia is due to expected NAV performance (Herzfeld, 1990; Malkiel, 1977). This prediction is not substantiated by the noncontemporaneous correlations in the fourth and fifth column plots. Statistical tests cannot reject the hypothesis that current premia are uncorrelated with future NAT/ return, supporting the assertion that the ability to predict future premia is almost entirely attributable to the ability to forecast stock returns as opposed to that of NAT/ returns.3 This finding is also interesting in light of the ability of market-to-book to predict return variation for typical firms (Chan, Hamao, and Lakonishok, 1991; Fama and French, 1992). In the spirit of Chan and Chen (1991), Fama and French posit that market-to-book might proxy for exposure to a distress risk factor. If market-to-book proxies for such a risk factor, then market-to-book should predict future distress. This does not appear to be the case with closed-end funds, since premia do not predict future NA V performance.

The average first-order autocorrelation of stock return minus market return and NAP’ return minus market return are both about -0.20 (the third row of column 3 and the fifth row of column 5, respectively). Because the first-order autocorrelation of market return is less than 0.03 during this time period, these autocorrelations can be interpreted as a measure of staleness due to inactive trading. Inactive trading would cause such a correlation since, if a security does not trade at the end of a time period and market level increases (decreases) during the inactive period, the next trade will incorporate this information and produce a return that will be high (low) relative to the market.

The contemporaneous correlation between net asset value returns and stock returns is about 0.60 (column 4, row 2) and the contemporaneous correlation between these two returns, after netting out the market return, is about 0.45 (column 5, row 3). From Eq. (3), recognizing that NA I/ return and stock return are not perfectly correlated, implies that premia vary. This provides a different framework for thinking about premium variation. Since squared correlations are the same as R’s from univariate regressions, these correlations imply that for the average fund, its net asset value return explains 36% of the variation of its stock return, and its NAT/ return minus the market return explains 20% of

3 Two tests were conducted. First, a t-test was conducted using the average fund-level correlation between current premia and future NAV returns, where the average is weighted by the inverse of the correlation’s standard error. The average parameter is therefore identical to the parameters presented in Fig. 1. This test was conducted for monthly NAV returns that led premia by one to six months. This test produces six t-statistics (52 degrees of freedom) ranging from -0.6 to 1.1. If net asset return minus market return is used as the return measure, the t-statistics range from -0.7 to 0.84.

The second test calculates the per fund average of the six correlations. The mean of these 53 average fund correlations is computed, where each fund is weighted by the average standard error from the six correlations between premia and future NAV returns. The mean (t-statistic) of the average fund correlation is -b.O04 (-0.10). I f net asset return minus market return is used as the return measure, the mean (t-statistic) of the average fund correlation is 0.004 (0.11).


the variation of its net stock return. It is unlikely that this finding is attributable to nonsynchronous trading, since this would imply positive correlation in adjacent months. The fact that these R2s are not 100% implies that either a portion of net asset value returns is noninformative, the fund’s stock return does not reflect all of the information impounded in the net asset value return, or the fund’s stock return reacts to information other than net asset value returns.

3. Explaining the premium-return relation

The empirical regularity documented in the previous section - current premia are correlated with future closed-end fund returns - is, on the surface, a direct violation of market efficiency. Information on closed-end fund premia is pub- lished weekly in the Wall Street Journal and in similar publications. An informationally efficient market precludes the opportunity to make ‘abnormal’ profits from public information. As Fama (1970) stresses, any test of market efficiency is a joint test of efficiency and a model of market equilibrium. With the exception of Barker (1991), who shows that the premium-return relation persists after controlling for business cycle risk, closed-end fund studies have made no attempts to reconcile the premium-return relation with an informationally efficient market. This section strives to motivate an extensive list of possible equilibrium relations that are consistent with premia being correlated with future returns. All of these predictions can be integrated within the framework of most asset pricing theories.

3. I. The bid-ask spread

Evidence from tests of the CAPM indicates that small firms yield positive abnormal returns (see, for example, Banz, 1981). This finding is often called the ‘small firm effect’. Amihud and Mendelson (1986) have argued that this effect could be caused by differences in bid-ask spreads. They provide evidence that after controlling for bid-ask spreads, the small-firm effect disappears.

Holding other attributes constant, investors prefer securities with lower bid-ask spreads. Thus, funds with smaller bid-ask spreads than the securities in their portfolios should command a higher premium over net asset value than funds with larger spreads. Moreover, funds with higher bid-ask spreads than the securities in their portfolios would sell at a discount, In these cases, the abnormal returns accrued from Thompson’s strategy might represent equilibrium compensation for transactions costs.

Another reason for spreads to be larger for low-premium stocks is purely mechanical. If the price of a fund fluctuates around net asset value, and if relative bid-ask spreads are larger for lower-priced securities, then low premia will be associated with high spreads.

350 J. PontiffJJournal of Financial Economics 37 (199.5) 341-370

3.2. DiJfferences in dividend taxation

There is both anecdotal and empirical evidence that during the period of this study, 1965 to 1985, the United States tax codes made dividends less attractive than capital gains to typical investors (see, for example, Barclay, 1987). Divi- dends are normally taxed as ordinary income, whereas long-term capital gains are usually taxed at a rate that is lower than the highest tax rate on ordinary income. In addition, capital gains are taxable when realized, whereas dividends are taxable when the firm pays them. Thus, individuals can decrease their tax burden by choosing to realize gains in a favorable tax environment.

Closed-end funds are unlike other corporations in that some of the dividends they pay are taxed as normal dividends and some are taxed as capital gains. The source of this difference stems from the portfolio’s return. The fund’s managers ‘pass on’ portfolio income to investors in the form of income and capital gains dividends. Dividend income is distributed to shareholders as a dividend that is taxable as ordinary income. Capital gains income from the fund’s portfolio is distributed to shareholders as a dividend that is taxable at the long-term capital gains rate.

Previous studies have documented that upon going ex-dividend, the prices of conventional stocks fall by an amount less than the amount of the dividend (for example, Karpoff and Walking, 1988). Some have attributed this effect to the tax treatment of dividends (for example, Elton, Gruber, and Rentzler, 1984). Regard- less of whether divided payments are tax-disadvantaged, the empirical evidence mentioned earlier implies that returns are predictably higher in ex-dividend periods than non-ex-dividend periods. This will affect both closed-end funds’ returns and returns to funds’ portfolios. Federal regulations require closed-end funds that elect to retain their beneficial tax status to return all dividend income to shareholders every year. Closed-end funds typically pay dividends quarterly or semi-annually. Funds which invest exclusively in bonds are exceptions in that they typically pay monthly dividends. These funds are a minor part of my sample. The average (median) fund in my sample has 2.7 (2.6) ex-dividend months per year. In periods in which a fund collects dividends on its portfolio, its net asset value return will be higher. In periods in which a fund pays these dividends to shareholders, the fund’s return will be higher. If the fund’s premium is sufficiently large, the premium will increase upon payment of accumulated dividends to shareholders.4 Thus, the premium before the dividend payment will

“If price responses to divided payments are solely tax-related, then the premium will increase as long as it is greater than negative one times the tax rate. When a fund pays a dividend, its net asset value falls by the entire dividend amount, whereas the price of the fund will fall by after-tax value of the dividend. Thus, if the time period is very short, we can write:

N,= N,-, -D, (Fl) P,=P,e,-(l-p)D, W4


be low, and the expected returns associated with the payment will appear to be ‘predicted’ in the same way described in Section 2.

3.3. Investor sentiment

De Long, Shleifer, Summers, and Waldman (1990) present a model of capital market equilibrium in which some agents have nonrational expectations regarding the future returns on some assets in the economy. These agents’ beliefs are driven by a common factor that De Long et al. label ‘investor sentiment’. Since all agents in this economy have finite investment horizons, risk caused by investor sentiment is not dissipated, and thus security prices are affected. Rational agents who are aware of misconceived investor sentiment are unwilling to fully offset noise trades, since they run the risk of having investor sentiment adversely affect security prices when they want to liquidate their holdings.

Lee, Shleifer, and Thaler (1991) offer investor sentiment risk as an explanation of what they term the ‘closed-end fund puzzle’. This puzzle has four parts. First, in initial public offerings, closed-end funds are issued at premia of nearly 10%. Second, within 120 days of their initial public offering, closed-end funds sell at an average premium of - 10%. Third, these premia fluctuate over time. Fourth, when closed-end funds are liquidated or open-ended, their premia become zero. Lee et al. argue that this puzzle can be explained in the framework of De Long et al. Funds are issued when noise trader demand is the greatest. After the initial public offering, closed-end funds are less valuable than the pool of assets they hold, since they are more subject to this stochastic, undiversifiable sentiment. Over time, premia change as investor sentiment changes. Upon open-ending, premia shrink to zero, since noise trader risk is eliminated.

An important implication of the De Long et al. model that is not pursued by Lee et al. is that discounted funds should have higher equilibrium expected returns. A funds premium is a measure of the fund’s exposure to investor sentiment risk. If premia are a manifestation of investor sentiment, then the abnormal returns associated with funds that sell, on average, at a negative

where N, and P, are, respectively, the time t net asset value and stock price, D is the dividend payment, and /,I is the marginal tax rate of dividend.

The premium of a fund (PREM) is defined as

PREM = (P, - N,)/N, , (F3)

or, from (Fl) and (F2),

PREM = (P,- 1 - N,m, + pD)/(N,- 1 - D).

The derivative of PREM with respect to D may be written as

aPREM/dD = (P,-1 - N,m,(l - /J))/(N,-1 - D)2.

This derivative will be positive, as long as P,-, > N,- ,(l - p), or PREM > -p

(F4)

(F5)

352 J. PontifSIJournal of Financial Economics 37 (1995) 341-370

premium simply reflect an added return for exposure to investor sentiment risk. Negative CAPM abnormal returns will accrue to funds that sell at a premium, since these returns are negatively correlated with investor sentiment, and thus provide a hedge against sentiment. In short, the returns earned by Thompson’s portfolio strategies are earned at the expense of being exposed to investor sentiment.

3.4. Omitted risk factors

Fama and French (1993) argue that three risk factors are useful in explaining stock return variation: the excess return of the market portfolio, the return to a portfolio that holds small firms and short-sells large firms, and the return to a portfolio that holds firms with high book-to-market ratios and shorts firms with low book-to-market ratios. Fama and French contend that these three portfolios do a good job of explaining the average returns of stocks. For example, conditioning returns on these three factors nearly eliminates the small-firm effect. Since a closed-end fund’s book-to-market ratio is its discount, controlling for market-wide book-to-market risk may be particularly important.

These three mimicking portfolios are also likely to be important in explaining closed-end fund returns. Specifically, Lee et al. show that changes in closed-end fund premia are correlated with small-firm returns. Thus, if small-firm risk affects expected returns, premia could forecast exposure to it. Since closed-end fund premia are analogous to market-to-book ratios, the ability of premia to predict closed-end fund returns might be explained by controlling for risk that is associated with book-to-market portfolios. If the risk associated with these portfolios ‘explains’ the ability of premia to forecast returns, the bothersome question remains as to why closed-end funds are subject to more risk than the risk in their portfolios.

3.5. The January eflect

Brauer and Chang (1990) present evidence that closed-end funds are subject to the ‘January Effect’. They document that closed-end prices increase in January, although their net asset values do not. They also find that share returns at the turn of the year are negatively related to the previous year’s returns. They interpret these findings as evidence of tax-loss selling. Brauer and Chang show that the return for the average fund in their sample is less than its asset value return for every month except January. This implies that, on average, premia are the highest in Janaury and decline during the year. If premia are lowest in December and stock returns are highest in January, then it is possible that the success of Thompson’s strategy is specific to these months. If this were the case, the ability to predict returns could be interpreted as a seasonal, tax-specific effect.

J. Pontiff/Journal of Financial Economics 37 (1995) 34X-370 353

3.6. Correlated risk changes

When Thompson (1978) documented abnormal returns from his strategy, he utilized market beta coefficients calculated from a three-year moving window. A potential explanation for the abnormal returns that Thompson found is that premia changes occur at the same time as beta changes. Fund managers might change the risk of the invested portfolio. Increases in risk and changes in premia may be correlated if managers are able to accrue abnormal returns in certain environments by changing portfolio risk, for example, by timing market move- ments. Another potential explanation is that managers attempt to eliminate discounts by increasing portfolio risk. Regardless of which explanation is more accurate, as long as increases in portfolio risk are met with lower premia, a test that constrains risk to be constant would detect abnormal returns when premia decrease.

4. Modeling the return-generating process

4.1. Discussion of the model

The preceding section proposed explanations consistent with the apparent ability of closed-end fund premia to predict future returns. This section incorporates these explanations into an empirically testable model of the process generating closed-end returns. These explanations can only be integrated into a multibeta model that allows risk and intercept parameters to vary.

The following model of the excess-return-generating process uses a general method of parameter specification, similar to that used by Shanken (1990), that is able to accommodate the previous explanations. Variable definitions are in Table 1. The model can be written as

Ri, - RF, = ai, + /$(RM, - RF,) + /3FMLHML, + /?iMBSMB,

+ j?y’ + ei,,

where

(5)

ai, = a + b JAN, + cINCDIt$ + d BIDASKi,- 1 +f PREMi,- 1,

Br = By +f”(PREMi,- 1 - AVGi) 3 /jfML = BFML +fHML(PREMi,- 1 - AVGi) 3

fi;“” = BsMB + fSMB(PREMi, - 1 - A VGi) 3

pi” = BFsT +fLS”‘(PREMi,- 1 - AV’Gi).

Excess returns are generated from exposure to four risk measures and fund- specific abnormal returns. Fama and French (1992) argue that the first three risk

354 J. Pontiff/Journal of Financial Economics 37 (1995) 341-370

Table I Variable definitions (i denotes the variable is for fund i, t denotes that the variable is for time t)

ai, = expected return of fund i that cannot be attributed to risk

AVGi = time-series average of fund i’s premium

BIDASK = fund’s estimated bid-ask spread

BY = beta of fund i with the CRSP value-weighted market index in excess of the risk-free

e,

HML

INCDI~

JAN

LST

PREMi

Ri

RF

RM

SMB

rate

= beta of fund i with the investor sentiment portfolio = beta of fund i with the Fama-French HML return

= beta of fund i with the Fama-French SMB return

= deviation of fund i’s premium from its time-series mean

= fund’s idiosyncratic price movement

= difference between the returns on high and low book-to-market equity portfolios with similar average size

= income dividend yield, taxable as dividend income, in excess of the risk-free rate

= indicator variable equal to one if time t is in the month of January, and equal to zero otherwise

= difference between the value-weighted returns on closed-end funds and their portfolios

= premium of fund i

= return of fund i

= risk-free rate

= return of the CRSP value-weighted market index

= difference between the returns on small-stock and big-stock portfolios with similar average book-to-market ratios

indices do a good job of explaining the cross-section of average expected stock returns. The fourth risk index is included to capture investor sentiment risk. The goal of these factors is to span all relevant risk.

The parameters of the model, the betas, and the abnormal return, ait, are allowed to be a function of variables of interest. The betas of the fund are affected by the deviation of the fund’s premium from its long-run mean. This allows us to interpret the Bi parameters as portfolio i’s average beta, while allowing premium to affect risk. The term ‘abnormal return’ refers to the expected excess return not attributed to risk. A fund’s abnormal return, ai,, is affected by the month of January, JAN,, the excess dividend yield that is taxable as ordinary income, ZNCDI1/,l, last month’s bid-ask spread, BIDASKi,- 1, and last month’s premium, PREMi,- 1.

The abnormal return conditioning variables can be ascertained before the return period. For example, PREM and BZDASK are observed the period

J. Pontiff/Journal of Financial Economics 3 7 (I 995) 34 I-3 70 355

before the return. The month of January is perfectly anticipated. Investors can anticipate future dividend payouts, since federal law requires that funds pay out 90% of portfolio dividends. Also, dividend payments are typically announced in advance of the actual payment.

Although Eq. (5) incorporates variation of abnormal returns and market beta, the impact of variables of interest on these parameters is the same for all funds, i.e., the parameters a, b, c, d, f, f”, f LST, fHML, and f”“” are identical for all funds. This specification is chosen in order to conserve degrees of freedom. Multiple betas are used in order to avoid adverse inferences from not taking into account the systematic risk not captured by the CRSP value-weighted stock index.

An investor sentiment beta, /?yT, is included to capture returns attributable to changes in sentiment. Since the sentiment index is the change in the value- weighted premium, this index can be considered the return from holding a value-weighted portfolio of closed-end fund shares and short-selling a value- weighted portfolio of the assets they hold. Thus, this index represents a zero investment portfolio. As long as closed-end funds are subject to more investor sentiment than the portfolios they hold and as long as both the fund and the portfolio are subject to equal amounts of other risks, subtracting NAT/ returns from closed-end fund returns provides a measure of sentiment risk.

This model is a multibeta extension of a simple market model. Since all risk measures are essentially portfolios, access to the risk-free security implies that, for all funds, ai, equals zero. This, in turn, implies that a, b, c, d, andfequal zero.

Rewriting DEVPi, as the deviation of the fund i’s premium from its time-series mean (i.e., DEVPi, = PREMi, - AVGi), the above model can be estimated with the following equation:

Ri, - RF, = u + b JAN, + cZNCDZl/i, + d BIDASK,- 1 +f PREM,- 1

+ B,F(RM, - RF,) + BHMLHML, + BfMBSMB,

+ ByTLSTt +f”DEVPit- l(RM, - RF,)

+fSMBDEVZ’it-lSMBt +fHMLDEVPif-fHMLf

+fLSTDEVPir-1LS7’t + ei,. (6)

All the coefficients have the same interpretation as in Eq. (5). Estimation involves estimating this equation for each fund, with the restriction that all parameters are identical across funds, except those parameters subscripted by i: BM, BHML, BSMB, and B,FST.

4.2. Market implications

Estimating Eq. (6) allows for a simple test of whether or not augmenting traditional approaches to asset pricing can mitigate the apparent relation

356 J Pontiff/Journal of Financial Economics 37 (1995) 341-370

between premia and future returns. This is directly tested by inferring whether the premium parameter,f, equals zero. Regardless of whether or not this can be rejected, other parameters are estimated from Eq. (6) that yield general insights into asset pricing.

Theories regarding the impact of bid-ask spreads on returns, such as that of Amihud and Mendelson (1986), postulate that the bid-ask spread parameter, d, is greater than zero. Since estimation of the return-generating process does not rely on a two-pass procedure, as does Amihud and Mendelson’s test, errors-in- variables problems are avoided. Also, because closed-end funds are claims to diversified portfolios, more accurate market model estimation is possible, since the relative amount of residual or idiosyncratic risk is less than individual securities. Unlike Amihud and Mendelson’s study, estimation of Eq. (6) incorporates other variables that influence or are expected to influence returns, such as the month of January and differential tax treatment of capital gains and dividends. A disadvantage of my test is the assumption that investors can trade the risk-free security. Since Amihud and Mendelson use a two-pass test, they do not rely on this assumption.

The impact of different combinations of dividends and capital gains on monthly returns has been studied by many, most notably Miller and Scholes (1982) and Litzenberger and Ramaswamy (1979). The results of these studies have been mixed. Most studies determine the impact of cash-flow mixes by regressing returns on measures of dividend yield and market beta. Studies that use long intervals to calculate dividend yields typically find no consistent relation between dividend yield and expected return. When shorter intervals (such as monthly) are used, there appears to be a consistent positive relation between dividend yield and expected return. Miller and Scholes (1982) stress that short-term dividend yield measures affect the conclusions of the test, because announcements of dividends convey information that is incorporated into security prices. They argue that this can lead to spurious estimation. Litzenberger and Ramaswamy (1982) conduct a test that addresses this criticism, and they conclude that information effects do not cause the relation between dividends and prices.

Closed-end fund dividend policy is constrained by tax law essentially to pay out all portfolio income. Closed-end funds report net asset value weekly, thus dividend payments do not convey information regarding NAV value. This avoids Miller and Scholes’s major criticism of short-horizon dividend tests, since stock prices will only react to an informationless payment if the value of the payment is different from the value of capital appreciation.

An investor sentiment explanation of closed-end fund premia attributes premia to investor sentiment risk exposure. Funds that have high average discounts should have high exposure to sentiment risk. A simple test of this model is to compare a fund’s premium with its sentiment beta, /3”“‘. Funds with higher premia should have higher sentiment betas.


The importance of different risk indices can also be ascertained by testing whether index betas are different. This is not a test of whether the risk of an index is priced, but a test of the necessary condition of whether or not the index explains any cross-sectional variation in returns.

The expected impact of the above effects on the parameters of the return- generating process are summarized in Table 2.

5. Estimating the return-generating process

5.1. Data

This section uses the same closed-end fund sample as Section 2. Excess fund returns are calculated by subtracting the current one-month Treasury-bill rate from the return of all funds. Similarly, the excess return of the market is computed by subtracting the one-month T-bill rate from the return of the CRSP value-weighted index. An index of the returns of small firms minus big firms (SMB) and an index of the returns of high minus low book-to-market firms (HML) are taken from Fama and French (1993).

The fourth excess return measure is the value-weighted closed-end fund return minus the value-weighted NAP’ return. The value weights are based on net asset value. While conceptually the same as the Lee et al. ‘Investor Sentiment Index’, this index is more convenient to use as a risk measure than the Lee et al. index because it is the excess return of a portfolio. The correlation between the two indices is 0.92. The average return of this portfolio is 0.34% per month.

It should be noted that since the difference between a closed-end fund’s return and its portfolio return represents a zero investment strategy, whether or not this index is priced can be ascertained by testing whether the average return of the index is different from zero (Shanken and Weinstein, 1990). The price of the index’s risk is 0.34% monthly. The t-statistic for this test is 2.35, with a p-value 1.95%. This test assumes that investors can trade the fund’s NAV. If the return of a fund’s net asset value is less than an investor can realize, perhaps due to managerial expenses, then the test statistic will be less than 2.35. For example, assuming managerial expenses of 1% annually reduces the price of risk to 0.26% monthly and the t-statistic to 1.79.

Excess income dividend yield was calculated from the CRSP data. If CRSP recorded that a dividend payment is taxable as ordinary income, the payment is noted as an income dividend, and if the payment is taxable as a realized capital gain, it is noted as a capital gain dividend. The excess income dividend yield is calculated by dividing the dividend amount by last period’s stock prioe and then subtracting the one-month T-bill yield.

Amihud and Mendeison (1986) use bid-ask spreads from Fitch’s Stock Quota- tions on the N YSE over the period 1961 to 1980. Their relative spread measure is

Table

2

Empi

rical

pr

edict

ions

fro

m t

he m

odel

of

the

close

d-en

d fu

nd r

etur

n-ge

nera

ting

proc

ess

The

retu

rn-g

ener

atin

g pr

oces

s is

spe

cifie

d as

Ri,

- RF

, =

ai,

+ j?f

(UM

I -

RF,)

+ jp

TLST

, +

/?tM

LHM

Lf +

fiEM

BSM

B,

+ ei

, ,

I- 2

wher

e $

ai,=a

+bJA

N,+c

INCD

I&,+

dBID

ASKi

,-,

+fPR

EM+,

, 2

/?f:

= BP

+f

”(PRE

Mi,-

1 --

AVGi

) ,

3 e

jjFM

L =

BFML

+

f “M

L(PR

EMi,m

1

- AV

Gi)

, 2

/?:M

B =

B,SM

E +

f SM

B(PR

EMi,m

1

- AV

Gi)

, S’

B

BE’

= Bi

uT

+ f L

ST(P

REM

i,- 1

- AV

Gi)

0.

k

R is

the

retu

rn

of th

e fu

nd.

RF

is th

e ris

k-fre

e ra

te.

JAN

is a

n in

dica

tor

varia

ble

equa

l to

one

if t

ime

t is

in t

he m

onth

of

Jan

uary

an

d eq

ual

to z

ero

2 5

othe

rwise

. IN

CDIV

is

the

inco

me

divid

end

yiel

d, t

axab

le

as d

ivide

nd

inco

me,

in

exc

ess o

f th

e ris

k-fre

e ra

te. B

IDAS

K is

the

fund

’s e

stim

ated

bid

-ask

8.

sp

read

. PRE

M

is th

e pr

emiu

m

of th

e fu

nd. R

M is

the

retu

rn o

f the

CRS

P va

lue-

weig

hted

m

arke

t in

dex.

HML

is

the

diffe

renc

e be

twee

n th

e re

turn

s on

high

2

and

low b

ook-

to-m

arke

t eq

uity

por

tfolio

s wi

th s

imila

r av

erag

e siz

e. SM

B is

the

diffe

renc

e be

twee

n th

e re

turn

s on

sm

all-s

tock

and

big

-sto

ck p

ortfo

lios

with

i=

; sim

ilar

aver

age

book

-to-m

arke

t ra

tios.

LST

is

the

diffe

renc

e be

twee

n th

e va

lue-

weig

hted

re

turn

s on

clo

sed-

end

fund

s an

d th

eir

portf

olio

s.

AVG

is th

e 2

time-

serie

s av

erag

e of

the

fund

’s p

rem

ium

. s *

Para

met

er

rest

ricte

d s

Coe

ffici

ent

Varia

ble

for

all

fund

s?

Pred

ictio

n I 2

a In

terc

ept

Yes

?

b JA

N Ye

s Fu

nd

retu

rns

are

subj

ect

to a

Jan

uary

Ef

fect

. b >

0.

C IN

CDW

Ye

s Fu

nd r

etur

ns

are

posi

tivel

y re

late

d to

con

tem

pora

neou

s di

viden

d yi

eld.

c >

0.

d BI

DASK

Ye

s Ex

pect

ed f

und

retu

rns

are

larg

er f

or fu

nds

with

hig

her

bid-

ask

spre

ads.

d >

0.

f PR

EM

Yes

The

abilit

y of

pre

mia

to

pre

dict

re

turn

s pr

oxie

s fo

r an

othe

r ef

fect

. f =

0.

J. PontifflJournal of Financial Economics 3 7 (I 995) 341-3 70

t; “i 4 .C

359

360 J. Pontiff/Journal of Financial Economics 37 (1995) 341-370

the average of beginning- and end-of-year relative spreads. For a given year, if a closed-end fund is included in the Amihud and Mendelson database, then their spread is used for all observations for that fund in the year. Since these data end in 1980 and since not all funds in my sample are listed on the NYSE, an estimate is used as the spread measure.

The following procedure was used to produce the estimated spreads. Earlier work, such as Masson (1989), has shown that bid-ask spreads are related to price level and the number of shares outstanding. Using closed-end funds that have price, number of shares, and spread data, the following pooled regression was estimated:

SPREAD = 0.071 - 0.00047 PRICE - 0.00032 PRZCEZO

+ 0.00067 PRICE15 - 0.0043 LN(MKTVAL)

+ 0.00017 SHARES, (7)

where PRICE is the fund’s price per share. PRICE20 is the maximum of PRICE minus 10 and zero. Likewise, PRICE15 is the maximum of PRICE minus 15 and zero. LN(MKTVAL) is the natural log of the fund’s market value (in thousands of dollars). SHARES is the fund’s number of shares outstanding (in millions). The adjusted R2 from this regression is 0.36. This regression equation is used to estimate spreads for funds that have price- and shares-outstanding data, but do not have Amihud and Mendelson spread data.

Premia are recorded in the Lee et al. database as the ratio of price per share to net asset value per share minus one. A similar way to express premia is as the log of the above ratio. This method is used, since one fund in the sample has had a reported premium of 1,000°~.5 This transformation reduces the skewness of the premium data.

5.2. Portfolio test

Estimation of Eq. (6) is achieved by applying the methodology of Zellner’s (1962) Seemingly Unrelated Regression (SUR), with cross-sectional restrictions on some parameters. Contemporaneous residuals from similar funds might be correlated, and some funds might consistently be associated with higher vari- ance residuals. This method accounts for correlated residuals between equations by estimating a cross-model residual correlation matrix that is used in second-pass estimation.

‘This fund is called Cyprus Corp. During the high-premium period, the fund purchased two small companies. Since these were the only companies in the fund’s portfolio, Cyprus ceased to legally be a closed-end fund, although net asset values, computed from the historic cost of these companies, were reported to the Wall Street Jounoal.


The test uses several portfolios of funds rather than individual funds. Portfolio formation is useful because if residual correlation is strong for funds with similar premia, then forming portfolios based on premium will reduce residual correlation. Also, most computer packages require the same number of cross-sectional observations for each period when accounting for residual correlation. The use of portfolios ensures this.

For every month in my sample, all funds with available data were placed into one of seven portfolios based on the fund’s premium in the previous month. Portfolio 1 is the low-premium portfolio and portfolio 7 is the high-premium portfolio. This yields seven cross-sectional observations with 245 months of data. Equally weighted averages of the variables of interest were computed for each portfolio and used as both independent and dependent variables. Eq. (6) was estimated with ordinary least squares for each portfolio and the residuals were used to compute the estimated cross-sectional covariance matrix.

To avoid spurious correlation between portfolio returns and the investor sentiment index, the index is restricted to funds that are not contained in the premium portfolio. Thus, each premium portfolio has a different investor sentiment factor that excludes the funds that are in the portfolio.

Information regarding the seven premium portfolios is presented in Table 3. The mean portfolio premium ranges from over 28% for portfolio 7 to about -35% for portfolio 1. The average monthly excess return for the low-premium portfolio is 1.75% per month, whereas the high-premium portfolio has a -0.55% average excess return. The average excess income dividend yield ranges from - 0.32 to -0.29%, and this variable is not monotonically related to premium. The average bid-ask spread is between 1.63 and 2.12%. The extreme portfolios are associated with the highest spreads. This finding is consistent with Pontiff (1993), who shows that the average absolute premium level is positively related to spreads.

5.3. Estimation results

Tables 4a and 4b present the results of the test. Model one allows for the basic CAPM relation between a firm’s return and the return of the market, as well as an alternative that relates expected returns to premium levels. The premium parameter,f, is -0.036 and statistically significant at all customary levels. Thus, funds with premium differences of 20% have monthly return differences of 0.72%. Since premia are mean-reverting, this does not imply that funds with 20% premium differences will have differences in return of 0.72% ad injnitum, rather only in the first month. Since the premium process can be approximated by an autoregressive process over the first n months, the expected return difference for funds with 20% premium differences is (0.2)(f) c:=, (ri), where ri is the autocorrelation between the contemporaneous premium and the premium i months away. Using this formula, funds with 20% premium differences will have annual return differences of 6.1%.

362 J Pontiff/Journal ofFinancial Economics 37 (1995) 341-370

Table 3 Summary statistics for seven closed-end fund portfolios

The portfolios are rebalanced monthly based on last month’s premium, using the 245-month period from S/65 to 12/U. The entire sample contains 53 closed-end funds. All variables are in percent.

Mean [Median]

Portfolio Premium, - r Excess return Excess income dividend yield

Bid-ask spread

1 - 34.66 [ - 33.291

2 - 22.63 [ - 25.671

3 - 17.21 [ - 19.661

4 - 12.29 [ - 13.07]

5 - 7.19 [ - 7.311

6 - 0.13 [ - 0.593

7 28.02 [18.81]

1.75 Cl.251

1.16 [0.90]

0.78 [0.40]

1.02 CO.861

0.17 co.331 0.02

[ - 0.381 - 0.55

[ - 0.791

- 0.32 [ - 0.411

- 0.27 [ - 0.321

- 0.22 [ - 0.303

- 0.21 [ - 0.271

- 0.15 [ - 0.211

- 0.19 [ - 0.231

- 0.29 [ - 0.361

2.00 [2.04]

1.67 Cl.611 1.65

Cl.631 1.67

Cl.621 1.63

Cl.631 1.67

Cl.611

2.12 cl.981

Tables 4a and 4b further demonstrate that market beta increases as premia increase. Using an F-test, we can reject the hypothesis that all firms have equal exposure to market risk.

The full return-generating model is estimated in Table 4b. A significant coefficient of 0.011 on JAN implies that, on average, closed-end funds outper- form the market in January by 1.1%. The parameter on INCDW is significantly different from zero and implies that, absent transaction costs, marginal investors are indifferent between a dollar dividend and 46.9e ($1 minus c) of price appreciation. The magnitude of this estimate draws attention to the role that transactions costs play in preventing short-term trading during this period. The parameter on the bid-ask spread variable is significantly different from zero and positive, which is consistent with the Amihud and Mendelson theory that bid-ask spreads increase expected returns. The January coefficient in the beta equation lends weak support to the assertion that market betas increase for closed-end funds in January.

The PREM coefficients in the beta equation are insignificant from zero. This result is not surprising, since the portfolios are formed on PREM. Thus, a large amount of risk variation associated with PREM will be picked-up by the portfolio beta coefficients.

J. Pontiff/Journal of Financial Economics 37 (1995) 341~370 363

Table 4a SUR estimation of the return-generating model for seven closed-end fund portfolios

The portfolios are. rebalanced monthly based on last month’s premium, using the 245-month period from 8/65 to 12/85. The entire sample contains 53 closed-end funds. The return-generating process is specified as

Ri, - RF, = air + bM(RM, - RF,) + ei,, ai, = a +f PREM+,

R is the return of the fund. RF is the risk-free rate. PREM is the premium of the fund. RM is the return of the CRSP value-weighted market index.

Parameters restricted to be the same across portfolios

ai, Intercept PREM

Parameter t-ratio”

- 0.000 - 0.102 - 0.036 - 6.760d

Unrestricted parameters (F-ratio for the hypothesis that all seven parameters are equal)

Portfolios 1 2 3 4 5 6 7 F-ratiob

PM 0.96 0.91 0.82 0.77 0.75 0.79 0.69 2.44’

a 17 13 degrees of freedom. b6 numerator degrees of freedom, 1713 denominator degrees of freedom. ‘Significant at the 5% level. “Significant at the 1% level.

Interestingly, although accounting for different risk exposure does not negate the ability of premia to forecast returns, premium portfolios have statistically significant cross-sectional exposure to all four types of risk. In other words, a fund’s premium level is related to the fund’s exposure to risk. With the exception of the lowest-premium portfolio, higher-premium portfolios are associated with lower exposure to market risk. Size risk (SMB) is largest for the extreme-premium portfolios. 141 fact, out of the four types of risk, size risk has the strongest rejection of the hypothesis of identical exposure across portfolios. Market-to-book risk appears to have no pattern across portfolios.

If premia are ‘caused’ by investor sentiment risk, then higher premium portfolios should have larger investor sentiment betas. This hypothesis was tested by re-estimating the Tables 4 results under the restriction that /?FST = ~0 + ~1 AV’Gi and that /?FST is constant through time. This specification yields an estimate for a, of -0.005, with a t-ratio of 1.69 and a p-value (two-sided) of 0.092. Thus, this provides weak evidence for the hypothesis that exposure to investor sentiment risk is greater for funds with larger discounts.

The bottom line of Table 4b is that inclusion of these variables has little influence on the relation between premia and future returns. The parameter

Table 4b SUR estimation of the return-generating model for seven closed-end fund portfolios

The portfolios are rebalanced monthly based on last month’s premium, using the 245month period from 8/65 to 12/85. The entire sample contains 53 closed-end funds. The return-generating process is specified as

Ri, - RF, = ai, + /lz(RM, - RF,) + /3yTLST, + jfMLHML, + BiMBSMB, + et,,

where

ai, = a + bJAN, + clNCDI& + dBIDAS&-, ffPREM+, ,

/3: = By +f”(PREMi,- 1 - AVGi),

p;“” = BrML + f HML(PREMi,-, - AVGi) ,

/?iMB = BfMB +fSMB(PREMi,- 1 - AVGi) ,

jfT = BFsT +fLST(PREMi,- L - AVGi)

R is the return of the fund. RF is the risk-free rate. JAN is an indicator variable equal to one if time t is in the month of January and equal to zero otherwise. INCDIV is the income dividend yield, taxable as dividend income, in excess of the risk-free rate. BIDASK is the funds estimated bid-ask spread. PREM is the premium of the fund. RM is the return of the CRSP value-weighted market index. HML is the difference between the returns on high and low book-to-market equity portfolios with similar average size. SMB is the difference between the returns on small-stock and big-stock portfolios with similar average book-to-market ratios. LST is the difference between the value- weighted returns on closed-end funds and their portfolios. AVG is the time-series average of the fund’s premium.

Parameters restricted to be the same across portfolios

Parameter t-ratio”

ai, P, Intercept - 0.008 - 2.290’ JAN 0.011 2.726“

i INCDIV 0.531 2.865“ BIDASK 0.366 2.038’ PREM - 0.028 - 5.372d

I# TM PREM - AVG 0.290 1.376 lc”” f SMB PREM - AVG - 0.066 - 0.219 a?” f HML PREM - AVG 0.241 0.741 BY f LST PREM - AVG - 0.111 - 0.299

Unrestricted parameters (F-ratio for the hypothesis that all seven parameters are equal)

Portfolios 1 2 3 4 5 6 I F-ratiob

Bf” 0.77 0.89 0.79 0.72 0.71 0.61 0.60 2.39’ BSMB 0.74 0.19 0.30 0.17 0.10 0.30 0.51 6.3gd p”ML 0.09 0.27 0.27 0.14 0.01 - 0.08 0.19 2.56” p= 0.33 0.43 0.07 0.28 0.12 0.47 - 0.19 3.09*

a 1678 degrees of freedom. ‘6 numerator degrees of freedom, 1678 denominator degrees of freedom. ‘Significant at the 5% level. dSignificant at the 1% level.


estimate of PREM shrinks approximately one and a half standard errors from -0.036 to -0.028, but remains statistically significant. Since SUR significance levels may be unreliable in small samples, bootstrap p-values were computed by maintaining the same cross-sectional residual correlation, under the null of no premium effect. 1,000 iterations generated a p-value on the parameter estimate of PREM of less than lohe

5.4. Conclusions and implications from the test

The preceding test demonstrated that closed-end fund premia have a strong ability to predict future returns. This ability is statistically robust, and it cannot be ‘explained’ by other factors that affect expected returns.

Fama and French (1992) cross-sectionally regress returns (in percent) on the log of book-to-market, whereas my tests incorporate a regression of returns (as a fraction) on the natural log of market-to-book (premium). Multiplying my result by - 100 yields a Fama-French comparable estimate of 2.8. Fama and French’s estimate (Table III) ranges from 0.33 to 0.50. If the ability of book-to- market to forecast returns is driven by the same factor for closed-end funds and typical firms, the difference in our results may be driven by an errors-in- variables problem specific to accounting data. Thus, book-to-market ratios for typical firms might be noisy proxies of the information contained in discounts, thus biasing results that use accounting book values.

Besides avoiding an errors-in-variable problem, using closed-end fund discounts to study book-to-market effects circumvents a selection bias criticism that is peculiar to Compustat firms. Closed-end fund premia are reported in the Wall Street Journal. Therefore, the inclusion of a fund in my sample is not based on ex-post performance. This avoids a selection bias that Kothari, Shanken, and Sloan (1992) claim contribute to the Fama and French findings.

The economic significance of my results can be addressed by estimating how large transactions costs must be to eliminate the ‘abnormal’ returns generated from trading on premium levels. The Appendix demonstrates that the round- trip transaction cost needed to eliminate CAPM abnormal returns is 8.25% for purchasing securities and 3.13% for short sales. These estimated transaction costs are larger than what traders typically pay, implying that the premium-return relation is not a mere statistical aberration.

The above tests also add new insight into other asset pricing issues. Both tests support the notion that differential taxation induces investors to prefer capital

6A second test was conducted that uses data at the individual fund level. The results are similar, and are available directly from the author. This test computes Fama-Macbeth $-statistics that are not subject to the same small sample bias as SUR c-statistics. This test produces a statistically significant slope coefficient on PREM, equal to -0.92, which is larger than that of the first test. This test is unable to reject the hypothesis that closed-end fund returns have a January effect.

366 J. PontiffJJournal of Financial Economics 37 (1995) 341-370

gains over dividend income. The estimated magnitude of this effect, 0.53, is larger than estimates from other studies. For example, Miller and Scholes (1982) find an estimate of 0.32, which they argue is spuriously biased upwards due to information effects, and Litzenberger and Ramaswamy (1979) estimate the parameter to be 0.23.

Barclay (1987) argues that as expected dividend yield increases, the effective tax rate, as inferred from ex-dividend stock price behavior, decreases. This is attributed to a clientele effect. High marginal tax rate investors are more apt to purchase low-dividend securities. Barclay estimates ex-dividend stock price responses for the two lowest dividend yield quintiles to be 66% and 83%. My estimate implies stock prices decline by 47% of the dividend payment (this is calculated by subtracting the dividend yield coefficient from one). Although my estimate is not statistically different from the estimates of previous studies, the low level of my estimate is consistent with the claim that closed-end funds attract high marginal tax rate investors, and transactions costs prevent profitable short-term trading by low marginal tax rate investors. Regarding the tax rate of closed-end fund investors, over 50% of NY SE securities are held by pension funds which are nontaxable. Pension fund advisors have a reputation for not purchasing closed-end funds, since benefici- aries view such purchases as the costly payment of two advisory fees - one to the advisor and one to the closed-end fund’s management. My estimate of the effective marginal tax rate for closed-end fund investors is consistent with such observations.

My test finds a positive relation between bid-ask spreads and expected returns. The estimate of 0.37 is less than one standard error from the Amihud and Mendelson estimate. This result, although consistent with Amihud and Mendelson, is overshadowed by the strong ability of premia to predict returns: closed-end fund premia appear to predict future returns more reliably than bid-ask spreads.

6. Conclusions

Closed-end fund book values are based on market prices, making them ideal for examining the ability of book-to-market to predict returns. This paper has shown that premia have an economically strong ability to predict returns, which is related to premium mean reversion. This relation is puzzling and evades explanation by factors that affect expected returns, such as multifactor risk exposure, bid-ask spreads, dividends, and varying risk exposure.

This investigation has also provided evidence that supports general financial theories. Consistent with a dividend taxation effect, a dollar dividend is shown to be associated with 47e of price appreciation. Similar to Amihud and Mendel- son (1986), bid-ask spreads are shown to be positively related to expected


returns. The cross-sectional pattern of premia is shown to be related to exposure to investor sentiment risk.

Appendix: Strategy feasibility

An anomaly can only be considered a serious blow to a financial model if profits can be earned. ‘Profits’ can be defined as abnormal returns minus costs. In the spirit of Thompson (1978), this section devises two strategies and con- siders the feasibility of each strategy to accrue CAPM profits. These strategies utilize the premium portfolios discussed in the text. Both strategies take into account that some funds cease to have their premium level reported in the Wall Street Journal.

Long strategy. Buy all funds that enter the low-premium portfolio (portfolio 1). Sell each fund when it enters portfolio 3 to 7, or six months after the last reported premium.

Short strategy. Short-sell all funds that enter the high-premium portfolio (portfolio 7). Cover each fund s position when it enters portfolio I to 5, or six months after the last reported premium.

Table A.1 provides summary information for these strategies and for the CRSP value-weighted index. The return from the long strategy is over three times that of the CRSP value-weighted index, while the standard deviation 17.1% greater than that of the CRSP index. The abnormal Jensen measure for this portfolio is about 0.8% per month.

Combining the long and short strategies lowers overall risk. This yields a strategy that has both lower risk and higher return than the CRSP index. The combination of these strategies assumes that the amount spent on the long portfolio is equal to the proceeds from the short portfolio, making interpretation of return measure difficult, since the portfolio is costless.

From the Table A.1 example, excessive risk exposure does not appear to be costly. The average number of monthly round-trip transactions amounts to about 10% of the long portfolio and 6% of the short portfolio. From these statistics the magnitude of transactions costs needed to negate the abnormal returns of these portfolios can be computed by dividing the abnormal return by the average monthly transactions. This implies round-trip transaction costs must be greater than 8.25% (0.806 divided by 9.767) to negate the long strategy and 3.13% (0.197 divided by 6.298) to negate the short strategy. The costs associated with the long strategy appear high, especially for large investors. Shorting securities is typically more expensive, due to margin requirements, suggesting that a 3.13% cost may not be far-fetched.

368 J. Pontiff/Journal of Financial Economics 37 (1995) 341.-370

Table A.1 Summary of information pertaining to the feasibility of a closed-end fund premium-based trading strategy

The strategies are: Long Strategy: Buy all funds that enter the low-premium portfolio (portfolio 1). Sell each fund when it enters portfolio 3 to 7, or six months after the last reported premium. Short Strategy: Short-sell all funds that enter the high-premium portfolio (portfolio 7). Cover each fund’s position when it enters portfolio 1 to 5, or six months after the last reported premium. The strategies are conducted over the 245month period from 8/65 to 12/85. The entire sample contains 53 closed-end funds.

Avg. excess return (monthly X)

Jensen abnormal return= (monthly X)

Standard deviation of return (annual %)

Beta with value-weighted index

Avg. round trip transactions b (monthly %)

Avg. number of funds in portfolio

Long Short strategy strategy

1.106 - omo

0.806 - 0.197

5.066 4.570

0.892 - 0.696

9.767 6.298

5.698 10.834

Combined CRSP value- strategies weighted

1.069 0.336

1.003 0.000

4.058 4.325

0.195 l.ooo

a The Jensen abnormal return is the intercept from a regression of excess return of the strategy on excess return of the market.

‘This is the percentage (monthly) of the closed-end funds in the portfolio that are traded.

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