The information content of discounts and premiums on closed-end fund shares

Journal

of Financial

Economics

6 (1978) 151. 186. 0

North-Holland

Publishing

Company

THE INFORMATION CONTENT OF DISCOUNTS AND PREMIUMS ON CLOSED-END FUND SHARES Rex THOMPSON* Carnegie-M&m

Received

Liniuersity,

May 1978, revised

Pittsburgh,

PA 15213, USA

version received August 1978

This paper investigates the extent to which discounts and premiums provide information about future expected rates of return on closed-end investment company shares. It is found that discounted fund shares, adjusted for risk, tended to outperform the market in the period 1940 to 1975. Funds selling at a premium appear to have been bad investments over the same time period. On the basis of these results it is argued that the two-parameter capital asset pricing model does not describe the return generating process of closed-end funds. Other potential areas to search for breakdowns in two-parameter pricing are suggested.

1. Introduction and summary Closed-end funds are publicly traded firms which earn their income from owning and managing a portfolio of financial securities issued by other corporations and legal entities such as the federal government. When a closed-end fund sells at a discount’ the market value of its outstanding stock is less than the market value of its net assets (portfolio holdings minus short term liabilities). Conversely, a closed-end fund which sells at a premium has a market value of its outstanding stock which exceeds the value of its net assets. Various authors have brought empirical evidence or theoretical arguments to bear on the reasons for closed-end fund discounts, including Pratt (1966), Boudreaux (1973), Roendfelt and Tuttle (1973), Sharpe and Sosin (1974), Vives (1975), Mendelson (1977), Malkiel (1977) and Thompson (1978). But it has been difficult arriving at a potential explanation for the existence of discounts and premiums which is simultaneously consistent with *The author has received helpful comments from the participants of the Finance Workshops at the Universtty of Rochester and Carnegie-Mellon University. In particular, the author would like to thank F. Black, K. Gaver, R. Kaplan, R. Holthausen, P. Malatesta, S. Richard, K. Schipper, G.W. Schwert, and especially M.C. Jensen and J.B. Long, Jr. ‘The discount on a closed-end fund is defined as the difference between the value of the net assets of the fund and the market value of the fund’s stock, divided by the value of the net assets. A premium is a negative discount. The appendix defines several other key terms used throughout the discussion of investment companies and gives both instnutional and historical background information.

152

R. Thompson.

Closed-end fund discvunrs

and efficient)

both a competitive market for fund management talent, and a semi-strong form efficient capital market which can be described by a two-parameter capital asset pricing model.’ In fact, in my Ph.D. thesis [Thompson (1978)] I argue that none currently exists. The purpose of this study is to examine some evidence concerning the association between closed-end fund discounts and the future expected abnormal return performance of their stock. An association between discounts and performance is predicted by an explanation which argues that discounts (premiums) occur because investors perceive closed-end fund shares to have unattractive (attractive) attributes associated with their cash flows not directly related to systematic risk. A review of the literature cited above indicates that most of the popular explanations of discounts and premiums explicitly or implicitly make this prediction. There are essentially five classes of *explanations for discounts and premiums: the effects of (1) discrepancies between the true market value of the assets and liabilities held by the fund and their quoted net asset value (i.e., accounting problems), (2) personal income taxes and accrued capital gains tax liabilities, (3) the existence of transactions costs and the demand for diversification by small investors, (4) the productivity of fund management and their ability to generate expenses, and (5) naive security market information inefficiency.3 Theories based on the existence of personal income taxes suggest that discounts are the result of price adjustments required to compensate investors, through a higher expected before tax return, for incurring a potentially higher capital gains tax liability than would be incurred were investors simply to purchase the fund’s net assets. The higher potential tax liability exists in funds with large unrealized gains in their portfolio which, when realized, must be distributed to shareholders (and therefore taxed at the personal income,level). Any capital loss on the shares as the result of the distribution cannot be realized by shareholders until the shares are sold. Theories based on a demand for diversification by small investors imply that poorly diversified funds will sell at discounts to compensate (via higher returns) for excess residual variance and well diversified funds, perhaps at premiums. Theories based on either the importance of personal income taxes or residual variance of return are clearly inconsistent with two-parameter asset pricing. *A market in which asset prices always incorporate available information about the assets traded is called ‘information efficient’, or just ‘efficient’. The hypothesis that prices fully reflect publicly available information is called the semi-strong form of Efficient Market Hypothesis. See Fama (1970) for a clarification of the Eflicient Market Hypothesis and its forms, and a review of several tests of market effLziency. ‘See Thompson (1978, ch. II) for a more complete discussion and clarification of these explanations.

R. Thompson,

Closed-end ,fund discounrs

and efficient)

153

In addition, both Pratt and Malkiel suggest that the higher (lower) required rate of return implicit in closed-end fund discounts (premiums) is not based on real effects but rather is simply the result of straightforward capital market information inefficiency. The inefficiency results from price adjustments reflecting capricious investor expectations of the productivity of management (net of expenses). In other words, closed-end fund share prices do not reflect unbiased expectations of their earning power. It is important to note that this explanation has a prediction in common with the taxes and demand for diversification explanations: discounted fund shares should yield positive risk adjusted abnormal performance, gross of personal income taxes. In other words, closed-end fund shares which are selling at significant discounts can be successfully used in profitable trading rules by large, tax exempt investors.4 In contrast, both the accounting explanations and the hypothesis that discounts reflect unbiased expectations of management productivity imply that fund shares are priced to yield normal returns, but net asset value has been inaccurately represented. Net asset value is incorrect either because of the difficulties involved in accounting for such things as contingent liabilities and infrequently traded securities, or because management, as a productive (or unproductive) asset, has not been capitalized and included in reported net asset value. These explanations imply that discounts and premiums provide no information which can be profitably used in trading rules involving the purchase or sale of closed-end fund shares. Discounts and premiums are simply an artifact of a complicated and perhaps unsolvable accounting problem, with investors determining market value on the basis of unbiased expectations and accountants estimating net asset value using accepted accounting principles. In this study, I examine the extent to which closed-end fund shares are priced in a fashion which is consistent with traditional capital asset pricing theory. I use discounts and premiums on individual closed-end funds as information in simple trading rules. Section 2 contains a description of, and justification for, the performance measures used in the trading rule tests. In section 3, a description of the data is provided along with a few summary statistics concerning the characteristics of the individual funds used in the trading rules. Sections 4 and 5 contain the results of the empirical investigation. The results indicate that portfolios of discounted closed-end fund shares tend to outperform the market using traditional, ex post, rate of return benchmarks. As a result, it is concluded that over the time period examined, tax exempt investors could have improved the risk-return characteristics of their investment portfolios (relative to the market as a whole) by holding more of their capital in discounted closed-end funds. 4Milter (1977) argues for the existence of market-wide information Inefficiencies caused by heterogeneous investor expectations. Applied to the closed-end fund industry, his theory predicts the same discount-performance relationship as Pratt and Malkiel.

154

R. Thompson, Closed-end find

discounts

and

efjciencp

In section 6, I offer an interpretation of the results and draw tentative conclusions and implications for the concept of capital market efficiency and two-parameter asset pricing. Other areas of capital market research which could lead to the same type of discrepancy between the prediction of twoparameter asset pricing and observed phenomena are suggested. The appendix contains definitions of some terminology used in the investment company industry and provides brief institutional background.

2. Measures of investment performance:

Methodology

Empirical work on the issue of asset pricing has found the following model to be a reasonably good representation of the stochastic process generating returns for financial assets traded on the NYSE:5

(1) where =rate of return on asset j during period t; =rate of return to the ‘market’ portfolio during period t; =cov(Fj,, F,,,,,)/var(?,,,,), often called the systematic risk of asset j in t; 2; = the disturbance of asset j during period t; zjr d,,,,di,=market determined parameters which describe (ex post) the average relationship between systematic risk and realized return during period t. ?jt

_

Given (exogenous) estimates of d,,, d,, and fij,, eq. (1) is solved for gjt, the estimate of the return to asset j during period t which is not attributable to general market influences6 The time series average of these residuals (sj,) is often used as an estimate of performance for the jth financial asset. Under the null hypothesis of neutral performance the average residual should be insignificantly different from zero. A statistically significant positive average residual implies that the asset is yielding rates of return in excess of the rate expected for assets of similar marginal risk (/Ij,). Several variations on the basic theme outlined above have been suggested as measures of performance of trading rules which call for the investor to hold a portfolio of securities whose composition (and therefore both systematic risk and residual variance) changes over time. Three such variations ‘See for example Black, Jensen and Scholes (1972) and Fama and MacBeth (1973). 6This technique and others like it are discussed in Brenner (1977). He describes the potential biases resulting from computing b, from a simple OLS regression, as a tirst stage in estimating abnormal returns (ij,). He demonstrates that for the problem at hand there is virtually no difference between using a simple regression (such as the one employed here) and a regression which includes the riskless rate of interest or the return on the zero beta portfolio. The difference is miniscule in our case because the average systematic risk of the closed-end funds is very close to unity [see table 3 below and Brenner (1977, p. 63)].

R. Thompson,

Closrd-end.firnd

discounts

and e,@ienc~

155

will be used in the empirical work below: the Abnormal Performance Index [Scholes (1972)], the Average Time Series Residual, and the Average Standardized Residual [Jaffe (1974)]. Each presupposes that the gi, described above have been calculated for the financial assets involved in the trading rule. The three performance measures represent summary statistics for the performance of combinations (portfolios) of financial assets; in our case, combinations of the securities of closed-end funds which have certain discount characteristics. These three performance measures are highly correlated, but they involve either different assumptions concerning reinvestment and rebalancing over time, or different procedures for measuring significance. Three statistics are reported (rather than just one) because they facilitate a comparison of my results with the results of virtually all previous studies investigating the performance of capital market trading strategies. 2.1. Abnormal

performance

index (API)

The API of a portfolio of N securities traces out the value of one dollar invested equally in all N securities and held through T compounding intervals with no rebalancing, after abstracting from general market effects,

The API will be close to unity if the ijt have a mean of zero.’ However, the sampling distribution of the API is not well understood and measures of significance are not generally reported for the API. Its magnitude is reported below because of its intuitive interpretation as the terminal wealth resulting from a strategy of investing $1/N in each security in the portfolio while agreeing to give away sequentially all ‘normal’ returns earned each month. 2.2. Average

time series residual (ATR)

The ATR of a portfolio of N securities is the time series average, between two points in time, of the average cross sectional residual of the N securities,

ATR= f i

r-1

f:

gj,/N,

J-1

where T is the number of time periods over which the average is taken. The ATR is equal to the Cumulative Average Residual of Fama, Fisher, Jensen and Roll (1969) divided by T, the number of months in the time interval. ‘See Ball and Brown hypothesis.

(1968) for a discussion of biases from unity of the API

under the null

R. Thompson.

156

2.3. Average

standardized

Clo.sed-cmi futd

residual

discounts

and efficiency

(ASR)

Computing the ASR of a trading rule requires several steps which are outlined more extensively in Mandelker (1974). The first step is to compute the average residual for the securities in the portfolio over each time interval (in our case, one month) for which the trading rule is operative. The second step is to estimate the standard deviation of each monthly average residual. This is done by computing the sample standard deviation of the residuals from the same portfolio held over the previous 36 months. The average residuals are then standardized (divided by the estimates of their standard deviations). Each standardized residual is an individual r-statistic for the residual of the trading rule in its respective month. The average (over time) of the standardized monthly residuals is ASR=;

T MR z +, I-1 I

where MR, is the average the estimate of the standard

portfolio deviation

residual at t=Cy= 1 (Zj,/N), and of the residual in period t,

S, is

The trading rule under consideration yields significant abnormal performance if the ASR is significantly different from zero. In the tables which summarize the trading rule tests the t-statistic of the ASR is reported under the heading ‘ASR (t-stat)‘.’

3. Data description Yearly data on market prices, net asset values, dividends and capital gains distributions, expense ratios, and other fund characteristics are available back to 1936 in Wiesenberger’s lwestment Companies. Between 1936 and 1976, approximately 100 closed-end funds are represented in this source. Some of these funds are listed for only short periods of time-many less than 10 years. ‘One problem with interpreting the significance of the ASR and its t-statistic is that the estimates of the standard deviations (S,) which are used in the standardization process are not independent over time. The dependence results from the tendency for trading strategies to contain the same securities for series of consecutive months. The time series estimates of the standard deviation of the residuals for consecutive months, therefore, contain common error terms which induce a form of serial dependence in the S, estimates. In the empirical work summarized in section 5 both the standardized and raw (MR, unstandardized) residuals are examined for serial dependence. For the problem at hand, the induced dependencies do not seem to be important.

157

R. Thompson, Closed-end fund discounts and efficiency

Most funds which terminate do so through a merger with another investment company, frequently an open-end fund. For example, all ten of the NYSE traded funds in the sample examined below which terminated did so through a merger. Other funds (not in my sample) have elected to liquidate, go open-end, or change to operating companies. The availability of monthly return data is primarily restricted to New York Stock Exchange (NYSE) traded funds. The Center for Research in Security Prices (CRSP) Monthly Return File has over 25 funds which have traded on the NYSE. Several of these funds began operations in the early seventies and have been eliminated from, the sample because they do not have suflicient data to adequately estimate performance. In all, 23 funds are Table ID no. 1

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23

CRSP

Fund

1

Name

ASA Ltd. (AmericanSouth African) Abacus Fund Inc. Adams Express Co. Alleghany Corp. American International Corp. American Research & Development Corp. Atlas Corp. Carriers & General Corp. Dominick Fund Inc. Eurofund International Inc. General American Invs. Inc. International Holdings Corp. Japan Fund Inc. Lehman Corp. Madison Fund Inc. National Aviation & Technique Newmont Mining Corp. Niagara Share Corp. Petroleum Corp. Am. Surveyor Fund Inc. Tri-Continental Corp. United Corp. U.S. & Foreign Sec. Co.

Period 1959-1975 1958-1971 1940-1975 1955-1973 194G-1968 1948-1966 1940-1956 194b-1975 1940-1974 196&1971 194%1975 1953-1974 1963-1975 194&1975 1951-1975 194c-1975 194tK1956 194&1975 194G-1975 194c-1973 194G1975 194&1975 1940-1975

included in the main sample analyzed in sections 4 and 5. The sample covers a wide spectrum of fund characteristics such as portfolio size and composition, fund objective, and length of tenure on the NYSE. The time period begins in January 1940 and ends in December 1975. Table 1 lists the funds and shows the time range for which beginning-of-the-year discounts are available. In order to provide a feel for the nature of the discount problem, end-ofyear discounts (stated in percent) for several of the major closed-end

J.F.E.

C

5

3 39 2 10 -5 -23 -6 3 0 5 16 13 E

61

7

4 35 7 -I -4 -28 3 -2 5 3 19 15 34

62

10

9 34 8 3 -1 -13 6 2 6 12 24 21 15

63

discounts’

Table

2

12

10 10 6 6 6 -3 0 10 3 21 26 24 32

64

11

12 -5 11 7 11 -2 8 2 -6 24 33 23 27

65

9

6 -12 19 11 9 -18 12 -14 0 20 29 25 32

66

-3

6 -77 21 -1 -16 -19 11 -33 3 19 17 16 9

67

-11

-10 -54 12 -14 -23 -32 -8 -26 -7 7 7 4 -5

68

for a sample of large closed-end

-2

-6 15 14 -8 -16 -51 -12 15 -4 14 11 2 -6

69

-1

6 -37 18 8 -14 -16 -5 12 3 15 3 5 -11

70

10

15 -10 20 12 8 3 13 15 14 26 7 14 -7

71

funds in the years

13

14 6 17 4 13 19 7 27 4 28 3 19 8

72

21

25 9 16 13 22 29 -4 43 10 25 26 14 43

74

16

23 -48 22 26 20 30 4 37 -2 28 25 22 16

75

value of the fund’s

17

14 -26 19 17 20 34 4 39 8 23 21 13 31

73

1960 to 1975.

‘Discount=(NAVMV)/NA I/: where N .t I’ 1, the net asset value of the fund. and MV is the market outstanding stock. hE = fund not traded.

11

14 30 12 19 -1 2 12 -2 0 4 22 23 E

3 1 8 11 14 15 18 16 19 21 22 23 13b

Average

60

ID no.

Year-end

R. Thompson,

Closed-end Jund discounts

und eflciewy

159

funds in the sample are listed in table 2. As the table indicates, discounts tend to be highly variable both cross-sectionally and intertemporally. Discounts in excess of 20% are quite frequent, with discounts exceeding 30 and 40% not uncommon. Premiums of a similar magnitude are also occasionally observed. Several authors have attempted to correlate discounts with various fund characteristics including portfolio composition, management fees, portfolio turnover rate, distribution policy, historical performance of the portfolio, and fund objective. These authors, including Roudreaux, Vives, Mendelson and Malkiel have met with varying degrees of success. These results are reviewed elsewhere [e.g., Thompson (1978, ch. III)] but generally, multiple regressions of discounts on groups of live to fifteen explanatory variables yield r-squared statistics in the neighborhood of 0.5 to 0.7. The sign and magnitude of the regression coefficients tend to be sensitive to model specification, the sample of funds selected, and the time period chosen. To gain an appreciation for the industry and the sample of NYSE funds used below, several fund characteristics should be highlighted. First, there are instances in the data where accounting problems exert considerable influence on the unadjusted discount quotations. For example, American-South African (ASA) holds primarily South African gold mining securities. ASA has chosen to quote asset values as the market value of their securities if traded on the Johannesburg Stock Exchange. The same securities often trade on the London Exchange at different prices. In 1966, London prices were approximately 17% lower than those in Johannesburg. Throughout most of the time period examined in this study, Tri-Continental had warrants outstanding which, if exercised would dilute the ownership of the firm. Several funds such as American Research and Development held substantial quantities of infrequently traded securities for which market value is difficult to determine. Three funds, ASA, Eurofund, and Japan Fund held foreign issues almost exclusively. International Holdings has significant Canadian holdings. The common stock of Alleghany Corporation was subject to significant leverage through the existence of preferred stock and bank loans. No attempt was made to adjust the quoted discounts for any accounting problems, and no funds were screened from the main sample on the basis of assets held. To the extent that accounting problems add to the size and variability of discounts, using unadjusted discounts will understate any link between performance and ‘corrected’ discounts. The data are used unadjusted primarily because, in most cases, it is unclear what an appropriate adjustment would be. The subsample investigated in section 5.5, however, is generally free of most accounting problems. No significant foreign holdings are contained in any of the fund portfolios and the vast majority of all holdings are NYSE securities. More will be said about this subsample in section 5.5.

160

R. Thompson,

4. Empirical estimation initial tests

Closed-end fund discounts

and efficiency

of time series performance,

benchmark

selection

and

The first step in the investigation of time series performance is to select a benchmark which accurately reflects the realized rate of return earned on financial assets having the same level of systematic risk as the trading rule or specific asset of interest. Limiting the scope of the benchmark to NYSE stock indices can be criticized since viable earning assets are arbitrarily excluded from the market portfolio proxy.’ However, the problems associated with using proxies for the market portfolio have not been solved operationally. The best that can be done currently is to demonstrate that the relative performance of the trading rule or financial asset is not highly sensitive to the choice of benchmarks. As a consequence, three popular benchmarks are used to estimate the performance of the trading rules examined below. The empirical results are essentially independent of the choice among these three, adding a measure of credibility to the overall findings. However, the issue of benchmark selection and its role in the interpretation of the results are discussed further in section 6. In terms of eq. (1) above, for a given level of systematic risk (pjl), define the benchmark rate of return as ?j, =d,, +dl,bj,. dot and d,, for each of the three benchmarks (FM, BJS,” and SLM”) used in the empirical work of sections 4 and 5 are defined in table 3. For each fund, the systematic risk (pj,) of the return on its stock is estimated from the following regression for each month in which there are sufficient data: ~j,=nj,+pj,(~~;n,)+~jr,

r=r-18,

t+17,

where fjK= the realized return for fund j over month r, = the realized return on the equal weighted market index, or, for use with i=nZ, the SLM benchmark, the return on the value weighted market index, gRoll (1977) summarizes the nature of the problems of using an arbitrary market portfolio proxy in capital market theory tests. “‘The Black, Jensen, and Scholes (1972) methodology is used to construct monthly security market line estimates. While Black, Jensen, and Scholes did not publish monthly security market line estimates they constructed portfolios of securities which enable monthly SML estimation. Their methodology was used to update the portfolio series from December 1965 (the end of their study) to December 1969 and monthly cross sectional regressions of portfolio returns on portfolio betas were run to estimate the monthly security market lines. “The Bildersee interest rates are rates of return from a portfolio of treasury bills. Part of the series can be found in Bildersee (1974), but the series has been updated using the Bildersee methodology through December 1975 by Mark Walsh and Lee Wakeman of the University of Rochester. Although not reported below, the equal weighted NYSE index was combined with the Bildersee riskless rates and used as a performance benchmark. Results were comparable to those reported.

R. Thompson,

Closed-end jiu~ul tliscoutlrs

Table

161

atld efficient>

3

Benchmark

d,,

d I,

Time range

FM

Fama and MacBeth intercepts as published in Fama (1976)

The Fama and MacBeth slope coelRients as published in Fama

1/4C-12/71

BJS

The intercepts as described in Black, Jensen and Scholes (1972)

The slope coeficient as described in Black, Jensen and Scholes

l/4&12/69

SLM

The return earned on a treasury bill index as defined in Bildersee (1974)

NYSE value weighted index minus the Bildersee riskless interest rate

1,14&12/75

nj, = intercept coefficient, pjt= the slope coefficient; fijI will be used as the estimate of systematic for the fund in month t, Cjr= the error term: Cjr is assumed to be normal, independently identically distributed with COV(?~,,r’,,,,)=E(1’,,)=0.

risk and

Note that the estimate of fijr for each month utilizes only 36 months of data. Although arbitrary, this technique is used because the true systematic risk may not be stationary over time. Potential weaknesses. of this methodology are discussed in section 6. Once the systematic risk estimates are obtained, the abnormal returns (Zj,) of eq. (2) are calculated. Table 4 presents the summary statistics of the gjt for each of the 23 funds, using the FM benchmark. As can be seen, the time series averages of the ij, (denoted (ij in the table) appear consistent with current capital asset pricing theory. Examining the average residuals of individual firms is a rather weak test of market efficiency, however. Table 4 also contains the time series average of the pj, computed from the 36 month windows. The global cross sectional average of the Bjt is 1.00 which suggests that closed-end funds do not have unusual systematic risk characteristics.

5. Portfolio performance of trading rules 5.1: Introduction

and summary

of the results

Since discounts fluctuate over time and across funds, it is difficult to infer a link (or lack of one) between discounts and performance by an examination of table 4. To highlight any relationship between discounts and performance, the individual funds are aggregated into portfolios based on the sign and magnitude of their discounts. The composition of the portfolios is

162

R. Thompson,

Average

abnormal

ID no.

Closed-end.jiind

monthly

0.00731 0.00015 0.00145 - 0.00372 - 0.00094 0.00830 - 0.00630 0.00067 -0.00191 -0.00281 0.00093 -0.00383 0.01615 0.00019 0.00225 0.00226 o.OQ107 0.00270 0.00282 - 0.00324 -0.00125 - 0.00264 - 0.00040

Avg.

0.00084

Table

4

return

for all funds

uud eflicienc)

FM benchmark

No. of observations

Avg. beta’

0.941 0.028 0.660 -0.513 -0.371 0.847 - 1.739 0.285 -0.936 - 0.397 0.406 -0.569 1.708 0.107 0.817 0.664 0.362 0.958 1.085 -0.569 -0.416 -0.505 - 0.146

I56 371 420 420 384 129 418 420 412 118 420 42 97 420 192 420 383 198 420 420 420 420 420

0.04 1.14 0.99 2.20 1.05 1.71 0.95 0.83 0.69 0.72 1.01 0.72 0.86 0.71 0.82 1.07 1.11 0.75 0.86 1.25 1.28 1.02 1.31

0.118

326

1.00

t,

ld 2 3 4” 5 6 7 8 9 10 11 12 I3 14 15 16 17 18 19 20 21 22 23

discounts

b

-

‘dj= the time series average of the ij, and has the dimensions of a monthly rate of return. bt = the r-statistic for dj assuming time series independence of the ej,. ‘Avg. beta=the average pj, for each fund over the time period in which the fund was listed on the NYSE. “Fund no. 1 is American-South African. This fund holds issues of South African firms many of which are involved in mining operations, It is interesting to note that the systematic risk of this fund is essentially zero. Fund no. 4 is Allagheny Corporation. The bulk of the assets of this fund were invested in a few large situations, primarily in financial services and railroads. The common stock of Allagheny was also subject to leverage via bank loans and the existence of preferred stock.

adjusted in response to changes in the discounts of the funds so that, in effect, each portfolio represents an investment strategy or trading rule. The trading rule results are presented in four parts: Section 5.2 contains a description of the trading rules and details of the performance estimation procedures. The results from utilization of the entire sample of closed-end funds are presented in section 5.3. In section 5.4 performance results are reported for the entire sample after an adjustment for industry specific risk. Results from the subsample of diversified funds are contained in section 5.5.

The primary

findings

can be summarized

as follows:

(1) Using

the entire sample of 23 funds over the period 194&1975, statistically significant superior performance is obtained by adopting trading strategies which utilize the discounts on fund shares. The superior performance is consistent across benchmark portfolios and arbitrary details of the performance estimation techniques. (2) Adjustments to the realized rates of return for tax receipt distributions and reinvestment options do not materially alter the results. (3) Superior performance of discounted funds relative to all the funds in the sample is obtained. A portfolio of discounted closed-end funds performs significantly better than an equally weighted portfolio of all the funds in the sample. (4) The subsample of diversified funds produces performance estimates similar to those of the entire sample.

5.2. A description

of the trading

strategies

Four investment strategies are employed. The ‘All Funds’ strategy serves as a control. At the beginning of each year, an equal investment is made in every fund in the sample. The performance of the ‘All Funds’ strategy represents an estimate of the performance of the entire closed-end fund industry, independent of the cross sectional distribution of discounts and premiums. The strategy labeled ‘Premium’ makes an equal investment in all the funds which are selling at a premium or exactly at NAV at the beginning of each year. If a fund should move to a discount during the year, it is not removed from the portfolio until the end of the year at which time the portfolio is revised and an equal investment is again made in all funds selling at a premium. The ‘Discount, Equal Weights’ strategy employs an equal weighting scheme like the Premium Strategy except that only funds selling at a discount are included in the portfolio at the beginning of each year. If a fund should go to a premium during the year, it is not sold until the end of the year, at which time the portfolio is revised to include all discounted funds with an equal investment in each. The ‘Discount Weighted’ strategy holds the identical securities as the ‘Discount, Equal Weights’ strategy. The portfolio weights, instead of being identical across funds however, are set proportional to the size of the discount at the beginning of the year. Funds with relatively large discounts receive relatively greater weight in the ‘Discount Weighted’ portfolio. The following the ‘Discount,

steps describe in detail how the performance estimates Equal Weights’ strategy are determined. The steps

for are

164

R. Thompson,

identical selection

for the criterion:

other

Closed-end fund discounts

strategies

except

for

and eflciettc)

the

weighting

scheme

and

(1) At

the beginning of each year, select each fund which was selling at a discount at the end of the previous year.12 (2) In the first year, divide $1 equally among all of these funds, reinvesting distributions back into the fund making the distribution. Without rebalancing, hold this portfolio until the end of the year. of the second and all subsequent years, reinvest the (3) At the beginning market value of the portfolio equally among all funds whose shares are selling at a discount. The API of the rule is defined as (4) ,@I=

‘ii’

{-&

YR=O

YR

‘5

r”ii”’

j=l

r=YR.I2+1

(I+&)

, I

where N,, is the number of funds selling at a discount in year YR. In the tables which report the trading rule results both the API and its geometric mean are reported. The geometric mean abnormal return is the 7th root of the API, minus unity. Expressed as a yearly return, the geometric mean aids in comparing performance across time periods of different lengths. It can be thought of as the yearly abnormal rate of return earned on the rule. Note that the API involves yearly rebalancing. (5) To compute the ATR and ASR of the rule: (a) In the first year, select the portfolio of funds and compute the residual for the portfolio for each month of the year. Continue to do this for all subsequent years. (b) The time series average of the monthly portfolio residual is the ATR. (c) Compute the average standardized residual of the entire period and each five-year subperiod as described above. (d) Compute the r-statistic for these averages.

I

F? .d

.

Results of the trading

rule tests: The entire sample

The results of the trading rules are presented in tables 5 through 8. Each table contains performance statistics for a particular trading strategy measured against each of the three benchmarks defined in table 3. Throughout “As a check against the possibility of a publication lag in the dissemination of year-end discounts the rules were also started in February rather than January of each year. This lag did not materially alter the results, although performance was reduced somewhat. Publication lag is not a serious problem for discounts and net asset values. The Wall Street Journal has published unaudited discounts on a weekly basis since 1965. Prior to that net asset values could have been obtained through correspondence with the funds themselves.

R. Thompson, Closed-end fund discounts

and
165

the discussion, results relative to the FM benchmark will be emphasized, but the general conclusions are also supported by the results from the other benchmarks. From tables 5 and 6, the performance estimates for the complete time period indicate that investors earned higher risk adjusted returns from closed-end fund shares selling at a discount than other NYSE stocks. This result is most noticeable in the ‘Discount Weighted’ strategy (table 5). While only a few of the j-year subperiods yield statistically significant performance, the cumulative effect is large. For example, over the 32 years between anuary 1940 and December 1971, an investor who adopted this trading ’ trategy would have ended with an abnormal performance index (measured I ,lative to FM) of 3.65. This represents an annual abnormal return in excess or 4%. Judging by the ASR T-statistic of 3.4, the abnormal performance is statistically significant at the 1 y0 level. It is also interesting to note that, relative to both the FM and BJS benchmarks, the average residuals are positive in every subperiod except 194@1944, where the average is negative but insignificantly different from zero. The performance of the ‘Discount, Equal Weights’ strategy is roughly consistent with the performance one would expect were it directly the result of the existence of discounts. For example, from table 5, the average discount of the funds in the ‘Discount, Equal Weights’ rule over the period 194&1971 was 20.06 percent. The geometric mean abnormal return of this rule over the same period was 2.37 percent per year. Over this period, the geometric mean return on the equal weighted market index and the geometric mean FM Intercept coefficient were approximately 15% and 8%, respectively. If it were possible to buy a stock portfolio at a constant 20% discount and continue to receive the dividends and capital gains on the true market value of the portfolio, the expected abnormal return would have been about 2% per year.’ 3 The ‘Premium’ strategy does not yield statistically significant negative performance when measured over the entire time period, although the API is return of an incredible 0.07.’ 4 This represents a geometric mean abnormal -7.9% per year. In other words, if an investor had adopted the ‘Premium’ strategy over the period 1940 to 1971, he would have lost approximately 8% “The expected return on a portfolio having a beta of 0.8 is 13.6% per year [yo+0.8(r,-~a)]. Purchased at a 2Op1; discount with the same expected dollar return, the expected rate of return would be 17% (13.6/0.8). The systematic risk of return to this arrangement would be unity (the original beta divided by the ratio of purchase prices). This implies a required return of 15 y0 and an abnormal return of 2 92. 14To check the sensitivity of the performance results to changes in arbitrary parameters such as.the dimension and orientation of the window used to compute pi,, performance was estimated under several different parameter specifications. No material changes in the results occur except that the 32-year performance of the ‘Premium’ strategy is statistically significant (with an API of 0.04 and ASR of -2.30) in the ca\e where the fi,, arc calculated using the 36 months of returns prior to month 1. The rcsul~s of table 7 used the 36 months of dara centered on month I

166

R. Thompson,

Closed-end find

discounts

and efficiency

per year relative to a comparably risky combination of all NYSE stocks. The tremendous variability in performance accounts for the lack of significance. The five-year period between 1940 and 1945 shows geometric means performance of -37 % per year! However, only four funds are held during this period and several of them sold at market prices well below $1.00 per share. Since price changes must take place in discrete jumps, realized rates of return on these funds are subject to infrequent but sizeable fluctuations. None of the four funds held foreign securities during the 1940-1944 period but two of the funds (Surveyor and United) were subject to extreme leverage. The period after 1944 also indicates negative average performance for the ‘Premium’ strategy, although smaller in magnitude and still statistically insignificant on the whole. The API from 1945 through 1971 is 0.77. The two subperiods 1945-1949 and 1965-1969 yield statistically insignificant positive abnormal performance. The All Funds strategy does not yield significant performance over the 32year period. However, the two subperiods 1945-1949 and 1965-1969 have statistically significant positive performance with geometric mean rates of abnormal return in excess of 8 y0 per year. It should be kept in mind that occasional short-term significance cannot be interpreted as indicative of expected abnormal future performance. Randomly selected portfolios occasionally yield statistically significant abnormal returns, particularly if estimated over as many subperiods as represented in the tables. As one of the checks for programmed errors, computer programs used to compute performance estimates in this study were also used to compute performance estimates for five portfolios of twenty randomly selected NYSE stocks. While no randomly selected portfolio generated significant abnormal performance over the entire time period, several significant five-year intervals were recorded. To give an indication of the sensitivity of performance to benchmark selection, table 9 contains the sample correlation coefficients between the ASR t-statistics from the different benchmarks using the six 5-year subperiods from 1940 to 1969. As can be seen, the Fama-MacBeth (FM) and Black, Jensen and Scholes (BJS) benchmarks give highly correlated performance statistics. None of the sample correlation coefficients are below 0.95. On the other hand, the value weighted NYSE index used in conjunction with Treasury Bill returns (SLM) is not highly correlated with either FM or BJS. For the ‘Discount Weighted’ strategy, the correlation coefficients are below 0.5.15 “Performance relative

to the equal weighted NYSE index used with treasury bills is more FM and BJS than performance relative to the value weighted index. Against the equal weighted index, only one correlation coeflicient was below 0.8 and four of the eight coeflicients were above 0.9. Performance relative to the equal weighted SLM benchmark is

highly

correlated

not reported.

with

R. Thompson.

Table Performance

statistics

167

Closed-end fund discounts and eflciency

5

for the ‘Discount ATR (avg. monthly) residual)

Weighted’

trading

strategy.

Period

API

Geometric mean (yearly)

194ck1971

3.65

0.04 13

0.0040

3.40

20.06

12.13

196Ck1971 194C-1959

1.96 1.97

0.0575 0.03 17

0.0050 0.0034

2.54 2.31

13.42 24.05

13.17 11.50

197&1971 1965-1969 196C-1964 1955-1959 1950-1954 1945-1949 194S-1944

0.99 1.44 1.37 1.09 1.27 1.55 0.87

- 0.0043 0.0759 0.0648 0.0176 0.0493 0.09 15 - 0.0280

0.0005 0.0061 0.0056 0.0020 0.0046 0.0077 -0.0009

0.12 2.07 1.62 0.50 1.67 2.59 -0.18

12.50 15.40 11.80 17.00 19.60 26.60 33.00

11.00 13.60 13.60 11.60 12.20 12.40 9.80

ASR (t-stat)

Avg. discount’

Avg. no. of funds

FM benchmark

BJS benchmark 194C-1969

3.19

0.0394

0.0039

3.18

20.57

12.20

196&1969 1940-1959

I .68 1.89

0.0535 0.0324

0.0048 0.0034

2.11 2.38

13.60 24.05

13.60 11.50

1965-1969 196&1964 1955-1959 195cL1954 1945-1949 194S1944

1.43 1.18 1.11 1.29 1.54 0.85

0.0745 0.0330 0.0214 0.0528 0.0906 -0.0314

0.0063 0.0033 0.0022 0.0048 0.0077 -0.0011

2.03 0.91 0.61 1.76 2.61 - 0.24

15.40 11.80 17.00 19.60 26.60 33.00

13.60 13.60 11.60 12.20 12.40 9.80

194&1975

3.27

0.0377

0.0037

2.75

20.06

12.13

1960-197.5 1940-1959

2.11 I.55

0.0640 0.0222

0.0057 0.0025

2.80 1.22

13.42 24.05

13.17 11.50

197&1975 1965-1969 196CL1964 1955-1959 1950-1954 1945-1949 194&1944 ~-.~---

0.98 1.73 1.24 1.01 1.01 1.23 1.25

- 0.0082 0.1160 0.0434 0.0013 0.0014 0.0417 0.0452

0.0005 0.0097 0.0037 0.0006 0.0005 0.0037 0.0054

0.05 2.84 1.14 -0.18 0.23 1.34 1.01

12.50 15.40 11.80 17.00 19.60 26.60 33.00

11.00 13.60 13.60 11.60 12.20 12.40 9.80

SLM benchmark

‘The average discount IS a simple average of all beginning-of-the-year discounts for the funds which \old at ~O\III\C diw>unt\ (;111d were therefore Included in this trading strategy).

R. Thompson, Closed-end find discoums

168

und c,$cienc~

Table 6 Performance statistics for the ‘Discount, Equal Weights’ trading strategy.

Period

API

Geometric mean (yearly)

1940-1971

2.12

0.0237

0.0024

2.96

12.13

1960-1971 194&1959

1.56 1.36

0.0375 0.0155

0.0032 0.0019

2.55 1.74

13.17 11.50

1970-1971 1965-1969 196&1964 1955-1959 1950-1954 1945-1949 194&1944

0.91 1.49 1.14 0.99 1.20 1.41 0.82

- 0.0439 0.0830 0.0269 - 0.0027 0.0373 0.0704 - 0.0395

- 0.0034 0.0066 0.0025 0.0002 0.0036 0.0060 -0.0021

- 0.99 3.17 1.15 - 0.04 1.55 2.28 -0.41

11.00 13.60 13.60 11.60 12.20 12.40 9.80

194&1969

2.03

0.0238

0.0025

2.86

12.20

196&1969 194&1959

1.48 1.37

0.0402 0.0158

0.0035 0.0020

2.33 1.81

13.60 11.50

1965-1969 196G1964 1955-1959 1950-1954 1945-1949 194&1944

1.50 0.99 0.99 1.23 1.39 0.81

0.0842 -0.0021 -0.0017 0.0418 0.0687 - 0.0422

0.0069 0.0002 o.ooo3 0.0040 0.0059 - 0.0022

3.25 0.06 0.01 1.69 2.30 - 0.45

13.60 13.60 11.60 12.20 12.40 9.80

ATR (avg. monthly residual)

ASR (r-stat)

Avg. no. of funds

FM benchmark

BJS benchmark

SLM benchmark 1940-1975

2.38

0.0275

0.0028

3.03

12.13

1960-1975 1940-1959

1.77 1.35

0.0485 0.0150

0.0042 0.0019

3.21 1.20

13.17 11.50

1970-1975 1965-1969 196&1964 1955-1959 1950-1954 1945-1949 1940-1944

0.96 1.63 1.12 1.01 1.01 1.15 1.15

-0.0192 0.1031 0.0236 0.0028 0.0015 0.0284 0.0279

-0.0011 0.0085 0.0022 0.0006 0.0005 0.0026 0.0039

-0.26 3.58 1.13 0.19 0.31 1.09 0.88

11.00 13.60 13.60 11.60 12.20 12.40 9.80 ---

-.

169

R. Thompson, Closed-end jund discounts and efficiency

Table 7 Performance statistics for the ‘Premium’ trading strategy. Geometric mean Period

API

(yearly)

ATR (avg. monthly residual)

ASR (t-stat)

Avg. no. of funds

FM benchmark 1940-1971

0.07

- 0.0788

- 0.0032

- 1.60

3.16

196&1971 194e-1959

0.93 0.08

- 0.0065 -0.1196

0.0001 - 0.0052

- 0.09 - 2.07

4.50 2.35

197&1971 1965-1969 196&1964 1955-1959 195&1954 1945-1949 194G-1944

0.72 1.57 0.81 0.64 0.77 1.71 0.09

-0.1493 0.0948 - 0.0407 - 0.0865 -0.0513 0.1132 - 0.3772

-0.0115 0.0078 - 0.0039 - 0.0070 - 0.0054 0.0130 -0.0213

- 1.91 1.86 - 1.09 - 2.35 - 1.65 1.31 - 1.07

6.50 5.30 3.00 3.00 1.80 1.60 3.00

1940-1969

0.10

0.0747

-0.0028

- 1.42

2.93

1960-1969 194&1959

1.18 0.08

0.0169 -0.1173

0.0019 -0.0050

0.28 - 2.05

4.10 2.35

1965-1969 196tXl964 1955-1959 195&1954 1945-1949 194(x1944

1.61 0.73 0.64 0.76 1.84 0.09

0.1006 -0.0604 -0.0854 -0.0533 0.1292 -0.3791

0.0082 -0.0060 -0.0070 -0.0057 0.0139 -0.0213

1.86 - 1.66 - 2.39 - 1.68 1.46 - 1.10

5.20 3.00 3.00 1.80 1.60 3.00

194G-1975

0.12

- 0.0633

-0.0012

- 1.46

3.16

196&1975 194@1959

0.88 0.14

-0.0104 - 0.0937

-0.0004

-0.0017

-0.50 - 1.49

4.50 2.35

197&1975 1965-1969 196&1964 1955-1959 1950-1954 1945-1949 194@1944

0.76 1.48 0.79 0.73 0.78 1.08 0.23

-0.1314 0.0820 - 0.0465 - 0.0606 -0.0481 0.0167 - 0.2579

-0.0100 0.0067 - 0.0045 -0.0051 - 0.0050 0.0064 -0.0035

- 1.66 1.39 - 1.39 - 1.45 - 1.86 0.22 -0.12

6.50 5.20 3.00 3.00 1.80 1.60 3.00

BJS benchmark

SLM benchmark

170

R. Thompson, Closed-end fund discounts and efficiency

Table 8 Performance statistics for the ‘All Funds’ trading strategy. Geometric mean

ATR (avg. monthly residual)

ASR (t-stat)

Avg. no. of funds

Period

API

194cLl971

1.19

0.0054

0.0012

1.68

15.28

196&1971 1940-1959

1.31 0.9 1

0.0227 - 0.0049

0.0019 0.0008

1.50 0.92

17.67 13.85

197&1971 196551969 1960-1964 1955-1959 1950-1954 19451949 194Gl944

0.83 1.49 1.05 0.91 1.13 1.53 0.57

- 0.0882 0.0837 0.0105 -0.0186 0.025 1 0.0890 -0.1049

- 0.0069 0.0061 0.0011 -0.0012 0.0026 0.0074 - 0.0057

- 1.78 2.77 0.54 -0.81 1.08 2.73 - 0.99

17.50 18.80 16.60 14.60 14.00 14.00 12.80

194c-1969

1.27

0.0081

0.0014

1.76

15.13

196&1969 194(x1959

1.40 0.91

0.0340 - 0.0046

0.0027 0.0008

1.62 0.97

17.70 13.85

1965-1969 196CL1964 1955-1959 195(x1954 1945-1949 194cL1944

0.52 0.92 0.91 1.15 1.54 0.56

0.087 1 -0.0165 -0.0184 0.0286 0.0906 -0.1086

0.0064 - 0.0010 -0.0012 0.0028 0.0074 - 0.0060

2.89 -0.54 -0.82 1.16 2.78 -1.04

18.80 16.60 14.60 14.00 14.00 12.80

1940-1975

1.58

0.0145

0.0021

1.89

15.28

196&1975 1940-1959

1.46 1.08

0.0323 0.0040

0.0027 0.0017

2.07 0.69

17.67 13.85

197Gl975 19651969 196&1964 1955-1959 1950-1954 194551949 1940-1944

0.87 1.61 1.04 0.95 0.98 1.23 0.94

- 0.0667 0.1004 0.0082 -0.0087 - 0.0033 0.0417 -0.0129

- 0.0050 0.0076 0.0009 - 0.0005 0.0000 0.0037 0.0036

- 1.17 3.10 0.48 - 0.23 0.08 1.38 0.39

17.50 18.80 16.60 14.60 14.00 14.00 12.80

(YeaW

FM benchmark

BJS benchmark

SLM benchmark

R. Thompson,

Closed-end

find

Table Sample

correlation

coefficients

between

ASR

discounts

171

and eflicienc)

9 r-statistics

for the live-year

subperiods

Discount Benchmarks

‘All Funds’

‘Premium’

‘Equal Weighted’

‘Discount

FM-BJS FM-SLM BJS-SLM

0.91 0.79 0.78

0.99 0.89 0.90

0.95 0.72 0.67

0.96 0.47 0.40

5.3.1. Adjustments

Weighted’

to the return series

In the performance tests summarized in tables 5-8, the rates of return were taken directly from the CRSP monthly return files. While expedient, the decision to use unadjusted rates of return can be criticized on two counts. One is related to the implicit assumption which such a procedure makes concerning the treatment of personal income taxes, and the other deals with the fact that several funds in the sample allow certain types of shareholder distributions to be reinvested in the fund at the lower of net asset value or market price. On the first count, most of the modern trading rule tests and methodology do not make adjustments for personal income taxes. In essence, the performance estimates reflect results obtainable by well diversified, tax exempt investors. In the case of closed-end funds the CRSP returns do not represent the true returns which would accrue to such an individual. The problem results from the treatment by CRSP of the distribution of tax receipts in the event that a closed-end fund elects to retain capital gains and pay income taxes on them on behalf of its shareholders. When a closed-end fund makes such a decision, it distributes to holders of record at the end of the year, a tax receipt which is deductible from federal income taxes. CRSP includes this tax receipt as if it were a cash distribution yet it has zero value to a tax exempt investor. Fortunately, few funds have ever elected to retain capital gains, but in the case of Tri-Continental, an adjustment to account for tax receipts affected the December rate of return for eight years. The trading rules were re-estimated after assigning zero value to tax receipts. The resulting impact on performance, though slight, was, of course, downward. The most noticeable effect occurred in the ‘Discount Weighted’ strategy rule since Tri-Continental sold at a rather large discount during the time that it distributed receipts. The adjustment for tax receipts reduces the API from 3.65 to 3.60 over the full 32-year period for the ‘Discount Weighted’ strategy. The t-statistic for the average standardized residual is still 3.37, well above the critical value for the 0.01 level of significance.

172

R. Thompsm.

Closed-end fund discounts

and efficiency

When selling at a premium, several closed-end funds allow shareholders to reinvest their capital gains distributions (and, in some cases, portions of dividend payments) in additional shares of the fund at net asset value (i.e., at a price below current market value). While the logistics of these arrangements vary across funds, the option to invest at a price below the market price is similar to a rights offering, having an exercise price equal to NA< issued concurrently with a cash distribution. Rather than attempt to explicitly value these rights, I adjusted the return series by simply assuming that, where advantageous, these options are exercised.16 As expected, the impact of the adjustment for reinvestment options increased the abnormal performance for all of the trading rules. The impact was most noticeable for the ‘Premium’ strategy where the t-statistic for the 32-year time period increased arithmetically from - 1.60 to - 1.51. On an individual fund basis, the adjustment has the biggest impact on the rates of return to shareholders of Madison Fund. All dividends and capital gains distributions from Madison are eligible and during the late 1950’s and 1960’s Madison almost always sold at a premium. Interestingly, the management of Madison Fund pointed out in their annual reports that about 20% of their shareholders did not participate in the reinvestment plan.

5.3.2.

Time series independence

Interpreting the ASR t-stats as student-t variates requires that each monthly abnormal return estimate from the trading rule be independent of the abnormal return from all other months. In addition, independence of the true abnormal returns is a necessary condition for market efficiency. Unfortunately, as was pointed out above, the standardization process utilized in the tests of significance induces a form of dependence in the standardized monthly performance estimates. As a result, the ASR t-stats could misstate the true significance of the average residuals. To investigate the extent of any misstatement, I calculated serial correlation coefficients for both the raw abnormal return series and the standardized series. Table 10 shows the first six autocorrelation coefficients for the ‘All Funds’ and both discount trading rules. The Box-Pierce statistic for the first 12 autocorrelations is also reported. Under the null hypothesis of serial independence, this statistic is distributed approximately chi-squared with 12 degrees of freedom in large samples. Several of the raw residual series display significant autocorrelation with the first order being negative. Dependence in the raw residuals causes an understatement in the individual monthly t-statistics. The understatement in the t-statistic results from using the sample standard deviation of the 16For a description of the algorithm used to compute ment options, see Thompson (1978, pp.. 101-102).

the approximate

benefits

of reinvest-

R. Thomgsotl,

Closed-end

fund

Table Serial correlation __~._

coefhcients

discounrs

173

and efjicienc)

10

for the abnormal returns benchmark.

of the trading

strategy

portfolios-FM

..~_ Lags

I

Period

2

3

_

4

5

6

BOX Pierce

‘AI! Funds’ 194tK 1971

Raw Res. Std. Res.

-0.17 0.00

0.08 0.05

- 0.03 -0.01

- 0.02 0.02

0.09 0.09

-0.04 - 0.00

35.8” 9.3

19601971

Raw Res. Std. Res.

0.08 0.13

0.00 0.01

0.01 - 0.04

0.02 -0.03

0.08 0.07

-0.07 -0.07

5.6 7.1

194& 1959

Raw Res. Std. Res.

-0.22 - 0.09

0.09 0.08

- 0.05 0.00

- 0.03 0.05

0.10 0.11

- 0.04 0.03

32.1” 12.8

194& 1971

Raw Res. Std. Res

-0.12 - 11.01

0.05 0.07

0.01 0.00

0.10 0.08

0.05 0.07

- 0.08 - 0.06

28.9” 12.9

19601971

Raw Res. Std. Re\.

0.12 0. I5

- 0.04 0.04

0.02 - 0.03

0.10 0.03

0.02 0.03

-0.14 -0.14

9.1 10.5

194& 1959

Raw Res. Std. Res.

-O.iY -0.12

0.07 0.09

-0.00 0.01

0 10 0.11

0.06 0.09

-0.07 - 0.03

28.7” 15.4

194% 1971

Raw Res. Std. Res.

-0.10 - 0.03

0.01 0.03

0.02 -0.01

0.08 0.07

0.01 -0.01

- 0.09 - 0.07

17.5” 8.6

196% 1971

Raw Res. Std. Res.

0.06 0.13

- 0.06 -0.01

- 0.03 -0.11

0.13 0.06

- 0.05 -0.11

-0.10 -0.10

8.8 13.0

194C 1959

Raw Res. Std. Res.

0.04 0.05

0.03 0.04

0.05 0.07

0.04 0.06

- 0.09 - 0.05

22.1” 13.4

‘Discount,

Equal

‘Discount

‘Significant

-0.18 -0.13

Weights’

Weighted

at the 0.05 level.

residuals in the denominator of the t without making an adjustment for the serial correlation in the residuals. This understatement of the r-statistic serves to understate the significance of the trading rule results reported in tables 58. The understatement is slight and if anything reinforces the significance of the results reported in the tables.” None of the standardized series displays significant autocorrelation at the 0.05 level. This result implies that there are no significant problems associated with interpreting the average standardized residuals. “For the case of a tirst-order autoregressive process, the variance of the abnormal returns overstates the variance of the ‘white noise’ in the abnormal returns by the factor l/(1 -p*) where p is the serial correlation coefficient. The largest serial correlation coefIicient (in magnitude) in table 9 is -0.22. If this is typical of the correlation throughout the trading rule portfolios, the overstatement in variance is less than 5%. The understatement in the r-statistic iscorrespondingly small.

174

5.4. Neutralizing

R. Thompson,

Closed-end find

discounrs

and ej’kienq

industry specijc risk

The possibility of overlooking an important component of marginal risk which may be indigenous to the closed-end fund industry motivates an additional test of the trading rule strategies. In table 11, the abnormal returns from the ‘All Funds’ strategy are subtracted from the abnormal returns to the discount rules. These return vectors represent the returns earned on the trading strategies after abstracting from both general market movements and closed-end fund industry movements. The performance of the strategies measured net of the ‘All Funds’ performance isolates the information content of the existence of discounts from the general information that the securities comprising the strategies are simply closed-end funds. For example, this differencing procedure should net out industry influences such as the effects, if any, of bad publicity concerning the advantages of purchasing open-end funds relative to closed-end funds, and the risk of management fraud or abuse of discretionary power. The performance estimates in table 11 are generally lower than in tables 5 and 6. This is because the ‘All Funds’ strategy yields positive performance estimates when measured relative to the market. The magnitude of the estimates in table 11 are essentially the difference between the estimate of the ‘All Funds’ strategy in table 8 and the discount strategies of tables 5 and 6. The differencing process, however, also reduces the variance of the abnormal return series to an extent sufficient to maintain statistical significance of the 32-year average residuals. For example, the ATR of the ‘Discount Weighted strategy falls from 0.004 to 0.0027 per month when the ‘All Funds’ abnormal returns are subtracted. However, the t-statistic of the ‘Discount Weighted’ strategy only falls from 3.4 to 3.0. The t-statistic for the ‘Discount Equal Weights’ strategy falls trivially from 2.96 to 2.85 when measured over the 32year period between 194&1971. 5.5. The subsample of diversified funds

As was pointed out in section 3 the entire sample of funds covers a wide spectrum of fund attributes. In terms of the asset structure of the funds, the variety represented in the entire sample may be greater than that of the New York Stock Exchange as a whole although interests in foreign and speculative investments, extensive diversification across investments or very poor diversification, could characterize the asset structure of other NYSE firms. While the basic question of the information content of discounts and premiums is not sensitive to differences in fund attributes, the empirical estimation of performance might be. Because of the shortcomings associated with using a NYSE index as a proxy for the market portfolio, firms which have extremely unusual characteristics relative to the index are the most likely to suffer from misestimation of true systematic risk.

R. Thompson,

Closed-end find

discounts

and eficiency

175

As a check against the possibility that a few extreme outliers are causing the results for the entire sample, I examined a conservative subsample of funds separately. This sample, listed in table 12, is identified by Vives (1975) Table Performance

11

statistics for the discount trading strategies after subtracting abnormal returns of the All Funds strategy-FM benchmark.’ ATR (Avg. monthly residual)

Geometric mean

ASR (t-stat)

Period

API

1940-1971

2.42

0.0280

0.0027

3.00

196c-1971 1940-1959

1.50 1.61

0.0346 0.0241

0.0030 0.0026

1.08 3.12

197&1971 1965-1969 1960-1964 1955-1959 1950-1954 1945-1949 194@1944 -

1.17 1.00 1.29 1.18 1.11 1.01 1.22

0.08 15 00001 0.05 17 0.0335 0.0205 0.0025 0.0402

0.0073 -0.0001 0.0044 0.0032 0.002 1 0.0003 0.0048

WW ‘Discount

Weighted

2.03 - 0.79 1.81 1.57 1.67 1.62 1.35

‘Discount, Equal Weights’ 194&1971

1.40

0.0106

0.0012

2.85

1960-1971 194&1959

1.20 1.17

0.0153 0.0078

0.0013 0.0012

1.66 2.31

197@1971 1965-1969 1960-1964 1955-1959 1950-1954 1941-1949 194&1944

1.08 1.04 1.08 1.07 1.04 0.92 1.15

0.0387 0.0069 0.0146 0.0129 0.0084 -0.0176 0.0279

0.0034 0.0004 0.0013 0.0014 0.0011 -0.0014 0.0036

0.00 -0.21 1.90 1.85 1.67 -0.22 1.08

‘Reinvestment

options

are allowed

to be exercised. Table

The subsample

12

of diversified

funds.

ID no.

Fund name

Period

Avg. beta

3 8 9 11 14 15 18 20 21 23

Adams Express Co. Carriers & General Corp. Dominick Fund Inc. General American Invs. Inc. Lehman Corp. Madison Fund Inc. Niagara Share Corp. Surveyor Fund Inc. Tri-Continental Corp. U.S. & Foreign Sec. Co.

1940-1976 194&1976 194&1974 1940-1976 194&1976 1951-1976 194&1976 194&1973 194&1976 194&1976

0.99 0.83 0.69 1.01 0.71 0.82 0.75 1.25 1.28 1.31

the

176

R. Thompson. Closed-end fund discounts and efficiency Table 13 Performance statistics for the subsample of diversified funds-FM ATR (avg. monthly residual)

benchmark.

Period

API

Geometric mean (yearly)

1940-1971

2.30

0.0264

0.0028

2.39

8.06

196&1971 194c-1959

1.26 1.82

0.0196 0.0305

0.0020 0.0033

1.23 2.11

8.00 8.10

197cL1971 19651969 196&1964 1955-1959 195&1954 1945-1949 194&1944

0.89 1.30 1.09 1.06 1.35 1.48 0.86

- 0.0540 0.0536 0.0169 0.0125 0.0615 0.0812 - 0.0295

- 0.0045 0.0047 0.0019 0.0013 0.0056 0.0076 -0.0014

-1.04 1.79 0.57 0.45 1.82 2.05 -0.38

1940-1971

1.82

0.0189

0.0021

2.22

8.06

196&1971 194&1959

1.29 1.41

0.0217 0.0171

0.0022 0.0021

1.40 1.72

8.00 8.10

1970-1971 1965-1969 196&1964 1955-1959 1950-1954 1945-1949 194tS1944

0.86 1.36 1.11 1.02 1.28 1.37 0.79

- 0.0739 0.0628 0.0216 0.0040 0.0500 0.0654 - 0.0469

- 0.0064 0.0054 0.0023 0.0007 0.0046 0.0062 --0.0031

- 1.64 2.01 0.89 0.20 1.79 1.97 -0.84

7.00 7.80 8.60 8.20 8.60 8.80 6.80

194&1971

0.06

-0.0821

- 0.0036

- 1.61

2.13

196&1971 194&1959

0.73 0.09

-0.0257 -0.1144

-0.0019 - 0.0046

-0.81 -1.40

3.00 1.60

197&1971 1965-1969 196@-1964 19551959 195G1954 1945-1949 1940-1944

0.7 1 1.31 0.79 0.63 0.77 1.29 0.14

-0.1589 0.0549 - 0.0456 - 0.0895 - 0.0497 0.0520 -0.3241

-0.0135 0.0048 - 0.0045 -0.0071 -0.0053 0.008 1 -0.0141

- 2.79 1.43 - 1.23 - 1.95 -0.84 0.94 -0.59

4.00 3.20 2.40 1.60 1.40 1.20 2.20

194&1971

0.96

-0.0012

0.0009

1.24

10.19

1960-1971 194S-1959

1.04 0.92

0.0037 - 0.0042

0.0007 0.0011

0.58 1.14

11.00 9.70

197c-1971 1965-1969 1960-1964 1955-1959 1950-1954 194551949 194@1944

0.80 1.28 1.02 0.94 1.19 1.38 0.60

-0.1057 0.0505 0.0042 -0.0128 0.0354 0.0667 - 0.098 1

-2.41 1.74 0.28 - 0.43 1.42 2.05 -0.74

11.00 11.00 11.00 9.80 10.00 10.00 9.00

‘Discount

ASR (r-stat)

Avg. no. of funds

Weighted

‘Disc own, Equal

7.00 7.80 8.60 8.20 8.60 8.80 6.80

Weights’

‘Premium’

-

‘A// Funds’

- 0.0089 0.0044 0.0007 - 0.0007 0.0033 0.0064 -0.0045

R. Thompson,

Closed-end

fund

discounts

177

and efjicienc)

as the ten closed-end funds which have traded on the NYSE and registered tinder the Investment Company Act of 1940 as diversified funds. The funds in this subsample tend to hold large numbers of securities, do not make significant investments in infrequently traded securities, hold primarily common stocks, and between 1940-1975 held almost no foreign securities. Note that the distribution of beta estimates conforms very closely to the ten Black, Jensen and &holes portfolios. In both cases, there are two funds (portfolios) which have average be:as less than 0.75 and two which have average betas greater than 1.25. Table 13 shows the trading rule results measured against the FM benchmark. While there are differences in the degree of significance. the basic relationships between performance and type of trading rule are generally in agreement

with

performance

the entire

resulting

from

sample.

Althou_gh

the discount

rules

significance falls

of the

somewhat.

abnormal

the

ASR I-

statistic for both rules is still greater than 2.0 over the 194s-1971 period. 6. Interpretation

of the performance results

6.1. Introduction

The apparent information content of discounts and premiums as it manifests itself in the trading rule performance summarized in section 5, could be the result of several different influences. It could result from: (1) a misspecification inherent in the empirical estimation procedures; (2) an ineffIcient capital market; or (3) a capital market which is information efficient, but which cannot be described by a two-parameter asset pricing model. The remaining parts of this section contain a discussion of these alternatives. 6.2. Problems

with the empirical

methodology

Even if we assume that the prices of financial assets conform to a traditional two-parameter pricing framework and that the capital market is information efficient, empirical estimation of performance requires the utilization of a pethodology which has several shortcomings. The major criticisms which could be leveled against the trading rule methodology employed above include: (1) There is considerable evidence that rates of return on NYSE common stocks are not strictly normally distributed.” The use of Gaussian ‘“See for example Fama (1965). Ollicer (1971) and Blattberg and Gonedes (1974). The distributional properties of monthly returns for the Dow Jones Industrials IS well summarized in Fama I 1976. pp. 26 3x).

178

(2)

(3)

(4)

(5)

R. Thompror~, Closed-end jund discounts und ejjicirucp

statistics and the associated measures of significance are technically incorrect. However, it has been the conclusion of most authors interested in the frequency distributions of rates of return that the assumption of normality is a sufficiently close approximation to reality for empirical work, particularly when portfolios of securities are involved.” The estimation of systematic risk in section 4 employs a moving window procedure which lacks theoretical justification. The moving window procedure is a compromise between (1) using all available data in computing flj (assuming stationarity of bj)” and (2) attempting to deal with the process by which managers might be adjusting the risk of the fund’s portfolio. In addition, the length of window and its location relative to the month of interest are arbitrary. Several different windows were investigated however, including the assumption of strict stationarity.*’ The results are not sensitive to the choice of time period over which to estimate systematic risk. The procedure used to standardize the residuals over time could induce dependencies in the individual standardized residuals, making the interpretation of significance of the average residual difficult. On the other hand, attempts to empirically test for serial dependence in the standardized residuals do not detect anything significant. The benchmark portfolios used as approximations to the true market portfolio omit many assets which should be included in a market portfolio proxy. Performance measured relative to a market proxy need bear no specific relation to the true, unobservable market portfolio. On the other hand, estimation errors are likely to be most severe for funds with atypical asset structures and systematic risk. When the subsample of diversified funds is examined separately, and thus the funds which trade in foreign securities and special situations are eliminated from the sample, the same basic discount-performance relationship holds. Further, the fact that the trading rule results of section 5 are not sensitive to the choice among several market benchmarks supports the contention that measurement errors in the market index are probably not the force behind the abnormal performance. The decision to use a monthly observation interval is arbitrary. Authors such as Levy (1972) have shown that, in principle, performance could be a function of the observation interval over which returns are measured.

“See Fama (1976, p. 33 and refs.). “If )9. is assumed stationary it might be considered appropriate to use the same time interval for estikrating B. as was used in the construction of the FM and BJS benchmarks. “After the dbmposition of the trading rules was determined, Jensen (1969) measures of performance were estimated using simple time series regressions of the excess return from the trading rule on the excess return of the equal weighted NYSE index. Although these results are not reported in section 5, they are in general agreement with the results from the more complex methodology described above. Both discount rules generated statistically significant intercept estimates (Jensen performance measures) over the 36year period 1940-1975.

My decision to use monthly observations is consistent with the vast majority of empirical tests of the Efficient Market Hypothesis and stems from the availability of the CRSP return files. Any consistent bias resulting from the use of monthly data has not shown up in similar tests. The crucial question is whether or not the criticisms of the methodology employed in this study are sufficient to explain the nature of the results. It seems unlikely in view of the tendency for previous efficiency tests employing similar methodology to fail to reject the hypothesis of semi-strong market efficiency. The emergence of exceptions to the rule of neutral performance may point to more substantive problems with capital asset pricing theory itself.22 6.3. Implications

for traditional

capital market

efficiency

In the light of the history of trading rules performance, the apparent information content of closed-end fund discounts is an interesting anomaly. The simple rules examined in section 5 almost certainly do not fully utilize the information content of discounts and yet the performance is remarkably high. 23 In addition, the rules do not require extensive purchases and sales of securities and no short positions are required. The following question must be asked: ‘Why are closed-end funds unique in the sense of affording feasible trading rules based on readily available and widely known discounts from net asset value? Any explanation must be consistent with the lack of performance of other weak and semi-strong form trading rules. Even if we grant the substance of Roll’s (1977) criticisms, we closed-end are left with the equally interesting question: ‘Why are discounted fund shares priced differently from other NYSE stocks? It is important to keep in mind that all of the funds included in the performance tests are traded on the NYSE and thus are a part of the market index. Taken out of context from other tests of the Efficient Market Hypothesis, the significant performance documented in section 5 flies directly in the face of the hypothesis that stock prices quickly reflect all publicly available information relating to the firm’s assets. The evidence is clearly inconsistent ‘*See Ball (1978) and Charest (1978) for discussions of apparent anomalous return behavior after public disclosure of accounting data and stock splits. Basu (1977) documents an apparent inverse relationship between P/E ratios and future abnormal performance. In addition, Jaffe (1974) indicates that a judicious use of the Ollicial Summary of Security Transactions and Holdings published by the SEC would have allowed investors to trade with corporate insiders and beat the Fama and MacBeth benchmark over the period 1962-1968. 23There are several refinements which should help select underpriced funds. One of these would be to correct the data for obvious accounting problems. Performance would probably be improved by adjusting discounts for management expenses and selecting funds on the basis of ‘net’ discounts. These relinements were not investigated because the apparent information content in discounts has hlready been demonstrated.

180

R. Thompson, Closed-end fund discounts and

e/ficiency

with traditional capital market efficiency in the semi-strong form. However, if the evidence is considered in context with the theories which originally motivated the trading rule tests, a somewhat different picture emerges. The prior empirical work concerned with semi-strong form trading rule performance has been concerned primarily with the speed of price adjustments to new information about the future profitability of firms. The literature dealing with the impact of public announcements perhaps epitomizes this line of research.24 The conclusions have generally been that investors do a good job of anticipating public announcements and, to the extent that investors are surprised, they tend to react very quickly. Price adjustments generally occur without a meaningful lag, so as to eliminate any short-run trading profits. On the basis of this prior research, it is reasonable to argue that the performance of discounted fund shares stems from something other than the fact that discounts are not widely disseminated pieces of information. In other words, it is possible, even probable, that investors are fully aware of discounts and that the prices of closed-end fund shares reflect what information is contained in them. Perhaps the most effective way to discriminate between the hypothesis that prior discounts are reflected in current prices (and therefore the apparent abnormal performance is a condition of equilibrium) and the hypothesis that the capital market is information inefficient is to examine the impact of the publication of results such as those described above on the level of discounts and the link between discounts and performance. If no change takes place in the next few years and the discount-performance relationship continues into the future then explanations relating to information inefficiency seem implausible. On the other hand, if the explanation lies with personal income tax effects or penalties for poor diversification, why don’t tax exempt institutions purchase closed-end funds and bid up prices (reduce discounts)? For some reason they have chosen not to do so. As of June 19, 1978 the average discount for the nine diversified common stock funds reporting their discount in the Wall Street Journal (p. 31) was 21.7%. Six of the nine funds had discounts above 20 %.

6.4. Limits of two-parameter

asset

pricing

Any strong conclusions concerning market efficiency and two-parameter asset pricing based on the results in section 5 must be hedged by the methodological shortcomings discussed above. On the other hand, the evidence could indicate the existence of a weakness in the concept of twoparameter asset pricing. As an abstraction of reality, it is used as an approximation for the purpose of making predictions concerning observed

R. Thompson,

Closed-end jitnd

discoyts

and efficirnc)

181

market phenomena. It is a useful abstraction only as long as the predictions it generates are consistent with these phenomena. In the original work on capital asset pricing, a stylized world was assumed in which the only relevant attributes for security selection were risk and expected rate of return (gross of any personal income taxes). In this world, every investor perceives the same tradeoff between risk and expected return and therefore holds the same reservation price per unit of systematic risk for all securities. When we allow for heterogeneous investor demands for attributes such as the timing, magnitude, and tax status of shareholder distributions this analysis breaks down. We have overlapping clienteles, each desiring different attribute packages. Every investor holds his own unique portfolio of securities. In this system there is no guarantee that all conceivable attribute packages will have the same risk-expected return tradeoff. This is not a condition of equilibrium. It will be approximately true if the relative supplies of attributes are proportional to the demand for these attributes. But otherwise, every investor could be holding his desired portfolio fully recognizing, for instance, that a shift in his portfolio holdings toward more taxable distributions would increase his expected gross of tax return per unit of systematic risk. There is no unanimity of investor preferences for attributes and therefore market value maximization on the part of managers will not necessarily be the preferred policy by all investors. If clienteles do lead to performance differences in the capital markets, the kind of research which potentially could uncover significant abnormal performance is that which results in a stratification of securities on the basis of characteristics which induce heterogeneous investor demands. Empirical investigations into the importance of dividend policy, such as Black and Scholes (1974), would seem likely to uncover performance dependencies if in fact supply is not ‘in proportion’ to demand. However, Black and Scholes are unsuccessful in their attempts to reject the null hypothesis. The question is whether the link between discounts and performance results from qualitatively different dependencies than those investigated by Black and Scholes or results from the opportunity to construct a more powerful test of the existence of these dependencies. Given the existence of discounts, it is not necessary to specify the nature of the interaction between share price and policy variables such as dividend and distribution policy, and residual variance of return. Instead it is possible to key on a proxy for the cumulative impact of all policy variables: the discount or premium. Black and Scholes specified a linear relationship between performance and dividend yield. Studies which require a less restrictive impact of policy variables on expected return seem fruitful areas to search for a breakdown between two-parameter pricing predictions and market realizations. In the context of a potential breakdown in two-parameter asset pricing. the results of section 5 and the empirical results of Basu on the information content of price-earnings (P/E) ratios for industrial firms have striking

182

R. Thompson,

Closed-end fund discounts

and efficiency

similarities. Basu finds an apparent cross sectional dependence between P/E ratios and abnormal returns. He stratifies firms on the basis of P/E ratios at the beginning of the year and aggregates into high, intermediate, and low P/E ratio portfolios. The ex post performance of these portfolios (using a Jensen measure of performance) is inversely related to the size of the P/E ratio. Notwithstanding the accounting problems inherent in measuring earnings, and the tendency for the P/E ratio to be correlated with the systematic risk of a firm’s cash flows, the P/E ratio of industrial firms could be thought of as an analogue of discounts on closed-end fund shares. An interesting area of future research is to compare the clientele related policies of low P/E firms with those of highly discounted closed-end funds. 6.5. Conclusions Discounts and premiums on closed-end funds which do not suffer from accounting problems in the estimation of net asset value must stem from one of four sources: (1) The existence of personal income taxes and related price adjustments to account for tax liabilities; (2) the existence of investor transactions costs and price adjustments to reflect distribution policy and portfolio diversification; (3) capital market information inefficiencies resulting from biased expectations of management productivity (the future performance of the funds portfolio, net of expenses) or, perhaps, the arbitrary exclusion of closed-end funds from the investment portfolios of institutional investors; and (4) the existence of a capitalized value (or cost) of management’s genuine ability, ex ante, to either outperform the market, thus inducing a premium, or generate expenses in the process of attempting, unsuccessfully, to outperform the market, thus inducing a discount. The evidence in section 5 indicates that, notwithstanding potential methodological shortcomings, discounted closed-end fund shares tend to outperform the market, adjusted for risk. This result is consistent with and, in fact, a prediction of each of the first three potential causes of discounts. One primary conclusion of this study is that, apparently, these forces play a role in the determination of capital asset prices. On the other hand, each is either inconsistent with the concept of two-parameter asset pricing theory or the considerable evidence in support of the semi-strong form of the Efficient Market Hypothesis. On the basis of the tests performed, it is not possible to identify the extent to which the results reflect capital market information inefficiency as opposed to a breakdown in the applicability of two-parameter asset pricing theory. Further resolution is left for future research. On the other hand, the evidence suggests that research directed at the identification of clientele related return differentials may helf unify the evidence which is beginning to accumulate against the joint hypothesis of market efficiency and two-parameter asset pricing.

R. Thompson.

Closed-end fund

discourrrs rend ~~ficirnc~

183

Appendix Closed-end funds:

Terminology

and institutional

setting

An investment company is a corporation which has as its earning asset a portfolio of corporate securities. The market value of the firm’s portfolio minus short-term liabilities is called its net asset value (NAT/). Investment companies have two possible organizational forms: closed-end and open-end. A closed-end investment company (or, equivalently, closed-end fund) is one which is organized similar to a traditional corporation. Claims to the earning assets of the fund are sold to investors through traditional means: an underwriting or perhaps warrants issued to existing shareholders. These claims are then traded among investors and the price determined through the forces of supply and demand. A closed-end fund may or may not elect to trade in its own securities but, in any event, the securities are traded on an exchange such as the American or New York Stock Exchanges. Differences between the market value of the claims to the fund and the NAV of the fund are described in terms of the discount. The discount is defmed as the difference between net asset value and market value, divided by net asset value, D=(NAV-MV)/NAL’.

A premium is a negative discount. Therefore, if a fund is selling at a premium, investors who wish to purchase shares of the fund must pay more than the net asset value per share, that is, more than the quantity of capita1 the shares have command over. Open-end funds deal directly with their shareholders in terms of issuing and redeeming shares. The claims to open-end funds are not traded among investors directly. Instead, investors come to the fund and exchange cash for claim to the same dollar amount of net asset value. Investment companies had their origins in Europe and Scotland in the early 1800’s. However, they began to gain in popularity in the United States shortly after the turn of the century. The stock market crash of 1929 and the resulting Securities and Exchange Commission brought a host of regulations pertaining to investment companies, the most significant legislation being the Investment Company Act of 1940. Under the Act, an investment company can receive special tax status if certain requirements are met. The Act essentially eliminates the double taxation (once at the corporate level, and once at the investor level) of income generated by the fund’s activities. Several of the provisions of interest to the discussion in this study are the following: (1) If at least 90% of dividends and interest income received by an investment company are distributed to its shareholders, the company

184

(2) (3)

(4) (5) (6)

R. Thornpoll.

Closed-end fund discounts

und @ciencJ

does not have to pay federal tax on the amount distributed. It must pay tax on the undistributed portion of net realized capital gains. Net realized capital gains in a given year are defined as the sum of all capital gains or losses realized from the sale of assets held in the company’s portfolio over the course of the year. If this total is negative, it may carry forward these losses to offset future capital gains. However it cannot distribute losses directly to its shareholders. If a fund elects to retain a portion of its realized capital gains it must pay taxes in accordance with the highest marginal personal tax rate. The fund then distributes to its shareholders a tax receipt which is deductible from personal income taxes due. At least 90% of income must be from portfolio activities (dividends, interest and capital gains). Owners of the fund’s shares must pay taxes on distributions from the fund in accordance with their own personal tax status. When a fund realizes capital gains, the determination of whether the gains are taxed as long-term or short-term depends on how long the securities have been held by the fund. It is not a function of how long the investor has held his shares in the fund. Unrealized capital gains are not taxed and need not be distributed until and unless realized. Investment companies may not hold in excess of 3% of the voting stock of another investment company. Certain requirements relating to portfolio composition must be met. The most stringent constraints are applied to those funds which desire to be classified as a diversified investment company. A diversified company is one which ‘75 y0 of value of its total assets is represented by cash and receivables, Government Securities, securities of other investment companies and other securities, limited for the purpose of this calculation in respect of any one issue to an amount not greater in value than 5% of (the investment company’s total assets) and not to more than 10% of the outstanding voting securities of such issuer.‘25

“From

section 5(b)(l)

of the Investment

Company

Act of 1950.

References Ball, R., 1978, Anomalies in relationships between securities’ yields and yield-surrogates, Journal of Financial Economics, this issue. Ball, R. and P. Brown, 1968, An empirical evaluation of accounting income numbers, Journal of Accounting Research 6, no. 2, 159-178. Basu, S., 1977, The investment performance of common stocks in relation to their price-earnings ratios: A test of the efficient market hypothesis, Journal of Finance, June, 663-682. Bildersee, J.S., 1974, Some new bond indexes: Extended and expanded results, Working Paper no. 2-74 (Wharton School. University of Pennsylvania, Philadelphia, PA).

R. Thompson, Closed-end fund discounts and efficiency

185

Black, F., M.C. Jensen and M. Scholes, 1972, The capital asset pricing model: Some empirical tests, in: M.C. Jensen, ed., Studies in the theory of capital markets (Praeger, New York) 79121. Black, F. and M. Scholes. 1974, The effects of dividend yield and dividend policy on common stock prices and returns, Journal of Financial Economics 1, no. 1, l-22. Blattberg. R. and N. Gonedes, 1974, A comparison of the stable and student distributions as statistical models for stock prices, Journal of Business, April, 244-280. Boudreaux, K.J., 1973, Discounts and premiums on closed-end funds: A study in valuation, Journal of Finance, May, 515-522. Brenner. M.. 1977. The effect of model missuecification on tests of the efficient market hypothesis, Journal of Finance, March, 57-66.’ Charest, G., 1978, Split and dividend information, stock returns and market efficiency; Part 1: The case of splitting stocks, Journal of Financial Economics, this issue. Fama, E.F., 1965, The behavior of stock market prices, Journal of Business 38, no. 1, 34-105. Fama, E.F., 1970, Efiicient capital markets: A review of theory and empirical work, Journal of Finance 25, no. 2, 383417. Fama, E.F., 1976, Foundations of Finance (Basic Books, New York). Fama, E.F., L. Fisher, M.C. Jensen and R. Roll, 1969, The adjustment of stock prices to new information, International Economic Review 10, no. 1, 1-21. Fama, E.F. and J.D. MacBeth, 1973, Risk, return and equilibrium: Empirical tests, Journal of Political Economy 81, 6077636. Investment Company and Investment Advisors Acts of 1940, Public. no. 768876th Congress, Chapter 686-3rd Session. Jaffe, J.F., 1974, Special information and insider trading, Journal of Business, July, 410-428. Jensen, M.C., 1968, The performance of mutual funds in the period 1945-1964, Journal of Finance 23, May, 389416. Jensen, M.C., 1969, Risk, the pricing of capital assets, and the evaluation of investment portfolios, Journal of Business 42, April, 167-247. Jensen, MC., 1972. Capital markets: Theory and evidence, The Bell Journal of Economics and Management Science 3, 357-398. Malkiel, B.G., 1977, The valuation of closed-end investment company shares, Journal of Finance, June, 847-859. Mandelker, G., 1974, Risk and return: The case of merging firms, Journal of Financial Economics 1, no. 4, 3033335. Mendelson, M., 1977, Closed-end fund discounts revisited, March (Center for Study of Financial Institutions, University of Pennsylvania Law School, Philadelphia, PA). Merton, R.C., 1973, Theory of rational option pricing, Bell Journal of Economics and Management Science 4, 141-183. Miller, E.M., 1977, Risk, uncertainty, and divergence of opinion, Journal of Finance 3, no. 4, 1151-1168. Officer, R.R., 1971, A time series examination of the market factor of the New York Stock Exchange, Ph.D. dissertation (University of Chicago, Chicago, IL). Pratt, E.J., 1966, Myths associated with closed-end investment company discounts, Financial Analysts Journal 22, 79-82. Roendfelt, R.D. and D.L. Tuttle, 1973, An examination of the discounts and premiums of closed-end investment companies, Journal of Business Research 1, 129-140. Roll, R., 1977, A critique of the asset pricing theory’s tests; Part 1: On past and potential testability of the theory, Journal of Financial Economics 4, no. 2, 129-176. Rozeff, M.S., 1974, Money and stock prices: Market efficiency and the lag in effect of monetary policy, Journal of Financial Economics 1, no. 3, 245-302. Scholes, MS., 1972, The market for securities: Substitution versus price pressure and the effects of information on share prices, Journal of Business 45, no. 2. Sharpe, W.F. and H.B. Sosin, 1974, Closed-end investment companies in the United States: Risk and return, Proceedings of the European Finance Association, Thompson, R., 1978, Capital market efliciency, two-parameter asset pricing and the market for corporate control: The implications of closed-end investment company discounts and premiums, Ph.D. dissertation (University of Rochester. Rochester, NY).

186

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Closed-end

/und discounts

and ejliciencv

Vives, A.. 1975, Discounts and premiums on closed-end funds: A theoretical analysis, Ph.D. dissertation (Carnegie-Mellon University, Pittsburgh, PA). Wiesenberger. A.. 1975. Investment companies (Arthur Wiesenberger. New York).

and

empirical