excess volatility and closed-end funds

American Economic Association

Excess Volatility and Closed-End FundsAuthor(s): Jeffrey PontiffSource: The American Economic Review, Vol. 87, No. 1 (Mar., 1997), pp. 155-169Published by: American Economic AssociationStable URL: http://www.jstor.org/stable/2950859 .

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Excess Volatility and Closed-End Funds

By JEFFREY PONTIFF*

If investors are rational, the variance of closed-end mutual fund returns should equal the variance of the underlying securities in their portfolios. In fact, this paper shows that the average closed-end fund's monthly return is 64 percent more volatile than its assets. Unlike variance-bounds tests, this facilitates an excess volatility test that does not rely on strong assumptions about discount rates or dividend streams. Although largely idiosyncratic, 15 percent of the average fund's excess risk is explained by market risk, small-firm risk, and risk that affects other closed-end funds. (JEL GIO, G12)

If investors are rational, the price of a share of stock should equal the present value of the stock's expected cash distributions to shareholders. However, there is a question as to whether share prices are more volatile than expected cash distributions. Robert J. Shiller ( 1989) argues that actual stock prices are more volatile than expected dividends, so that some portion of price movements can be attributed to psychology or irrationality. Excess volatility is typically tested using a variance-bounds test, which compares the variability of stock returns to the variability of dividends.

This paper addresses whether stocks are excessively volatile by comparing the volatility of closed-end fund returns to the volatility of their underlying portfolio returns. A closed- end fund holds an asset portfolio managed by the fund's officers. Market prices of the underlying assets are used to compute the value of the fund's portfolio (net asset value). Be- cause closed-end funds, themselves, are traded on stock exchanges, the price of a fund can

differ from the fund's net asset value (NAV). Open-end funds are similar to closed-end funds except that they are purchased and sold directly from the fund at NAV, thus ensuring that price volatility and NAV volatility are equal. Nonetheless, since a share in a closed- end fund is a claim on the fund's portfolio, the volatility of a closed-end fund should equal the volatility of its underlying portfolio.

Previous closed-end fund research has documented that closed-end funds typically sell at a discount relative to the price of the fund's underlying portfolio and that discounts vary through time (Rex Thompson, 1978). Rational explanations of discounts have had little, if any, empirical support (for example, Burton G. Malkiel, 1977; Pontiff, 1995, 1996; Charles M. C. Lee et al., 1991 ). Volatility tests based on a comparison of fund returns and NAV returns provide a more general test of efficiency, since discount variation does not imply that closed- end fund volatility will be greater (or less) than NAV volatility. Also, volatility tests avoid testing a specific model of discounts.

My findings contradict the efficient markets model. Even though closed-end fund prices underreact to changes in NAV, the average fund has monthly return variances that are 64 percent greater than the variance of its NAV return. This volatility is not caused by infrequent trading or bid-ask bounce since it persists even when returns are calculated for longer holding periods. The excess volatility

* Department of Finance and Business Economics, Box 353200, University of Washington, Seattle, WA 98195. I thank Brad Barber, Michael Barclay, Kalok Chan, Kathy Dewenter, Wayne Ferson, Alan Hess, David Ikenberry, Avi Kamara, John Long, Bob Shiller, Jay Shanken, Michael Weisbach, Ivo Welch, an anonymous referee, and participants at the University of Washington Finance Workshop. Ken French and Charles Lee provided some of the data used in this study.

155



156 THE AMERICAN ECONOMIC REVIEW MARCH 1997

finding is puzzling since open-end funds are not exposed to this volatility, yet closed-end and open-end NAV returns are highly correlated, and risk-adjusted closed-end NAV returns are not statistically different from those of open-end funds.

Closed-end fund excess volatility appears to be largely idiosyncratic. For the average fund, only 15 percent of its excess volatility is explained by market risk, small-firm risk, book-to-market risk, or the risk associated with the discount movements of other closed- end funds. From these four risk factors, three factors appear to affect the entire population of funds-small-firm risk, market risk, and risk associated with other closed-end funds. Book-to-market risk affects only the volatility of funds with low premiums. If other securities are exposed to similar risk factors, my findings have implications for other studies. Since 85 percent of the excess volatility documented in this study is idiosyncratic, this risk will not be detected by volatility tests that use portfolio returns because placing securities in diversified portfolios eliminates idiosyncratic risk. Thus, previous volatility tests, such as Shiller ( 1989) and Lucy F. Ackert and Brian F. Smith ( 1993 ), underestimate the excess volatility in financial markets.

The simple excess volatility test conducted in this paper avoids some of the pitfalls associated with variance-bounds tests. For example, most variance-bounds tests compare dividend volatility with return volatility. Since this comparison involves a variance bound and a point estimate, the role of sampling errors and statistical biases can be important. In a literature survey, Christian Gilles and Stephen F. LeRoy (1991) document the evolution of econometric tests designed to overcome these problems.

Inferences from variance-bounds tests also are sensitive to the inclusion of different types of shareholder distributions. For example, most variance-bounds tests use dividends as the relevant cash distribution. Thus, other distributions to shareholders, such as cash generated from share repurchases and takeovers, are not considered. Although variance-bounds tests usually reject the null hypothesis of no excess volatility when dividends are used as

the relevant distribution, Ackert and Smith (1993) fail to reject the null when a broader definition of distribution is used. Problems with distributions are avoided with volatility tests that use closed-end funds, since they facilitate the comparison of two market-based prices.

Both John H. Cochrane (1991) and G. William Schwert ( 1991), in reviews of Shiller's work, stress the importance of the joint hypothesis of excess volatility and a time- varying discount rate model. For example, many variance-bounds papers assume constant expected returns and, hence, constant discount rates through time. Even if a test allows time variation in expected returns, a variance- bounds test might reject the null hypothesis if the expected return process is misspecified. The test conducted in my paper assumes that the discount rate of the fund is equal to the discount rate of the fund's portfolio. Thus, a model of time-varying discount rates is unnecessary.

The paper proceeds as follows. Section I uses the definition of a closed-end fund's premium to motivate the relation between fund returns and net asset value returns. Section II documents the findings of this study. Section III concludes.

I. Premium and Return Identities

Closed-end funds use market prices to compute the value of their portfolios. The financial press defines a fund's premium as the difference between one and the ratio of the fund's price per share to its net asset value per share. Defining a fund's premium as the log of this ratio allows the interpretation of changes in premiums as returns, which can be used to motivate implications regarding the relation between premiums and returns. Therefore, I express a fund's premium as

( 1 ) (~~ Nt)

Pt is the closed-end fund's price per share and Nt is the fund's net asset value per share. Changes in a fund's premium are computed by time-differencing equation (1) yielding



VOL. 87 NO. I PONTIFF: EXCESS VOLATILITY AND CLOSED-END FUNDS 157

(2) PREM,-PREM, - I = ln P,-ln N,

.-InPt_ I+ nN,-,.

A\PREMt is defined as this period's premium minus last period's premium. If the fund pays no dividends, we can write

(3) /PREMt = Rts- Rn

Rs is the return of fund's shares, referred to as the fund's stock return, and Rn is the return accruing to the fund's net asset value, referred to as the fund's net asset value return.

The definition of premium also can be used to evaluate the relation between return variances. Equation (3) can be written as

(4) Rt = APREMt + Rt.

Using the basic properties regarding the variance of sums,

(5) Var(Rs) = Var(A\PREMt)

+ Var(Rn) + 2 Cov(APREMt, Rn).

Thus,

Var(Rs) > Var(Rn)

if, and only if,

(6) Var(A\PREMt)

> -2 Cov(A\PREMt, Rt)

or

Cov(L\PREMt, R n) 1

Var(A\PREMt) 2

From (6), the difference between the fund variance and the portfolio variance is related to the covariance of premiums with portfolio returns. This covariance must be sufficiently negative for the variance of a fund to be less than the variance of its portfolio. As demon- strated by (7), this condition also may be interpreted as a slope coefficient from a regression of net asset value returns on premium

changes. If the NAV return typically decreases by more than half of the premium change, then the NAV return is more volatile than the stock return. Put another way, if NAV (stock) returns have a larger effect on changes in premiums than stock (NAV) returns, then NAV returns are more (less) volatile than stock returns. For a specific fund, this condition may or may not hold. Recent studies have shown that premiums vary (Thompson, 1978) and that premium changes are related to small-firm risk (Lee et al., 1991). However, these findings do not compare return variances or covariances, making it impossible to conclude whether stock returns are more volatile than fund returns or vice versa.

The only recent closed-end fund study that provides some of the details needed to ascertain whether closed-end funds are more or less volatile than their portfolios is Kathleen W. Hanley et al. (1997). Their paper shows that the price of the median closed-end fund does not change during the month after its initial public offering (IPO). All premium changes during this period will be perfectly negatively correlated to NAV return. From equation (7), this implies that the volatility of the closed- end fund will be less than the volatility of the fund's NAV. The authors attribute this finding to price stabilization by the IPO's underwriters.

II. Empirical Tests

A. Data

The sample of closed-end funds used in this study is identical to that in Lee et al. ( 1991 ). It includes 68 funds covered in The Wall Street Journal's publicly traded funds column during the period July 1965-December 1985. Funds with six or fewer months of discount data were deleted, yielding a sample of 53 funds. Cyprus Corporation also was deleted since this fund reports NAVs based on historic cost, reducing the sample to 52 funds (although including Cyprus Corporation has no impact on this study's conclusions). Returns and price data are from the Center for Re- search in Security Prices (CRSP) database. Monthly NAV returns are computed using both sets of data. The return of a fund's NAV




can be computed from the premium and stock return information. Specifically,

(tPREMt-, 1I NR = (1+ SRX) V PREM +1 J

+ (SR - SRX)(PREMt_, + 1)- 1,

where NR is the net asset value return, SRX is the stock return without dividends, SR is the stock return, and PREMt is the time t premium. In months in which 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.

B. Excess Volatility Estimates

Using the sample of 52 closed-end funds, the components of the variance decomposition in equation (5) are estimated with monthly data for each fund. The left and right sides of the equation do not equate exactly, because the identities developed in the previous section as- sumed no dividends and continuously com- pounded returns. Averages [medians ] for each component are:

Var(Rs) = Var(?APREMt) + Var(R7)

51.15 37.33 37.89

[37.52] [19.62] [24.72]

+ 2 Cov(ZAPREMt, Rf)

-25.42

[ -7.74].

Thus, the average monthly closed-end fund return variance is greater than the average NAV return variance. The covariance between changes in premiums and NAV returns is negative.' Since the premium change is the dif-

ference between the fund return and the net asset value return, this negative covariance implies that closed-end fund prices underreact to NAV returns. If NAV is the fundamental value of the fund, these findings imply that closed-end fund prices are excessively volatile, despite the fact that they underreact to fundamentals.

For each fund in the sample, the ratio of the stock return variance to the NAV return variance is computed. To reduce skewness, the log of this ratio is taken. This log variance ratio will be zero if the volatility of a fund's return is equal to the volatility of its NAV return.2 Summary statistics of these ratios, computed for return intervals of one through four months, are presented in Figure 1. The return of a closed-end fund is, on average, more volatile than the return of its portfolio. The average (median) log variance ratio of monthly returns is 0.494 (0.474), implying that, for the average (median) fund, the variance of its return is 64 percent (61 percent) greater than the variance of its portfolio return. If a fund's portfolio return is a measure of the return that would accrue to the fund if it were open- ended, my results imply that the mechanism of public trading adds volatility to the returns of these funds.

These results are suspect to the extent that infrequent trading or bid-ask spreads bias the variance estimates. Since the magnitude of these biases is the same regardless of the return interval, and since variance increases as the return interval increases, the fraction of the variance attributable to biases should decrease. The average log variance ratios of two-, three-, and four-month returns also are significantly different from zero, implying that these biases are not severe.

' This equation was reestimated using bimonthly returns, but the negative covariance between changes in premiums and NAV returns persists. Using monthly data, Nai-fu Chen et al. (1993) find a negative covariance be-

tween changes in premiums and NAV returns. Using weekly data on country closed-end funds, James N. Bodurtha, Jr. et al. (1995) and Peter Klibanoff et al. (1996) find the same result. Using annual data, James Brickley et al. (1985) find a positive covariance between premium changes and NAV returns. This evidence suggest that the negative relation dissipates when longer time intervals are considered.

2Log variance ratios are used for presentation pur- poses. The conclusions of this paper are not affected if the tests are conducted with simple ratios.




Mean Median t-value Histogram H: log ratio=0 Vertical line at zero

9-

One-month return interval

0.494 0.474 6.20 3

Two-month return interval

0.559 0.483 6.81

Three-month return interval 411

0.721 0.486 6.49 3IVIALAA

Four-month return interval 6

0.434 0.361 4.89 A 4

FIGURE 1. HISTOGRAMS OF THE LOG RATIO OF THE VARIANCE OF A CLOSED-END FUND S RETURN TO THE VARIANCE OF THE FUND'S PORTFOLIO RETURN FOR 52 CLOSED-END FUNDS FROM JULY 1965 THROUGH DECEMBER 1985




William F. Sharpe and Howard B. Sosin (1975) document share price volatility in excess of net asset value volatility on another sample of closed-end funds. Using annual data from 1933 to 1972 on ten closed-end funds, they report that the variance of the median fund is 17 percent greater than that of its underlying assets. Using quarterly data from 1966 to 1973 on eight funds, they find that the median fund has a variance that is 36 percent greater than its portfolio. However, they do not report any test of the statistical significance of their findings.

C. Similarity with Open-End Funds

For open-end funds, NAV must represent fundamental value since open-end funds trade at NAV. The previous results suggest that a closed-end fund could reduce volatility by "open-ending" and, therefore, redeeming shares at NAV. Whether or not this is accurate depends on the similarity of the portfolios of closed-end and open-end funds. Without ob- serving portfolio composition, it is impossible to pinpoint exactly how similar the investments of these types of funds are. However, one way to address the similarity between closed-end funds and open-end funds is to re- gress closed-end NAV returns on the NAV returns of open-end funds. The parameter estimates on each security return used as an independent variable can be interpreted as the weight of each asset in the replication portfolio. Adjusted R2s are estimates of how closely a closed-end fund's NAV can be replicated with a portfolio of open-end funds.

Since the premium information required to compute NAV returns is only available once per week, noise (due to nonsynchroneity) is added to the NAV returns. However, length- ening the time interval increases the return variances without affecting the size of the nonsynchrony, so that relative amount of noise in regressions with longer return intervals will be less than in those with shorter intervals.

Table 1 addresses the ability of NAV to be replicated by investments in open-end funds. The first two rows report median and quartile adjusted R2s from regressions utilizing the

NAV return in excess of a month T-bill yield as a dependent variable, and the excess CRSP value-weighted index return and the excess returns of ten no-load, open-end funds as independent variables. The open-end funds se- lected are indicative of the different types of open-end funds available to investors.:

As expected, increases in the return interval are associated with increases in the adjusted R2, implying that these R2s are biased down- ward. Thus, I concentrate on the results for the longer return intervals. For the median fund, 54 percent of its NAV return can be explained by the CRSP value-weighted index, and 70 percent can be explained by the ten open-end fund returns. Open-end fund returns are interesting since, like closed-end funds, they represent returns to managed portfolios. A median adjusted R2 of 70 percent implies that the assets and management styles used by closed- end funds are not unique to the industry.

The third row of Table 1 presents the adjusted R2s from regressions of one of the open- end fund's excess returns on the excess return of the CRSP value-weighted index. The fourth row uses the excess returns of the remaining nine funds as independent variables. These tests are conducted at the monthly level since all returns are calculated using the mutual fund's price on the last day of the month. The results of this test are similar to tests using closed-end NAVs, although the typical open- end fund is better replicated than a closed-end fund. For example, the median open-end adjusted R2 from the nine-fund regression is 78 percent. Since Table 1 does not present a for- mal statistical test, the reader must use his or her judgment in interpreting the similarity of open- and closed-end fund investment strategies.

D. Redundancy of NA V Returns

Table 1 suggests that the investment strategies of open-end funds and closed-end funds

' The following open-end funds were chosen: Energy Fund, T. Rowe Price Growth Stock Fund, Scudder Com- mon Stock Fund, Keystone High Grade S-1, Guardian Mutual, Loomis-Sayles Fund, Penn Square Fund, Stein Roe International Fund, Keystone Income K-1, Keystone B-2, and Keystone B-4.




TABLE 1-SUMMARY STATISTICS OF ADJUSTED R2 S FROM OLS REGRESSIONS

Return interval

One- Two- Three- Dependent variable Independent variables month month month

Closed-end fund net CRSP value-weighted 0.246 0.293 0.289 asset value return index return 0.435 0.552 0.535 (52 regressions) 0.600 0.680 0.769

Returns of ten open- 0.346 0.51 ia 0.567b end funds 0.505 0.645a 0.702b

0.630 0.768a 0.854b

Open-end fund return CRSP value-weighted 0.484 (ten regressions) index return 0.694

0.781

Returns of nine open- 0.627 end funds 0.775

0.844

Notes: Summary statistics of adjusted R2 s from OLS regressions of: 1) closed-end fund net asset value returns on the return of the CRSP value-weighted index and returns of ten open-end funds (52 closed-end funds); and 2) open-end fund net asset value returns on the return of the CRSP value-weighted index and returns of nine open-end funds (ten open-end funds).

Lower-quartile adjusted R2

Median adjusted R2

Upper-quartile adjusted R2 a These statistics are generated from a cross section of 48 funds, since four funds do not

have enough data to estimate a regression equation. bThese statistics are generated from a cross section of 38 funds, since 14 funds do not

have enough data to estimate a regression equation.

are similar. This inference is based on the correlation of open-end and closed-end NAV returns. Since open- and closed-end funds are highly correlated, these funds pursue investment strategies with similar risk exposure. Besides risk, investors must consider the expected return of open- and closed-end funds; thus, this section goes one step further by con- sidering risk-adjusted return performanice.

Arthur D. Roy ( 1952) demonstrates that the weight of an asset in a mean-variance efficient portfolio is equal to the expected excess return of the asset conditioned on the excess return of all other available assets being zero, divided by the variance of the asset's return conditioned on all other available asset returns. This reasoning can be used to ascertain whether closed-end fund NAVs are redundant

given open-end funds. Using the regression estimation that produced Table 1, the weight of a given closed-end fund in a portfolio of ten mutual funds is equal to the intercept from the regression of excess closed-end fund returns on open-end fund returns, divided by the residual standard deviation from the same regression. If a closed-end fund is redundant given the ten open-end funds, then an investor would not choose to hold the closed-end fund's NAV in a portfolio that contains the ten open-end funds. In this case, the ratio of the intercept to the residual variance will be zero.

From the regression estimation used to pro- duce Table 1, the portfolio weight measure was constructed for all 52 funds. The average (median) measure is 0.009 (0.025). The t-value under the null hypothesis that the average




measure is zero, is 0.67, implying that the average closed-end fund NAV is redundant given the ten open-end funds. A test of inter- cepts is similar. The average (median) intercept is -0.0004 (0.0010). The t-value under the null hypothesis that the average intercept is zero, is -0.44.

E. Sources of Volatility

Figure 1 implies that closed-end fund returns are more volatile than their NAV returns. This section addresses the extent to which this volatility is related to market-wide risk. The findings of this section relate to Richard Sias (1992), who performs regressions of changes in closed-end fund discounts on risk measures. He finds that changes in premiums generally are positively correlated with consumption growth, default premiums, changes in the slope of the yield curve, and T-bill rates. Un- expected inflation is negatively related to discount changes, and market returns appear unrelated. It is impossible to infer from Sias's results whether or not these factors proxy for the investor sentiment risk claimed by some to affect fund discounts (Lee et al., 1991).

Eugene F. Fama and Kenneth French (1993) argue that three risk measures explain cross-sectional differences in average stock returns: market risk, book-to-market risk, and small-firm risk. They create three return measures that proxy for these risks. Their market risk measure is the value-weighted average return of the CRSP index. Their book-to-market risk measure is the difference between the value-weighted return of firms with the highest book-to-market ratios and the value-weighted returns of firms with the lowest book-to- market ratios. Similarly, their small-firm risk measure is the difference between the returns on small-firm portfolios and large-firm portfolios. The formation of these portfolios is discussed extensively by Fama and French (1993).

Lee et al. (1991) propose that closed-end funds are subject to systematic "investor sentiment risk." They use a value-weighted index of changes in closed-end fund discounts in order to control for this risk. From equation (3), this measure is analogous to the return of a

portfolio that holds closed-end funds and short-sells the assets held by the funds. Since the number of closed-end funds (especially in the 1960's) is limited, a regression of the change of a closed-end fund's discounts on the change in an index of closed-end fund discounts will yield a positive slope coefficient, even if all changes in discounts are independent. This occurs because the fund's change in discount is included in the index. In order to avoid any spurious findings, the fourth risk measure is the value-weighted difference between each fund's return and each fund's NAV return, where all funds except the fund of interest are included.

Each fund's stock price return is regressed on its NAV return. In order to control for nonsynchroneity, the residuals are modeled as a first-order autoregressive process. The residuals from this regression are used to measure the stock return that is unexplained by NAV movements. Thus, these residuals are the source of the excess volatility documented in Figure 1. The average slope coefficient from these regressions is 0.85, and the average autoregressive parameter is -0.23.4

This unexplained stock return measure is regressed on the excess return of the market portfolio over the one-month T-bill yield, the excess of small-firm returns over large-firm returns, the excess of high book-to-market firm returns over large-firm returns, the excess of high book-to-market firm returns over low book-to-market returns, and the value- weighted difference between closed-end fund returns and their NAV returns (for all funds other than the fund of interest). The results of all 52 regressions are summarized in Figures 2-4.

Figure 2 reports summary statistics and a histogram of the adjusted R2s from the regressions. Surprisingly, the returns of closed-end

4 If the slope coefficient on NAV return were one, then the residual from this regression essentially would be the change in the fund's premium. The estimation procedure in this section also was conducted using changes in premium, instead of residuals. The main difference in this estimation is that it produces weaker coefficients on small- firm risk and market risk.



VOL 87 NO. 1 PONTIFF: EXCESS VOLATILTY AND CLOSED-END FUNDS 163

Mean Median t-value Histogram H: mean adj. R2=0 Vertical line at zero

Adjusted R2

9 0.15 0.14 8.45 6-

FIGURE 2. HISTOGRAM OF ADJUSTED R2S FROM REGRESSIONS OF THE RETURN OF A CLOSED-END FUND THAT IS

UNEXPLAINED BY NAV RETURN ON FOUR INDEPENDENT VARIABLES

Notes: The four independent variables are: 1) the return of aggregate closed-end fund returns minus net asset value returns; 2) the return of the CRSP value-weighted index; 3) the Fama-French high-minus-low book-to-market return; and 4) the Fama-French small-minus-big capitalization return. A separate regression is conducted for all 52 closed-end funds.

funds that are not explained by NAV returns appear to be mostly idiosyncratic. For the median fund, the four systematic risk measures explain 14 percent of closed-end fund returns in excess of their portfolios. This result implies that most excess closed-end fund volatility is unrelated to market factors. The results of Figure 2 also were computed from regressions that used only market return as the independent variable. This estimation produced a mean (median) adjusted R2 of 0.02 (0.05). This finding is interesting since virtually all excess volatility studies use market indexes. If typical stocks are similar to closed-end funds, 98 percent of their excess volatility will be not be captured by tests that use a market index.

Figure 3 reports the slope coefficients on the four risk factors. Most funds have a positive exposure to investor sentiment risk, as proxied by the value-weighted return of other closed- end funds in excess of their portfolios. The median fund has an investor sentiment beta of 0.49, reaffirming Lee et al.'s ( 1991 ) conclusion that changes in closed-end fund discounts co- vary. The mean exposure to this risk is 0.46, and is highly significant with a t-value of 10.04.

The histograms of market beta and size beta offer evidence of pervasive exposure to these

risks. Exposure to these risks is less pro- nounced than investor sentiment risk. For average funds, the market and size betas are close to zero (0.13 and 0.20, respectively). The t-values for these ratios are 5.61 and 4.91, rejecting at most common levels the null hypothesis of no average exposure to these risks. Exposure to book-to-market risk does not appear to affect the typical closed-end fund; the mean slope coefficient is 0.03, and is insignif- icantly different from zero.

Figure 4 summarizes the 52 t-values for each risk measure. The t-value may be more inform- ative than slope coefficients if the standard errors of the slope coefficients vary. The results using t-values are similar to the parameter estimates reported in Figure 3. The mean t-value for the slope coefficients on investor sentiment, market, and size are significantly different from zero at common significance levels.

F. Exposure to Risk and Premium Level

From Figures 2-4 it is impossible to infer whether risk exposure is related to premium level. J. Bradford De Long et al. (1990a) model the effects of investor sentiment risk on asset prices. An implication of their




Mean Median t-value Histogram H: mean slope=0 Vertical line at zero

12 Investor sentiment beta 8

0.46 0.49 10.04

Market beta

0.13 0.11 5.61

Book-to-market beta

0.03 0.02 1.07

'~ ~ ~~~s 'i Cs.

12 Size beta

0.20 0.14 4.91 _.~~~~~~'

FIGURE 3. HISTOGRAMS OF SLOPE COEFFICIENTS FROM REGRESSIONS OF THE RETURN OF A CLOSED-END FUND

THAT IS UNEXPLAINED BY NAV RETURN ON FOUR INDEPENDENT VARIABLES

Notes: The four independent variables are: 1) the return of aggregate closed-end fund returns minus net asset value returns; 2) the return of the CRSP value-weighted index; 3) the Fama-French high-minus-low book-to-market return; and 4) the Fama-French small-minus-big capitalization return. A separate regression is conducted for all 52 closed-end funds.




Mean Median t-value Histogram H: mean t-value =0 Vertical line at zero

Investor sentiment t-value

2.27 2.11 9.17

Market t-value

1.10 1.12 5.19

-0, en @0 C0 o0 ' 0

Book-to-market t-value

0.32 0.09 1.73 k A

Size t-value

1.13 0.87 6.06 A A A . .' , @ . . @0,.................. .}

. : 9 ' f9 y

FIGURE 4. HISTOGRAMS OF THE t-VALUES FOR THE HYPOTHESIS THAT THE FIGURE 3 SLOPE COEFFICIENTS ARE EQUAL TO ZERO

Notes: These t-values are generated from regressions of the return of a closed-end fund that is unexplained by NAV return on the following four independent variables: 1) the return of aggregate closed-end fund returns minus net asset value returns; 2) the return of the CRSP value-weighted index; 3) the Fama-French high-minus-low book-to-market return; and 4) the Fama-French small-minus-big capitalization return. A separate regression is conducted for all 52 closed- end funds.




TABLE 2-UNRELATED REGRESSION OF THE RETURN OF HIGH- AND LOW-PREMIUM CLOSED-END FUNDS

Dependent variable Closed-end fund return minus net asset value return

Independent variables Discount level

High-premium Low-premium F-ratio (p-value] portfolio portfolio H: both coefficients equal

Intercept -0.01 0.01 42.47 (-6.55) (3.85) [0.00]

Return of the CRSP value- 0.10 0.20 2.52 weighted index minus (2.75) (5.03) [0.11] the one-month T-bill yield

Return of the Fama-French 0.02 0.22 5.04 high-minus-low book- (0.29) (3.68) [0.03] to-market portfolio

Return of the Fama-French 0.13 0.16 0.14 small-minus-large (2.46) (2.94) [0.70] capitalization portfolio

Value-weighted return of 0.38 0.37 0.01 the opposite closed-end (6.62) (5.14) [0.92] fund portfolio in excess of net asset value return

Notes: A seemingly unrelated regression of the return of high- and low-premium closed-end funds that is unexplained by net asset value return on the following independent variables: 1) the excess return of the CRSP value-weighted index; 2) the Fama-French high-minus-low book-to-market return; 3) the Fama-French small-minus-big capitalization return; and 4) the value-weighted return of the opposite closed-end fund portfolio minus net asset value returns. Estimation uses 245 monthly observations (t-values in parentheses).

model, as extended to closed-end funds, is that funds that have stronger exposure to investor sentiment risk should also have, on average, larger discounts. This result stems from the fact that investor sentiment risk is systematic, so that sophisticated investors must be compensated for this risk through larger discounts.

Table 2 addresses the issue of whether financial market risk is related to the premium level. Using the 52-fund sample, funds are placed in portfolios based on their premiums in the previous month. If a fund's previous month's premium is greater than the median premium in that month, it is placed in the high- premium portfolio; otherwise, it is placed in the low-premium portfolio. The portfolio returns are computed by value-weighting the portion of each fund's stock return that is not

explained by its NAV return. On average, the high-premium portfolio sells at a discount of 1.4 percent (standard deviation of 9.8 percent), whereas the low-premium portfolio sells at a discount of 17.1 percent (standard deviation of 7.6 percent). Both of these portfolio returns are used as the dependent variables in a seemingly unrelated regression with the four risk measures as independent variables. A seemingly unrelated regression is used instead of an ordinary least-squares regression in order to facilitate a test of the hypothesis that the respective slope coefficients for the two portfolios are the same. For this test, the investor sentiment risk measure is the value-weighted average of the stock return minus the NAV return of the other portfolio. Again, this avoids a spurious correlation problem.




Consistent with Figures 2-4, both portfolios have significant exposure to market risk, small- firm risk, and investor sentiment risk. Interest- ingly, a fund's exposure to book-to-market risk is related to its premium level. Specifically, the low-premium portfolio has strong exposure to book-to-market risk, whereas the high-premium portfolio does not. These differences in book-to-market risk exposure are significant at the 3-percent level. There is weak evidence that the low-premium portfolio has higher exposure to market risk (p-value = 11 percent). Both portfolios have similar exposure to small-firm risk and investor sentiment risk.

III. Conclusions

This paper demonstrates that closed-end funds are more volatile than is implied by efficient financial markets. Despite the fact that closed-end fund returns underreact to net asset value returns, the average fund is 64 percent more volatile than its assets. This finding is not attributable to nonsynchronous trading since it persists over long time intervals. Also, this finding cannot be attributed to distorted NAVs since open-end funds trade at NAV and the return characteristics of closed- and open-end fund NAVs are similar. The implication of my study is that prices are more volatile than fundamentals, even though there is a tendency for prices to underreact to fundamentals.

Various authors have modeled the reaction of security prices to fundamental information. My finding that fund prices do not fully re- spond to information in NAV is consistent with models such as Albert Kyle (1985) that predict underreaction to fundamentals, and in- consistent with models that predict overreaction, such as De Long et al. (1990b). Kyle's model is based on an economy with informed and uninformed investors. The uninformed participants in this model also can be interpreted as noise traders who have information about fundamentals, yet ignore this information in their decision-making. Kyle shows that the informed traders choose to trade in such a way that fundamentals are not immediately re- vealed in prices. De Long et al.'s (1990b) model is based on noise traders who irration- ally overreact to fundamentals and informed

investors who anticipate noise trades and, therefore, "front-run" by buying before noise trader purchases (and selling before noise trader sales). This trading increases the overreaction of prices to fundamentals.

Unlike other studies, my paper documents excess volatility and underreaction for the same securities. Empirical studies regarding the broad underreaction of prices to information are much more recent than the excess volatility literature. These studies show that information contained in announcements is not immediately reflected in prices. For example, Tim Loughran and Jay Ritter ( 1995) show that the stocks of companies that issue equity un- derperform for five years after the announcement of the offerings. Analogously, David Ikenberry et al. ( 1995) show that open-market share repurchases are associated with over- performance in the four years after the announcement. Similar results have been documented with dividend omissions and initia- tions. Roni Michaely et al. (1995) show that in the three years after the announcement, firms that initiate dividends have positive abnormal returns while firms that omit dividends have negative abnormal returns. The accounting literature has documented similar findings regarding earnings surprises. Victor L. Bernard and Jacob K. Thomas (1989) show that after earnings announcements, shares in firms with improved earnings have positive abnormal returns and firms with lowered earnings have negative abnormal returns. Similar to these studies, news about closed-end fund fundamentals (NAV) is not fully reflected in prices. The difference between these papers and my study is that these papers do not have a measure of fundamental value. Rather, they must identify events that presumably have value implications.

My study also sheds light on the source of excess volatility. Although most of the excess risk is idiosyncratic, 15 percent is related to risk that affects other closed-end funds, small-firm risk, market risk, and book-to-market risk. Mar- ket risk alone explains only 2 percent of the average fund's excess volatility. Although book-to-market risk is not related to the average fund's excess risk, book-to-market risk does affect funds with larger discounts. Whether or not similar excess volatility exists in the returns




of other securities remains to be examined. Since the excess volatility documented in this study is largely idiosyncratic and unrelated to aggregate market risk, tests that examine the volatility of diversified portfolios (such as the Standard & Poor's 500) will overlook this large component of volatility.

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