Mean-reversion in closed-end fund discount: evidence from half-life

Abstract

This article examines the mean-reversion properties of the discount on UK and US closed-end funds. While the discounts are tested I(1), strong statistical evidence of mean-reversion is ascertained by bias-corrected bootstrap half-life estimates. The estimates also indicate that equity-based funds converge to the steady-state level faster than fixed income funds. In addition, although an equilibrium pricing condition postulates an inverse relation between half-life and the discount size, correlation estimates fail to show strong support for the relation.

Keywords:

• closed-end funds discount
• mean-reversion
• half-life
• high-density region

JEL Classifications:

• C22
• G11

Acknowledgement

The authors are grateful to Laurence Copeland for helpful comments, and Daniel Chai and Raphael Park for assistance with computing work.

Notes

1.  The assumption of fixed variance will be relaxed shortly in the bootstrap procedure to account for a (conditionally) heteroscedastic error term.

2.  The full details can be found in Kim et al. (2007).

3.  The number of bootstrap iterations B₁ and B₂ is set to 5000 and 5000, respectively, with the wild bootstrap conducted using the standard normal distribution for η_t.

4.  h still denotes the half-life estimate.

5.  Copeland (2007) uses 736 observations for the period of 5 May 1990–12 May 2004.

6.  The data frequency largely depends on availability. Because the ITC and US data differ in frequency, their half-life is calculated in years for a comparative analysis.

7.  Because 25% and 10% significance levels are used in subsequent sections for statistical inference, the ADF test was conducted at these significance levels for consistency.

8.  Copeland (2007) finds consistent results with this based on KPSS test and Phillips-Perron test.

9.  This is because it would be hard to argue that the discount mean-reverts if it does not revert within the fund’s life. The average length of the fund life is approximately 10 years across the funds except for Loan Participation which shows a shorter average of 6 years. Also, funds less than two years old are excluded from the analysis.

10.  Based on their Monte Carlo results, Kim et al. (2007) report that 90% confidence interval provides sufficient true value coverage and recommends the use of 90%. Past published applications (Sisira et al., 2007; Kim and Ji, 2011) of the HDR estimators all use 90% and 75% intervals.

11.  Most of the funds that tested I(1) in the unit root test had finite upper limits in the intervals. None of the funds that tested I(0) showed infinite limits.

12.  In principle, an alternative approach is to estimate half-life from fractionally integrated (ARFIMA) models embracing what Copeland (2007) has documented. However, the primary interest of the present study is to provide evidence of mean-reversion for the closed-end fund discount via half-life. More importantly, as a foregoing section observed, Copeland (2007) himself states that it is impossible to be more specific about half-life in ARFIMA models because there is wide variation in the ARMA components for his data, which is the gap void in the literature that this study attempts to fill in reliance on the documentation on the half-life bias correction in AR context by several authors including Kim et al. (2007).

13.  The median is adopted in preference to the mean in current context to avoid the outlier effects of infinite values.

14.  As discussed in the introduction, however, Copeland (2007) warns that the long memory tests could not be more specific than this about half-life.

15.  These include India, Indonesia, Korea, Malaysia, Mexico, Taiwan, Turkey, Russia and other markets under more stringent investment restrictions compared to industrialized countries.

16.  If the test statistic is negative and significant, it indicates that the null of the same location is rejected against the alternative that funds in row are located to the left of funds in column. To conserve space, the two-sided test p-values are not presented but are available upon request.

17.  An exception occurs with General and International. The test statistic of 3.17 in column International ranks International higher than General contrary to Table 7. The median confidence intervals for General from Table 5 are larger than International but the Mann–Whitney tests suggest General is located to the left of International. This may be due to the skewness of the distributions. These two distributions may be skewed in the opposite direction.

18.  The correlations between returns on NAV and half-life have been examined, but the results are qualitatively the same because of strong correlation between price returns and NAV returns. This adds indirect evidence that the discount should be mean-reverting.

19.  One may find the positive correlations self-evident by reasoning that frequent occurrences of a large discount lead to strong persistence. However, the size of discount is not required to have any relation with the half-life unless a relation is theorised. For example, large discounts can occur frequently but die out quickly giving rise to weak persistence – a small half-life.

20.  In order to make an (rather crude but simple) adjustment for risk, the correlations have been estimated too between the coefficients of variation for returns and discount and half-life, but the results are much weaker.