Arbitrage Bounds and the Time Series Properties of the Discount on UK Closed-End Mutual Funds

Abstract

The persistence of discounts on UK (and US) closed-end mutual funds (investment trusts) is well known, both in the academic literature and in the financial sector. In a dataset of 135 UK ITC's, sampled at weekly intervals, it is shown that while prices and net asset values clearly have unit roots, the evidence suggests that discounts are for the most part not stationary, a finding which supports Cheng, Copeland and O'Hanlon (1994) and more recently Gemmill and Thomas (2002). On the other hand, it is shown here that discounts almost certainly do not have a unit root. A possible statistical reconciliation would be a long memory process, and results are presented to show that for most UK investment trusts the discount is well described by a fractionally-integrated process. This type of model has been widely applied to financial markets ever since it was introduced by Granger and Joyeux (1980). In most cases, the ITC discount process appears to have a root of around 0.7, which implies nonstationarity, but reversion to the mean. In other words, ITC discounts have a long run mean level (of around 13%) to which they eventually return, but disturbances are so persistent that reversion may be an extremely slow, protracted process.

This conclusion is in some respects unsatisfactory, given that many of the ITC's in the sample are large, frequently traded, and quite liquid stocks. The long run mean discount estimated here is entirely consistent with the Gemmill and Thomas (2002) arbitrage-induced level. But if arbitrage is at all effective, it is difficult to reconcile with such slow adjustment in the aftermath of disturbances. A possible explanation is to be found in the broader arbitrage bounds generated by the threat of open-ending. If the discount process is actually a bounded random walk, then it is shown here that it will mimic a fractionally-integrated process, a conclusion which may well have relevance to a number of other financial markets which have been shown to display apparent long memory behaviour.

The implication is that a more appropriate model of the typical ITC discount would take explicit account of the arbitrage forces at work. Specifically, it is argued that the process would be better characterised by a smooth-transition autoregression (STAR), implying that the speed of adjustment is an increasing function of the gap between the current discount and its long run level. Two specific formats are considered here: the exponential STAR (ESTAR) model, which postulates a symmetric adjustment process, and the logistic (LSTAR) model, which allows for asymmetry. The latter has to be a candidate in the present context, because of the possibility that the speed of adjustment to above-average and below-average discounts are not necessarily the same, since the arbitrage involved is different in the two cases and may involve different transaction costs. In the event, tests on 5 ITC's provide clear evidence of nonlinearity in the discount process, but they are inconclusive about whether the ESTAR or LSTAR model better describes the process.

Keywords: Closed-end mutual funds, ESTAR, LSTAR, long memory

JEL Classification: C22, G12, G14