Many emerging markets funds active in the world today are closed-end funds. Closed-end funds issue a fixed number of shares, which are then traded either on a securities exchange or over the counter. The fund's share price is determined by the interplay of supply and demand. Some closed-end emerging markets funds are listed on the New York Stock Exchange, thereby mitigating the risks associated with investing in the local markets. Only in the rarest cases does a closed-end fund's share price coincide with its net asset value (NAV). When the share price exceeds the NAV, investors must pay a premium to acquire the shares held by the closed-end fund, while when the share price falls below the NAV, investors acquire the shares at a discount. Considering this inefficiency, it interesting to test whether it is possible to realise excess returns when applying quantitative investment strategies.

Early in the 19th century, both Carl Friedrich Gauss and Francis Galton made significant contributions to risk management by using the normal distribution curve to estimate results of large samples of scientific data. In both cases, they noticed that the data seemed to cluster around a central point. Galton further observed that in cases where the data were higher or lower than the mean, the data eventually reverted back to the mean. He also noted that two conditions are necessary for observations to be distributed normally around their averages. First, there must be a large number of observations. Second, the observations must be independent.

Burton G. Malkiel in his 1975 book 'A Random Walk Down Wall Street' argued that markets are perfectly random, which would imply that stock price movements are completely independent. In a more recent study, Peter Bernstein in 'Against the Gods' used normal distribution analysis to test the random walk theory. His results confirmed that the market supports the random walk theory when the stock prices are trading near their mean. However, at the extremes of the distribution curve, the market is not random. This occurs because investors have a tendency to overweigh recent events in their decision-making process and to lose sight of the long run. The brief retreat from the significant area around the mean provides a trading opportunity.

The vast majority of closed-end country funds trade around their 52-week means throughout the year. However, sometimes the prices significantly deviate from their respective mean. By subtracting the discount from the 52-week mean and dividing by the standard deviation, one can derive the z-score. The z-scores indicate the relative magnitude of the discount's deviation from the mean, thereby serving as buy and sell signals. In both statistical and portfolio contexts, this calculation is superior to using absolute discounts and premiums to the NAV.

We used the weekly US$ price and net asset values for 31 NYSE closed-end emerging market equity country funds from January 1989 to June 1997. We also collected the weekly US$ prices of the IFC Investable Country Indices for each of the 18 countries represented during the same time period. The sample included all of the quoted NYSE funds that had been trading for at least 52 weeks prior to the study and for which an IFCI Index was available. The 31 funds included in the study account for 80.8% of the assets of all the quoted NYSE emerging markets country funds.

We analysed five alternative strategies, the buy and sell points appear in Table 1. For example, under strategy one, we would purchase shares when the z-score fell to -1.25 for the first time, and would sell when the z-score rose to +1.25. At this point, we would invest into the respective IFC Investable Country Index until the z-score declined to -1.25 again. Obviously, the frequency of trades would be a function of the level of z-score required for the purchase or sale decision to be made. If these rules produce excess returns, given the performance of the market and risk level, the weak form of the efficient market hypothesis will not be supported. Moreover, the excess returns will demonstrate that the discount levels to the NAV are not as relevant as the discount to the 52 week mean.

The country funds had to have been trading for a minimum of 52 weeks to be included in the portfolio; this was necessary to attain the initial 52 week mean, standard deviation, and z-score. Beginning in January 1989, each portfolio was worth $100,000, which was equally distributed between those funds meeting the 52-week criterion. As additional funds satisfied the 52-week criterion, the equally weighted portfolio was rebalanced to include those funds.

Investors should note, however, that the trading strategy would be more costly to administer than others that could be developed, as it would be necessary to trade shares whenever a buy or sell signal occurred. Since transaction costs were assumed to be zero, the number of trades w ere not of concern. Obviously, however, transaction costs are real, which means that trading strategies minimising the number of transactions are necessary and require testing.

We also evaluated two different buy and hold strategies. In the first, we equally distributed $100,000 among the individual IFC Investable Country Indices with funds that met the 52 week criterion. We added countries as the 52 week criterion was met but never sold the positions. In the second equally weighted portfolio, the invest-or bought and held each of the 31 funds as they met the 52 week criterion. Table 2 summarises the total re-turn, standard deviation, and number of buy and sell signals for each strategy. The most successful investment strategy called for the funds to be purchased when their z-score was at -0.5 and sold when their z-score reached +0.5. Figure 1 depicts the terminal value of $100,000 invested in January 1989 and at the end of June 1997.

Any of the buy and sell point strategies provided higher returns than a simple buy and hold strategy involving all of the funds. Moreover, all five strategies produced higher returns than would have been received from the individual IFC Investable Country Indices. Admittedly, the weekly returns were slightly more variable than were the returns from investing in the IFC Investable Indices.

Importantly, the country funds outperformed in both rising and falling markets when applying the z-score strategies, even when the funds themselves underperformed their respective IFC Indices. The individual funds underperformed a total of 40 times in rising markets, but outperformed the index 65% of the time when applying the z-score strategies. On the other side of the market, the funds underperformed a total of 17 times, but outperformed the index 71% of the time using our strategies.

The most compelling benefit of an emerging market country fund is the downside protection it provides. For example, there were 34 strong market corrections (declining more than 15% in less than three months) between 1989 and 1997 in the emerging markets; the country funds outperformed their respective IFC Indices 95.9% of the time. Hence, country funds have the characteristics of a put option in falling markets.

The results of this study demonstrate that investors can realise excess returns in the emerging markets irrespective of the individual country fund's absolute discount or premium to the NAV. This study also provides several different trading strategies to realise these rates of return. Consequently, these findings support the conclusion drawn by earlier research-ers about possible inefficiencies of the market for closed-end fund shares.

Arbitrary buy and sell points using z-scores produced returns in excess of those obtainable by holding the individual IFC Investable Country Indices or by following a buy and hold strategy with the closed-end country funds. Also, returns of the various strategies did not appear to be significantly more risky than the return of the individual markets. Thus, these results generally fail to support weak form efficiency.

In conclusion, investors can im-prove the likelihood of trading profits by employing strategies using z-scores in quoted emerging market country funds similar to those tested and found successful here.

László Gömöri and Karen Oeser are with Bank Sarasin & Co in Basle