I. Introduction to Closed End Funds

II. Comments on Data

III. Benchmarks

IV. Trading Strategy 1

V. Trading Strategy 2

VI. Trading Strategy 3

VII. Areas for Further Research

VIII. Conclusion

Much work has been done to try to explain the presence of premiums and discounts in prices of closed end funds. A review of the research on this topic reveals that the controversy is still being hotly debated.

On thing is certain, however. Since the inception of the closed end fund industry, funds have traded at discounts and premiums and there is no end in sight to this phenomenon. This project does not attempt to explain or justify discounts or premiums. Instead, we seek ways to profit from them.

In our study of about 50 closed end fund price and NAV data for the 1990’s we noticed two trends that form the basis for the trading strategies presented in this paper:

1) There is negative correlation between the monthly movement of the premium/discount and the return of proceeding month. Increases in premiums lead to decreases in monthly returns. As an example, the following correlations were observed:

2) Premiums and discounts exist for long periods of time for individual funds. Most funds do not change between premium and discount funds very often.

The first observation led to the simple trading strategy 1. For strategies 2 and 3, both observations were taken into account. Our fundamental objective was to try and select funds that would provide excess returns by taking advantage of premiums and discounts that change through time as well as the changing underlying NAV. We realized that predicting increasing premiums often means predicting positive returns and predicting increasing discounts often predicts negative returns.

Throughout this project, we focused our efforts on monthly trading strategies. We believe the basic concepts could be extended to both shorter and longer trading horizons, but we don’t have a theory on the expected performance of these strategies in these different horizons.

We ended up using a subset of the available closed end funds. We used price and NAV data for 29 country funds for the period 1/1/92 through 12/31/99. The time constraint of needing to manually entering NAV data prevented us from analyzing a wider data sample. Before implementing these trading strategies, we would recommend that these algorithms be repeated with a more complete data set.

Another area of potential problem with our data is the presence of dividend paying funds. We did not include dividend payments into the price and NAV data we used. Although this certainly causes some of the price returns to be inaccurate for up to 25% of the periods analyzed (4 dividend payments per year), we feel the effects of this problem are minimized due to the following:

a) Many of the funds pay only a small dividend that does not in many cases get fully reflected in the fund price.

b) The dividend should affect both the price and the NAV approximately equally, so the premium calculation would not be affected. Our trading strategies depend on the premium, so the decisions would not be affected if dividends were added to the price and NAV data.

c) Our trading strategies are all equally long and short in each period. The dividends we would earn on the long positions on average should equal the dividends to be paid on the short positions, so overall returns should not be affected greatly. This assumption obviously breaks down if for some reason our short funds tended to be higher dividend paying funds, although this seems unlikely, given the nature of our short and long selection.

A final note on the results presented in the report is that the returns do not include trading costs. However, since our strategies require only 20 trades per month we believe the trading costs would have only a minimal downward impact on the reported returns. However, closed end funds have higher bid-ask spread costs than other equity assets, so it would be prudent to analyze potential trading costs before these strategies are implemented.

There are two benchmarks that we have used to attempt to judge the performance of our trading strategies. The first is the simple strategy of holding (long) an equally weighted portfolio of all 29 funds. A more realistic benchmark would be the MSCI World Price Index. The results presented below generally are compared to this MSCI index.

A simple strategy of holding an equally weighted portfolio of all 29 funds produces the following performance:

As can be seen, this simple strategy yields poor results in comparison with the world market. The top chart shows an average monthly return for the strategy of .4% with a standard deviation of 5.7%. In the bottom chart, the performance variables were calculated as follows:

Our first strategy is a simple strategy based on the observation that there is negative correlation between movements in the premium and the next period’s price return. It is important to note that a negative change in price return does not mean that the return will necessarily be negative. The data does show that the higher a premium is, the more likely a reversal will occur in the next period. To be the highest premium fund, it must have had a positive movement in the premium during the previous period. A reversal in the premium of the highest premium funds often results in a negative price return. The same theory can be applied to the reversal of the largest discount funds.

To take advantage of this reversal, this strategy simply buys the 5 highest discount funds and shorts the 5 lowest discount funds. The position is held for one month only. The number 5 was chosen based on the total number of funds in the data sample and the fact that during the observation period many more funds were trading at a discount than a premium, which led to limited selection for the short position.

In order to maximize the reversal effect, weights were chosen to be unequal. The following weights were used:

Strategy 1 resulted in the following performance:

 Strategy 1 is marginally better than the MSCI World index, as judged by its higher Sharpe ratio. It also provides a higher return than the benchmark 61% of the time, while yielding a respectable 30% annual return.

The persistence of premiums and discounts gives rise to our second strategy. The market is willing to pay a premium for some funds and demands a discount on others. We theorized that a premium is paid for a ‘good’ fund and a discount demanded for a ‘bad’ fund. Additionally, we think that when the market is prepared to change a fund’s status from discount to premium (and visa versa) it looks to the average premium or discount given to other funds to determine an appropriate level. Thus if we could identify funds that the market considers ‘good’ or ‘bad’ we could base a trading strategy on the relative premium or discount compared with other funds of the same category.

In our implementation, we defined a ‘good’ fund as one that has a 3-month moving average premium and a ‘bad’ fund as one that has a 3-month moving average discount. Our strategy then buys 5 ‘good’ funds that are trading at the lowest premiums relative to other ‘good’ funds, and shorts 5 ‘bad’ funds that are trading at the lowest discount (highest premium) relative to other ‘bad’ funds. The strategy was implemented using simple sorting algorithms.

The weights used for this strategy are as follows:

Ideally, we would have like to have used equal weights for both the longs and the shorts. However, during the 1990’s, many more funds were trading at a discount than a premium. This severely limited our selection pool for our longs. In fact, in some months there weren’t even 5 funds trading at a premium. So we opted to choose only 2 of the ‘good’ funds and weigh them equally.

The results of this strategy are as follows:

This strategy gives the same average monthly return as strategy 1 with a lower standard deviation. Additional, this strategy achieves a slightly higher Sharpe ratio, and has a lower Beta, which implies a lower exposure to the volatility of the world market.

A closer examination of the results of strategies 1 and 2 leads to strategy 3. In strategy 1, about 84% of the average monthly return comes from the long positions. In strategy 2, about 36% of the return comes from the short position. Strategy 3 then combines the long position of strategy 1 with the short position of strategy 2.

While it may be tempting to reject this strategy on the grounds of data snooping, we believe there is solid theory behind its performance. The long position of strategy 1 is to buy the funds with the largest discount (which are also part of the ‘bad’ group). The short position of strategy 2 is to short the ‘bad’ funds (those trading at a discount) that have the smallest discount. Strategy 3 then just focuses of the ‘bad’ funds, and is a mean-reverting strategy. This strategy makes some sense considering a market where in effect the discounts themselves really make no sense. If the discounts have no real financial reason for existing, how does the market know the appropriate level of discount? We believe the market looks at other funds trading at discounts and succumbs to market discount level peer pressure. Further, due to overreaction and slow response times, a mean-reverting trading strategy seems to make sense.

The same strategy may perform well if concentrated only on the ‘good’ funds. Unfortunately, in our limited data sample set, there were not enough ‘good’ funds to test this theory. This is an area of further research that would require more extensive data. This lack of data may also bias lower the results of strategies 1 and 2.

The results of strategy 3 are as follows:

Strategy 3 gives the best results in terms of both return and standard deviation and consistency. This strategy also has a low (and negative) exposure level to the world market.

In addition to the areas mentioned previously for further study, there is one area that we believe may hold promise at least for country funds. The price of a closed end fund is of course highly correlated with the underlying NAV. Our data shows correlations of 80-95%. However, the price of some funds is more sensitive to underlying NAV changes than others. It is for this reason that the data shows significant volatility in the premiums and discounts.

In order to try to exploit the difference in sensitivities, we propose the following:

a) View the fund price as a separate asset from the underlying NAV

b) Calculate a Beta for each fund based on the covariance of the price with the NAV

c) Use predictive regressions to try to predict country index movements. These predictive regressions have shown some promise in some countries.

d) Develop a trading strategy based on selecting funds with the highest Betas. For example, sort the countries by the predicted movement in the country market, up or down. Within each group, sort the funds by the betas. Short the highest beta funds in the ‘down prediction’ group and long the funds with the highest betas in the ‘up prediction’ group.

Recent years have seen an attack on the closed end fund industry by activists. Some funds have been liquidated or converted to open funds. Possibly within 10 years there will no longer be closed end funds.

Until closed end funds disappear, however, we believe there is a significant opportunity to take advantage of inefficiencies in this market. The strategies presented in this paper represent some basic ideas we believe can be extended to even better, more consistent, trading strategies. It is probably to the advantage of the few investors that focus on closed end funds that this industry has not received as much attention as other equity opportunities. Perhaps with more attention, the inefficiencies exploited by the simple strategies presented here will disappear long before the closed end fund industry itself.