Jason C - NYU



Predicting Net Asset Value Discounts/Premiums

of Closed-End Funds

Data Analysis: Prof. Simonoff

The first investment decision I ever made was to buy the Asia Pacific Fund, a closed end fund that invests in companies located in the Asia Pacific region. Unlike open-end, mutual funds, closed end funds do not allow redemption of their shares at the underlying value of the stocks in which the fund invests (Net Asset Value). Rather, the shares of closed end funds trade on an exchange like a normal equity and thus a discount, or premium, can emerge if the trading price of the fund’s shares diverges from the fund’s net asset value.

When I bought the Asia Pacific Fund, in 1993, it was trading at a premium to its net asset value (i.e., the fund’s market price was higher than the underlying value of the fund’s investments). The Asia Pacific markets were very popular with investors at the time and had drummed up lots of interest in the financial media. However, shortly after I purchased the fund, the premium that I paid for the shares turned into a discount and has not recovered since. I have since learned that this is a common occurrence with closed end funds. However I have never heard a good explanation for this puzzling aspect of market demand.

If a fund trades at a discount, it means that the shareholders would gain more value if the fund disbanded and liquidated its shares. Since the underlying investments of the fund are usually market-listed stocks or bonds, the underlying net-asset value could tangibly be realized. When a fund trades at a discount for a long period of time, major investors often try to have the fund either i) liquidated and disbanded or ii) converted into an open-end fund so that shares of the fund could be redeemed on a daily basis at the net asset value per share. Given the large number of closed end funds in the market trading at a discount and the rare occurrence of liquidation, it is unlikely that discounts can be generally explained by investor sentiment.

I chose this issue as the subject for my project to try to gain a better understanding of this enigma. All the data I used for my analysis is readily available on Bloomberg and on the Internet at Morningstar’s web site[1]. Thus the funds selected for this project are limited to those funds rated by Morningstar. I am not aware of any bias that may exist in Morningstar-rated funds versus funds not rated by the company, yet in any case the results of this study are limited to Morningstar-rated funds. To obtain my data, I looked at the 192, alphabetically listed, closed-end funds available on the web page and selected every fourth fund, leaving a data set of 48 funds. Obviously studying all 192 would have been preferable but the data had to be manually entered into Minitab and a good portion of the data had to be searched for, individually for each fund, on Bloomberg. I chose the week ending October 24, 1997 as the ending date for the data in my study since at the time of gathering, it was the most recent. Thus the information I am trying to predict is the Net Asset Value Discount of a Morningstar-rated fund on October 24, 1997. However, to the best of my knowledge, there were no market events that made this week any different from any other,[2] and thus the results may be extrapolated to cover any weekly period. To build the model for this prediction, I selected the following information to study:

1. 1-Year Average Share Price: This represents the average market price of each fund over a 365 day period ending October 24, 1997. I chose this variable due to the fact that most companies pursue a share price above $10 for no clear economic reason. It is simply more attractive to investors to purchase a stock above $10. I would expect this to be the case with closed end funds as well. Thus it is possible that funds with lower share prices might attract less interest than those with higher share prices, and therefore could account for a deeper discount. I chose a one-year average to avoid temporary movements in prices. Below is a scatter plot showing 1-Year Average Share Price on the x-axis and Net Asset Value Discount on October 24, 1997 on the y-axis.

While there appears to be a positive linear relationship in the lower left corner of the graph, there are many outliers and influence points. Yet without looking at all the other variables, it is difficult to tell whether any of these points should be excluded.

2. Morningstar Rating: Morningstar rates funds on a scale from 1-5 stars based on its performance, risk profile and expenses. One would think that lower rated funds would have less market interest and would therefore trade at larger discounts to NAV. The scatter plot below doesn’t seem to support this.

There are a considerable number of 4 and 5-star funds trading at discounts, which seems to disprove the strength of Morningstar’s ratings as a predictor of NAV discounts/premiums. There is a noticeable outlier on this graph, a 1-star fund with a NAV premium over 40%. This represents the Thai Fund, a fund that invests exclusively in Thai equities. It is difficult to tell exactly why the premium is so large, but it is clearly a function of the Southeast Asian turmoil. I would have expected an unusually large discount but perhaps there is not a lot of liquidity in the fund and investors were forced to hold the fund’s shares despite drastic declines in the underlying equities. In any case, the abnormality of this fund and the special circumstances of Thai equities justify its removal from the data set before a regression is performed.

3. 5-Year Return: Many investors look at 5-year return to determine fund performance. This can be measured in terms of NAV or in terms of stock price. Both of these show the absolute return of the fund over the 5-year period ending October 24, 1997. The difference between the 5-year NAV return and the 5-year market return, is a measure of the 5-year NAV discount/premium. All three variables are shown in scatterplots against current NAV discount below.

Judging from these three scatterplots, the strongest relationship seems to exist with the difference between 5-year NAV and 5-year market return, shown above as 5-year discount. Once again, the Thai Fund is a noticeable leverage point. This finding seems to imply that past performance is the best measure of current performance. It will be interesting to see how this plays out in a regression. Significantly, there are 11 funds that have not been around long enough to have a 5-year history, thus the actually number of funds in the data set will be reduced to 37 in the regression.

4. 1-Year Average NAV Discount: This measures the average discount over the one-year period ending October 24, 1997. The scatterplot below shows a strong relationship. It is not surprising that the best predictor of current NAV discount is the average discount over the past year. The Thai Fund again is a noticeable leverage point.

5. Type of Fund / Investment Goal: There are two yes or no variables being measured here. The first measures whether the fund invests in bonds (1) or equities (0). If a fund invests in both, I marked it as an equity fund. Since equities have a higher expected return and standard deviation, they have more of an effect on a portfolio’s risk and return than bonds. It would be ideal to measure the percentage of equities in the fund as a variable, but that information was not available. The second variable measures whether the fund invests in foreign (1) or domestic (0) securities. If a fund invests in both, I labeled it as foreign with the same argument used in the equity / bond case. Side by side boxplots show the distribution of current NAV broken down by the two variables.

In the case of bond funds, there appears to be a smaller median discount and a narrower distribution than equity funds. Given the higher variability of equities, this is not surprising. Foreign funds seem to have a larger discount than domestic funds with a slightly wider distribution. This is also unsurprising given the inherent political risk in many foreign funds. The Thai Fund is once again noticeably different than all other funds.

REGRESSION ANALYSIS

The initial regression using all variables, except 5-Year NAV Return and 5-Year Market Return (since they both are represented in 5-Year Discount), with the Thai-Fund removed from the data, gave the following results.

The regression equation is

NAV Discount = 0.0283 -0.000745 1-Year Avg Price + 0.00043 Morn. Rating

+ 0.690 5-yr discount + 0.752 1-yr Avg NAV Disc + 0.0033 Bond =1

- 0.0397 For=1

36 cases used 11 cases contain missing values

Predictor Coef StDev T P VIF

Constant 0.02833 0.02540 1.12 0.274

1-Year A -0.0007451 0.0007835 -0.95 0.349 1.2

Morn. R 0.000426 0.005394 0.08 0.938 1.2

5-yr dis 0.6901 0.2821 2.45 0.021 2.0

1-yr Avg 0.75227 0.09339 8.06 0.000 2.6

Bond =1 0.00334 0.01244 0.27 0.790 1.5

For=1 -0.03966 0.01265 -3.13 0.004 1.5

S = 0.03009 R-Sq = 91.6% R-Sq(adj) = 89.8%

Analysis of Variance

Source DF SS MS F P

Regression 6 0.285690 0.047615 52.58 0.000

Error 29 0.026259 0.000905

Total 35 0.311950

Source DF Seq SS

1-Year A 1 0.017689

Morn. R 1 0.000001

5-yr dis 1 0.151241

1-yr Avg 1 0.106678

Bond =1 1 0.001184

For=1 1 0.008898

Unusual Observations

Obs 1-Year A NAV Disc Fit StDev Fit Residual St Resid

19 12.1 -0.00290 0.04748 0.01941 -0.05038 -2.19R

29 15.3 0.08870 -0.00731 0.00803 0.09601 3.31R

41 45.6 -0.06790 -0.06260 0.02619 -0.00530 -0.36 X

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

The R-squared is very high at 91.6%. However some of the variables (Morningstar Rating and Bond/Equity) have very high p-values. Thus they are not likely to be relevant to the model. Additionally, there is a data point (#29) with a very high standard residual (3.31). This represents the MuniYield Fund that invests in municipal bonds. The fund is unusual in that its 5-year discount and 1-year average discount are both negative, yet it is currently trading at a premium. There can be two explanations for this. Either i)something unusual has happened to the fund in recent weeks creating enough buy-side interest that the discount has become a premium (this seems unlikely given the steady performance of most municipal bond funds), or ii) I made an error inputting the data. It is impossible to tell which is the cause without having access to Bloomberg, which I currently do not. Nevertheless, if either case is true, the fund is unrepresentative of most funds and should therefore be excluded from the analysis.

Therefore I re-ran the regression without the MuniYield Fund and without the Morningstar Rating and Bond/Equity variables. The results are listed below.

The regression equation is

NAV Discount = 0.0304 -0.000957 1-Year Avg Price + 0.714 5-yr discount

+ 0.748 1-yr Avg NAV Disc - 0.0365 For=1

35 cases used 11 cases contain missing values

Predictor Coef StDev T P VIF

Constant 0.030421 0.008830 3.45 0.002

1-Year A -0.0009567 0.0005743 -1.67 0.106 1.0

5-yr dis 0.7145 0.2097 3.41 0.002 1.8

1-yr Avg 0.74772 0.06638 11.26 0.000 2.1

For=1 -0.036467 0.009170 -3.98 0.000 1.3

S = 0.02342 R-Sq = 94.4% R-Sq(adj) = 93.6%

Analysis of Variance

Source DF SS MS F P

Regression 4 0.276890 0.069222 126.18 0.000

Error 30 0.016457 0.000549

Total 34 0.293347

Source DF Seq SS

1-Year A 1 0.019408

5-yr dis 1 0.148079

1-yr Avg 1 0.100726

For=1 1 0.008676

Unusual Observations

Obs 1-Year A NAV Disc Fit StDev Fit Residual St Resid

19 12.1 -0.00290 0.05043 0.01184 -0.05333 -2.64R

32 18.2 -0.03460 -0.08376 0.00824 0.04916 2.24R

40 45.6 -0.06790 -0.07211 0.02043 0.00421 0.37 X

R denotes an observation with a large standardized residual

X denotes an observation whose X value gives it large influence.

The R-Squared is now even higher at 94.4% with at least 90% significance of all variables. The F-statistic is extremely high at 126.18 providing an extremely strong regression. The VIF of all variables is relatively low and therefore collinearity is not a problem. Yet before concluding anything about the model, we must look at the error assumptions and regression diagnostics

Regression Diagnostics

I first looked at the standard residuals. There is one data point with a residual of -2.64. This is the India Growth Fund, a fund that invests primarily in Indian equities. The situation with this fund is similar to the MuniYield fund. That is, it is currently trading at a discount (-.029%) despite a 1-year average premium (5.59%) and a 5-year premium (3.67%). However, the Indian market is a lot more volatile than the US munibond market and the current discount is very small. Therefore I cannot see a good reason to exclude this data.

With four predictors and 35 data cases, the relevant leverage factor is 2.5*(4+1)/35 = .3571. At this level there is one case with high leverage. The Source Capital Midcap Value Fund has a leverage value of .7611. This is likely due to the fact that the fund’s 1-year average share price is 45.86 versus a mean for the data set of 13.76. This made me take another look at 1-Year Average Share Price as a predictor in the model. Its coefficient in the model is -0.0009567. Despite a low p-value, this coefficient is still pretty close to 0 and thus may not have much significance in the model. So I re-ran the regression with the three remaining predictors.

The regression equation is

NAV Discount = 0.0186 + 0.704 5-yr discount + 0.766 1-yr Avg NAV Disc

- 0.0363 For=1

35 cases used 11 cases contain missing values

Predictor Coef StDev T P VIF

Constant 0.018622 0.005423 3.43 0.002

5-yr dis 0.7040 0.2155 3.27 0.003 1.8

1-yr Avg 0.76611 0.06731 11.38 0.000 2.1

For=1 -0.036274 0.009428 -3.85 0.001 1.3

S = 0.02408 R-Sq = 93.9% R-Sq(adj) = 93.3%

Analysis of Variance

Source DF SS MS F P

Regression 3 0.275367 0.091789 158.26 0.000

Error 31 0.017980 0.000580

Total 34 0.293347

Source DF Seq SS

5-yr dis 1 0.158615

1-yr Avg 1 0.108167

For=1 1 0.008586

Unusual Observations

Obs 5-yr dis NAV Disc Fit StDev Fit Residual St Resid

19 0.0367 -0.00290 0.05101 0.01217 -0.05391 -2.59R

32 -0.0036 -0.03460 -0.08044 0.00822 0.04584 2.03R

R denotes an observation with a large standardized residual

Without 1-year average share price, the R-squared is still extremely strong at 93.9%. The remaining three variables now reject the Beta Null hypothesis at a 99% confidence level and the regression F statistic is still extremely high at 158.26. The Regression diagnostics still shows the India Growth Fund with a high standard residual, yet as explained before I am choosing to ignore this.

With three predictors now, the relevant leverage value is 2.5*(3+1)/35 = .2857. At this level there are two funds with significant leverage values. These are the First Financial Fund (#13) and the High Income Advantage Fund (#18). Their leverage values are 0.322191 and 0.288414 respectively. The High Income Advantage Fund falls has the highest 1-Year Average Discount in the data set and the highest current NAV, thereby explaining its leverage. However, there is nothing that intrinsically makes this fund different from the others. The First Financial Fund has no characteristics that differentiate it from the data set. Therefore I can see no reason to exclude them. Furthermore, running the regression without them barely changed the results. Thus despite high leverage values, I can conclude that the model is stable with or without these points.

Finally, there are no data with cook values above 1. Thus there are no influence points in the data set.

Error/Residual Assumptions

The standard residuals vs. fits plot on the left shows no apparent relationship among residuals; thus the residuals are not correlated. The graph on the above left shows that the residuals are roughly normally distributed. The normality assumption is further reinforced by the histogram of the residuals below showing a roughly Gaussian distribution.

Therefore, our regression assumptions are valid and we can conclude that the model is significant.

CONCLUSION

The regression equation of the model is:

NAV Discount = 0.0186 + 0.704 5-yr discount + 0.766 1-yr Avg NAV Disc - 0.0363 For=1

Thus with an intercept of .0186, we would expect a brand new domestic closed end fund (i.e. with no discount history) to trade at a premium of .0186. The Beta coefficients say that i)for every 1 percentage point increase in five year discount/premium, the current NAV discount/premium increases by .704 percentage points, ii)for every 1 percentage point increase in 1-year average discount, the current NAV discount/premium increases by .766 percentage points, and iii)if a fund invests in foreign securities, its discount increases, or its premium decreases, by .0363 percentage points. In addition to the statistical significance of the model, the coefficients make practical sense. We would expect past discount performance to give a good indication of current performance, despite the many disclaimers in all fund prospectuses. Additionally, we would expect the higher risk in foreign funds and the lackluster performance of foreign markets, relative to the US bull market over the past five years, to detract from a fund’s discount/premium.

Now that we have a good predictive model it is interesting to test its accuracy on data not included in the study data set. I ran a prediction interval on the Colonial Intermediate High Income Fund, a domestic high-yield bond fund. It’s 5-year discount is -.001, its one year average discount is.0294, and it doesn’t invest in foreign securities. The model predicted a fit of .04044 with a 95% prediction interval of (-0.01037, 0.09125). The fit is very close to the actual premium of .0374 that the fund was trading at on October 24, 1997 and thus the model seems to be accurate with market data.

It is interesting to know that past performance is the best indicator of current performance. However, current performance tells us nothing about future performance. A model that could predict future discounts/premiums would be of strong practical value and might have saved me some money in my Asia Pacific Fund investment. Perhaps I already have a topic for next semester’s regression project.

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[1] Morningstar is a research company that rates mutual funds based on performance and risk profile.

[2] This was before the 500 point “crash” of October 27, 1997.

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