Closed-End Discount and Liquidity Constraint
A closed-end equity fund listed on the Pakistan Stock Exchange trades at PKR 9.20 per share while its NAV is PKR 10.00 per share. The fund's annual distribution yield is 7.0% based on NAV, and its total expense ratio is 1.5%. An open-end diversified equity fund with a similar portfolio has a total expense ratio of 2.0% and an expected distribution yield of 6.5% based on NAV, but it can be redeemed daily at NAV with no exit load after 30 days. The investor has PKR 2,000,000 and a three-year horizon. The closed-end fund's average daily trading volume is 50,000 shares, and the investor would need to sell within five business days if an emergency arises. The investor expects the closed-end fund's discount to narrow from 8% to 3% over three years. Ignore tax and brokerage commissions. Assume distributions are reinvested at market price for the closed-end fund and at NAV for the open-end fund.
1. Calculate the closed-end fund's distribution yield on market price and the open-end fund's distribution yield on NAV. Explain why the closed-end yield on market price is higher.
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Closed-end distribution per share = 7.0% x PKR 10.00 NAV = PKR 0.70. Yield on market price = 0.70 / 9.20 = 7.61%. Open-end distribution yield = 6.5% on NAV. The closed-end yield on market price is higher for two reasons: the distribution is based on a higher NAV than the market price because the fund trades at an 8% discount, and the open-end fund's stated yield is lower. The market-price yield is not a free lunch: if the discount widens, the investor can lose more on price than the extra yield. The yield on NAV is the better measure of the portfolio's distribution capacity; the yield on market price is the cash yield actually received relative to the purchase price.
2. Assume NAV stays at PKR 10.00 and the discount narrows to 3%. Calculate the closed-end fund's expected three-year price return and approximate annual total return including distributions. Compare with the open-end fund if its NAV also stays constant.
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Target closed-end price at a 3% discount = 10.00 x (1 - 0.03) = PKR 9.70. Current price = PKR 9.20. Price gain = (9.70 - 9.20) / 9.20 = 5.43% over three years, or about 1.78% per year simple. Distribution yield on market price = 7.61% per year. Approximate annual total return = 7.61% + 1.78% = 9.39%.
Open-end fund: distribution yield 6.5%, no discount narrowing, NAV constant, so approximate total return = 6.5%. The closed-end fund looks better by about 2.9 percentage points per year if the discount narrows as expected. But that return depends on a forecast of discount narrowing, which is not guaranteed. If the discount instead widens to 12%, the target price would be 8.80, a 4.35% price loss over three years, and the total return would fall to about 6.16% per year. The open-end fund has no discount risk but a higher expense ratio.
3. Assess the liquidity risk for the PKR 2,000,000 investment and decide whether the closed-end fund is suitable given the emergency sale requirement. What position size or order strategy would you suggest?
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Shares needed = 2,000,000 / 9.20 = about 217,400 shares. Average daily volume = 50,000 shares, so five-day volume is about 250,000 shares. The order is about 87% of five-day volume. That is too large for a reliable five-day exit, especially in a stress scenario when volume may fall and the discount may widen. The investor would face market impact, a wider bid-ask spread, and the risk of selling at a deeper discount.
For a hard five-day emergency requirement, the closed-end fund is not suitable at this position size. The investor should keep the emergency reserve in a money market fund or open-end fund with daily redemption. If the investor still wants the closed-end exposure, size it so the position is a small fraction of expected volume, for example no more than 20-30% of five-day volume, which would be about 50,000-75,000 shares, or PKR 460,000-690,000 at PKR 9.20. Use limit orders and split the sale across several days rather than a single market order. Monitor the discount and the fund's distribution sustainability. A closed-end fund can be appropriate for a patient investor with no near-term liquidity need, not for money that may be needed within five business days.