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There’s a formula that tells you whether a closed-end is cost-effective.

Finding bargains in closed-end funds is quite the challenge these days. I went looking and found a few. Very few.

What follows is a short list of closed-ends that look cheap and a long explanation of why you should be stay away from the rest of the bunch.

A closed-end fund is a special kind of investment company that has its exit door locked. Once capital is inside, it can’t leave. If you want to cash out, you have to find another buyer willing to take your place, and you might have to accept a stingy offer.

Contrast open-end and exchange-traded funds. Open-end, a.k.a. mutual, funds, cash out unhappy investors by selling off portions of their portfolios. ETFs leave the problem of liquidity in the hands of market makers who assemble and disassemble blocks of shares.

U.S.-registered closed-ends, which hold $250 billion of assets, have long since been overtaken by mutual funds and ETFs, which hold a combined $29 trillion. But there was a time when closed-ends towered over the competition. Bankers concocted them at a furious pace and unloaded the shares at fat prices.

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At the climax of the 1929 bubble, closed-ends traded at an average 50% premium to the value of their assets. In their appeal to the naive and in their ability to enrich insiders they were the counterpart to today’s special-purpose acquisition companies.

Noteworthy: a leveraged closed-end called Goldman Sachs Trading Corporation. Shares peaked above $200. A few years later those shares were going for $1.75. That entity was eventually put out of its misery, but the closed-end category survived, and new members occasionally come into being.

Nowadays closed-ends often trade at a discount to their asset value. But a discount by itself does not make a fund into a good buy. Remember that the operators of the fund are plucking fees from the portfolio and that the exit door is bolted. There is, meanwhile, a tiny escape of dollars to freedom, in the form of cash distributions.

Any dollar you get in the form of a payout is a dollar you bought at a discount, and you have an instant profit on it. If a fund is trading at a 20% discount to its assets, and is paying out 5% of assets, then you are earning an extra 1% a year on top of whatever the portfolio is doing for you. This arbitrage gain may be enough to cover, or more than cover, the amount being drained away in fund fees.

So here’s my formula for determining if a closed-end is a value play. Multiply the discount by the payout rate. If that product is bigger than the expense ratio, then the fund is worth a look.

I pawed through a Morningstar database of 418 closed-ends with at least $100 million in assets. Potential bargains: a mere seven, displayed in the table.

There’s potential here, but not any fabulous buys. These bargains come with caveats: The expenses might go up, and the payouts might decline.

The most intriguing of the lot is Highland Global Allocation Fund. It’s easy to see why shareholders are anxious to depart. The last annual report details such holdings as pipeline partnership shares worth a third of the $51.6 million paid for them, a collection of senior bank loans with similar performance, bonds from Argentina and a short position in technology stocks. Yikes.

You might be willing to wager that these very contrarian plays are about to pay off. If they do, the discount would probably narrow and you’d have a double win. In the meantime, the distributions give you a stream of modest arbitrage gains worth not quite 3% a year, comfortably more than losses to fund fees.

This is, as I said, a wager. Highland’s investments might continue to sag. If they do, the discount will probably widen. In that case your losses will be accentuated.

Sorry that this is the best I can do for a bullish case on closed-ends. The category simply isn’t very promising at the moment, with the market hitting new highs. If we get a crash of the 1929-1932 variety you might see bargains reappearing.

Don’t overlook that caveat about distributions falling. This is a potential hazard at the Highland fund, and is all the more so at the next two funds on the list. These closed-ends, investing in German and in Asian stocks, have been paying out capital gains that you can scarcely count on.

There are two more things to be wary of. One is the notion that a discount deeper than the historical average for a fund is particularly likely to narrow, delivering a windfall to you. It’s just as likely to go the other way.

The other is the idea that when you buy at a discount your returns are magnified because you have more dollars working for you in the portfolio. Alas, the arithmetic doesn’t work in that fashion. Say you buy a $10,000 portfolio at a 20% discount and the portfolio returns 50%, growing to $15,000. At the same 20% discount your fund shares are now worth $12,000. You’ve earned precisely the 50% return on a $8,000 investment you would have had putting your money into an open-end fund.

Before buying a closed-end fund, consider the alternative: a low-expense ETF or mutual fund. There are plenty to choose from that have tiny expense ratios. See Guide To Stock Index Funds: 97 Best Buys. To be attractive, a closed-end should have an effective holding cost that is lower than tiny. It should be below zero.

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