If anyone tells you that all the big dividends have been bought up in this inflated market, do yourself a favor: tune them out, asserts Michael Foster, investment strategist and editor for CEF Insider.

Because while stocks are up -- and dividend yields are down as a result -- there are still high, cheap payouts to be had out there. And we closed-end fund investors know exactly where to find them.

The average CEF pays 6% now, crushing the meager 1.3% payouts you get on stocks and US Treasuries. In addition to high yields, closed-end funds offer a great play for diversification.

You can see that diversification in action through a CEF like General American Investors (GAM), whose portfolio includes Microsoft (MSFT), waste-management firm Republic Services (RSG) and semiconductor-industry supplier ASML Holding (ASML).

GAM's smartly built portfolio has helped it outperform the benchmarks for REITs, BDCs and corporate bonds over the last five years And today we can buy this fund at a 16.4% discount to NAV, or about 84 cents on the dollar, in other words.

CEFs are also a great choice if you don't want all-in-one diversification, like GAM offers, but instead want to target certain sectors of the economy.

A good example of a more sector-specific CEF is the 6.1%-yielding Nuveen NASDAQ 100 Overwrite Fund (QQQX), which holds the stocks in the tech-laden NASDAQ 100 Index and sells call options on its portfolio.

Selling calls is a savvy strategy that lets the fund pull in additional income, which it hands to us in the form of its large payout.

Selling calls does limit the fund's upside somewhat (it tends to underperform the NASDAQ, for example), but in return this strategy offers greater stability and supports QQQX's high dividend, which is 13 times bigger than the payout on the typical NASDAQ stock.

Plus, QQQX has delivered a sparkling 125% total return in the last five years. QQQX does trade at a premium. But at 0.6%, it's barely above par, so you're not at risk of overpaying, especially when this fund has traded at premiums as high as 4.3% in the past year.

Among CEFSs, we much prefer the Adams Diversified Equity Fund (ADX), a long-time buy recommendation in our portfolio.

As with all our CEFs, dividends are a big reason for our loyalty: ADX boasts a healthy 6.9% trailing-12-month dividend (recall that this fund pays most of its dividend in the form of a year-end special payout).

Second, ADX delivered a bigger total return than QQQX over the past five years without being tied as tightly to just one sector. It has nicely outperformed GAM, too.

Despite that track record, ADX boasts an attractive 14% discount today! That's an insult to ADX's management, and the fund's performance is likely to stay strong, helped by a discount that's bound to narrow as more investors jump into CEFs, and fewer of these funds are available at a discount.

This is just one reason among many why ADX remains one of our most beloved portfolio picks, even in this overbought market.

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