I think investors should sell or trim their holdings in Fannie Mae, Five9 Inc. and Coca-Cola Consolidated Inc. The month of May is a reasonable time to do it.

The adage “Sell in May and Go Away” dates back to Britain more than 100 years ago. Though the expression is old, the saying still has some validity: On average, most of the U.S. stock market’s gains come in November through April.

I suggest you do an annual review of your portfolio, with the aim of weeding out 10% of the stocks you own — losers whose comeback chances look weak and winners that may now be overpriced.

Here are some stocks I would sell — or at the very least, lighten up on. Each of these is up a lot in the past year, has a lot of debt and has posted losses or scanty earnings.

Fannie Mae

Shares in Federal National Mortgage Association (FNMA), known popularly as Fannie Mae, have more than doubled this year.

Before the financial crisis, Fannie Mae bought mortgages right and left from issuing banks, which freed the banks to issue more mortgages — but also tempted them to get sloppy about lending standards. Because Fannie Mae was originally a government agency, people figured that the government would bail it out if necessary.

In the crisis, it did become necessary. Shareholders weren’t shielded; they took a body blow. From a peak of about $84 in 2001, the stock plummeted to $1.06 as this year began. It now fetches $2.76 a share.

In the past 15 years, Fannie Mae has shown a profit six times and a loss nine times. Last year was a profit, but the stock sells for 138 times that profit. The company’s debt towers, at 633 times stockholders’ equity.

Five9 Inc.

Based in San Ramon, California, Five9 Inc. (FIVN) makes cloud software for customer-service centers and other contact centers. Sales have grown rapidly, from about $43 million in 2011 to almost $258 million last year. The company hasn’t yet turned a profit, but almost did last year.

Analysts figure it will be in the black this year, but I don’t like the stock’s multiples. The stock sells for about 60 times this year’s projected earnings, almost 11 times revenue and nearly 20 times book value (corporate net worth per share). This is what some people call “priced for perfection.”

Perfection rarely happens.

Coca-Cola Consolidated

Coca-Cola Consolidated Inc. (COKE) is a major bottling company, bottling Coca-Cola beverages (and some others) in more than a dozen states.

The company’s debt is more than three times stockholders’ equity. Most investors figure the debt is harmless because soft-drink bottling is a super-steady business. Well, maybe. But even steady businesses sometimes get disrupted by changes in consumer tastes, or by new competition.

The company’s profit margins have been declining for a while, and it fell into a loss last year.

Iridium

I recommended Iridium Communications Inc. (IRDM), a satellite communications company, in June 2013, when it was unloved and selling for about $7. Today it fetches $24 and is recommended by the majority of analysts who follow it. I think most of the juice has been squeezed out of this one.

While the stock has become expensive, profits have tailed off, and most analysts expect a loss in the coming year. That doesn’t discourage them, but it discourages me.

Past record: My sell recommendations from a year ago did what they should — they lagged behind the Standard & Poor’s 500 Index by about 5 percentage points. They rose 1.80% while the index rose 6.59%. My best pick was UBS Group AG (UBS), which declined about 21%. Worst was Southern Co. (SO), which rose about 30%.

Longer-term, my 11 columns focused on sell recommendations haven’t done so well — but most of the egg on my face comes from a single stock I said to sell in 2005. That was Hansen Natural Corp., now known as Monster Beverage Corp. (MNST). It defied me by rising 492% in 12 months.

Without Monster, my “sells” underperformed the Standard & Poor’s 500 by 6.5 percentage points a year. With Monster, my “sells” have beaten the index by 2.4 percentage points a year.

Bear in mind that my column recommendations are theoretical and don’t reflect actual trades, trading costs or taxes. Their results shouldn’t be confused with the performance of portfolios I manage for clients. And past performance doesn’t predict future results.

Disclosure: I have no positions, long or short, in the stocks discussed this week.

John Dorfman is chairman of Dorfman Value Investments in Newton Upper Falls, Massachusetts, and a syndicated columnist. He can be reached at jdorfman@dorfmanvalue.com.

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