Cut your losers and run your winners” is the old investing mantra. But when does it make sense to sell your most profitable holdings? Let’s look at one FTSE 100 success story and the case for replacing it with two of its peers.

Running out of puff?

Savvy investors will have done exceedingly well from Imperial Brands (LSE:IMB) over the years. Those who invested back in 2000 will have enjoyed watching the shares rise over 1,200% since. Imperial’s shares currently trade on a fairly decent price-to-earnings (P/E) ratio of just under 16. The yield is over 4% and covered by earnings. What’s not to like?

Well, while the company may benefit from a Brexit vote due to a depreciation in sterling, there are reasons to be cautious regarding the tobacco industry’s long-term future. More than 170 countries have now introduced smoking bans in public places and recent academic research has shown that, where a ban exists, fewer people are smoking. Indeed, last month, Imperial reported falling sales in the UK. The industry as a whole also lost its case against the Government’s plain packaging policy.

True, the addictive nature of the company’s products and the growing popularity of vaping can probably deal with obstacles such as standardised packaging. Nevertheless, in my view, long-term holders of the stock should consider the benefits of leaving the party when they’re having the most fun.

Pipeline potential

A complete alternative to Imperial Brands is pharmaceutical giant AstraZeneca (LSE:AZN). Since Pfizer’s infamous approach back in 2014, things have gone relatively quiet. That May, its shares reached 4,808p. They’re now 3,964p, suggesting that investors are growing tired of the obligatory if understandable ‘jam tomorrow’ message on its pipeline and/or are concerned about the impending referendum.

Nonetheless, the company’s shares now trade on a P/E of just under 15, which indicates they could be a decent buy, despite ongoing concerns about when its next blockbusting product will arrive. The yield, at around 4.75% for the current year, will also be attractive to income investors desperate for better returns than those offered by cash.

AstraZeneca next updates the market in July. This should provide clues on the likely direction of the share price in the near term, as long as global events don’t interfere.

Shaky foundations?

Taylor Wimpey (LSE:TW), like Imperial Brands, is another example of when it can be beneficial to invest at the point of maximum pessimism. Back in November 2008, shares fell to 7.5p. Last month, they reached 210p. However, the general belief that housebuilders will suffer in the event of a Brexit has upset things somewhat and the price is now back to 188p. While a Brexit is likely to affect those with significant exposure to the London housing market (Berkeley Group, for example), it’s very unlikely Taylor Wimpey will escape unscathed. Yesterday’s prediction by surveyors that house prices are expected to fall in the short-term isn’t helping matters either.

The housebuilder currently trades on a P/E value of just under 11, according to Stockopedia with its massive 5.89% yield adequately covered by earnings.

The general media circus surrounding opinion polls over the past few weeks is unlikely to go away before the crucial vote. Nervous investors may wish to hold off completely but those confident of the UK remaining in the EU may be regard this uncertainty as a golden opportunity to build a holding in the company.

Tough call

While the tobacco industry is arguably in slow decline, Imperial Brands offers perhaps more security in the near term. Astrazeneca's immediate future after the referendum is hard to say but it will still depend heavily on the success of its pipeline. And Taylor Wimpey's shares could see greater volatility as 23 June approaches but could soar if more people vote for the status quo.

As always in investing, buy and sell decisions depend on a whole host of factors in addition to a company's prospects, including your attitude to risk, investing horizon and financial goals.

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Paul Summers has no position in any shares mentioned. The Motley Fool UK has recommended AstraZeneca. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.