I’m seeing a lot of cheap shares around these days, and there are surely some great candidates for a price doubling. The trick is finding them before it’s too late, so here are three ideas…

Undervalued insurance

The insurance sector still seems to be inexplicably in the dumps after the financial crisis, and I reckon there are plenty of bargains to be had. Aviva (LSE: AV) remains my favourite, even though the share price has stubbornly stagnated since I bought some — despite a recent rally, it’s still down 13% over the past 12 months, at 450p.

And that’s a year in which the company has seen its restructuring strategy coming to fruition. At results time in March, chief executive Mark Wilson said that

With a Solvency II ratio of 180% and a surplus of £9.7 billion, our balance sheet is one of the strongest and most resilient in the UK market. Over the last four years, we have tripled our economic capital surplus“.

Forecasts suggest a doubling in EPS this year to put the shares on a P/E of under 10, dropping to under nine on 2017 forecasts, and dividend yields of 5.4% and 6.1% are expected for this year and next. I think Aviva could double your money (and mine) in two or three years — providing we don’t leave the EU and plunge into a fresh economic crisis.

A great track record

One approach is to examine our past growth stars and look for ones that are likely to continue, and I think the obvious one is ARM Holdings (LSE: ARM). The designer of the chips that power iPhones and all manner of other devices has seen its shares soar by a stunning 1,025% since the end of 2008, as smartphone mania has taken hold.

For years I’ve been saying that the mobile computing revolution is still in its infancy, and that’s still true today — I doubt we’re seeing even 5% of the processor usage that we’ll have in another 10 years. There’s no guarantee that ARM will still dominate, of course, but while demand for its designs is still climbing and analysts are still forecasting double-digit rises in annual earnings, I can see a lot more share price growth to come.

Oh, and the stagnation of the past couple of years has put ARM shares, at 977p, on a P/E of 25 based on 2017 forecasts — their cheapest for a good few years.

Mining recovery?

Could a recovery in the downtrodden mining sector do the trick for you? It might surprise you to see that I’m considering Anglo American (LSE: AAL) as a candidate for doubling. The South Africa based miner has, after all, suffered from its own internal problems, in addition to the slump in metal and mineral prices, and as a result the share price has lost 80% since the end of 2010.

But since this year’s low on 20 January, we’ve seen a 180% rise to 636p, nearly trebling your money if you managed to get in at the right time. Can it continue?

Well, the prices of some of Anglo’s products have been recovering nicely of late, and analysts are predicting a bottoming in the firm’s declining earnings this year — there’s a 37% EPS rise forecast for 2017, which would put the shares on a P/E of 15.5.

Sustained rises will probably still be needed to keep Anglo’s shares rising, but I can’t help feeling we’ll be looking back at early 2016 as the moment of maximum pessimism and the perfect time to buy.

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Alan Oscroft owns shares of Aviva. The Motley Fool UK has recommended ARM Holdings. We Fools don't all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors.