You might think I’m mad to suggest Barclays (LSE: BARC) as a candidate for some of your 2016 ISA allowance. After all, the bank has decided to slash its 2016 dividend by more than half, and there are investigations into some of its past practices going on that most people suspect will lead to more fines.

And Barclays did set aside a further £1.45bn in the final quarter of 2015 to cover PPI mis-selling costs, taking its total so far to £7.4bn. But you know what? I think there’s more than a reasonable amount of pessimism built into today’s share price which, at 156p, is down 39% over the past 12 months.

Forecasts are hard to get right, but with earnings per share (EPS) expected to return to modest growth this year and with a 34% boost pencilled-in for 2017, the shares would be on a P/E multiple of nine this year, dropping to under seven for 2017. Even with the uncertainties and risks, I see that as just too cheap, and I think Barclays is likely to be heading for a period of slow but sure share price growth — just what you need for an ISA.

A risky one

And if you thought that was mad, how about Premier Oil (LSE: PMO)? Yes, the heavily indebted oil explorer is a big risk. Yes, oil could still go lower and send the share price down. And yes, it could even go bust, or at least require refinancing that would dilute out existing shareholders if the low oil price leads to a default on debt payments. And the shares have lost 75% of their value since May 2015’s high point, to 43p — though they have been lower, at just 19p.

But on the upside, if the oil price recovery does continue, I reckon Premier Oil shares could be seriously uprated. After all, the company does still have cash and untouched borrowings to draw on, and it did take advantage of the downturn to snap up the whole of E.ON’s North Sea assets for the bargain price of $120m.

But is it too much of a gamble for an ISA? I’d usually say yes, but if you already have a few years of ISA allowances used up with safer shares, there’s nothing wrong with adding a small bit of high-risk excitement.

Back to safety

And one safe candidate that could help offset any Premier Oil risk is insurer Legal & General (LSE: LGEN), which has been handing out very attractive dividends. The shares have fallen 18% over the past 12 months to 238p, but that suggests a prospective P/E of around 12 this year, dropping to 11 on 2017 forecasts. That’s for a company which has recorded EPS growth for four years in a row with two more predicted, and is expected to pay dividend yields of around 6%.

Full-year results on 15 March were impressive, revealing a 14% rise in net cash generation, a 10% lift in pre-tax profit, and adjusted EPS up 11% on the previous year. The dividend was hiked by 19%, as chief executive Nigel Wilson told us: “We remain confident in the outlook for our business“.

The results gave the share price a boost, and it’s already up 20% since February’s low — and I can only see more progress over the next couple of years.

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