Since the EU referendum, shares in Barclays (LSE: BARC) have slumped by 27%. Clearly, this is disappointing for existing investors but it also presents a potential opportunity for new investors to buy-in at a heavily discounted share price. For example, Barclays trades on a price-to-earnings (P/E) ratio of just 11.2 and this indicates that a significant upward rerating is on the cards.

Although Barclays’ near-term future is rather uncertain, given the challenging outlook for the UK economy, its longer-term potential remains high. Its new CEO is set to implement a refreshed strategy that should see Barclays’ financial standing improve and with it being a global bank, a downturn in the UK economy may not hit it as hard as the market currently believes.

Certainly, Barclays’ decision to reduce dividends has hurt investor sentiment and it seems unlikely that the bank will become a strong income stock in the short run. However, with profit due to rise next year and it having a sound strategy, its current valuation seems to make it a value play rather than a value trap.

Wait and see

Also trading lower after the EU referendum are shares in Arbuthnot (LSE: ARBB). The bank’s valuation has fallen by 15% since the UK decided to leave the EU and, like Barclays, its near-term forecasts are likely to come under pressure as the UK faces the real threat of a recession.

With Arbuthnot being heavily UK-focused, its retail and private banking offerings could be hurt over the medium term. Therefore, while it’s forecast to record a 232% rise in earnings this year, there’s a very real possibility that this figure could be downgraded over the coming weeks and months. Likewise, Arbuthnot’s expected fall in earnings of 32% next year may prove to be a rather modest forecast.

Due to Arbuthnot trading on a forward P/E ratio of 11.4, many investors may be tempted to buy-in following the recent share price fall. However, it may be prudent to await further news flow on the state of the UK economy before doing so. That’s not to say that Arbuthnot is necessarily a value trap, but rather that it lacks a sufficiently wide margin of safety to merit investment.

Emerging markets exposure

Meanwhile, Prudential (LSE: PRU) has seen its share price fall by as much as 19% since the EU referendum. However, it has recovered somewhat to now be down by around 12%, but even so its international focus means that it’s in a strong position to overcome any downturn in the UK economy.

In fact, the main driver of Prudential’s share price over the coming years is likely to be its exposure to the emerging world. This presents a major opportunity since the wealth and size of the middle class across the developing world is likely to rise rapidly in the coming years. With Prudential well-positioned in a number of key markets, it should be able to capitalise on this growth trend.

Prudential’s P/E ratio of 10.3 therefore indicates that it’s a value play rather than a value trap. Its near-term share price volatility may be high, but for long-term investors it’s a bargain.

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Peter Stephens owns shares of Barclays and Prudential. 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.