The rampant sell-off across the banking sector has seen both Barclays (LSE: BARC) and HSBC (LSE: HSBA) plunge to fresh multi-year lows in February.

Shares in the banks have fallen 26% and 16% respectively since the start of 2016 as jitters concerning the global economy have weighed heavily. With worries over the firms’ exposure to the commodities markets also circulating, not to mention concerns over mounting PPI bills, there appears to be plenty in the tank to send stock prices still lower.

However, I believe this weakness makes both HSBC and Barclays terrific value picks for brave investors.

An emerging market marvel

For HSBC in particular, the prospect of cooling emerging economies could present further reverberations on the top line — the business sources more than 60% of total profits from Asia alone.

Still, I believe HSBC’s long-term revenues outlook in these regions remains strong, thanks to a combination of breakneck population growth and rising personal affluence levels, factors that should support strong banking product demand.

Meanwhile, the impact of vast cost-cutting across the business — the Financial Times announced this week that management pay freezes at HSBC’s Retail Banking and Wealth Management arms are in the pipeline — should help the bank weather the current storm.

Sure, HSBC may be expected to endure a 4% earnings dip in 2016. But I believe a consequent P/E rating of 10.2 times is an attractive point at which to buy into the bank’s long-term growth prospects.

Earnings primed to explode

Barclays may not have the same exposure to developing markets as HSBC, but this has not prevented the stock from diving as well.

Concerns over the shape of Barclays’ investment bank business , and more recently the fate of its Africa banking division, allied with fears over escalating financial penalties, have all served to suppress investor appetite in recent times.

However, I believe the success of Barclays’ high street operations — allied to the effects of its vast Transform scheme in slashing costs and improving its digital operations — should undergird strong earnings growth in the near-term and beyond.

This view is shared by the City, and the bank is expected to punch a 21% bottom-line bounce in 2016, resulting in a quite-exceptional earnings multiple of 8.2 times.

Perfect payout contenders

On top of this, the City expects dividends at both Barclays and HSBC to provide plenty of bang for shareholders’ bucks in the near-term and beyond.

The effect of massive restructuring on Barclays’ balance sheet, not to mention the firm’s improving earnings outlook, are expected to give dividends an imminent shot in the arm.

The ‘Square Mile’ currently forecasts a payout of 6.6p per share for 2015, up from a figure of 6.5p in recent years. And the dividend is projected to surge to 8.3p this year, creating a market-beating yield of 3.6%.

And things are even better over at HSBC. Sure, a hike to 52 US cents per share in 2016 from a predicted 51 cents for last year may not be as impressive as the increases pencilled in at Barclays. But a subsequent yield of 6.4% blasts most of London’s blue-chips clean out of the water. I believe both banks offer plenty of upside for savvy bargain seekers.

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Royston Wild has no position in any shares mentioned. The Motley Fool UK has recommended Barclays and HSBC 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.