Banks have been in the spotlight recently, and some of them are getting attention for all the wrong reasons. With the massive rise in interest rates over the past year putting pressure on bank balance sheets, shares of some sizable financial companies have suffered.

With the market bouncing back more recently, some investors have hoped that the worst of the banking crisis might be over. Even if that's the case, though, it doesn't mean smooth sailing for bank stocks is directly ahead. Indeed, downward moves from State Street (STT 0.14%) and Charles Schwab (SCHW 0.13%) Monday morning show that there are still a host of concerns facing bank-stock investors right now.

State Street sinks on sliding earnings

Shares of State Street were down 11% in early trading Monday morning. The financial services provider behind the well-known SPDR line of exchange-traded funds has had to deal with the impact of the bear market in stocks for more than a year now, and even a rebound on Wall Street hasn't translated to the financial results from State Street that shareholders have wanted to see.

First-quarter financial results showed the disparities across its two businesses. On one hand, rising interest rates helped boost net interest income by 50% year over year. However, fee revenue from its asset management business dropped 9%, and that limited the gains in overall sales to just 1% at $3.1 billion.

And State Street wasn't able to live up to expectations on its bottom line. Earnings of $1.52 per share were actually down 3% from year-ago levels. Despite efforts to control costs, total expenses grew 2% year over year to $2.37 billion.

The company relies on its massive asset base of $37.6 trillion under custody and administration to generate its revenue, and weak markets have caused its asset levels to drop 10% from where they were 12 months ago. Until markets recover more broadly, State Street could continue to see pressure in its financial metrics.

Schwab sees deposit outflows

Shares of Charles Schwab were down 4% early Monday. Despite several parts of the brokerage giant's business faring better than State Street, investors nevertheless saw some signs of trends with which they weren't entirely comfortable.

Schwab's first-quarter financial results were largely positive. Net revenue climbed 10% year over year to $5.12 billion, driven largely by a 27% jump in net interest revenue. Asset management and administration fees also moved higher by nearly 5%. Net income of $1.53 billion was 20% higher than in the year-ago period, working out to earnings of $0.83 per share.

However, Schwab did see some of the same customer trends that other consumer-oriented financial institutions have dealt with lately. Bank deposit account fees plunged by nearly half to $151 million, as bank deposits dropped 30% year over year to $326 billion. Levels of cash and available-for-sale securities on Schwab's balance sheet were sharply lower, while short-term borrowings soared, showing the liquidity crunch that much of the industry is facing currently.

Higher interest rates have helped part of Schwab, but no company wants to deal with substantial outflows in a key part of its business. Investors with cash to put to work increasingly want higher-interest options, and Schwab will need to respond in a way that encourages customers to remain loyal if it wants to hang on to them.