Bank of New York Mellon (NYSE:BK) on Thursday announced its final set of separate financial results for its two legacy banks. The firms combined July 1 to form an asset-servicing and -management giant with a market cap topping $52 billion. Its second-quarter results were largely undisturbed by issues of credit quality and tight interest rate spreads, which have recently dampened earnings across much of the banking industry.

Overall, both Bank of New York and Mellon Financial showed strong performance in the second quarter. BoNY reported income from continuing operations of $448 million, or $0.59 per share. Excluding merger and integration expense of approximately $0.04 per share, earnings per share increased 21% from the previous year's $0.52.

Mellon's earnings growth was similarly impressive, rising from $223 million to $281 million year over year. On a per-share basis, excluding merger expenses and other special items, Mellon's earnings improved by 28% to $0.69 per share, from the previous year's $0.54.

Bank of New York and Mellon enjoyed a more successful quarter than most banks because the majority of their income comes from selling fee-based services to corporate customers. That frees their bottom line from dependence on the shaky finances of individual consumers, or the shape of the yield curve. (Both banks have disposed of their retail branch systems in recent years.)

BoNY increased asset-servicing fees -- mainly revenue from trust and custody services that the bank provides to other financial services companies, retirement funds, and other large institutional customers -- by 17% to $427 million. Issuer servicing fees jumped by 77% to $367 million, largely as a result of acquiring the corporate trust business of JPMorgan Chase (NYSE:JPM) in the first quarter. Such sources of steady fee income provided 78% of BoNY's total revenue in the second quarter.

Mellon, with a substantial asset management business, received an even higher percentage of its revenue from fee-based sources than its merger partner did. A whopping 91% of second-quarter revenue came from fees. Asset management fees, buoyed by strong net inflows and rising equity prices, grew by 29% to $678 million. Mellon also increased its asset servicing revenue by 16%, thanks to new business development and rising market values.

The dimensions of the combined bank are eye-popping. With $20 trillion in assets under custody or administration, Bank of New York Mellon leaps ahead of rivals JPMorgan Chase, State Street (NYSE:STT), and Citigroup (NYSE:C) to become the largest custody bank. Bank of New York Mellon also ranks among the largest asset-management firms, with more than $1 trillion under management. The bank services approximately $11 trillion of debt. Such commanding positions in various business activities benefit the bank by enhancing its operating leverage and providing stable revenue streams for the future.

Investors expected that merging BoNY and Mellon would create new cross-selling opportunities among their existing clients. Mellon's large asset-management franchise boasted a greater number of relationships with pension funds and endowments than the legacy BoNY enjoyed. Those clients were expected to be good prospective customers for BoNY's superior securities lending and foreign exchange platforms, among other services.

In the near term, however, investors seem anxious about Bank of New York Mellon's disclosure that it may lose some clients during its integration process. Given BoNY's reputation as a thrifty provider of custody services, it is probably inevitable that some clients will decide to defect to high-touch rivals. Many investors, however, apparently believe that the attrition could be greater than the 2%-3% rate that bank executives are now predicting. That may explain the recent sell-off in the bank's shares.

Such pessimism about Bank of New York Mellon's ability to retain clients may be misplaced, but on the other hand, the bank's current stock valuation gives shares little room to run. The bank's share price rallied when the merger was first announced last year, and the bank's shares now trade at multiples comparable to its peers.

Accordingly, Bank of New York Mellon remains an attractive investment for long-term investors seeking to profit from the increasing size and vigor of global trade and investing. However, any near-term appreciation in the bank's shares will probably be somewhat muted. In the meantime, investors may take comfort in its decent dividend, which was just raised to $0.24 per quarter, giving the bank a 2.1% yield.

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Fool contributor Michael Leibert welcomes your feedback. He owns shares of Bank of New York Mellon. The Fool's disclosure policy is merger-proof.