The U, the V, the W -- no, this is not your kid's homeschooling agenda, it's all the various scenarios analysts say could transpire with the markets and the economy during this COVID-19-fueled downturn. A U-shaped recovery is one that's longer at the bottom and more drawn out, while a V-shaped recovery is one where the markets bounce back sharply. The W is the double dip, with a recovery followed by another drop. Which letter we get depends on a variety of factors, foremost of which is how we handle the coronavirus going forward.

That said, one thing we know for certain is that we are in a recession, and that has hit a lot of industries hard, including the financial sector. Banks, in particular, have struggled mightily on 0% interest rates and credit losses. Those looking for a stock to add stability to their portfolios in uncertain times might want to consider Bank of New York Mellon (NYSE:BK). Here's why.

Stable fee income

BNY Mellon is not a traditional bank that makes loans and takes deposits. BNY Mellon is a custody bank, which holds and protects financial assets for mostly large institutional clients, like mutual fund companies, hedge funds, and pension funds. It also provides account servicing, like account administration, transaction settlements, passing along dividend and interest payments, preparing disclosures, handling taxes, and conducting foreign exchange trading.

Negative phrases on small pieces of paper, like panic, COVID-19, virus worries, and impact, on top of paper money

Image source: Getty Images.

BNY Mellon is the largest custodian bank in the country, with $37.3 trillion in assets under custody. State Street is its main competitor, with $31.8 trillion in custody assets, while JPMorgan Chase and Citigroup are other major players. BNY Mellon's income for custodian services comes from fees paid based on assets under custody. Thus, its revenue is far more stable than traditional banks, which count on net interest on loans for much of their income. When interest rates are low or loan volumes decrease, banks feel the pinch.

In the second quarter, while many banks struggled for earnings, BNY Mellon made $3.1 billion in fee revenue, a 2% increase over the second quarter of 2019. That accounted for most of its $4 billion in revenue, which was up 2% overall. The rest came from its investment and wealth management business, which generated $886 million, down 3%.

Assets under custody grew 5% in the quarter to $37.3 trillion, reflecting higher client inflows, market values, and net new business. As CEO Thomas Gibbons explained on the second-quarter earnings call, more asset managers are outsourcing asset servicing due to the challenges they are facing in this market. "Our unique capabilities in fund accounting and transfer agencies, as well as investments we've made in building out our digital and data capabilities positions us well," Gibbons said.

Another big plus is that the company only had to set aside $143 million for provision of credit losses, down from $169 million in the first quarter. Meanwhile, competitors like JPMorgan Chase and Citigroup had to set aside $10.5 billion and $5.6 billion for anticipated credit losses, respectively, resulting in a drag on earnings. BNY Mellon's earnings stayed flat in the second quarter at $1.01 per share.

Analysts at Jefferies recently upgraded BNY Mellon to a buy, saying trust banks are "recovering faster than the economy" and for their "lack of meaningful credit risk."

A good value

BNY Mellon also has a strong capital position, posting a common equity tier 1 (CET1) ratio of 12.6% in the second quarter, up from 11.3% in the first quarter. This metric gauges a bank's capital strength and solvency by measuring its core capital against its risk-weighted assets. The company's CET1 capital totaled $20 billion, up $1.57 billion from the first quarter. The Federal Reserve's recent stress test of global systematically important banks (G-SIBs) confirmed the strength and resiliency of BNY Mellon's business, Gibbons said on the second-quarter earnings call: "We had the lowest peak-to-trough reduction in CET1 capital under the Fed's model relative to other U.S.-based G-SIBs at just 20 basis points, and that's well below the minimum SCB [stress capital buffer] requirement."

BNY Mellon is still down about 28% year to date, but since dropping to a 52-week low of $26.93 on March 23, it has gradually climbed to $36.12 as of Friday's close -- a gain of about 34% in four months or so. Yet it comes at a great value, with a price-to-earnings (P/E) ratio of almost 8 times earnings. BNY Mellon is not going to be a high flier, but it should continue to have steady growth throughout the recession, which is a nice alternative to the volatility you might find elsewhere.