To understand those developments, Kleintop is following alternative data such as data on rush-hour commuting, air pollution, retail foot traffic and electricity usage in addition to the usual economic indicators.

His colleague, Liz Ann Sonders, chief investment strategist at the Schwab Center for Financial Research, says the U.S. stock market is not paying enough attention to "second-order economic effects" of the COVID-19 pandemic. 

U.S. stocks, for example, rose slightly the day the government reported that 20.5 million people had lost their jobs in April because it also reported that 80% of those job losses were temporary. But with a growing number of corporate defaults and bankruptcies at small and large companies, those temporary losses may become permanent, says Sonders, adding that such factors "need to be included in market expectations."

The University of Chicago's Becker Friedman Institute predicts that 42% of U.S. jobs lost through April 25 — or 11.6 million — due to the coronavirus will become permanent.

Sonders also notes that recent stock buying sprees are being propelled not only by quantitative and algorithmic buyers but also by small traders and individual investors, including sports bettors who are now turning to making stock bets, which adds another risk factor for the U.S. stock market.

Also underpinning the stock market recovery from the March lows — and the corporate bond market — is the Federal Reserve. It has been supporting the U.S. economy with near zero interest rates, asset purchases and multiple liquidity programs to backstop various bond market segments as well as Treasury programs to aid businesses, such as the Payroll Protection Program and Main Street Lending program.

Most of those programs haven't even started yet, and those that have begun have used just a fraction of the money available, leaving the Fed with "lots of firepower" to do more, says Kathy Jones, chief fixed income strategist at the Schwab Center. "The Fed has even had success just by signaling what it can do," says Jones.

Among bond markets, the municipal market especially faces challenges, says Jones. "State revenues are declining while costs are going up, much of it for health care" due to the COVID-19 pandemic and the economic shutdowns that followed.

The Fed has announced a municipal liquidity fund, which it recently extended to three years, to provide muni issuers bridge loans they desperately need, but ultimately more federal support will be needed, says Jones. "States can't file for bankruptcy."

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