"We still think we're in a favorable environment for risk markets. The risks of a recession are both low and diminishing," he said. The positives, he added, include the fact that the dollar and oil are steadying and emerging markets have stopped being a big drag.
"The macro backdrop has gotten less bad," said Turnill.
But at the same time Turnill sees a pickup in default rates, and BlackRock expects they will be higher than the 4.7 percent expected by Moody's.
"High yield isn't cheap anymore," Turnill wrote in a note Monday. "Spreads remain above typical levels associated with an economic expansion, but they reflect today's low-growth world, highlighted by back-to-back quarters of around 1 percent annualized growth in U.S. gross domestic product."
As for the dollar, he sees it acting as much less of a headwind for emerging markets.
"We think it's an environment where investors should be participating in emerging markets. What's stopping us from being more aggressive is we're not yet seeing a change in the fundamentals," Turnill said.
As for U.S. stocks, Turnill expects to see mid- to high-single-digit returns.
"The areas leading the market higher still look cheap," he said. "Value, as a style, still trades at a 35 percent discount to the market." Historically, the discount is about 20 percent, he said.
The improvement in oil prices has been important, though Turnill does not expect them to rise significantly.
"Oil prices are being driven largely by changing sentiment in the economy. We see oil going forward as less of a leading indicator for the economy," said Turnill.
An important factor for markets is the activity of central banks, with the Bank of Japan and European Central Bank easing and the Fed slowly moving to tighten. "We're still in this environment of policy divergence, but the pace of divergence slowed down and (Fed Chair Janet) Yellen's comments last week emphasized that," Turnill said in a phone interview.
Yellen said the Fed would move cautiously to raise rates, and she emphasized the risks to the Fed's outlook including low inflation and the slowdown in China. Traders took the message as a sign the Fed would now move more slowly to raise interest rates.