(Reuters) -As Wall Street puts April's tariff shakeout in the rearview mirror and indexes set record highs, investors remain wary of U.S. President Donald Trump's rapid-fire, sometimes chaotic policymaking process and see the rally as fragile.      

The S&P 500 and Nasdaq composite index advanced past their previous highs into uncharted territory on Friday. Yet traders and investors remain wary of what may lie ahead. 

Trump's April 2 reciprocal tariffs on major trading partners roiled global financial markets and put the S&P 500 on the threshold of a bear market designation when it ended down 19% from its February 19 record-high close.

This week's leg up came after a U.S.-brokered ceasefire between Israel and Iran brought an end to a 12-day air battle that had sparked a jump in crude prices and raised worries of higher inflation. But a relief rally started after Trump responded to the initial tariff panic that gripped financial markets by backing away from his most draconian plans.

JP Morgan Chase, in the midyear outlook published on Wednesday by its global research team, said the environment was characterized by "extreme policy uncertainty."

"Nobody wants to end a week with a risk-on tilt to their portfolios," said Art Hogan, market strategist at B. Riley Wealth. "Everyone is aware that just as the market feels more certain and confident, a single wildcard policy announcement could change everything," even if it does not ignite a firestorm of the kind seen in April.

Part of this wariness from institutional investors may be due to the magnitude of the 6% S&P 500 rally that followed Trump's re-election last November and culminated in the last new high posted by the index in February, said Joseph Quinlan, market strategist at Bank of America.

"We were out ahead of our skis," Quinlan said. A focus on deregulation, tax cuts and corporate deals brought out the "animal spirits," he said. Then came the tariff battles. 

Quinlan remains upbeat on the outlook for U.S. stocks and optimistic that a new global trade system could lead to U.S. companies opening new markets and posting higher revenues and profits. 

But he said he is still cautious. "There will still be spikes of volatility around policy unknowns."

Overall, measures of market volatility are now well below where they stood at the height of the tariff turmoil in April, with the CBOE VIX index now at 16.3, down from a 52.3 peak on April 8. 

UNSTABLE MARKETS 

"Our clients seem to have become somewhat desensitized to the headlines, but it's still an unhealthy market, with everyone aware that trading could happen based on the whims behind a bunch of" social media posts, said Jeff O'Connor, head of market structure, Americas, at Liquidnet, an institutional trading platform. 

Trading in the options market shows little sign of the kind of euphoria that characterized stock market rallies of the recent past.

"On the institutional front, we do see a lot of hesitation in chasing the market rally," Stefano Pascale, head of U.S. equity derivatives research at Barclays, said.

Unlike past episodes of sharp market selloffs, institutional investors have largely stayed away from employing bullish call options to chase the market higher, Pascale said, referring to plain options that confer the right to buy at a specified future price and date.

Bid/ask spreads on many stocks are well above levels O'Connor witnessed in late 2024, while market depth - a measure of the size and number of potential orders - remains at the lowest levels he can recall in the last 20 years.

"The best way to describe the markets in the last couple of months, even as they have recovered, is to say they are unstable," said Liz Ann Sonders, market strategist at Charles Schwab. She said she is concerned that the market may be reaching "another point of complacency" akin to that seen in March.

"There's a possibility that we'll be primed for another downside move," Sonders addded.

Mark Spindel, chief investment officer at Potomac River Capital in Washington, said he came up with the term "Snapchat presidency" to describe the whiplash effect on markets of the president's constantly changing policies on markets. 

"He feels more like a day trader than a long-term institutional investor," Spindel said, alluding to Trump's policy flip-flops. "One minute he's not going to negotiate, and the next he negotiates."

To be sure, traders seem to view those rapid shifts in course as a positive in the current rally, signaling Trump's willingness to heed market signals.

"For now, at least, stocks are willing to overlook the risks that go along with this style and lack of consistent policies, and give the administration a break as being 'market friendly'," said Steve Sosnick, market strategist at Interactive Brokers.