By Suzanne McGee

(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.

"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.