Nothing is invincible, but JPMorgan doesn't see too much right now that could derail the stock market rally.

And, it's trying to convey that to a growing number of skeptic clients.

Stephen Parker, head of thematic equity solutions at the firm's private bank, argues there are hardly any signs of investor euphoria right now — a critical element of a bull market on its last legs.

"This is really a fundamental story. We're seeing a market that's being driven by growth, by earnings and by improving expectations," Parker said recently on CNBC's "Futures Now."

But a new wave of stock market highs appears to be breeding fresh bearishness among investors. Parker said nearly every client conversation lately has been beginning with a "laundry list of things that can go wrong."

"We'd be a lot more nervous if this was taking the form of expanded market multiples showing some signs of froth. But to us, this is a growth story, and we're seeing the best synchronized global growth since the crisis," he added.

Parker has been firmly in the bull camp. During a September appearance on CNBC "Futures Now," he predicted stocks would keep grinding higher. As of Wednesday, the is up 4 percent since then.

To score the biggest profits, Parker is urging investors to look at secular growth stocks such as technology and health care. He also likes cyclical value areas, particularly financials and energy.

And, he views any sell-offs over at least the next 12 months as key buying opportunities, and not a sign that a recession is on the horizon.

"Stay invested and buy any pullbacks," Parker said.