In a post-rate-hike world, here's where LMM's Bill Miller would invest

Bill Miller: Long the S&P, short the 10-year Treasury

A Federal Reserve interest rate hike will cause near-term reallocations in the stock market but not long-term problems, legendary mutual fund investor Bill Miller said Tuesday.

"The underlying value of the businesses don't really change," the chief investment officer of LMM said in an interview with CNBC's "Closing Bell" after his appearance at CNBC/Institutional Investor's Delivering Alpha conference.

Therefore during any short-term adjustment, he'd look to invest in companies where prices fell far more than warranted by a change in interest rates or a drop in the overall market.

"Broadly speaking, if the yield curve is shifting up, then that's going to be good for banks, good for financials, credit-sensitive names," Miller said.

For example, a 100 basis point move in the Fed funds rate is probably around $4 billion to $5 billion of pre-tax earnings for JPMorgan and Bank of America Merrill Lynch, he pointed out.

Miller said he'd also look at deep value names, like the "very attractive" Credit Suisse.

"Many of the deep value names, as expressed in a low price to tangible book, have already had a big move this year but in a strengthening global economy, even if it's not strengthening very much, those names should continue to do well," he said.

Miller thinks signs like the fact the U.S. economy is "chugging along" and approaching full employment seem to show that extraordinary accommodation isn't needed anymore.

Plus, "at the end of the day, the central banks around the world are at least in a rethink about the ability of lower rates to make any difference in the overall economy."