Can the CBA share price regain its $100 crown in October?

The Commonwealth Bank of Australia (ASX: CBA) share price is off to a strong start in October.

The big four bank share slipped 0.1% on Monday. But its shares closed up 4.6% yesterday and are up 2.64% in afternoon trading today.

That's a fair bit more than the 1.51% gain posted by the S&P/ASX 200 Index (ASX: XJO) at this same time.

Following the past two days' gains, the CBA share price stands at $97.29. But will it regain its $100 crown in October?

Can the CBA share price regain its $100 crown?

CommBank first breached the psychologically significant $100 mark in May last year, going on to top $110 per share in November.

But the CBA share price hasn't been immune to the impacts of rising interest rates since that high water mark.

While higher rates do enable the bank to increase its net interest margins (NIMs), there are also potential headwinds from lower demand for new mortgage lending and higher levels of bad debts among its customers.

It's also worth noting that the bank trades on a significant premium to the other big listed lenders.

CBA trades at a price-to-earnings (PE) ratio of 18.7 times, compared to a PE ratio of 11.2 times for rival Australia and New Zealand Banking Group Ltd (ASX: ANZ).

So, can the CBA share price regain its $100 mark this month, a level it last saw on 7 June this year?

With the past few days' bullish run in mind, it's certainly possible.

But Evans & Partners doesn't expect that to hold.

The broker raised its rating for CBA to neutral with a price target of $85.