Commonwealth Bank of Australia (ASX: CBA) shares have continued their incredible run this week, reaching an all-time high of $157.28 during Tuesday's session. 

Since then, CBA shares have cooled off a little but are still trading at $156.11 at the time of writing this Thursday after pushing as high as $157.05 earlier this morning.

This week's all-time high is just the latest in an avalanche of new records for CBA in 2024. It's difficult to imagine today, but remember, this ASX 200 bank stock was asking just $103.70 this time last year and had never been over $112 a share.

Over the past 12 months, CBA has now gained a whopping 10.5%, which includes the 37.4% the bank has put on over 2024 to date. Check that out for yourself below:

Although these gains for CBA have no doubt been welcomed by shareholders and, by extension, anyone who is invested in ASX index funds or indeed with a superannuation fund, it is probably leaving shareholders feeling nervous today. After all, it's not like this share price growth has matched the fundamental performance of CBA's underlying business, which we went into last month.

As such, many investors might wonder whether it is worth switching their CBA shares for an ASX S&P 500 Index (SP: .INX) fund, another top-performing investment.

S&P 500 tracker vs. CBA shares

I've made my personal views on CBA clear, which you can read here. Anyone who has read that will know that I am probably open to an alternative investment to the ASX bank today.

But it's not just me. Just today, analysts at fund manager L1 Capital stated that the CBA share price "makes no logical, analytical sense". Those analysts anticipate CBA, along with the other major bank stocks, to "revert to the norm" soon.

It's not that I would buy any other ASX share over CBA right now. But an S&P 500 Index fund is, in my view, a decent alternative and one that offers several advantages.

The ASX's sole S&P 500 Index fund – the iShares S&P 500 ETF (ASX: IVV) – has also had a massive year. IVV units have soared by 20.85% since this time in 2023, driven by its underlying index's performance. Gains from large S&P 500 stocks like Amazon, NVIDIA and Tesla have seen this flagship American index deliver this historically outsized gain.

However, I would still pick the iShares S&P 500 ETF over CBA in a heartbeat.

Why? Well, for one, the iShares S&P 500 ETF offers something that CBA doesn't, inherent diversification. With CBA, your fortunes are entirely tied up with what investors are willing to pay for a small company. In this case, a company with stagnant earnings and profits.

However, with the IVV ETF, a single company's pricing doesn't really matter. The value of your investment will instead reflect what investors are willing to price the entire market at, or at least the largest 500 companies listed on the American markets.

That doesn't make the iShares S&P 500 ETF immune from a big tumble, of course. But it does dilute that single-company risk.

Buying shares that are actually growing

What's more, the S&P 500's 2024 rally looks like it is being driven, at least partly, by actual fundamentals. Unlike CBA, most of the largest holdings in IVV's portfolio, such as those mentioned above, are continuing to grow their own revenues and earnings at a healthy rate.

For example, at the start of this month, Amazon dropped its latest quarterly earnings report. This showed the e-commerce giant increasing its revenues by 11% compared to the same quarter in 2023. Its net income exploded by an even more impressive 57%.

Again, compare that with CBA's recent earnings.

So, all in all, it would be a no-contest for me if I had to choose between investing in CBA shares today or an S&P 500 Index fund. Who knows what will happen going forward? CBA could continue to push higher and hit $160 or $170 a share. The S&P 500 could have an awful year in 2025. The opposite could also occur.

But I know which one I'd sleep better at night with.