A naked put is synthetically equivalent to a covered call, where both are opening transactions with the same strike and same expiration. They will have a similar risk graph and about the same performance regardless of what the stock price does. Therefore, you can use a "put writing ETF" or a "covered call writing ETF" and you can find them by googling the phrase with the quotations.
For informational purposes, the CBOE has a dozen or so option writing indexes. Two of the more popular ones are:
The CBOE's BXM index represents the returns of a monthly buy-write strategy where the S&P 500 is bought and one at-the-money call is written. Over the past 30 years, the S&P 500 has returned an annual rate of 9.9% with a standard deviation of 15.3%. The BXM has returned 8.9% with a standard deviation of 10.9%. Tthis would be equivalent to writing the ATM put.
The CBOE's BXMD index represents the returns of a monthly buy-write strategy where the S&P 500 is bought and one call 30% out-of-the-money is written. Over the 30 past years, the S&P 500 has returned an annual rate of 9.9% with a standard deviation of 15.3%. The BXMD has returned 10.7% with a standard deviation of 13.2%. This would be equivalent to writing the 30% ITM put (where the 30% is based on the underlying's price).
Here are some others with some stats:
I'm not a fan of this concept because covered calls (and naked puts) have an asymmetric R/R ratio. You bear all of the downside risk while having only a modest amount of upside potential (the premium). Imagine what the performance would be in 2000 or 2008 bears when the market lost over 50%. Not pretty. I'd sooner chase a smaller premium and write vertical spreads and a more balanced R/R spectrum along with a defined floor of loss. Tail risk is a bitch.