Your link to the BLS website says exactly what I said. Did you read it? The cost to purchase a home is not included in CPI. Mortgage interest is not included in CPI. What an owned home would rent for is included in CPI. This is all in your link, it’s only like 3 paragraphs long. Just read it next time.

As for the stock market, you’re using nominal numbers to “correct” a claim about real numbers.