The purpose of this question is to see if you are truly passionate about investing and are following the markets. Most individuals with a passion for investing will be actively following the markets, even if it just means investing in a paper portfolio if they are limited by capital or regulatory limitations.
Presumably, if you are interviewing for a PE firm and are passionate about investing, you do invest in stocks. However, there are some valid reasons why you might not, and it’s worth explaining if you say you don’t invest in stocks. If you work at an investment bank, there are often quite a number of restrictions on which stocks you can buy, and how long you must hold them before you sell, so your preference might be to buy index funds rather than hold individual stocks. Maybe you have had to focus your cash flow on repaying student debt or perhaps you have been investing in real estate / paying off a mortgage.
However, if you say you don’t invest in stocks and provide a legitimate reason, it’s important to then follow up with stocks you would hypothetically own if you could. Make sure to have a short rationale prepared as to why you like those stocks; perhaps it’s part of a larger industry trend and you think the company is undervalued, or the stock has great growth potential that is not being fully priced in. It’s good to know roughly how large the market cap is, what their LTM revenue is, and what multiples they are trading at in terms of EV / EBITDA or whatever multiple is relevant for that industry.
Similarly, if you do invest in stocks and begin listing your holdings, it’s better to list stocks that you can provide a quick rationale as to why you like them. The interviewer could ask you about any of those stocks at any moment to test if you’ve truly done your due diligence. It’s not necessary to list every single stock you own if you have a large portfolio; it’s more important to list stocks that you can pitch effectively.