What is the industry average conversion rate for cold emailing?

I run a new productized service. Initially, I was focused on sales and cold emailing customer prospects, but it totally failed. I've emailed over 400 prospects with different approaches, using well-tested templates and even custom tailored uber-personalized emails. Not a single cold prospect has converted. The other week I spoke to a guy who runs a similar business model. His main acquisition channel is cold email and is working well for him. When I told him I sent 400 emails and didn't convert a single user, he was like: "Buddy, we had to send 4000 emails to convert 20 customers." That is 0.5% conversion rate. He also mentioned that's the industry standard. Now, in my books 0.5% conversion rate is rather horrible for all type of acquisition channels. But you can't argue with the fact his business has more customers than ours ATM due to that tactic. So two questions here: 1. Is cold emailing a game of numbers, and is really volume crucial? 2. Do you have any stats or benchmarks from personal experience what is the average conversion rate for cold emailing? I know this depends heavily on the type of business, and price points, so let's say we're talking about a service around the $100-400 price range.