What is the relationship between risk and return of an investment?

Higher risk investments must have higher returns in order to attract investors. Suppose you can get, say, a 4% return by just putting your money into an FDIC insured account at your bank. This is a very low risk investment, right? Or, you could put your money into a stock that may double in value within a year, but the company could go bankrupt, and you investment is not insured. So this investment is risky. The only reason you would put your money into that stock rather than just putting it in the bank is if you expect to make more money, right?