In Chapter 1, I explain the prices of semi-variances at the individual stock level using model-free semi-variance indices. In Chapter 2, I quantify downside and upside semi-variance risk premiums for stocks with a model-free and fully tradable approach. I show that these premiums have opposite signs, contrasting magnitudes, and exhibit different variation patterns. In Chapter 3, I study the relationship between the semi-variance risk premiums and stock returns. I report the differential impact of the semi-variance risk premiums on stock returns. My results imply the need to analyze downside and upside semi-variance risks separately.