4. Certainty Equivalent, Risk Premium and Asset Pricing

This chapter explores the methods to determine a discount rate. After examining the prevailing alternatives to determine a discount rate, the bad news is: none of them is correct in theory. This implies that we cannot incorporate (asset, project, etc.) risk into valuation effectively. Based on the option pricing model, the chapter finds two ways to solve the problem of incorporate risk: via certainty equivalent and via the risk-adjusted discount rate. Correspondingly, a series of models (the ZZ models of certainty equivalent and its coefficient, the ZZ risk equivalent and its coefficient, the ZZ risk premium model and the ZZ CAPM) are derived. Both the forms and the variables of these models are derived via strict logic processes rather than chosen subjectively, which implies these models are sound in theory and versatile in practice.