The risk-free rate is the theoretical return on an investment with zero risk. It represents the interest an investor would expect from an absolutely riskless investment over a given period. In practice, short-term U.S. Treasury bills are commonly used as a proxy because they are backed by the U.S. government.
The risk-free rate serves as the baseline for evaluating other investments. When comparing opportunities or valuing assets, investors typically start with the risk-free rate and then add premiums for taking on additional risk.
In the Capital Asset Pricing Model (CAPM), the expected return \(E[R_i]\) of an asset is \[E[R_i] = R_f + \beta_i (E[R_m] - R_f)\] where \(R_f\) is the risk-free rate, \(\beta_i\) measures how the asset moves with the market, and \(E[R_m]\) is the expected market return.