What is stochastic discount factor?

Stochastic discount factor (SDF) is a tool that is widely used in financial economics to model asset prices and expected returns. It is a measure of the risk premium that investors demand for holding a risky asset over a riskless asset. The SDF is a function that relates the price of an asset to the underlying economic factors that affect its returns.

The SDF is a stochastic variable, meaning that it varies over time and is dependent on random factors that cannot be predicted with certainty. The SDF is usually modeled as a function of various macroeconomic or financial variables such as interest rates, inflation rates, or stock prices.

The SDF is an important concept in many financial models, including asset pricing models such as the capital asset pricing model (CAPM) and the arbitrage pricing theory (APT). These models attempt to explain the behavior of asset prices and expected returns using the SDF as a tool.

One of the key advantages of using the SDF in financial modeling is that it allows for a more realistic representation of the risk and uncertainty associated with investing in financial assets. By incorporating stochastic factors into the model, the SDF can help investors better understand the risks and potential rewards of different investment strategies.