## Asset Pricing Models

## Introduction

Asset pricing models are used to determine the expected return on an investment. They take into account the riskiness of the investment and the overall market conditions. Asset pricing models are used by investors to make informed decisions about their investments.

There are a number of different asset pricing models, each with its own strengths and weaknesses. The most common asset pricing model is the capital asset pricing model (CAPM). The CAPM is based on the idea that investors are compensated for taking on risk. The riskier an investment is, the higher its expected return should be.

## The Capital Asset Pricing Model (CAPM)

The CAPM is a single-factor model that assumes that the only risk that investors care about is systematic risk, or market risk. Systematic risk is the risk that an investment cannot be eliminated by diversification. The CAPM formula is as follows:

“`

Expected return = Risk-free rate + Beta (Market risk premium)

“`

Where:

Expected return is the expected return on the investment

The CAPM is a simple and easy-to-use model, but it has a number of limitations. One limitation is that it assumes that investors are rational and risk-averse. Another limitation is that it does not take into account any non-systematic risk, or idiosyncratic risk. Idiosyncratic risk is the risk that can be eliminated by diversification.

## Arbitrage Pricing Theory (APT)

Arbitrage pricing theory (APT) is a multi-factor model that assumes that investors are compensated for taking on a number of different risks. APT is based on the idea that there are a number of factors that can affect the price of an investment, and that investors will demand a premium for taking on risk associated with any of these factors.

The APT formula is as follows:

“`

Expected return = Risk-free rate + Σ (Factor premium Factor sensitivity)

“`

Where:

Expected return is the expected return on the investment

APT is a more general model than the CAPM, but it is also more complex. One limitation of APT is that it is difficult to identify and measure all of the factors that can affect the price of an investment.

## Fama-French Three-Factor Model

The Fama-French three-factor model is a multi-factor model that is based on the idea that there are three factors that can explain the returns on stocks:

Market risk premium: The difference between the expected return on the market and the risk-free rate

The Fama-French three-factor formula is as follows:

“`

Expected return = Risk-free rate + Beta_M (Market risk premium) + Beta_SMB (SMB premium) + Beta_HML (HML premium)

“`

Where:

Expected return is the expected return on the investment

The Fama-French three-factor model is a more successful explanation of stock returns than the CAPM. It is able to explain a larger percentage of the variation in stock returns, and it is less sensitive to changes in the risk-free rate.

## Carhart Four-Factor Model

The Carhart four-