Asset Pricing Models: A Comprehensive Overview

Asset Pricing Models

Meta Description: Asset pricing models are used to determine the expected return on an investment. This article will discuss the different types of asset pricing models, how they work, and their limitations.

Meta Keywords: asset pricing models, CAPM, arbitrage pricing theory, Fama-French three-factor model, Carhart four-factor model

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

Risk-free rate is the rate of return on a risk-free investment, such as a government bond

Beta is a measure of the investment’s systematic risk

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

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

Risk-free rate is the rate of return on a risk-free investment, such as a government bond

Factor premium is the premium that investors demand for taking on risk associated with a particular factor

Factor sensitivity is the investment’s sensitivity to a particular factor

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

SMB (size): The difference between the returns on small stocks and the returns on large stocks

HML (value): The difference between the returns on high-book-to-market stocks and the returns on low-book-to-market stocks

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

Risk-free rate is the rate of return on a risk-free investment, such as a government bond

Beta_M is the investment’s sensitivity to market risk

Beta_SMB is the investment’s sensitivity to size

Beta_HML is the investment’s sensitivity to value

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

SMB premium is the difference between the returns on small stocks and the returns on large stocks

HML premium is the difference between the returns on high-book-to-market stocks and the returns on low-book-to-market stocks

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-

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