Theoretical Overview: Capital Asset Pricing and Arbitrage Pricing Theory SpringerLink

Other commonly used factors are gross domestic product (GDP), commodities prices, market indices, and exchange rates. When evaluating the efficacy of asset pricing models, the historical performance is a critical yardstick. It’s not just about the theoretical underpinnings or the elegance of the equations; it’s about how these models perform in the real world, with real data. The Capital Asset Pricing Model (CAPM) and the Fama-French Three Factor Model are two of the most discussed frameworks in finance. They both aim to explain and predict returns on securities, but they take different routes to reach their conclusions.

A risk-neutral pricing formula is easily derived, showing the equivalence between CAPM and the Black and Scholes’ model. Extensions to higher moments like skewness and kurtosis are straightforward, providing a generalized valuation equation. Finally, the generalized equation is derived in a different, more rigorous way, as a result of a classical intertemporal general equilibrium model. ________________ We would like to thank Emilio Barone, Umberto Cherubini and Fabio Panetta for encouragement and helpful comments to a previous version. The APT’s multi-factor model allows for a broader range of determinants impacting security returns, as evidenced by its reliance on variable external factors rather than just beta.

On the other hand, the CAPM relies on the difference between the expected and the risk-free rate of return. Systematic risk factors refer to broad economic forces that impact the entire financial market, affecting asset prices and investment returns across various sectors. Key systematic risks include interest rate fluctuations, inflation rates, GDP growth, and geopolitical events, which cannot be mitigated through diversification. The Capital Asset Pricing Model (CAPM) quantifies systematic risk using beta, measuring an asset’s sensitivity to market movements. Investors must consider these factors when constructing portfolios to manage exposure to market-wide uncertainties effectively. CAPM is based on the assumption that markets are efficient, meaning all available information is fully reflected in asset prices.

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Nevertheless, CAPM’s influence on modern financial theory and practice remains undisputable. The fundamental assumption of arbitrage theory is that there are no arbitrage opportunities available in a market. This means that it is impossible to achieve risk-free profits without any investment. The primary difference stems from how each model identifies the factors that impact asset prices. Both CAPM and APT start from different assumptions about market structures and asset pricing mechanisms.

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This means that the market is well-diversified and that the idiosyncratic risk (the risk that is specific to each asset and not related to the market) of any asset is negligible. This assumption allows the APT model to ignore the idiosyncratic risk and focus only on the systematic risk (the risk that is common to all assets and related to the market) of any asset. This assumption also implies that the covariance matrix of the asset returns is diagonal, meaning that the assets are uncorrelated with each other.

• Capital budgeting is the process of evaluating and selecting long-term investments that are consistent with the firm’s goal of maximizing owner wealth.
• A beta of 1 means the asset’s price moves in line with the market, while a beta greater than 1 indicates higher volatility.
• While CAPM provides a foundational understanding of the risk-return tradeoff, the Fama-French model offers a more complex and arguably more realistic view of the factors that drive asset returns.
• In this section, we will explain how to use the APT formula to calculate the expected return and risk premium of an asset, and compare it with the CAPM approach.

A firm using capital budgeting, their goal is to see if there fixed income will cover itself for profit. To do this, they have to calculate a discounted cash flow (DCF) for each project. The DCF is the present value of the future cash flows that the project is expected to generate. However, to calculate the DCF, the firm needs to estimate the required rate of return for each project, which is the minimum acceptable return that the firm should earn on the investment. An asset’s or portfolio’s beta measures the theoretical volatility in relation to the overall market. For example, if a portfolio has a beta of 1.25 in relation to the Standard & Poor’s 500 Index (S&P 500), it is theoretically 25 percent more volatile than the S&P 500 Index.

What are the limitations of the Arbitrage Pricing Theory?

If any stock is plotted above SML, i.e. it has higher expected return per unit of systematic risk i.e. beta, it is underpriced and vice versa. Arbitrage pricing theory states that any portfolio can deviate from the SML because it is exposed to a different systematic risk factors and such deviation doesn’t necessarily mean that the security is underpriced. The APT is a powerful and elegant model that extends the CAPM with multiple risk factors. The APT can explain the expected returns of assets better than the CAPM, and can capture the effects of various sources of systematic risk. The APT can also provide insights into the sources and the magnitude of the risk premiums, and can help investors to construct optimal portfolios that match their risk preferences.

N – Risk premium associated with respective factor

Investors use beta to assess expected return adjustments in the Capital Asset Pricing Model (CAPM). For example, a beta of 1.2 indicates the stock theoretically changes 20% more than market movement, informing portfolio risk management. CAPM assumes that there exists a risk-free asset, typically represented by government bonds, which offers a guaranteed return. The risk-free rate is the baseline return an investor can earn without taking any risk. It is used as the starting point to difference between capm and apt calculate the expected return on risky assets, making it a critical factor in CAPM’s overall framework.

B – Sensitivity of the stock with respect to the factor; also referred to as beta factor 1, 2 …

• Extensions to higher moments like skewness and kurtosis are straightforward, providing a generalized valuation equation.
• The expected values and the variances of the risk factors can be estimated using historical data, forecasts, or other methods.
• The role of risk and return in the APT is an important topic for understanding how to price any investment using multiple factors.
• It multiplies the risk-free rate by the asset’s beta coefficient and adds the market risk premium.

The two theories are thus unified, and their individual asset-pricing formulas shown to be equivalent to the pervasive economic principle of no arbitrage. In making an investment in an instrument, investors need to know how much risk they are taking. They have to assess whether the instrument is properly priced, or whether they are getting sufficient returns for the chance they are taking.

Our understanding of financial markets is being improved by the continued study of asset pricing models, which also aims to develop more reliable frameworks for projecting asset returns. Researchers work to create more thorough and accurate models that can represent the complexities of real-world asset price dynamics by addressing concerns and improving existing models. Furthermore, researchers are also investigating how non-financial elements including environmental, social, and governance (ESG) considerations affect asset price.

Modigliani-Miller models (MM models) of capital structure theory

The main advantage of APT is that it allows investors to customize their research because it provides more data and it can suggest multiple sources of asset risks. Read more about how CAPM and arbitrage pricing theory differ for more on the differences between the CAPM and APT. Four or five factors will usually explain most of a security’s return, however. Working capital is the lifeblood of any business, representing the short-term assets available to… Where \(s_i\) is the stock’s sensitivity to the size premium (SMB, or «Small Minus Big») and \(h_i\) is its sensitivity to the value premium (HML, or «High Minus Low»). An example of this model in action is when small-cap stocks outperform large-cap stocks, which is often attributed to the SMB factor.

Arbitrage Pricing Theory (APT) and the Capital Asset Pricing Model (CAPM) are prominent frameworks used to determine asset prices and expected returns in financial markets. APT relies on multiple macroeconomic factors to explain asset returns, offering a multifactor approach compared to CAPM’s single-factor model based solely on market risk. Explore the differences and applications of APT and CAPM to understand their impact on investment strategies and risk assessment.