**Introduction to CAPM**

The world of finance is filled with models and theories that aim to explain and predict the behaviour of financial markets. Among these models, the Capital Asset Pricing Model (CAPM) stands out for guiding investors to make financial decisions. This model seeks to determine the expected return on an investment, given its risk relative to the market. We will dive a bit deeper into understanding CAPM, shedding light on its fundamental elements, applications, and critiques.

**Behind the model: The pillars of the formula**

The CAPM was introduced by Sharpe and Linter in the early 1960s to mainly highlight the relationship between risk and return: the principle that with a higher risk, comes the demand for higher rewards (as described by Sharpe in the "Capital asset prices: A theory of market equilibrium under conditions of risk." Journal of Finance)

The CAPM formula is expressed mathematically as: **E(Ri)=Rf+βi(E(Rm)−Rf)**

Where:

- Risk-Free Rate, (Rf): This is the return on an investment that is considered free of risk (usually a government bond). It is the minimum return an investor expects for any investment.

-Beta, (β): measures the volatility of an asset compared to the overall market.

- Market Return, E(Rm): represents the expected return of the overall market.

The graph shows the correlation between risk and return: higher risk leads to higher expected returns and vice versa:

**Figure 1**. Graph showing Market risk (Beta) and Expected return (%). Image source: Toolshero

**A popular model for investment analysis**

CAPM is widely used in finance for various purposes for both individual investors and corporates. The model gives insights on how to balance a portfolio between risk and returns. For analysis purposes, it enables capital allocation, allowing corporations to channel resources into ventures that bring returns balanced with their risks. Furthermore, in business valuation, the CAPM linked with models like the Discounted Cash Flow (DCF), ensures that valuations reflect not only current standings but future potentials and inherent risks. Far from being just an academic concept, CAPM's principles are commonly used in the financial environment, highlighting its lasting importance.

**Illustrating CAPM in Action: A Tale of Two Stocks**

An investor is looking to buy one of the stocks of company A or company B with different risk profiles. Company A, known for its aggressive expansion strategies and bold market moves, has a beta of 1.2 (this indicates that its stock price is likely to move 20% more than the market average). Company B, with its more conservative approach, has a beta of 0.8 (suggesting it might move 20% less than the market average).

Now, let's factor in the current risk-free rate, which stands at 3%, and the market risk premium, which is 6%. Using the CAPM formula, the investor can determine the expected returns for both companies:

For Company A: Expected Return = 3% + (1.2 x 6%) = 10.2%

For Company B: Expected Return = 3% + (0.8 x 6%) = 8.8%

The calculations reveal that Company A (with its higher beta), is anticipated to yield a return of 10.2%, while Company B's expected return is 8.8%. This difference underscores the essence of CAPM: higher risk (as indicated by a higher beta) often comes with the potential for higher returns. So, if the investor has a high-risk appetite, company A might be more appealing, while if he is seeking a more stable venture, he might choose to buy the stock of company B.

This example showcases how CAPM can be a valuable tool for investors, helping them determine the risk and potential return of different investment opportunities in the real world.

**While CAPM is a valuable tool, it has its limitations and critiques**

While CAPM stands as a cornerstone in modern financial theory, it's not without its detractors and acknowledged limitations. The main critique leans on certain simplifying assumptions, such as the efficient market hypothesis and a constant beta, which might not always align with the complexities of financial markets. This is further complicated by the model's assumption that all investors share the same expectations in terms of risks and returns, sharply contrasting with the varied perspectives and anticipations observed in the markets. The model's dependence on quality and timely data is often criticized as past data might become less indicative of future market behaviours. Its focus predominantly on systematic risk (the market risk) often overshadows the idiosyncratic risks inherent to individual assets. The notion of an absolute risk-free rate, combined with the idea that investors can easily borrow and lend at this rate, makes CAPM appear somewhat detached from realistic financial dynamics.

These limitations have prompted critics to explore other models. Notably, the Fama-French three-factor model and the Arbitrage Pricing Theory (APT) are often highlighted for their broader and more nuanced insights into risk and return.

**Conclusion **

In conclusion, the Capital Asset Pricing Model (CAPM) is a vital tool in finance that helps investors make informed decisions by quantifying the relationship between risk and return. While it has its limitations, CAPM remains a widely used framework for estimating expected returns on investments. It empowers investors and financial professionals to assess and compare the risk-return tradeoffs of various assets, ultimately contributing to the construction of diversified portfolios and investment decision-making. Despite its limitations, its widespread use of CAPM in various financial applications shows its importance. As with all models, it's essential to understand its assumptions and use it as one of many tools in the financial toolkit.

This article was written by Ardi Kuka, Banking Supervision Analyst at the ECB, Kedge Business School, France.

**References**

Ang, A., Hodrick, R. J., Xing, Y., & Zhang, X. (2006). "The cross-section of volatility and expected returns." The Journal of Finance, 61(1), 259-299.

Fama, E. F., & French, K. R. (1992). "The cross‐section of expected stock returns." The Journal of Finance, 47(2), 427-465.

Fama, E. F., & French, K. R. (2004). "The capital asset pricing model: Theory and evidence." Journal of Economic Perspectives, 18(3), 25-46.

Frazzini, A., & Pedersen, L. H. (2014). "Betting against beta." Journal of Financial Economics, 111(1), 1-25.

Jack, F., Jensen, M. C., & Scholes, M. (1972). "The capital asset pricing model: Some empirical tests." In Studies in the theory of capital markets (pp. 79-121). Praeger Publishers Inc.

Lewellen, J., & Nagel, S. (2006). "The conditional CAPM does not explain asset-pricing anomalies." Journal of Financial Economics, 82(2), 289-314.

Lintner, J. (1965). "The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets." Review of Economics and Statistics, 47(1), 13-37.

Sharpe, W. F. (1964). "Capital asset prices: A theory of market equilibrium under conditions of risk." Journal of Finance, 19(3), 425-442.

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