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Beta, CAPM, Cost of Capital, Equity Risk Premium, Markowitz, Modern Portfolio Theory, Pablo Fernández

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Over the last decades, finance has developed widely, not only in the real-world industry, but also at an academic level. Since Markowitz’s modern portfolio theory (1952), many theories have emerged. The most known of all these theories is the Capital Asset Pricing Model (CAPM), which states that the market expected return of a stock is driven by the risk-free rate, the stock beta and the market risk premium. Analytically, the CAPM can be summarised as follows:

Where E[Ri] is the expected return of the stock, Rf is the risk-free rate, β is the stock beta, and E[Ri]-Rf is the market risk premium.

The formula is intuitive and do not requires much explanation: the expected return of a company is the return of the risk-free asset plus the market risk premium adjusted by the stock systematic risk. The theory seems obvious and self-evident. Yet, empiric evidence doesn’t support the CAPM theory, nor the assumptions are realistic. Therefore, it has no real applications, and trusting it can lead to problems.

In order to be valid, the model assumes that there are homogeneous expectations on the systematic risk and the equity risk premium. Thus, it implicitly assumes that the value of future beta and equity risk premium are observable and unquestionable, so every investor has the same risk expectations for every stock. Still, evidence and common sense show that risk is a subjective estimation so there is no such thing as market expected return, but rather, a lot of individual expected returns.

Frequently, expected beta and market risk premium are estimated with historical data, assuming that these are the market expectations, but evidence do not support this process. The main two reasons are that historical equity risk premium and betas differ from one index to another, and that both two variables are very unstable.

On top of that, the main problem comes when investors try to apply the CAPM to calculate the so-called cost of capital. This measure is one of the most important ones when using the discounted cash flow valuation, since it is the number that is used to discount the free cash flow to equity (or combined with the cost of debt, the free cash flow to the firm). In fact, the cost of capital is not a cost, but a required return by investors. And here comes the problem: CAPM is about expected return, while cost of capital is about required return. Both measures are not the same, not only because there are not homogeneous expected and required returns, but also because the market is not fully efficient. That is, even if market expectations and preferences were equal for all investors, the market has some frictions and sources of inefficiencies that would lead to differences between expected and required returns.

Thus, using the CAPM to estimate the cost of capital by calculating beta and market risk premium with historical data is worth nothing in the valuation process and may lead to errors. Cost of capital is subjective and depends on how risky the cash flow generation is according to each investor. Therefore, using qualitative risk measures may be better than quantitative ones, applying common sense and rational-based expectations.

Suggested readings:

- Fernandez, Pablo, CAPM: An Absurd Model (November 19, 2015). Available at SSRN: https://ssrn.com/abstract=2505597
- Fernandez, Pablo, Are Calculated Betas Good for Anything? (November 21, 2015). Available at SSRN: https://ssrn.com/abstract=504565
- Fernandez, Pablo, Equity Premium: Historical, Expected, Required and Implied (November 18, 2015). Available at SSRN: https://ssrn.com/abstract=933070

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