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EdgarStat® contains an internal regression model to calculate the beta-risk coefficient of an individual enterprise stock price return compared to the return of the S&P 500 stock price (market) index. This stock price return regression model is known as CAPM.

Let the individual stock price return be calculated with the investment gain or loss formula:

(1) **R**(*t*) = {[**P**(*t*) / **P**(*t* − 1)] – 1}, such that we postulate the linear relation:

(2) **Y**(*t*) = α + β **M**(*t*)

where the dependent variable is **Y**(*t*) = [**R**(*t*) + 1] = [**P**(*t*) / **P**(*t* − 1)] or **P**(*t*) = [1 + **R**(*t*)] **P**(*t* − 1).

The variable **M**(*t*) is the stock market price return, measured using the same eq. (1).

In eq. (2), the intercept (= α) is the adjusted stock price return, equivalent to the local short-term sovereign bill return. Some call the intercept “seeking alpha." The slope coefficient (= β) is the derivative of the individual stock price return with respect to the stock market price (index) return.

In EdgarStat, we use monthly **R**(*t*) to calculate α, β, and σ = √Var(**Y**(*t*)) for individual companies selected by the user. It’s sensible to calculate (2) using quarterly data, because dividends are reported per quarter of year.

Example 1: The CAPM Coefficients of Chevron Corp. (GVKEY 2991, Mergent 7846)

(5) **Y**(*t*) = 0.8379 **M**(*t*) – 0.111, σ = 6.2558

where σ is the residual standard error.

The intercept is not significant (Newey-West *t-*Statistics are –0.3893), and the slope coefficient is significant with the Newey-West corrected *t*-Statistics = 11.2001. Count = 490 observations from 2023-01-1 back to 1982-01-31. The R^{2} = 25.45%, showing that for Chevron the CAPM linear model is a bad fit.

Example 2: The CAPM Coefficients of ConocoPhillips (GVKEY 8549, Mergent 6630)

(3) **Y**(*t*) = 1.017 **M**(*t*) – 0.1052, σ = 8.2715

The intercept is not significant (Newey-West *t-*Statistics are –0.2761), and the slope coefficient is significant with the Newey-West corrected *t*-Statistics = 9.4952. Count = 490 observations from 2023-01-1 back to 1981-12-31. The R^{2} = 22.34%, showing that for ConocoPhillips the CAPM linear model is a bad fit.

Example 3: The CAPM Coefficients of Exxon Mobil Corp. (GVKEY 4503, Mergent 7846)

(4) **Y**(*t*) = 0.681 **M**(*t*) – 0.0189, σ = 6.285

The intercept is not significant (Newey-West *t-*Statistics are –0.0642), and the slope coefficient is significant with the Newey-West corrected *t*-Statistics = 8.0272. Count = 490 observations from 2023-01-1 back to 1982-01-31. The R^{2} = 18.26%, showing that for Exxon Mobil the CAPM linear model is, again, a bad fit.

The principal takeaway is that canned beta coefficients are unreliable to discount the expected future stock prices of a selected enterprise to the present. Also, canned beta coefficients are an unreliable measure of risk.

Richard Brealey & Stewart Myers, ** Principles of Corporate Finance** (6th edition), McGraw-Hill, 2000, § 8.2 (Relationship between risk and return) and § 9.1 (Measuring betas).

Zvi Bodie & Robert Merton, ** Finance**, Prentice Hall, 2000, § 13.3 (Beta and risk premiums on individual securities).

Chart 1: Chevron Corp. (GVKEY 2991, Mergent 7846)

Chart 2: ConocoPhillips (GVKEY 8549, Mergent 6630)

Chart 3: Exxon Mobil Corp. (GVKEY 4503, Mergent 7846)

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