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Interpreting the CAPM Expected-Return Factor in a Price Formula

Article Quant Q&A · Author: Night Walker
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Summary

The document interprets the denominator in a rearranged capital asset pricing model relation. CAPM links an asset’s expected return to the risk-free rate plus its beta multiplied by the market’s expected excess return. Applying that expected return over one period gives a relation between the asset’s current price and its next-period expected price.

Under this model, the denominator represents the one-period price appreciation factor implied by the asset’s beta and the market risk premium. The explanation depends on CAPM being an adequate description of the asset’s risk and return, and it concerns expected pricing rather than a guarantee of the realized next-period price. The brief exchange provides no empirical test or discussion of model limitations beyond that assumption.

Key ideas

  • CAPM relates an asset’s expected return to the risk-free rate and its beta-scaled market risk premium.
  • The expected next-period price equals the current price multiplied by one plus the CAPM expected return.
  • In the rearranged price equation, the denominator is the modeled one-period price appreciation factor.
  • This interpretation depends on CAPM accurately describing the asset’s risk and return.

Tags

Risk managementStatisticsEquities
Full text
# CAPM as pricing formula


# CAPM as pricing formula












P - price that the asset was purchased. Q - price that it was sold

P = Q/(1+r+B(R_m - r))

What is the financial meaning of denominator.

Thanks for help.

## Answer by pbr142 (score 4)

https://quant.stackexchange.com/a/10662

The CAPM states that the expected return of an asset i is related to the expected market return by $$\mathbb{E}[R_i] = r_f + \beta_i (\mathbb{E}[R_M] - r_f) $$

If the CAPM is a correct description of risk and return, then the next period price Q should be given by

$$ Q = P (1+r_f + \beta_i (\mathbb{E}[R_M] - r_f)) $$

In your formulation, the denominator is the factor by which the asset's price should apprecitate over the period of observation.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.