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CAPM Expected Returns and Portfolio Beta Inputs

Article Quant Q&A · Author: Svit
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Summary

The document presents a question about applying the Capital Asset Pricing Model to a two-stock portfolio. The investor supplies portfolio weights and estimated betas, then asks how to obtain the expected return and whether a correlation inferred from the beta relationship can be used. The questioner reports two calculated correlation candidates, both outside the feasible range for a correlation, and also lacks the risk-free rate and market return needed for the CAPM calculation.

No answer or worked solution is included, so the document does not resolve the calculation. Its instructional value lies in identifying the required CAPM inputs and the consistency check that correlation must lie between negative one and positive one. The stated portfolio weights and betas alone are insufficient to determine expected returns; the relevant market and risk-free returns, and valid covariance inputs for beta, would also be needed.

Key ideas

  • CAPM expected return requires a risk-free rate, a market expected return, and the asset or portfolio beta.
  • The question supplies portfolio weights and individual stock betas but not the return inputs needed for CAPM.
  • Correlation estimates outside the interval from negative one to positive one are mathematically invalid.
  • The document contains no answer showing how to resolve the reported calculation.

Tags

EquitiesFactor investingStatistics
Full text
# Expected return


# Expected return












I apologize if similar question has already been asked.

I have to calculate expected return on the stocks A & B via CAPM.

I know $w_A = 0.2$ & $w_B = 0.8$ (weights computed from given prices and quantities)

$β_A = 1.2$. I have calculated also $β_B = 0.95$ using above data.

Now, the task is to solve this equation:

$E(r_A,_B = r_F + β_A,_B(r_M - r_F)$

I think I can find $ρ$ (that I need for the covariance) from formula for $β_A$, and I get two solutions: $ρ_1 = 1.88$ & $ρ_2 = -1.13$

I don't know which is the right one, besides I can't find $r_F$ & $r_M$ so I'm stuck here.

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