Math Problem Statement

The risk-free rate is 1.91% and the expected return on the market 12.23%. A stock with a β of 1.14 will have an expected return of ____%.

Solution

To calculate the expected return of the stock, we can use the Capital Asset Pricing Model (CAPM) formula:

E(Ri)=Rf+β×(E(Rm)Rf)E(R_i) = R_f + \beta \times \left(E(R_m) - R_f\right)

Where:

  • E(Ri)E(R_i) = Expected return of the stock
  • RfR_f = Risk-free rate = 1.91% = 0.0191
  • E(Rm)E(R_m) = Expected return on the market = 12.23% = 0.1223
  • β\beta = Beta of the stock = 1.14

Step-by-step calculation:

  1. Calculate the market risk premium: E(Rm)Rf=0.12230.0191=0.1032(10.32%)E(R_m) - R_f = 0.1223 - 0.0191 = 0.1032 \, (10.32\%)

  2. Multiply the market risk premium by the beta of the stock: β×(E(Rm)Rf)=1.14×0.1032=0.117648(11.7648%)\beta \times \left(E(R_m) - R_f\right) = 1.14 \times 0.1032 = 0.117648 \, (11.7648\%)

  3. Add the risk-free rate to the result: E(Ri)=Rf+β×(E(Rm)Rf)=0.0191+0.117648=0.136748(13.6748%)E(R_i) = R_f + \beta \times \left(E(R_m) - R_f\right) = 0.0191 + 0.117648 = 0.136748 \, (13.6748\%)

Final Answer:

The expected return of the stock is approximately 13.67%.


Would you like a breakdown of related concepts or further clarification?

Here are 5 related questions you might explore:

  1. What does the beta (β\beta) of a stock represent in CAPM?
  2. How would a change in the market's expected return affect the stock's expected return?
  3. Can a stock have a negative beta, and what does it imply for expected returns?
  4. How does the CAPM compare to other models like the Fama-French three-factor model?
  5. What are the limitations of using CAPM for estimating expected returns?

Tip: Always double-check the risk-free rate and market return assumptions, as small errors can significantly impact the result.

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Math Problem Analysis

Mathematical Concepts

Finance
Expected Return
CAPM (Capital Asset Pricing Model)

Formulas

E(R_i) = R_f + β × (E(R_m) - R_f)

Theorems

CAPM Theory

Suitable Grade Level

Undergraduate/Finance Students