Question

Given the information below about stock XYZ and the market portfolio (Mrkt), please answer the questions in the Essay Box provided. Note that σaσa denotes a standard deviation, and σa,bσa,b denotes a covariance.

• σXYZ=0.34σXYZ=0.34
• σMrkt=0.16σMrkt=0.16
• σXYZ,Mrkt=0.019623σXYZ,Mrkt=0.019623
• riskfreerate=0.0250riskfreerate=0.0250
• E(RMrkt)=0.1200E(RMrkt)=0.1200

A. What is the ββ (beta) of stock XYZ

According to the CAPM, what is the E(RXYZ)E(RXYZ)?

Answer 1

Given that

SD of stock XYZ ( σXYZ ) = 0.34

SD of Market portfolio ( σMrkt ) = 0.16

Co-variance ( σXYZ,Mrkt ) = 0.019623

Risk free rate (Rf) = 0.0250 or 2.5%

Return of the Market portfolio (Rm) = 0.1200 or 12%

A. Beta (β) of the stock XYZ can be calculated as : -

= Covariance / σMrkt²

= 0.019623 / 0.16²

  = 0.019623 / 0.0256

= 0.7665 or 0.767.

Beta (β) of the stock XYZ is 0.767.

B. As per CAPM, Expected return of the stock XYZ (ER of XYZ) =

ER (XYZ) = Rf + Beta ( Rm - Rf )

= 2.5% + 0.767 ( 12% - 2.5% )

= 2.5% + 0.767 ( 9.5% )

= 2.5% + 7.2865%

ER (XYZ) = 9.7865% or 9.79%

Conclusion: -

A. Beta (β) of the stock XYZ is 0.767.

B. Expected return of the stock XYZ as per CAPM = 9.79%.