Consider two stocks, Stock D, with an expected return of 15 percent and a standa

Question

Consider two stocks, Stock D, with an expected return of 15 percent and a standard deviation of 30 percent, and Stock I, an international company, with an expected return of 8 percent and a standard deviation of 18 percent. The correlation between the two stocks is –.16. What is the weight of each stock in the minimum variance portfolio? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Consider two stocks, Stock D, with an expected return of 15 percent and a standard deviation of 30 percent, and Stock I, an international company, with an expected return of 8 percent and a standard deviation of 18 percent. The correlation between the two stocks is –.16. What is the weight of each stock in the minimum variance portfolio? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

Explanation / Answer

The parameters which are provided in the question are as under:

Expected return of Stock-D = E(RD ) = 15%,  

Expected return of Stock-I = E(RI )= 8%,  

Standard deviation of Stock-D = D = 30%,

Standard deviation Stock-I = I = 18%,

Correlation between the fund returns = P= -0.16

From the standard deviation and correlation coefficient we generate the covariance matrix:

Stock-D

Stock-I

Stock-D

30*30= 900

30*18*-0.16 = -86.4

Stock-I

18*30*-0.16 = -86.4

18*18= 324

As the portfolio is a minimum variance portfolio so the portfolio weights can be found by using this formula:

Wmin(D) ={ I2 – Cov(B, S)} / {D2+I2- 2 Cov(D, I)}

              = {324 + 86.4} / {900+324 + 2*86.4} = 410.4 / 1396.8 = 0.2938

Therefore,   Wmin(I) = 1- 0.2938 = 0.7062

Stock-D

Stock-I

Stock-D

30*30= 900

30*18*-0.16 = -86.4

Stock-I

18*30*-0.16 = -86.4

18*18= 324

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