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An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.4. The risk-free rate of return is 5%. The standard deviation of the returns on the optimal risky portfolio is :_______

a. 25.5%
b. 22.3%
c. 21.4%
d. 20.7%

Respuesta :

Answer:

Option c (21.4%) is the right approach.

Explanation:

As we know.

  • wA and wB = weights of the securities    
  • SDA and SDB = standard deviations    
  • Cor(A,B) = correlation coefficient.

On applying the formula:

⇒  [tex]SD \ Portfolio = [wA^2\times SDA^2+wB^2\times SDB^2+2\times wA\times wB\times SDA\times SDB\times Cor(A,B)]^{0.5}[/tex]

On substituting the values, we get

⇒  [tex](0.29^2\times 39^2+0.71^2\times 20^2+2\times 0.29\times 0.71\times 39\times 20\times 0.4)^{0.5}[/tex]

⇒  [tex]21.40 \ Percent[/tex] (%)

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