An investor can design a risky portfolio based on two stocks, a and b. the standard deviation of return on stock a is 24%, while the standard deviation on stock b is 14%. the correlation coefficient between the returns on a and b is .35. the expected return on stock a is 25%, while on stock b it is 11%. the proportion of the minimum-variance portfolio that would be invested in stock b is approximately

Calculate the Covariance of both stock A and B

=  × ∝A × ∝B

 = 0.35 × 0.24 × 0.14

 = 0.01176

Therefore, the Covariance of AB is 0.01176.

Calculate the proportion of investment in stock – A  

Proportion of A = \frac{∝_{B}^{2}  - Covariance_{AB} }{∝_{A}^{2} + ∝_{B}^{2} - (2 Covariance_{AB}) }

Proportion of A = \frac{0.14^{2}  - 0.01176 }{0.24^{2} + 0.14^{2} - (2 * 0.01176)}

Proportion of A = 0.1461 or 14.61%

Therefore, the proportion of investment in stock – A is 14.61%

Calculate the proportion of investment in stock – B  

Proportion of B = 1 – Proportion of A

Proportion of B = 1 – 0.1461  

Proportion of B = 0.8539 or 85.39%

Therefore, the proportion of investment in the stock – B is 85.39%  

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