The stock of Bruin, Inc., has an expected return of 25 percent and a standard de

Question

The stock of Bruin, Inc., has an expected return of 25 percent and a standard deviation of 38 percent. The stock of Wildcat Co. has an expected return of 12 percent and a standard deviation of 43 percent. The correlation between the two stocks is .43. Calculate the expected return and standard deviation of the minimum variance portfolio. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

The stock of Bruin, Inc., has an expected return of 25 percent and a standard deviation of 38 percent. The stock of Wildcat Co. has an expected return of 12 percent and a standard deviation of 43 percent. The correlation between the two stocks is .43. Calculate the expected return and standard deviation of the minimum variance portfolio. (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

As per  minimum variance portfolio

Weight of Stock Bruin = (Variance of Stock wildcat co - covariance)/(Variance of Stock Bruin co+ Variance of Stock wildcat co -2 covariance)

Weight of Stock Bruin = (43^2 - 38*43*0.43)/(38^2 + 43^2 - 2*38*43*0.43)

Weight of Stock Bruin = 0.60727

Weight of Stock Wildcat Co   = 1- Weight of Stock Bruin

Weight of Stock Wildcat Co   = 1-0.60727

Weight of Stock Wildcat Co   = 0.39273

Expected return of Portfolio = Weight of Stock Bruin * Expected Return of Bruin + Weight of Stock Wildcat Co * Expected Return of Wildcat Co

Expected return of Portfolio = 0.60727*25 + 0.39273*12

Expected return of Portfolio = 19.89%

Standard deviation of Portfolio = (Weight of Stock Bruin^2 * Standard deviation of Bruin^2 + Weight of Stock Wildcat Co^2 * Standard deviation of Wildcat Co^2 + 2* Weight of Stock Bruin *Weight of Stock Wildcat Co * Standard deviation of Wildcat Co* Standard deviation of Bruin *Correlation)^(1/2)

Standard deviation of Portfolio = ( 0.60727^2*38^2 +  0.39273^2*43^2 + 2*0.60727*0.392673*43*38*0.43)^(1/2)

Standard deviation of Portfolio = 33.95%

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