Question

Your current portfolio has a value of $60,000, with an expected return of 30%, and a standard deviation of 40%. You decide you want to purchase $12,000 of ABC, which has an expected return of 26%, a standard deviation of 60%, and is perfectly negatively correlated to your current portfolio. What will be your new portfolio’s standard deviation after the addition of ABC?

please show how it is calculated

Answer 1

Assume current portfolio = Stock A New stock = Stock B Weight of stock A = $60000/(60000+12000) =0.83333 Weight of Stock B = 12000/(60000+12000) =0.16667 Standard Deviation of portfolio=√(W Stock A^2 × σ Stock A^2) +(W Stock B^2 × σ Stock B^2)+2 × r × W Stock A × W Stock B × σ Stock A × σ Stock B
Where,
W Stock A=Weight of Stock A
W Stock B=Weight of Stock B
σ Stock A=Standard Deviation of Stock A
r = correlation coefficient
=√(0.83333^2 × 40%^2) +(0.166667^2 × 60%^2) + 2×-1 × 0.83333 × 0.166667 × 40% × 60%
=√1111.10222224+100.0004000004+-666.665333328
=√1211.1026222404
=23.33%