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
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% 
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