Security Standard Deviation (σ) Weights (w) R 20% 0.8 S 50% 0.2 Calculation upto two decimal place. From the information given above, you are…

(i) Portfolio Variance and Standard Deviation of Portfolio if securities returns are independent: σ p 2 = x 1 2 σ 1 2 + x 2 2 σ 2 2 Accordingly, Variance (σ p 2 ) = (0.80) 2 (20) 2 + (0.20) 2 (50) 2 Variance (σ p 2 ) = 256 + 100 = 356 Standard Deviation (σ p ) = √356 = 18.87% (ii) Portfolio Variance and Standard Deviation of Portfolio if securities returns are perfectly negatively related: σ p 2 = (x 1 σ 1 - x 2 σ 2 ) 2 σ p = x 1 σ 1 - x 2 σ 2 Accordingly, Variance (σ p 2 ) = (0.80x20 - 0.20x50) 2 Variance (σ p 2 ) = (6) 2 = 36 Standard Deviation (σ p ) = √36 = 6% (iii) Portfolio Variance and Standard Deviation of Portfolio if securities returns are perfectly positively related: σ p 2 = (x 1 σ 1 + x 2 σ 2 ) 2 σ p = x 1 σ 1 + x 2 σ 2 Accordingly, Variance (σ p 2 ) = (0.80x20 + 0.20x50) 2 Variance (σ p 2 ) = (26) 2 = 676 Standard Deviation (σ p ) = √676 = 26%