βp = ∑{wi?βi} = [ βi=1 ; wi=1/n ] = n?∑{βi/n) = βi

βi = 1 → βp = 1

σp2 = βp2?σI2 + ∑{wi2?σi2} = [wi=1/n] = βp2?σI2 + σi2/n

σp=√σp2

βp = 1.0

σi = 0.3

σI = 0.2

{a} n=4 ; σp = √((12?0.22) + 0.32/4) = √ 0.0625 = 0.25 = 25%

{b} n=10; σp = √((12?0.22) + 0.32/10) = √ 0.049 ≈ 0.221359 ≈ 22.136%

Consider two portfolios, one composed of four securities and the other of ten securities. All the securities have a beta of 1 and idiosyncratic risk of 30%. Each portfolio distributes weight equally among its component securities. If the standard deviation of the market index is 20%, calculate the total risk of both portfolios.