Suppose that the standard deviation of returns from a typical share is about 0.3

Question

Suppose that the standard deviation of returns from a typical share is about 0.35 (or 35%) a year. The correlation between the returns of each pair of shares is about 0.2. Required: (a) Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. (Round "Variance" to 6 decimal places and "Standard deviation" to 3 decimal places.) No. of Standard Shares Variance Deviation 1 2 3 4 5 6 7 8 9 10 (b) How large is the underlying market risk that cannot be diversified away? (Round your answer to 3 decimal places.) Market risk (c) Assume that the correlation between each pair of stocks is zero. Calculate the variance and standard deviation of the returns on a portfolio that has equal investments in 2 shares, 3 shares, and so on, up to 10 shares. (Round "Variance" to 6 decimal places and "Standard deviation" to 3 decimal places.) No. of Standard Shares Variance Deviation 1 2 3 4 5 6 7 8 9 10

Explanation / Answer

a) variance (2) (for 2 share case) = xa^2*a^2 + xb^2*b^2 + 2a*b*ab*xa*xb

= .5^2*35^2 + .5^2*35^2 + 2*35*35*.2*.5*.5

= 735

standard dev = 27.111%

for equal investments in 3 shares just change the weights xa,xb,xc...and so on

b) underlying market risk cant be diversified away

c) if correl = 0

then 2 (for 2 share case) = .5^2*35^2 + .5^2*35^2

= 612.5

s.d = 2 = 24.749%

similarly while calculating for 3,4....10 share case just add the variances of each individual share to get the variance of the portfolio...

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