Explore BrainMass
Share

Explore BrainMass

    Assets/variance/portfolio question

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    B. Assume there are only two assets in a portfolio. If this portfolio has a positive weight for each asset, can its (portfolio.s) variance be greater than the variance of returns on the asset in the portfolio that has the higher variance of the two? Explain. Can the variance of the portfolio be smaller than the variance of returns on the asset in the portfolio that has the smaller variance? Explain.

    I'm looking for a mathematical proof along with theory to explain
    thanks!

    © BrainMass Inc. brainmass.com October 9, 2019, 4:20 pm ad1c9bdddf
    https://brainmass.com/economics/principles-of-mathematical-economics/assets-variance-portfolio-question-29348

    Solution Preview

    Assuming the two assets are A and B, then
    Asset A has a variance of Va, a standard deviation of SDa and a share of Wa;
    Asset B has a variance of Vb, a standard deviation of SDb and a share of Wb;
    Let Va > Vb,
    and since SD = SQRT(V),
    SDa > SDb
    Also, by definition, Wa+Wb = 1

    The variance of the portfolio is:
    Variance (P) = Variance(A) * (Wa)^2 + Variance(B) * (Wb)^2 +2(Wa)*(Wb)*Covariance(A,B)
    Variance (P)= Va* (Wa)^2 + Vb * (Wb)^2 +2 Wa * Wb* SDa * SDb) *Corr(A,B)
    (* where "^2" means "squared", and Corr(A,B) is the Correlation ...

    Solution Summary

    Assets/variance/portfolio question is solved.

    $2.19