shown that Var[Rp] =w, Cov[R, R], Pip], that is, the variance of a portfolio equals the...
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shown that Var[Rp] =w, Cov[R₁, R₂], Pip], that is, the variance of a portfolio equals the weighted average covariance of each asset with the portfolio. (a) Based on this equation, show that SD[R] - Σ i=1 Σw. Pip SD[R], where pi, is the correlation between the asset i's return with the portfolio return. (b) Based on the equation in (a), prove the argument that "the volatility of a portfolio is less than the weighted average volatility of assets in the portfolio." E (c) Now consider asset 1 in the portfolio and assume Pip 0.5 and SDR₁] = 40%, both of which are fixed. If we increase w, (the portion of wealth invested in asset 1), by 1% (i.e., if w₁ used to be 4%, now it is 5%), how much will SD [R,] change according to the equation you've proved in (a)? (d) Dropping the assumption that pip is always 0.5. If we increase w₁. how will pp change in reality and why? shown that Var[Rp] =w, Cov[R₁, R₂], Pip], that is, the variance of a portfolio equals the weighted average covariance of each asset with the portfolio. (a) Based on this equation, show that SD[R] - Σ i=1 Σw. Pip SD[R], where pi, is the correlation between the asset i's return with the portfolio return. (b) Based on the equation in (a), prove the argument that "the volatility of a portfolio is less than the weighted average volatility of assets in the portfolio." E (c) Now consider asset 1 in the portfolio and assume Pip 0.5 and SDR₁] = 40%, both of which are fixed. If we increase w, (the portion of wealth invested in asset 1), by 1% (i.e., if w₁ used to be 4%, now it is 5%), how much will SD [R,] change according to the equation you've proved in (a)? (d) Dropping the assumption that pip is always 0.5. If we increase w₁. how will pp change in reality and why?
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Statistics The Art And Science Of Learning From Data
ISBN: 9780321997838
4th Edition
Authors: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
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