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Benefits of Diversification

# Benefits of Diversification - average of the individual...

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Benefits of Diversification We will prove the benefits of diversification for the case where n = 2. σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2w 1 w 2 σ 1 σ 2 ρ 12 Suppose that ρ 12 = 1, i.e. the two assets are perfectly correlated (hence no benefits of diversification). σ p 2 = w 1 2 σ 1 2 + w 2 2 σ 2 2 + 2w 1 w 2 σ 1 σ 2 (1) (*) = (w 1 σ 1 + w 2 σ 2 ) 2 So, σ p = w 1 σ 1 + w 2 σ 2 , i.e. when ρ 12 = 1 the portfolio risk is the weighted average of the individual risk. Therefore, there are no benefits from diversification, as the investor receives the weighted average of returns, but also takes on the weighted average of the risks. It follows that if ρ 12 < 1 then the portfolio risk must be less than the weighted
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Unformatted text preview: average of the individual risks [since the third term in the sum is now smaller than in (*) ]. In this case there are benefits from diversification, as the investor receives the weighted average of returns, but takes on less than the weighted average of the risks. n portfolio return = R p = ∑ w i r i • the portfolio return is the weighted i=1 average of the individual returns n Key result: σ p < ∑ w i σ i • but, the portfolio risk is less than the i=1 weighted average of the individual asset risks...
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