H11 - Portfolio Variance with Many Risky Securities William...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Portfolio Variance with Many Risky Securities William L Silber and Jessica A. Wachter Case 1: Unsystematic risk only. Recall that when the correlation ρ between two securities equals zero, the portfolio vari- ance is given by: σ 2 p = w 2 1 σ 2 1 + w 2 2 σ 2 2 A simple generalization of this formula holds for many securities provided that ρ = 0 between all pairs of securities : σ 2 p = w 2 1 σ 2 1 + w 2 2 σ 2 2 + ··· + w 2 N σ 2 N . (1) We will prove the following result. As N → ∞ , the portfolio standard deviation σ p → 0. To make the notation simpler, assume that σ 1 = σ 2 = ··· = σ N = σ . This means that each asset is equally risky. Under those circumstances, we try the simple diversification strategy of dividing our wealth equally among each asset such that w i = 1 N . These assumptions allow us to rewrite expression (1) as σ 2 p = 1 N 2 σ 2 + 1 N 2 σ 2 + ··· + 1 N 2 σ 2 (2) There are N identical terms in expression (2), which means: σ 2 p = N 1 N...
View Full Document

{[ snackBarMessage ]}

Page1 / 2

H11 - Portfolio Variance with Many Risky Securities William...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online