Lecture08

# Lecture08 - FINM2401 Financial Management Portfolio...

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Unformatted text preview: FINM2401 Financial Management Portfolio Analysis 2 Lecture 8 2 Diversification of Portfolio Risk In the last lecture, we demonstrated the measurement of risk in a two-asset portfolio Recap: When considering portfolio risk, it is necessary to look at the variability of returns from each investment in relation to other assets in the portfolio This leads to what is known as the “portfolio effect” 3 Recap: Two-asset portfolio E[r] σ w σ 1,2 Asset 1 10% 15% 0.6 0.01875 Asset 2 18% 25% 0.4 () () () = + 1 1 2 2 E E E p r w r w r () ( ) ( ) = + = E 0.610% 0.418% 13.2% p r 2 2 2 2 2 1 1 2 2 1 2 1,2 2 p w w w w σ σ σ σ = + + ()( )()( ) ()()( ) = + + = 2 2 2 2 0.6 0.15 0.4 0.25 20.60.40.01875 0.0271 σ = = 0.0271 16.46% p 4 Portfolio Risk and Return 2-asset N-asset () () = = ∑ 1 E E n p j j j r w r () () () = + 1 1 2 2 E E E p r w r w r σ σ σ σ = + + 2 2 2 2 2 1 1 2 2 1 2 12 2 p w w w w σ σ = = = ∑∑ 2 , 1 1 n n p i j i j j i w w Return Risk 5 N Asset Portfolio Risk For a larger portfolio, the variance is: ρ σ σ = = ∑∑ , 1 1 n n i j i j i j i j w w w 3 w 3 ρ 3,3 σ 3 σ 3 w 3 w 2 ρ 3,2 σ 3 σ 2 w 3 w 1 ρ 3,1 σ 3 σ 1 w 2 w 3 ρ 2,3 σ 2 σ 3 w 2 w 2 ρ 2,2 σ 2 σ 2 w 2 w 1 ρ 2,1 σ 2 σ 1 w 1 w 3 ρ 1,3 σ 1 σ 3 w 1 w 2 ρ 1,2 σ 1 σ 2 w 1 w 1 ρ 1,1 σ 1 σ 1 6 3 Asset Portfolios 3-asset N-asset () () = = ∑ 1 E E n p j j j r w r () () () () = + + 1 1 2 2 3 3 E E E E p r w r w r w r σ σ σ σ σ σ σ = + + + + + 2 2 2 2 2 2 2 1 1 2 2 3 3 1 2 1,2 1 3 1,3 2 3 2,3 2 2 2 p w w w w w w w w w σ σ = = = ∑∑ 2 , 1 1 n n p i j i j j i w w 7 3 Asset Portfolio 0.2 2 x 0.12 2 3 2 x0.3x0.2x0.006 0.3 2 x 0.25 2 2 2 x0.5x0.2x0.0144 2 x0.5x0.3x0.01875 0.5 2 x 0.15 2 1 3 2 1 ∑ = 0.021 σ p = 14.5% E(r p ) = 0.5 x 10% + 0.3 x 18% + 0.2 x 7% = 11.8% E[r] σ w 1 2 3 Asset 1 10% 15% 0.5 0.02250 0.01875 0.01440 Asset 2 18% 25% 0.3 0.06250 0.00600 Asset 3 7% 12% 0.2 0.01440 Variance-Covariance Matrix 8 Diversification With Multiple Assets For a well-diversified portfolio (i.e. a portfolio with a large number of assets), the variance of the individual assets contributes little to the risk of the portfolio The risk depends largely on the covariances(correlations) between the returns on the assets. This point is expanded under the N-asset case next. 9 Equally Weighted Portfolios The equally weighted N-asset case allows us to generalize measurement of portfolio risk to a portfolio consisting of any number of assets The expected portfolio return for the N-asset case is still the weighted average of the expected returns of each asset (as seen with the 2-asset case) 10...
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Lecture08 - FINM2401 Financial Management Portfolio...

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