FM11_Ch_05_Tool_Kit

# The expected return on the portfolio is the weighted

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Unformatted text preview: is the weighted average of the expected returns on asset A and asset B. ^ ^ ^ r p = w A r A + (1 − w A ) r B The standard deviation of the portfolio, σp , is not a weighted average. It is: 22 2 σ p = WAσ A + (1 − WA ) 2 σ B + 2WA (1 − WA ) ρA B σ A σ B ATTAINABLE PORTFOLIOS: THE TWO ASSET-CASE Asset A 5% 4% Expected return, r hat Standard deviation, σ Asset B 8% 10% Using the equations above, we can find the expected return and standard deviation of a portfolio with different percents invested in each asset. Correlation = 1 Proportion of Proportion of P ortfolio in Portfolio in Security A Security B (Value of wA) (Value of 1-wB ) 1.00 0.00 0.90 0.10 0.80 0.20 0.70 0.30 0.60 0.4 0 0.50 0.50 0.4 0 0.60 0.30 0.70 0.20 0.80 0.10 0.90 0.00 1.00 ρΑ Β = + 1 : σp rp 5.00% 5.30% 5.60% 5.90% 6.20% 6.50% 6.80% 7.10% 7.4 0% 7.70% 8.00% 4 .0% 4 .6% 5.2% 5.8% 6.4 % 7.0% 7.6% 8.2% 8.8% 9.4 % 10.0% Α ττα ιν αβ λ ε Σ ε τ ο φ Ρισ κ/ Ρετ υ ρ ν Χο µβιν α τιο ν σ E xp e ct e d r e t u r n 10 % 5% 0% 2% Correlation = 4% 6% 8% Risk, sp 1 0% 12% 0 Proportion of Proportion of P ortfolio in Portfolio in Security A Security B (Value of wA) (Value of 1-wA) 1.00 0.00 0.90 0.10 0.80 0.20 0.70 0.30 0.60 0.4 0 0.50 0.50 0.4 0 0.60 0.30 0.70 0.20 0.80 0.10 0.90 0.00 1.00 σp rp 5.00% 5.30% 5.60% 5.90% 6.20% 6.50% 6.80% 7.10% 7.4 0% 7.70% 8.00% 4 .0% 3.7% 3.8% 4 .1% 4 .7% 5.4 % 6.2% 7.1% 8.0% 9.0% 10.0% ρ ΑΒ = 0 : Α ττα ιν αβλ ε Σ ετ ο φ Ρισ κ/Ρ ετυ ρν Χοµ βιν ατ ιον σ E xpe ct e d r et ur n 10% 5% 0% 2% Correlation = 4% 6% 8% Risk, sp 10% 12% -1 Proportion of Portfolio in Security A (Value of wA) 1.00 0.90 0.80 0.70 0.60 0.50 0.4 0 0.30 0.20 0.10 0.00 Proportion of P ortfolio in Security B (Value of 1-wA) 0.00 0.10 0.20 0.30 0.4 0 0.50 0.60 0.70 0.80 0.90 1.00 σp rp 5.00% 5.30% 5.60% 5.90% 6.20% 6.50% 6.80% 7.10% 7.4 0% 7.70% 8.00% 4 .0% 2.6% 1.2% 0.2% 1.6% 3.0% 4 .4 % 5.8% 7.2% 8.6% 10.0% ρ Α Β = −1 : Α τ τα ιν α βλ ε Σ ετ ο φ Ρ ισ κ/Ρ ετυ ρν Χ οµ βιν ατ ιον σ 1 0% E xp e ct e d r e t u r n 983ee486f2b383ac35dd7b729bba9bf726517f7e.xls 5% 0% 0% 2% 4 % 6% 8 % 10 % 12% Risk, sp ATTAINABLE AND EFFICIENT PORTFOLIOS: MANY A...
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