The expected return on the portfolio is the weighted

Info iconThis preview shows page 1. Sign up to view the full content.

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

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...
View Full Document

Ask a homework question - tutors are online