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FM12 Ch 07 Tool Kit

# FM12 Ch 07 Tool Kit - Chapter Chapter 7 Tool Kit for...

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8360eabc3b2248d44fb4229d7d3ee523369569d7.xls Chapter Michael C. Ehrhardt Page 1 06/15/2011 12/2/2006 Chapter 7. Tool Kit for Portfolio Theory and Other Asset Pricing Models PORTFOLIO RISK AND RETURN: THE TWO-ASSET CASE ATTAINABLE PORTFOLIOS: THE TWO ASSET-CASE Asset A Asset B Expected return, r hat 5% 8% 4% 10% EFFICIENT PORTFOLIOS (Section 7.1) Suppose there are two assets, A and B. w A is the percent of the portfolio invested in asset A. Since the total percents invested in the asset must add up to 1, (1-w A ) is the percent of the portfolio invested in asset B. The expected return on the portfolio is the weighted average of the expected returns on asset A and asset B. The standard deviation of the portfolio, σ p , is not a weighted average. It is: Standard deviation, σ Using the equations above, we can find the expected return and standard deviation of a portfolio with different percents invested in each asset. B A AB A A 2 B 2 A 2 A 2 A p ) W 1 ( W 2 ) W 1 ( W σ σ ρ σ σ σ - + - + = B ^ A A ^ A p ^ r ) w 1 ( r w r - + =

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8360eabc3b2248d44fb4229d7d3ee523369569d7.xls Chapter Michael C. Ehrhardt Page 2 06/15/2011 Correlation = 1 1.00 0.00 5.00% 4.0% 0.90 0.10 5.30% 4.6% 0.80 0.20 5.60% 5.2% 0.70 0.30 5.90% 5.8% 0.60 0.40 6.20% 6.4% 0.50 0.50 6.50% 7.0% 0.40 0.60 6.80% 7.6% 0.30 0.70 7.10% 8.2% 0.20 0.80 7.40% 8.8% 0.10 0.90 7.70% 9.4% 0.00 1.00 8.00% 10.0% Correlation = 0 1.00 0.00 5.00% 4.0% 0.90 0.10 5.30% 3.7% 0.80 0.20 5.60% 3.8% 0.70 0.30 5.90% 4.1% 0.60 0.40 6.20% 4.7% 0.50 0.50 6.50% 5.4% 0.40 0.60 6.80% 6.2% 0.30 0.70 7.10% 7.1% 0.20 0.80 7.40% 8.0% 0.10 0.90 7.70% 9.0% 0.00 1.00 8.00% 10.0% Proportion of Portfolio in Security A (Value of w A ) Proportion of Portfolio in Security B (Value of 1-w B ) r p σ p Proportion of Portfolio in Security A (Value of w A ) Proportion of Portfolio in Security B (Value of 1-w A ) r p σ p 3% 4% 5% 6% 7% 8% 9% 10% 11% 0% 5% 10% Ατ τ αιν αβ λε Σετ ο φ Ρ ισ κ /Ρ ετ υρ ν Χο μ β ιν ατ ιο Risk, sp Expected return 10% 0 Ατ τ αιν αβλε Σετ οφ Ρ ισ κ/Ρ ετ υρν Χομ βιν ατ ιο
8360eabc3b2248d44fb4229d7d3ee523369569d7.xls Chapter Michael C. Ehrhardt Page 3 06/15/2011 Correlation = -1 1.00 0.00 5.00% 4.0% 0.90 0.10 5.30% 2.6% 0.80 0.20 5.60% 1.2% 0.70 0.30 5.90% 0.2% 0.60 0.40 6.20% 1.6% 0.50 0.50 6.50% 3.0% 0.40 0.60 6.80% 4.4% 0.30 0.70 7.10% 5.8% 0.20 0.80 7.40% 7.2% 0.10 0.90 7.70% 8.6% 0.00 1.00 8.00% 10.0% Table 1 Expected Return and Standard Deviation under Various Assumptions 1.00 0.00 5.00% 4.0% 4.0% 4.0% 0.75 0.25 5.75% 5.5% 3.9% 0.5% 0.50 0.50 6.50% 7.0% 5.4% 3.0% 0.25 0.75 7.25% 8.5% 7.6% 6.5% Proportion of Portfolio in Security A (Value of w A ) Proportion of Portfolio in Security B (Value of 1-w A ) r p σ p Proportion of Portfolio in Security A (Value of w A ) Proportion of Portfolio in Security B (Value of 1-w A ) r p σ p Case I ρ AB = +1.0 Case II ρ AB = 0.0 Case III ρ AB = -1.0 3% 4% 5% 6% 7% 8% 9% 10% 11% 0% 5% Risk, sp Expected return 0% 2% 4% 6% 8% 10% 12% 0% 5% 10% 1

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