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CHAPTER SEVEN PORTFOLIO ANALYSIS

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THE EFFICIENT SET THEOREM n THE THEOREM An investor will choose his optimal portfolio from the set of portfolios that offer 3 maximum expected returns for varying levels of risk, and 3 minimum risk for varying levels of returns

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THE EFFICIENT SET THEOREM n THE FEASIBLE SET DEFINITION: represents all portfolios that could be formed from a group of N securities

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THE EFFICIENT SET THEOREM THE FEASIBLE SET rPrP PP 0

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THE EFFICIENT SET THEOREM n EFFICIENT SET THEOREM APPLIED TO THE FEASIBLE SET Apply the efficient set theorem to the feasible set 3 the set of portfolios that meet first conditions of efficient set theorem must be identified 3 consider 2nd condition set offering minimum risk for varying levels of expected return lies on the “western” boundary 3 remember both conditions: “northwest” set meets the requirements

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THE EFFICIENT SET THEOREM n THE EFFICIENT SET where the investor plots indifference curves and chooses the one that is furthest “northwest” the point of tangency at point E

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THE EFFICIENT SET THEOREM THE OPTIMAL PORTFOLIO E rPrP PP 0

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CONCAVITY OF THE EFFICIENT SET n WHY IS THE EFFICIENT SET CONCAVE? BOUNDS ON THE LOCATION OF PORFOLIOS EXAMPLE: 3 Consider two securities – Ark Shipping Company E(r) = 5% = 20% – Gold Jewelry Company E(r) = 15% = 40%

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CONCAVITY OF THE EFFICIENT SET PP rPrP A G r A = 5 A =20 r G =15 G =40

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CONCAVITY OF THE EFFICIENT SET n ALL POSSIBLE COMBINATIONS RELIE ON THE WEIGHTS (X 1, X 2 ) X 2 = 1 - X 1 Consider 7 weighting combinations using the formula

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CONCAVITY OF THE EFFICIENT SET Portfolioreturn A 5 B 6.7 C 8.3 D 10 E 11.7 F 13.3 G 15

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CONCAVITY OF THE EFFICIENT SET n USING THE FORMULA we can derive the following:

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CONCAVITY OF THE EFFICIENT SET r P P=+1 P=-1 A52020 B6.71023.33 C8.3 026.67 D101030.00 E11.72033.33 F13.33036.67 G154040.00

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CONCAVITY OF THE EFFICIENT SET n UPPER BOUNDS lie on a straight line connecting A and G i.e. all must lie on or to the left of the straight line 3 which implies that diversification generally leads to risk reduction

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CONCAVITY OF THE EFFICIENT SET n LOWER BOUNDS all lie on two line segments 3 one connecting A to the vertical axis 3 the other connecting the vertical axis to point G any portfolio of A and G cannot plot to the left of the two line segments which implies that any portfolio lies within the boundary of the triangle

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CONCAVITY OF THE EFFICIENT SET G upper bound lower bound rPrP PP

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CONCAVITY OF THE EFFICIENT SET n ACTUAL LOCATIONS OF THE PORTFOLIO What if correlation coefficient ( ij ) is zero?

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CONCAVITY OF THE EFFICIENT SET RESULTS: B =17.94% B =18.81% B =22.36% B =27.60% B =33.37%

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CONCAVITY OF THE EFFICIENT SET ACTUAL PORTFOLIO LOCATIONS C D F

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CONCAVITY OF THE EFFICIENT SET n IMPLICATION: If ij < 0line curves more to left If ij = 0line curves to left If ij > 0line curves less to left

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CONCAVITY OF THE EFFICIENT SET n KEY POINT As long as -1 < the portfolio line curves to the left and the northwest portion is concave i.e. the efficient set is concave

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THE MARKET MODEL n A RELATIONSHIP MAY EXIST BETWEEN A STOCK’S RETURN AN THE MARKET INDEX RETURN where intercept term r i = return on security r I = return on market index I slope term random error term

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THE MARKET MODEL THE RANDOM ERROR TERMS i, I shows that the market model cannot explain perfectly the difference between what the actual return value is and what the model expects it to be is attributable to i, I

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THE MARKET MODEL i, I CAN BE CONSIDERED A RANDOM VARIABLE DISTRIBUTION: 3 MEAN = 0 VARIANCE = i

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DIVERSIFICATION n PORTFOLIO RISK TOTAL SECURITY RISK: i 3 has two parts: where = the market variance of index returns = the unique variance of security i returns

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DIVERSIFICATION n TOTAL PORTFOLIO RISK also has two parts: market and unique 3 Market Risk – diversification leads to an averaging of market risk 3 Unique Risk – as a portfolio becomes more diversified, the smaller will be its unique risk

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DIVERSIFICATION 3 Unique Risk – mathematically can be expressed as

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END OF CHAPTER 7

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