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CHAPTER SEVEN PORTFOLIO ANALYSIS. THE EFFICIENT SET THEOREM n THE THEOREM An investor will choose his optimal portfolio from the set of portfolios that.

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Presentation on theme: "CHAPTER SEVEN PORTFOLIO ANALYSIS. THE EFFICIENT SET THEOREM n THE THEOREM An investor will choose his optimal portfolio from the set of portfolios that."— Presentation transcript:

1 CHAPTER SEVEN PORTFOLIO ANALYSIS

2 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

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

4 THE EFFICIENT SET THEOREM THE FEASIBLE SET rPrP PP 0

5 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

6 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

7 THE EFFICIENT SET THEOREM THE OPTIMAL PORTFOLIO E rPrP PP 0

8 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%

9 CONCAVITY OF THE EFFICIENT SET PP rPrP A G r A = 5  A =20 r G =15  G =40

10 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

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

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

13 CONCAVITY OF THE EFFICIENT SET r P  P=+1  P=-1 A52020 B C D E F G

14 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

15 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

16 CONCAVITY OF THE EFFICIENT SET  G upper bound lower bound rPrP PP 

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

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

19 CONCAVITY OF THE EFFICIENT SET ACTUAL PORTFOLIO LOCATIONS  C D  F

20 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

21 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

22 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

23 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

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

25 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

26 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

27 DIVERSIFICATION 3 Unique Risk – mathematically can be expressed as

28 END OF CHAPTER 7


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