*CHAPTER EIGHTPORTFOLIO ANALYSIS

*THE EFFICIENT SET THEOREMTHE THEOREMAn investor will choose his optimal portfolio from the set of portfolios that offermaximum expected returns for varying levels of risk, andminimum risk for varying levels of returns

*THE EFFICIENT SET THEOREMTHE FEASIBLE SETDEFINITION: represents all portfolios that could be formed from a group of N securities

*THE EFFICIENT SET THEOREMTHE FEASIBLE SETrPsP0

*THE EFFICIENT SET THEOREMEFFICIENT SET THEOREM APPLIED TO THE FEASIBLE SETApply the efficient set theorem to the feasible setthe set of portfolios that meet first conditions of efficient set theorem must be identifiedconsider 2nd condition set offering minimum risk for varying levels of expected return lies on the western boundaryremember both conditions: northwest set meets the requirements

*THE EFFICIENT SET THEOREMTHE EFFICIENT SETwhere the investor plots indifference curves and chooses the one that is furthest northwestthe point of tangency at point E

*THE EFFICIENT SET THEOREMTHE OPTIMAL PORTFOLIO

ErPsP0

*CONCAVITY OF THE EFFICIENT SETWHY IS THE EFFICIENT SET CONCAVE?BOUNDS ON THE LOCATION OF PORFOLIOSEXAMPLE:Consider two securitiesArk Shipping CompanyE(r) = 5% s = 20%Gold Jewelry CompanyE(r) = 15% s = 40%

*CONCAVITY OF THE EFFICIENT SET sPrPAGrA = 5sA=20rG=15sG=40

*CONCAVITY OF THE EFFICIENT SETALL POSSIBLE COMBINATIONS RELIE ON THE WEIGHTS (X1 , X 2)X 2 = 1 - X 1Consider 7 weighting combinations

using the formula

*CONCAVITY OF THE EFFICIENT SETPortfolioreturnA 5B 6.7C 8.3D 10E 11.7F 13.3G 15

*CONCAVITY OF THE EFFICIENT SETUSING THE FORMULA

we can derive the following:

*CONCAVITY OF THE EFFICIENT SETrPsP=+1sP=-1A52020B6.71023.33C8.3 026.67D101030.00E11.72033.33F13.33036.67G154040.00

*CONCAVITY OF THE EFFICIENT SETUPPER BOUNDSlie on a straight line connecting A and Gi.e. all s must lie on or to the left of the straight linewhich implies that diversification generally leads to risk reduction

*CONCAVITY OF THE EFFICIENT SETLOWER BOUNDSall lie on two line segmentsone connecting A to the vertical axisthe other connecting the vertical axis to point Gany portfolio of A and G cannot plot to the left of the two line segmentswhich implies that any portfolio lies within the boundary of the triangle

*CONCAVITY OF THE EFFICIENT SETAGupper boundlower boundrPsP0

*CONCAVITY OF THE EFFICIENT SETACTUAL LOCATIONS OF THE PORTFOLIOWhat if correlation coefficient (r ij ) is zero?

*CONCAVITY OF THE EFFICIENT SETRESULTS:sB=17.94%sB=18.81% sB=22.36% sB=27.60% sB=33.37%

*CONCAVITY OF THE EFFICIENT SETACTUAL PORTFOLIO LOCATIONSBCDEF

*CONCAVITY OF THE EFFICIENT SETIMPLICATION:If rij < 0line curves more to leftIf rij = 0line curves to leftIf rij > 0line curves less to left

*CONCAVITY OF THE EFFICIENT SETKEY POINTAs long as -1 < r< +1 , the portfolio line curves to the left and the northwest portion is concavei.e. the efficient set is concave

*THE MARKET MODELA RELATIONSHIP MAY EXIST BETWEEN A STOCKS RETURN AN THE MARKET INDEX RETURN

where aiI = intercept term ri = return on security rI = return on market index Ib iI = slope terme iI = random error term

*THE MARKET MODELTHE RANDOM ERROR TERMS ei, Ishows that the market model cannot explain perfectlythe difference between what the actual return value is and what the model expects it to be is attributable to ei, I

*THE MARKET MODELei, I CAN BE CONSIDERED A RANDOM VARIABLEDISTRIBUTION:MEAN = 0VARIANCE = sei

*DIVERSIFICATIONPORTFOLIO RISKTOTAL SECURITY RISK: s2ihas two parts:

where = the market variance of index returns

= the unique variance of security i returns

*DIVERSIFICATIONTOTAL PORTFOLIO RISKalso has two parts: market and uniqueMarket Riskdiversification leads to an averaging of market riskUnique Riskas a portfolio becomes more diversified, the smaller will be its unique risk

*DIVERSIFICATIONUnique Riskmathematically can be expressed as