Chapter 6 Efficient Diversification I Diversification Portfolio Risk a Market Risk risk that remains even after diversification i Also called Systematic Risk or Nondiversifiable Risk b Unique Risk risk that can be eliminated through diversification i Also called firm specific risk nonsystematic risk diversifiable risk ii SEE PAGE 146 Diagram II Asset Allocation with 2 Risky Assets a Covariance and Correlation i Even though the portfolios expected return is the weighted average of the fund a portfolios standard deviation can be less than either individual stocks standard deviation ii Correlation is denoted by rabge from 1 to 1 1 a 1 perfect negative correlation b 1 perfect positive correlation c 0 returns are unrelated to each other b The 3 Rules of a Two Risky Asset Portfolio i The rate if return on the portfolio is a weighted average of the returns on the component securities with the invesments porpotrions as weights 1 rp wbrb wsrs ii The Expected rate of return of the portfolio os a weighted average of the expected returns on the component securities with the same portfolio proportions as weights 1 E rp wbE rb wsE rs iii The variance of a rate of return 1 2 p wb b 2 ws s 2 2 wb b ws s bs a bs correlation coefficient between the two assets c The Mean Variance Criterion i If a portfolio lies northwest of an oter portfolio then all investors would prefer that portfolio a If we add a risk free asset to the portfolio we can draw a line from this point to the frontier This Line is Called the Capital Allocation Line CAL i Slope Sharpe Ratio ratio of excess return to standard deviation 1 SP E rP rf P 2 You want a large Shape Ratio ii Keep moving CAL Up until it is tangent to the Fronteir only once this is called the Optimal Risky Portfolio the best combination of risky assets to be mized with safe assets to form the complete portfolio b SEE Page 160 III The Optimal Risky Portfolio with a Risk Free Asset 1 E rA E rB and A B c Seperation Principal into two independent tasks the property that implies portfolio can be separated i 1 determination of the optimal risky portfolio 1 technical problem ii 2 the personal choice of the best mix of the risky portfolio and the IV Single Index Asset Market risk free asset a Too many securities to construct efficency frontiers for every combination i Use index to model this b Ri iRm ei i Variance Systematic Risk Firm Specific Risk i Ri Rate of return in excess of reisk free rate 1 Ri ri rf ii Rm Excess return on a broad market fund 1 reflects the influence of economy wide or macroeconomic events that effect ALL stocks iii B Beta the sensitivity od a securities return to the systematic risk factor 1 sensitivity to macroecominc evetns 2 Systematic Risk iv ei Firm Specific Risk component of return variability that is independent of broad market events v expected return of the stock beyond any return induced by movements in the market index 1 Positive Alpha means stock is under priced
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