Portfolio Analysis Project

Portfolio Analysis Project - Professor Frank J. Jones Bus....

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Professor Frank J. Jones Bus. 172 B. Project 1 November 2, 2009 1. Using these date in the portfolio optimization program develop the EF (efficient frontier). Also develop the CML (capital market line). Provide the equation for the CML. What is the composition of the PM? The data in the portfolio optimization: PORTFOLIO OPTIMIZATION ONE PLUS INPUTS EXPECTED STANDARD EXP RATE RETURN DEVIATION {1+E®} ONES Riskless Rate ® 5.00% 0.00% 105.00% 14.72% 17.49% 114.72% 100.00% IA All Value 14.55% 16.23% 114.55% 100.00% IA All Growth 14.31% 20.52% 114.31% 100.00% IA Monthly Convertible Bond 11.81% 12.96% 111.81% 100.00% LB Aggregate Bond 9.25% 6.34% 109.25% 100.00% LB Hi-Yld 10.76% 13.51% 110.76% 100.00% The EF (efficient frontier) and the CML (capital market line): EFFICIENT TRADE OFF LINE & EFFICIENT FRONTIER CURVE -0.05 0 0.05 0.1 0.15 0.2 0.25 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00% STANDARD DEVIATION EXPECTED RETURN Series1 Series2 Series3
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The equation of the CML: r = r f + ( r m - r f / σ m ) σ The composition of the PM: EFFICIENT FRONTIER CURVE EFFICIENT TRADE OFF LINE INDIVIDUAL ASSET INDEX STANDARD DEVIATION EXPECTED RETURN EXPECTED RETURN OPTIMAL COMBINATION OF RISKY ASSETS IN TANGENT PORTFOLIO 17.49% 14.72% 11.86% IA All Value 16.23% 14.55% 13.53% IA All Growth 20.52% 14.31% 8.25% IA Monthly Convertible Bond 12.96% 11.81% 15.13% LB Aggregate Bond 6.34% 9.25% 39.46% LB Hi-Yld 13.51% 10.76% 11.78% No, there are no negative weights. If there are negative weights involved this means the investor who borrows money to fund his/her purchase of the risky assets has free weights. 2. Select the point on the CML which is your personally optimal point. Why did you select this point? At this point, how much borrowing/ lending of the risk free asset is involved? The point which I selected is the standard deviation is 9.92% and the expected return is 18.20%. Comparing with the related EF point which is the standard deviation is 9.92% and the expected return is 14.90%, the EF and the point I selected both have the same risk (9.92%); however, the point I chose has a higher rate of return (18.20%) than the EF (14.90%). This is the reason why I would chose this point. σ p = w x x ) 9.92% = w x (4.96%) w x = 2 Risk free rate is 5%
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r p = ( w rf * r f ) + ( w x * r x ) 0.1820 = w rf * 5% + (2* 0.1160) 0.1820 = w rf * 5% + 0.232 -0.05 = w rf * 5% w rf = -1 = -100% From the calculation, it shows that lending -1% of risk free asset is involved. 3. What is the Sharpe Ratio for this PM and your personally optimal point? Standard Deviation Expected Return OPTIMAL COMBINATION 4.96% 11.60% EFFICIENT TRADE OFF LINE 0.00% 0.00% 5.00% 100.00% 4.96% 11.60% 200.0% 9.92% 18.20% The point I selected: standard deviation is 9.92%, and the expected return is 18.20% Sharpe Ratio= ( r m - r f ) / σ m The risk free rate is 5% The Sharpe Ratio for the PM = (11.60% - 5%) / 4.96% = 1.331 The Sharpe Ratio for the point I selected = (18.20% - 5%) / 9.92% = 1.331 4. Identify the two points on the CML with risks 5.0% higher and 5.0% lower than your
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Portfolio Analysis Project - Professor Frank J. Jones Bus....

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