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Project1-Fall09

# Project1-Fall09 - Hrolessor lrank J Jones Bus 172 B Project...

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Hrolessor lrank J. Jones Bus. 172 B. Project I November 1,2009 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 INPUTS EXPECTED RETURN STANDARD DEVIATION ONE PLUS EXP RATE ONES Riskless Rate @ 5.00% 0.00% 105.00% s&P 500 114.72% 100.00% lA AllValue 114.5s% 100.00% lA All GroMh 114.31o/o 100.00% lA Monthlv Convertible Bond '111.91% 100.00% LB Aqqreqate Bond 109.25% 100.00% LB Hi-YId 110.76% 100.00% The EF (efficient frontier) and the CML (capital market line): EFFICIENT TRADE OFF LINE & EFFICIENT FRONTIER CURVE z t f F lrJ t o IJJ F o lJl o- x lrJ 0.25 0.2 0.15 0.1 0.05 0 0. -0.05 l--r- Seriesl ---r--- Series2 Series3 I 30.00% STAT{DARD DEVIATION

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Th The equation of the CML: f: f1* (fnl- rr / om) o f the PM No, there are no negative weights. If there were negative weights involved it would mean 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 9,92o/o and the expected retum is 18.20%. Comparing with the related EF point which is the standard deviationis9.92Yo and the expected return rs 14.90o/o, the EF and the point I selected both have the same risk (9.92%); however, the point I chose has the higher rate of retum (18.20%) than EF (14.90%). T'his is the prime reason why I chose this point. oo: w^(o^) 9.92%: wx (4.96%) Wx:2 e ono EFFICIENT FRONTIER CURVE EFFICIENT TRADE OFF LINE INDIVIDUAL ASSET INDEX STANDARD DEVIATION EXPECTED RETURN EXPECTED RETURN OPTIMAL GOMBINATION OF RISKY ASSETS IN TANGENT PORTFOLIO s&P 500 17.49o/o 14.72% 11.860/r lA AllValue 16.23Yo 14.55% 13.53% lA All GroMh 20.52o/o 14.3'l% 8.25% lA Monthly Gonvertible Bond 12.96% 11.9'l% 15.13% LB Aqqreqate Bond 6.34% 9.25% 39.46% LB Hi-YId 13.51% 't0.76% 11.78%
Risk free rate is 5oZ rp: ( w.f * rt+( w^ * r*) 0.1820:Wrf * 5o/o+(2* 0.1160) 0.1820: Wrf * 5oA+0.232 -0.05:W6*5o/o Wrf : -1 : -l00Yo From the calculation, it shows that lending -100% 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.OYo 9.92% '18.20% The point I selected: standard deviation is 9.92Yo, and the expected return is 18.20% Sharpe Ratio: (f.- fr ) I o^ The risk free rate ts 5Yo The Sharpe Ratio for the PM: (11.60%- 5n I 4.96% : 1.331 The Sharpe Ratio for the point I selected : (I8.20o/o - 5%) I 9.92% : 1.331 4. Identify the two points on the CML with risks 5.0% higher and 5 .0o/o lower than your personally optimal point and determine the Sharpe Ratios of these two points.

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