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CAPM 4 Assets Expected rate of return Standard deviation p security 1 p security 2 p security 3 p security 4 Security 1 12.00% 10.00% 1.0000 0.0500 0.3500 0.2500 Security 2 15.00% 14.00% 0.0500 1.0000 0.6000 -0.4000 Security 3 13.00% 15.00% 0.3500 .6000 1.0000 0.4500 Security 4 25.00% 26.00% 0.2500 -0.4000 0.4500 1.0000 Risk-free interest rate 5.00% Efficient frontier of risky assets: The picture can't be - a= 0.210356735 b= 1.469289662 C= 0.0035569 MARKET PORTFOLIO RM = 23.2538% OM = 5.2495% Sharpe 3.47726469 X1= 26.1077% X2= 137.2046% X3= -128.069% X4= 64.7565% 3.5 composition of M 2.5 2 1.5 0 4 0 1 01 1 18% 02 0.5 0 . 2 39% 03 -0.5 0.2 0.4 90 0.8 3 04 -1 -36% security 1 security 2 security 3 security 4 cov with M 0.0011 0.0015 0.0012 0.0030 B 0.3835 0.5478 0.4383 1.0957 systematic risk 0.0201 0.0288 0.0230 0.0575 specific risk 0.0980 0.1370 0.1482 0.2536 total risk .1000 0.1400 0.1500 .2600 contribution to oM 0.0053 0.0395 -0.0295 0.0372Market data Consider a market with only the following four stocks with the following returns and standard deviations: S1 S2 83 S4 Return % 8 15 17 25 0 % 10 14 18 26 With correlation coeficients Pi,j : P1,2 = 0.05; P1,3 = 0.35; P1,4 = 0, 25; p2,3 = 0, 60; p2,4 = 0, 40; p3,4 = 0, 45 and Risk Free Rate Return : Trfr = 5%Questions Using the provided Excel spreadsheet find the optimal portfolio, and answer the following ques- tions: 1. Which is the expected return of the portfolio? 2. Which is the standard deviation (risk) of the portfolio? 3. Which are the weights of each asset in the portfolio w1, w2, w3, w4? 4. Is the specific risk of the portfolio the weighted average of assets specific risk? 5. Is the total risk of the portfolio the weighted average of assets systematic risk? 6. Which return can expect the investor if leverages the optimal portfolio with risk free rate asset and is willing to accept a op = 20%? 7. Which composition (weights of assets A, B, C, D and Risk Free Asset respectively, separated with ";") will have his new leveraged portfolio? 8. Which of the four securitiess could be labelled as agressive in the equity market jargon? Questions 9, 10, 11 and 12 refer only to Stock 3. 9. By means of diversification, how much variance can be removed from S3? 10. How much variance of S3 can not be diversified? 11. Which is the total risk o3 of S3? 12. A financial analyst estimates that the Expected Return of S3 is 22%. Based in the SML valuation, is the asset underpriced or overpriced? Finally, evaluate the change that would entail in the initial optimal portfolio a change in the correlation coefficients of stock 1 to: p1,2 = 0, 15, p1, 3 = 0, 45, p1,4 = 0, 35 13. Has the risk of the portfolio increased or decreased? 14. If an investor invests 10000 EUR in this optimal portfolio, which transaction and for which amount will make with S1
