Principal Component Analysis (PCA) is a stable and good way of calculating VaR on a portfolio using a modelbuilding approachThere has been several attempts to estimate factors for a PCA analysis. The well known model, for a longperiod of time, below can be usedFactor loadingsPCA modelPC1PC2PC310,216-0,5010,62720,331-0,4290,12930,372-0,267-0,15740,392-0,11-0,25650,4040,019-0,355Factor scoresFactorScorePC 117,55PC 24,77PC 32,08Question 2.3What is the 99% 10 day VaR for the portfolio using all three factors estimated in the PCA modelWould you use all the factors in reality

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Answered: Principal Component Analysis (PCA) is a…

Essentials Of Investments

11th Edition

ISBN:9781260013924

Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.

Chapter1: Investments: Background And Issues

Section: Chapter Questions

Problem 1PS

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A diagram of the CML and SML for the market M, risk-free asset ry, an inefficient portfolio P, and a complete portfolio C is shown below. The diagram is not to scale. E(r) E(13) CML & CALP E(12) P C E(r) M 01 02 03 P βρ SML M Вм The values of the labeled variables are E[1] = 3.0%, E[12] = 10.3%, E[3] = 16.7%, σ₁ = 17.9%, σ = 30.0%, 03 = 44.3%. What is the standard deviation of nonsystematic risk for the complete portfolio σc under the CAPM? O a. 0.1374 O b. 0.1180 O c. 0.0988 d. 0.1105 O e. 0.0791 O f. 0.0913 Og. 0.0858 O h. 0.1443
2. The following table gives information on the return and variance of assets A and B, whose covariance is 0.0003: A B 0} 0,0009 0,0012 E (R₂) 0,05 0,06 a. Does the portfolio (1/3 of A and 2/3 of B) dominate the portfolio (2/3 of A and 1/3 of B)? b. Does the portfolio (1/2, 1/2) belong to the efficient frontier? c. If there were the possibility of lending and borrowing at 2%, would the portfolio (1/2, 1/2) belong to the new efficient frontier?
The Sharpe ratio Select one: O is computed using idiosyncratic risk only is computed using systematic risk only Ois maximized for the risk-free asset is the highest for a minimum variance portfolio is the same along the capital market line
6. On the basis of the utility formula below, which investment would you select if you were risk averse with A = 4? Standard Expected return E(t) deviation Investment 0.12 0.30 0.15 0.50 0.21 0.16 0.24 0.21
Manipulating CAPM Use the basic equation for the capital asset pricing model (CAPM) to work each of the following problems. a. Find the required return for an asset with a beta of 1.48 when the risk-free rate and market return are 8% and 13%, respectively. b. Find the risk-free rate for a firm with a required return of 14.684% and a beta of 1.47 when the market return is 12%. c. Find the market return for an asset with a required return of 12.040% and a beta of 0.95 when the risk-free rate is 5%. d. Find the beta for an asset with a required return of 13.312% when the risk-free rate and market return are 10% and 12.3%, respectively. C a. The required return for an asset with a beta of 1.48 when the risk-free rate and market return are 8% and 13%, respectively, is %. (Round to two decimal places.)
<Urgent> please answer M9,M10,M11
We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
In order to create an efficient set of portfolios thru optimization using concepts from Markowitz portfolio theory, you would need to forecast only 2 variables including expected return and standard deviation or variance for the asset classes or securities in focus. True or false
Please calculate CAPM of Asset J with the following information: where, kj = required return on asset j, Rf = risk-free rate of return, (6%) bj = beta coefficient for asset j, (1.75) %3D Rm = market return. (10%) The equation for CAPM is kj = Rf + [bj x (Rm - Rf)] kj = Solve for required return on asset j (kj is CAPM) Please be detailed when answering and show all work, thank you.

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