Assignment 2 IPT 1 PDF
Investment and Portfolio Theory 1 (6012B0233Y)
Universiteit van Amsterdam
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QUESTION 3 DATA ANALYSIS VRSN STOCK SAMENVATTING UITVOER Gegevens voor de regressie Meervoudige 0,644054 R Aangepaste 0,414573 kleinste kwadraat Standaardfout 0,01677 Waarnemingen 2515 Vrijheidsgraden Kwadratensom Gemiddelde kwadratenF Significantie F Regressie 1 0,500958 0,500958 1781,301 Storing 2513 0,706734 Totaal 2514 1,207692 Standaardfout statistische gegevens Hoogste Laagste Hoogste Snijpunt 0,001294 2,854315 0,004348 0,002184 0,002184 1,058873 0,025089 42,20546 1,009677 1,10807 1,009677 1,10807 DATA ANALYSIS STOCK SAMENVATTING UITVOER Gegevens voor de regressie Meervoudige 0,776472 R Aangepaste 0,602751 kleinste kwadraat Standaardfout 0,008974 Waarnemingen 2516 Vrijheidsgraden Kwadratensom Gemiddelde kwadratenF Significantie F Regressie 1 0,307415 0,307415 3817,046 0 Storing 2514 0,202471 Totaal 2515 0,509886 Standaardfout statistische gegevens Hoogste Laagste Hoogste Snijpunt 0,829397 0,013425 61,78225 0 0,803073 0,855721 0,803073 0,855721 DATA ANALYSIS FB STOCK SAMENVATTING UITVOER Gegevens voor de regressie Meervoudige0,31829 R Aangepaste 0,100319 kleinste kwadraat Standaardfout 0,025617 Waarnemingen 910 Vrijheidsgraden Kwadratensom Gemiddelde kwadratenF Significantie F Regressie 1 0,067169 0,067169 102,3577 Storing 908 0,595846 Totaal 909 0,663015 Standaardfout statistische gegevens Hoogste Laagste Hoogste Snijpunt 0,00146 0,001499 0,974112 0,330261 0,004402 0,004402 1,044551 0,103245 10,1172 0,841924 1,247178 0,841924 1,247178 DATA ANALYSIS APL SAMENVATTING UITVOER Gegevens voor de regressie Meervoudige 0,587375 R Aangepaste 0,344748 kleinste kwadraat Standaardfout 0,01748 Waarnemingen 2516 Vrijheidsgraden Kwadratensom Gemiddelde kwadratenF Significantie F Regressie 1 0,404612 0,404612 1324,22 Storing 2514 0,768146 Totaal 2515 1,172758 Standaardfout statistische gegevens Hoogste Laagste Hoogste Snijpunt 0,620978 0,534671 0,00122 0,00122 0,951523 0,026148 36,38984 0,900249 1,002797 0,900249 1,002797 SD of daily excess returns SD of systematic risk component SD of idiosyncratic risk component 0 0 X the annualized risk premium is the annualized return minus the risk free rate. In order to calculate the return of the Russell we used this formula: and took the average of the daily returns and at least squared this number to the power of 252 days to get the annualized return. To get the annual risk premium we used the following formula: Rm rm rf. Rm So the annualized idiosyncratic risk of the Russell Index is zero and the annualized return of the Russell Index is b) The Single Index Model is as follows: ri E(ri) ei To calculate the and the annual idiosyncratic risk we did a regression on Excel and regressed for each stock the daily excess return (explainable variable Y) with respect to the daily excess return of the market index (unexplainable variable X). Because is a coefficient, the is shown in the output summary of the regression analysis shown here above. Estimating for each stock is also possible with the output summary, because you have to take the standard deviation of the residuals of all given dates. Later on, we annualized these standard deviations multiplying with (because there exists 252 trading days) and then at least you have to square these standard deviations of the residuals and you have annual idiosyncratic risk of each stock. For calculating the annual risk premium of each stock, we did first calculated the daily risk premium which equals systematic risk, because you can assume that the daily rate is zero. The daily risk premium SD of the daily excess return of RUA betai At least, we annualized these risk premium multiplying the daily risk premiums the root of 252. VRSN FB APL Annual Beta 1 0 1 0 Annual risk premium c) i) To calculate the active alpha and active beta for the portfolio we have to use the procedure. Step 1: w0i Stock VRSN FB APL w0i 0 0 0 Step 2: w0i Stock w0i VRSN FB APL 1 0 step 3: (1 0) (0 0) 0 step 4: So the expected active alpha of the portfolio is and the active beta of the portfolio is ii) For calculating how much to invest in each asset, we have to continue with the procedure: step 5: 0) 0) 0, or step 6: wA0 ( The ) is given in the matrix above and is 0 wA 0 0 step 7: 0 en 1 1 0 0 step 8: E(Rp) E(Rm) and 0 E(Rp) 0) 0, or step 9: (0 0 0, or
Assignment 2 IPT 1 PDF
Vak: Investment and Portfolio Theory 1 (6012B0233Y)
Universiteit: Universiteit van Amsterdam
