Graphical derivation of beta A firm wishes to estimate graphically the betas for
ID: 2765375 • Letter: G
Question
Graphical derivation of beta A firm wishes to estimate graphically the betas for assets, A and B. It has gathered the return data shown in the following table market portfolio and for both assets over the last 10 years, 2006-2015. On a set of "marker return (x-axis) -asset return (y-axis)"axes,use the data given to draw the characteristic line (x-axis)asset A and foe asset B. Us the characteristic line from a to estimate the betas fo assetsA and b. Use the betas found in part b to comment on the relatyive risks of A and B.Explanation / Answer
a = Y - Bx = 9.8-0.7906*4.5
= 6.2423
FOR ASSETS A YEAR Return Return xy x2 x-x x-x2 y-y y-y2 Y market 2006 11 6 66 36 1.5 2.25 1.2 1.44 2007 8 2 16 4 -2.5 6.25 -1.8 3.24 2008 -4 -13 52 169 -17.5 306.25 -13.8 190.44 2009 3 -4 -12 16 -8.5 72.25 -6.8 46.24 2010 0 -8 0 64 -12.5 156.25 -9.8 96.04 2011 19 16 304 256 11.5 132.25 9.2 84.64 2012 14 10 140 100 5.5 30.25 4.2 17.64 2013 18 15 270 225 10.5 110.25 8.2 67.24 2014 12 8 96 64 3.5 12.25 2.2 4.84 2015 17 13 221 169 8.5 72.25 7.2 51.84 98 45 1153 1103 900.5 563.6 B = Exy-nxy/Ex2-n(x)2 = 1153-10*9.8*4.5/1103-10*4.5*4.5 = 0.7906a = Y - Bx = 9.8-0.7906*4.5
= 6.2423
hence character line is 6.24 + 0.7906 (Rm) total risk of market = E(x-x)2/n = 90% total risk of stock = 563.6/10 = 56.36% Systematic risk = B2 * market risk = 0.79*0.79 *.90 = 56.16% unsystematic risk = total - sys.risk = 56.36-56.16 = 0.20% FOR ASSETS B YEAR Return Return xy x2 x-x x-x2 y-y y-y2 Y market 2006 16 6 96 36 1.5 2.25 1.7 2.89 2007 11 2 22 4 -2.5 6.25 -3.3 10.89 2008 -10 -13 130 169 -17.5 306.25 -24.3 590.49 2009 3 -4 -12 16 -8.5 72.25 -11.3 127.69 2010 -3 -8 24 64 -12.5 156.25 -17.3 299.29 2011 30 16 480 256 11.5 132.25 15.7 246.49 2012 22 10 220 100 5.5 30.25 7.7 59.29 2013 29 15 435 225 10.5 110.25 14.7 216.09 2014 19 8 152 64 3.5 12.25 4.7 22.09 2015 26 13 338 169 8.5 72.25 11.7 136.89 143 45 1885 1103 900.5 1712.1 B = Exy-nxy/Ex2-n(x)2 = 1885-10*14.3*4.5/1103-10*4.5*4.5 = 1.378 a = Y - Bx = 14.30-1.378*4.5 = 8.1 hence character line is 8.1 + 1.378 (Rm) total risk of market = E(x-x)2/n = 90% total risk of stock = 1712/10 = 171.2% Systematic risk = B2 * market risk = 1.378*1.378*90 = 122.642 % unsystematic risk = total - sys.risk = 171-122 = 49 %Related Questions
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