Graphical derivation of beta A fund manager wishes to estimate graphically the betas for two assets, X and Y. It has gathered the return data shown in the following table for the market portfolio and for both assets over the past 10 years, 2010–2020.

a. On a set of “market return (x-axis)–asset return (y-axis)” axes, plot the data given and draw the characteristic line for asset X and for asset Y.

b. Use the characteristic lines from part a to estimate the betas for assets X and Y.

c. Use the betas found in part b to comment on the relative risks of assets X and Y.

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Year 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020 Market portfolio 4% 5 -3 5 6 12 15 9 5 4 6 Annual return Asset X 11% 8 -5 4 3 19 22 18 11 12 15 Asset Y 16% 11 -6 4 5 25 30 27 24 18 25