Case Study - Measuring Stock Market Risk
One measure of the risk or volatility of an individual stock is the standard deviation of the total return (capital appreciation plus dividends) over several periods of time. Although the standard deviation is easy to compute, it does not take into account the extent to which the price of a given stock varies as a function of a standard market index, such as the S&P 500.
As a result, many financial analysts prefer to use another measure of risk referred to as beta. Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock and the independent variable is the total return for the stock market. For this case problem we will use the S&P 500 index as the measure of the total return for the stock market, and an estimated regression equation will be developed using monthly data. The beta for the stock is the slope of the estimated regression equation (b1). The data contained in the file named Beta provides the total return (capital appreciation plus dividends) over 36 months for eight widely traded common stocks and the S&P 500.
The value of beta for the stock market will always be 1; thus, stocks that tend to rise and fall with the stock market will also have a beta close to 1. Betas greater than 1 indicate that the stock is more volatile than the market, and betas less than 1 indicate that the stock is less volatile than the market. For instance, if a stock has a beta of 1.4, it is 40% more volatile than the market, and if a stock has a beta of .4, it is 60% less volatile than the market.
Managerial Report
You have been assigned to analyze the risk characteristics of these stocks.Conduct analysis in RStudio.
- A Compute descriptive statistics for each stock and the S&P 500. Comment on your results. Which stocks are the most volatile?
- B Compute the value of beta for each stock. Which of these stocks would you expect to perform best in an up market? Which would you expect to hold their value best in a down market?
- C Comment on how much of the return for the individual stocks is explained by the market.
Beta file:
Month, Microsoft, Exxon Mobil, Caterpillar, Johnson & Johnson, Mcdonald's, Sandisk, Qualcomm, Procter & Gamble, S&P 500 Jan-03,-0. 08201,-0.02261,-0.0304,-0.00186,-0.11443,-0.24867,0.0349,0.000465,-0.027415 Feb-03, 0. 00211, 0.00293, 0. 06867,-0.01781, -0.04424,0.09363,-0.08178, -0.043356,-0.017004 Mar-03,0. 02152, 0.02734, 0.04681, 0. 10334,0.06245,0.00839, 0.04251,0.087833,0.008358 Apr-03, 0. 05576, 0.00715, 0.07622,-0.02609, 0.18257,0.43876,-0.11444, 0.013588, 0.081044 May-03,-0. 03717, 0. 04119,-0.00856,-0.03141, 0.09532, 0.50165, 0.05395, 0.021925, 0.050899 Jun-03,0. 04185,-0.01346,0.06731,-0.04876,0.17779,0.1164,0.07124,-0.028752,0.011322 Jul-03,0.03003, -0.00919,0.21847,0.00174, 0.04306, 0.39734, 0.04285,-0.009587,0.016224 Aug-03,0. 00417, 0.06661, 0.06462,-0.03804,-0.02564,0.06633, 0.10459,-0.006601,0.017873 Sep-03, 0.04827, -0. 02918,-0.04163,-0.00121,0.04996, 0.05409,0.00823,0.063352, -0.011944 Oct-03, -0. 05396, -0.00055, 0.06987,0.01636, 0.06202,0.26491, 0.13967,0.063833, 0.054962 Nov-03,-0. 01645, -0.00355, 0.0378,-0.0157,0.0412,0.00273,-0.06043,-0.020857,0.007129 Dec-03,0. 06457, 0.1326, 0.09165, 0.04787,-0.03121,-0. 24276,0.21055,0.037822,0.050765 Jan-04,0.01023, -0. 00512,-0.05444, 0.03407,0.03665,-0.11275,0.08678, 0.01657,0.017276 Feb-04, -0. 04051, 0. 03996,-0.03046, 0.01367,0.09946,-0.06372,0.07763, 0.014147, 0.012209 Mar-04,-0.06031,-0.01375, 0.04383,-0.05917,0.00954, 0.11566, 0.05072,0.02312,-0.016359 Apr-04,0. 04813, 0.02308,-0.01227,0.06526, -0.0469,-0.18371,-0.05778, 0.013063, -0.016791 May-04, 0. 00383, 0.0228,-0.03062,0.03637,-0.03048,0.06479,0.07541,0.019574,0.012083 Jun-04,0. 08883, 0.02682, 0.05428,-0.00018, -0.01515,-0.12008,0.08812,0.009831,0.017989 Jul-04,-0. 00245, 0.04256,-0.06974,-0.00772,0.05769, 0. 12125,-0.05166,-0.037472,-0.034291 Aug-04,-0. 03896, 0. 00151,-0.01075, 0.05636,-0.01745, -0.03988,0.10157,0.07325,0.002287 Sep-04, 0. 01282, 0.04837, 0. 1066, -0.03046,0.03738, 0.24711, 0. 02602,-0.033053,0.009364 Oct-04,0. 01157, 0.01842, 0. 00622, 0.03639,0.03996,-0.28331,0.06557,-0.049704,0.014014 Nov-04,0. 06864, 0.04673, 0.1367, 0.03811, 0. 07341, 0.08194,0.00048, 0.044939,0.038595 Dec-04,-0.00336, 0. 0002, 0.0651, 0.05139, 0. 04294,0.10585, 0.02042, 0.029918,0.032458 Jan-05,-0. 01647,0. 00663,-0.08204, 0.02018,0.01029,-0.01081,-0.1217,-0.029049,-0.02529 Feb-05,-0. 03957,0.23217,0.06678, 0.01832, 0.0213,0.08826,-0.03008,-0.00263,0.018903 Mar-05,-0.03935,-0.0586,-0.03798,0.02378,-0.05865,0.03423,0.01609,-0.001695,-0.019118 Apr-05, 0. 04675, -0.04312,-0.03259, 0.02189,-0.05877,-0.14748,-0.0475, 0.026981,-0.020109 May-05 , 0. 02292, -0. 00947, 0.06882, -0.01749,0.05561,0.09578, 0.07079, 0.018467,0.029952 Jun-05,-0. 03721, 0. 0226, 0.01275,-0.0313,-0.1031,-0.08625,-0.1143,-0.043518,-0.000143 Jul-05,0.031, 0. 02227,0.1365,-0.016, 0.12324, 0. 4252, 0.196, 0.059905,0.035968 Aug-05, 0. 07224, 0.02451, 0. 02931, -0.00375, 0.04107,0.14814,0.00811,-0. 002696,-0. 011222 Sep-05,-0. 06026, 0.06077,0.05875,-0.00174, 0.03205,0.24234, 0.12692,0.071738,0.006949 Oct-05,-0. 00117,-0.11646, -0.1006,-0.01043,-0.05643,0.22056,-0.11151,-0.053649,-0.017741 Nov-05,0. 08016, 0.03883, 0. 09869,-0.00862, 0.0924,-0.13281, 0.14361,0.021432,0.035186 Dec-05,-0. 05527,-0.03205, -0.00017,-0.02672,-0.00384, 0.23032, -0.05058,0.012065,-0.000952