In: Statistics and Probability
HOW TO DO B PLEASE EXPLAIN IN DETAIL
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. Prepare a report that includes but is not limited to the
following items.
A (30 points). Compute descriptive statistics for each stock and
the S&P 500. Comment on your results. Which stocks are the most
volatile?
B (30 points). 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 (40 points). Comment on how much of the return for the individual
stocks is explained by the market.
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 |
ANSWER::
GIVEN DATA IS ABOUT MEASURING STOCK MARKET RISK
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