Problem 1:

Below I have listed a set of phenomena that have been empirically documented to hold on average. For each of these phenomena, I want you to identify the weakest form of the efficient market hypothesis that each phenomena is inconsistent with. For each, circle the correct answer.

A. The January Effect:A portfolio of stocks in small cap firms (i.e., firms in the bottom 5 percentile ranked by market capitalization) has a higher average return than predicted by its risk in the first week in January.

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

B. The average returns over a 3-year period following an existing publicly traded company issuing new shares (a seasoned equity offering or SEO) are on average less than those of similar firms (in terms of risk and business) that did not issue new equity.

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

C. Immediately after an existing public firm announces that it is going to issue new equity (do an SEO), the price of its current equity falls on average.

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

D. Immediately after an existing public firm announces that it is going to issue new equity (an SEO), on average the price does not change.However, by the end of the day the SEO occurs and the new equity is sold, the stock price rises on average.

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

E. Every year there are a bunch of professional fund managers who beat the market (i.e., have larger returns than a passive portfolio invested in the market portfolio).

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

F. When it is announced that a CEO has died while in office, the stock price of the firm rises on average.

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

G. Whenever the Dow Jones Industrial Index rises by more than 1 percent in a given day, the stocks included in the index have negative returns the next day on average.

Weak Form Semi-Strong Form Strong Form It is consistent with all forms

Problem 2:

See the data in the attached spreadsheet called data.xlsx.

The spreadsheet contains data on the closing price of an unidentified stock for one (undisclosed) year (252 trading days). The spreadsheet also plots price over time. Weekly data for this security is also provided starting at row 260.

Questions:

1. Does there appear to be a pattern in price movements? If today is day 252, what do you predict will happen to the price over the next day? What do you predict will happen to price over the next two to three weeks? Why?

2. If there is truly a pattern in price movements, then it should be the case that you can predict the next intervals return (albeit imperfectly) knowing the previous periods return. To see if this is true, calculate the series of returns over each interval. (The security paid no dividends.) Then create a plot of the return at t (on the vertical axis) against the return at t-1 (on the horizontal axis). If the prior return (at t-1) is useful a predicting the next periods return (at t), then this plot should show non-zero correlation. Does the data at the daily or weekly level show any correlation?

3. Is there a difference between what you perceived when you answered Question 1 and what you perceived when you answered Question 2? If so, which perception is correct? Why?

Daily t= Price 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 80 80.16607 80.12718 80.1901 80.34944 80.49639 79.92348 79.90402 79.64494 79.60603 79.88645 79.87341 80.01697 80.7255 80.29098 79.93891 80.00372 79.77348 79.68303 79.2309 79.13209 79.38338 79.49518 79.09849 78.88981 78.3517 78.84115 78.57304 78.33952 78.2393 78.18404 77.74334 77.99141 78.21822 78.20861 78.05359 78.16176 77.93218 77.96233 77.76458 77.37813 77.38783 77.94882 78.00102 77.65313 77.51911 77.52075 76.967 77.34267 77.38828 76.91452 76.75627 76.57772 76.35125 76.27895 76.74123 76.79644 76.74855 76.78126 76.75314 76.84942 77.01324 76.95561 77.08792 76.89943 76.5408 76.61163 77.08906 77.10426 76.62601 76.43815 76.5687 76.96109 77.30804 77.61297 77.59143 77.38655 76.76404 86 84 82 80 Column D 78 76 74 72 0 50 100 150 200 250 300 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 76.98777 76.91255 77.43462 77.8881 78.26001 78.46858 78.37497 78.67258 78.1928 78.22431 78.61791 79.10905 79.23709 79.18537 78.86331 78.32288 78.91809 79.49027 79.29118 79.44946 79.66016 79.57894 79.96136 80.22727 80.3249 80.9953 81.47187 81.38149 80.93325 81.12261 81.26333 80.60383 81.15954 81.55883 81.82921 81.743 81.77295 81.43149 81.437 80.54985 80.21566 79.63268 79.8727 79.73746 80.60639 80.92561 80.97525 81.10417 81.53628 81.59385 81.65522 80.67784 80.59384 80.29366 80.35289 80.19361 80.27433 79.87791 79.63352 79.91552 79.50045 79.21374 79.14578 79.1552 78.85257 78.6138 78.4142 78.50523 78.57088 78.76433 79.13611 79.06993 78.95653 78.96988 78.79151 79.32592 79.56121 79.53647 79.94979 79.85843 80.06957 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 79.8227 80.52657 81.1231 80.81533 81.25725 80.1364 80.38727 80.09139 79.67902 79.88471 80.20267 80.25672 80.04684 79.80523 79.69915 79.82294 79.52841 80.03398 80.27764 80.79822 80.29266 80.76826 80.65484 80.54132 80.96673 80.73832 80.55494 80.18706 80.664 80.62575 80.74178 80.60199 81.12971 81.17894 81.06059 81.03289 80.88985 81.47836 81.31708 81.74373 81.97093 81.77855 81.66891 81.56631 81.34887 81.75285 82.50203 82.50045 82.43056 82.83383 82.90073 82.54764 82.66801 82.64207 82.29118 82.26566 82.3059 82.01076 81.92286 82.22295 82.30234 82.48762 82.94603 83.30521 83.57508 83.91229 83.79178 83.96887 83.73874 84.10374 84.63644 84.64301 84.20111 84.2123 84.45373 83.83198 84.42107 84.5305 84.48369 84.0701 83.51484 240 241 242 243 244 245 246 247 248 249 250 251 252 83.31984 83.52184 83.75521 83.87475 84.10831 84.65427 84.2255 83.60533 83.9911 83.74938 83.98509 83.59817 84.43051 Weekly t (days) = Price 0 80 5 80.49639 10 79.88645 15 79.93891 20 79.13209 25 78.3517 30 78.18404 35 78.05359 40 77.37813 45 77.51911 50 76.91452 55 76.74123 60 76.84942 65 76.5408 70 76.43815 75 77.59143 80 77.43462 85 78.67258 90 79.23709 95 79.49027 100 79.96136 105 81.38149 110 81.15954 115 81.43149 120 79.8727 125 81.10417 130 80.59384 135 79.87791 140 79.14578 145 78.50523 150 78.95653 155 79.53647 160 80.52657 165 80.38727 170 80.25672 175 79.52841 180 80.76826 185 80.55494 190 80.60199 195 80.88985 200 81.77855 205 82.50203 210 82.54764 215 82.3059 220 82.48762 225 83.79178 230 84.64301 235 84.42107 240 83.31984 245 84.65427 250 83.98509