Problem 2. In this problem you are asked to construct and analyse your own asset pricing factor based on the illiquidity measure ILLIQ from "Illiquidity and stock returns: cross-section and time-series effects" by Amihud (2002). The data for the problem can be found in the file "aap-2024-amihud-data.xlsx," which contains daily dollar volumes of trade, daily returns, and monthly returns for 40 stocks, as well as monthly Fama-French-Carhart factor returns from Jan-1996 to Dec-2015. Each of the stocks is identified by a five-digit code that is derived from the Center for Research in Security Prices (CRSP) database. Factor Construction (i) For each stock and each day, calculate the daily ILLIQ measure ILLIQid=106 × Vid dvolid' where rid and dvolia are the return and dollar volume of trade of stock i on day d. (ii) For each stock and each month, calculate the monthly ILLIQ measure by taking the equally weighted average of the daily ILLIQ values in a given month. (iii) For each month, sort the stocks into quintiles based on the monthly ILLIQ values, with the most illiquid stocks in quintile one and the most liquid stocks in quintile five. (iv) For each month excluding Jan-1996, calculate the equally weighted average returns of the stocks in the most illiquid quintile and the stocks in the most liquid quintile. By taking the difference between these returns, calculate the returns of the IML (illiquid minus liquid) factor. To calculate the returns for month t, use the quintile sorts from month t - 1. For example, the most illiquid quintile returns for Feb-1996 are calculated using the returns from Feb-1996, but the ILLIQ quintiles from Jan-1996. Analysis (a) Calculate the monthly average return, monthly volatility, and monthly Sharpe ratio of the IML factor. When calculating the Sharpe ratio, assume for simplicity that the risk-free rate is zero. [3 points] (b) Repeat the calculations in (a) for the subperiods Feb-1996 to Dec-2005 and Jan-2006 to Dec-2015. Briefly discuss the results. [1 point] (c) Suppose you invested $1 into the IML factor at the beginning of Feb-1996. Plot the value of the investment over the sample period. What is the final value of the investment at the end of Dec-2015? [0.5 points] (d) Regress the IML factor returns on the Fama-French-Carhart factors: IML₁ = a + B₁Mkt-Rft + B2SMB+ + ẞ3HML + ẞ4UMD+ + εt. Does the IML factor generate a statistically significant alpha that is not explained by the Fama-French-Carhart model? [0.5 points] (e) The IML factor in this problem is a simplified version of the IML factor in "The pricing of the illiquidity factor's conditional risk with time-varying premium" by Amihud and Noh (2021). An extract from their Table 1 is reproduced below. Briefly discuss the similarities and differences between your results from (d) and their results. [3 points] Table 1 Time-series estimation results for the illiquidity return premium factor IML (1) 1947-2017 Panel B: Regression of IML alphaIML 0.341 (5.47) (2) 1947-6/1982 0.441 (4.94) (3) 7/1982-2017 0.288 (3.33) BRMrf -0.287 (-15.59) -0.328 (-13.00) -0.234 (-10.08) BSMB 0.606 (18.87) 0.595 (13.56) 0.574 (12.88) BHML 0.404 (12.34) BUMD -0.078 (-3.77) 0.468 (8.02) -0.206 (-5.37) 0.366 (10.00) -0.006 (-0.26) R² 0.61 0.66 0.61 A B с D E F G H J K L M N P R S 1 Date 10147 10890 11850 11891 15720 2 1/2/1996 0.1057 0.1136 -0.0062 -0.0109 3 4 1/3/1996 -0.0441 0.0612 1/4/1996 -0.0154 5 1/5/1996 0.0000 0.0417 6 1/8/1996 0.0156 7 1/9/1996 -0.0462 -0.0769 8 1/10/1996 0.0242 001,95 16600 17144 17750 17778 17929 18411 19166 20204 20415 0.0142 0.0173 0.0195 -0.0181 -0.0187 0.0060 0.0000 0.0018 0.0071 -0.0029 0.0034 0.0050 0.0207 0.0000 0.0031 0.0330 0.0140 0.0151 -0.0212 -0.0046 -0.0183 -0.0120 0.0000 0.0295 -0.0106 -0.0117 0.0068 0.0050 -0.0018 0.0000 0.0062 0.0851 -0.0070 -0.0149 -0.0195 -0.0155 -0.0137 0.0061 -0.0051 -0.0108 0.0249 -0.0075 0.0034 0.0149 -0.0037 -0.0135 0.0246 0.0931 0.0070 -0.0113 -0.0199 0.0016 -0.0164 0.0000 0.0102 0.0072 0.0139 -0.0045 0.0134 -0.0049 0.0019 0.0137 0.0200 0.0120 0.0359 0.0070 0.0038 0.0017 0.0016 0.0058 0.0181 -0.0051 0.0000 0.0034 0.0121 -0.0099 0.0196 -0.0074 0.0068 -0.0588 -0.0193 -0.0216 -0.0069 0.0019 -0.0091 0.0094 -0.0058 0.0059 0.0102 0.0126 -0.0444 -0.0060 0.0033 -0.0192 -0.0261 -0.0268 0.0625 -0.0302 -0.0398 0.0070 -0.0057 -0.0252 -0.0295 0.0000 -0.0118 0.0000 -0.0213 -0.0536 -0.0075 -0.0199 -0.0147 0.0038 -0.0345 9 1/11/1996 0.1024 0.0392 0.0062 0.0553 0.0000 -0.0038 0.0047 0.0080 0.0167 0.0000 0.0000 -0.0073 0.0491 -0.0136 0.0102 -0.0050 0.0038 0.0286 10 1/12/1996 -0.0143 0.0566 -0.0139 -0.0131 0.0139 -0.0077 0.0094 0.0079 0.0164 0.0238 -0.0101 -0.0165 -0.0144 0.0031 -0.0201 -0.0050 -0.0114 0.0000 11 1/15/1996 -0.0507 0.0179 -0.0110 -0.0088 -0.0137 0.0058 0.0070 -0.0016 -0.0065 -0.0116 0.0152 0.0204 -0.0146 0.0061 0.0137 0.0101 0.0000 -0.0208 12 1/16/1996 0.0153 0.0000 0.0143 -0.0134 0.0139 0.0288 0.0115 0.0094 0.0000 0.0176 0.0100 0.0000 0.0000 0.0319 -0.0135 -0.0299 0.0346 0.0000 13 1/17/1996 0.0226 -0.0526 0.0047 0.0045 -0.0137 -0.0093 0.0046 -0.0031 0.0097 0.0116 0.0099 -0.0055 0.0111 -0.0103 0.0137 0.0256 -0.0520 0.0213 14 1/18/1996 0.0368 0.0000 0.0093 0.0045 0.0069 -0.0019 -0.0045 0.0000 0.0129 0.0229 -0.0098 -0.0037 0.0220 -0.0045 -0.0034 0.0200 -0.0176 0.0208 15 1/19/1996 -0.0284 -0.0185 0.0015 -0.0179 -0.0138 -0.0038 0.0023 0.0172 -0.0159 0.0112 -0.0099 0.0074 -0.0072 0.0104 0.0034 0.0588 0.0000 0.0068 16 1/22/1996 0.0657 0.0189 -0.0185 -0.0183 0.0070 0.0000 0.0023 -0.0046 0.0161 -0.0110 -0.0100 -0.0036 0.0217 -0.0059 0.0439 0.0000 17 1/23/1996 0.0274 0.0556 -0.0204 0.0558 0.0069 0.0133 -0.0023 -0.0077 0.0000 -0.0223 0.0152 0.0000 0.0035 0.0238 0.0259 0.0000 18 1/24/1996 0.0267 0.0000 -0.0016 0.0176 0.0207 0.0375 0.0205 0.0078 0.0032 0.0114 0.0199 0.0000 0.0070 0.0058 0.0126 0.0046 0.0120 -0.0263 19 1/25/1996 0.0649 0.0000 0.0112 0.0130 0.0068 -0.0144 -0.0200 0.0015 0.0000 -0.0056 -0.0146 -0.0018 -0.0140 -0.0072 -0.0031 0.0138 0.0059 0.0203 20 1/26/1996 -0.0427 -0.0175 0.0127 0.0171 -0.0067 0.0110 -0.0023 0.0123 -0.0063 -0.0057 0.0000 0.0055 0.0142 0.0087 -0.0125 -0.0045 0.0255 0.0596 21 1/29/1996 -0.0191 0.0536 -0.0063 -0.0252 0.0000 -0.0018 -0.0046 -0.0061 0.0096 0.0000 0.0000 0.0164 0.0140 0.0058 0.0222 0.0000 -0.0019 -0.0063 22 1/30/1996 0.0000 0.0000 -0.0079 0.0043 0.0000 0.0200 0.0343 -0.0245 0.0126 0.0000 0.0050 0.0162 0.0448 0.0100 0.0124 0.0183 -0.0115 -0.0126 23 1/31/1996 -0.0065 0.0169 0.0207 0.0129 0.0000 0.0053 0.0177 0.0142 -0.0062 0.0171 0.0000 0.0300 -0.0099 0.0043 -0.0306 0.0090 0.0019 -0.0127 24 2/1/1996 0.0065 0.0000 0.0109 -0.0254 -0.0135 -0.0106 -0.0043 -0.0171 -0.0031 0.0056 -0.0122 0.0000 0.0000 -0.0028 0.0126 -0.0044 0.0116 -0.0194 25 2/2/1996 -0.0390 -0.0167 -0.0046 0.0217 0.0068 -0.0107 -0.0328 0.0063 0.0031 -0.0056 0.0000 -0.0051 0.0067 -0.0057 0.0062 0.0045 0.0057 0.0395 26 2/5/1996 0.0068 0.0169 0.0000 0.0851 0.0000 0.0307 0.0045 -0.0235 -0.0063 -0.0056 0.0051 -0.0069 0.0066 0.0142 0.0000 -0.0089 0.0152 -0.0063 27 2/6/1996 0.0134 -0.0500 0.0077 0.0196 -0.0068 0.0333 0.0360 -0.0112 0.0000 0.0000 -0.0050 0.0156 -0.0132 -0.0056 -0.0062 0.0045 0.0019 0.0000 28 2/7/1996 -0.0132 0.0351 0.0015 -0.0115 0.0068 -0.0034 -0.0065 0.0162 0.0032 0.0000 0.0152 -0.0017 -0.0333 0.0113 0.0093 0.0134 0.0056 0.0000 29 2/8/1996 -0.0201 0.0000 0.0230 0.0039 -0.0068 0.0170 0.0240 0.0192 0.0094 -0.0113 0.0000 0.0137 0.0069 0.0000 0.0216 0.0132 0.0168 0.0127 30 2/9/1996 -0.0068 0.0000 0.0000 -0.0078 -0.0068 0.0034 0.0213 0.0110 -0.0078 0.0057 0.0050 0.0017 0.0171 -0.0042 0.0121 -0.0043 0.0018 0.0118 31 2/12/1996 -0.0207 0.0339 0.0091 0.0078 0.0138 0.0067 -0.0146 -0.0031 0.0016 0.0057 0.0099 0.0185 0.0438 -0.0168 0.0000 -0.0044 0.0128 0.0000 32 2/13/1996 0.0000 0.0000 0.0000 -0.0116 0.0000 -0.0116 0.0042 -0.0062 -0.0063 0.0056 0.0098 -0.0066 -0.0032 0.0114 0.0030 0.0000 -0.0108 -0.0125 33 2/14/1996 -0.0282 -0.0656 -0.0090 0.0039 -0.0204 -0.0017 0.0063 -0.0094 0.0473 -0.0112 -0.0097 -0.0017 0.0259 -0.0099 0.0060 -0.0044 0.0000 0.0127 34 2/15/1996 0.0145 0.0000 0.0015 0.0000 -0.0069 0.0202 -0.0063 0.0095 0.0271 0.0114 0.0000 -0.0083 -0.0221 -0.0014 -0.0207 0.0176 -0.0146 0.0188 35 2/16/1996 0.0071 -0.0526 -0.0151 -0.0039 -0.0140 0.0082 -0.0063 -0.0047 -0.0381 0.0056 -0.0049 -0.0051 -0.0452 -0.0100 0.0000 -0.0043 -0.0148 -0.0123 26 2/20/1006 00077 0.0275 0.0071 00270 ก กวาว 00126 0.0061 0.0296 19350 19393 22592 23393 0.0060 0.0068 -0.0079 0.0201 0.0056 0.0024 0.0024 0.0115 00101 00217 0.0000 0.0000 returns-daily dollar-vols-daily returns-monthly ff-factors Ready Accessibility: Good to go B + + 100%