ASSIGNMENT 2 Due: 10/12/2023 at 11:59 pm In this assignment you will apply mean variance analysis for an asset allocation decision using real data. Mean Variance Analysis in Practice Assume you are a portfolio manager for a large pension fund and in charge of allocating funds across major asset classes. Specifically, today is 12/31/2014 and you are assembling a portfolio for January of 2015. Your investment universe consists of T-bonds (Barclays U.S. Treasury index), investment grade corporate bonds (Barclays U.S. Corp index), domestic stocks (S&P 500), international stocks (MSCI World index), commodities (Goldman Sachs Commodity In- dex), and gold. Asset allocation decisions are made based on mean variance analysis. On Canvas, you will find an Excel file containing historical monthly net returns for these assets. Assume that the risk-free rate for 1/2015 equals 25 basis points per month. QUESTIONS: A Report the mean and variance-covariance matrix for all assets. B Based on the moments you estimated in A, find the tangency portfolio and the minimum variance portfolio. Report the mean, standard deviation, and portfolio weights for both portfolios. C Compute the optimal share invested in risky assets for an investor with the utility function U = pu ac? and values for risk aversion, a, between 10 and 40.! Plot the optimal risky asset share as a function of . Is the function increasing or decreasing? Explain economically why you find the slope that you do. D Plot the frontier of risky assets. To do so, use the minimum variance portfolio and the tangency portfolio found above, along with the two fund separation property. Use weights between -25 and 15 on the minimum variance portfolio (i.e. -2500% to 1500%). Add the individual assets as 'dots' to the plot. E Suppose you form a portfolio that invests in both the minimum variance portfolio and the tangency portfolio. If the weight on the minimum variance portfolio equals 40%, what are the weights on the individual assets (T-bonds, corporate bonds, etc.)? IStart by computing the optimal share in risky assets for a value of o = 10. Repeat for o = 11, a = 12 ete. Fixed Income Equities Commodities Date T-Bonds Corp. Bonds S&P 500 MSCI World GSCI Gold 197301 -0.010 -0.002 -0.0168 0.003 0.034 0.020 197302 -0.003 0.004 -0.0338 0.008 0.043 0.292 197303 0.000 0.000 -0.0011 0.002 -0.024 0.058 197304 0.009 0.010 -0.0401 -0.050 0.060 0.005 197305 0.002 -0.004 -0.0140 -0.002 0.182 0.262 197306 0.003 -0.011 -0.0052 0.007 -0.017 0.079 9 197307 -0.021 -0.035 0.0391 0.025 0.258 -0.067 10 197308 0.020 0.037 -0.0315 -0.041 0.025 -0.097 11 197309 0.022 0.032 0.0422 0.030 -0.050 -0.036 12 197310 0.008 -0.011 0.0003 0.011 -0.053 -0.030 13 197311 0.006 0.011 -0.1072 -0.129 0.052 0.031 14 197312 -0.001 -0.013 0.0180 -0.007 0.105 0.120 15 197401 0.007 0.001 -0.0081 0.009 0.112 0.187 16 197402 0.003 0.002 0.0020 0.016 -0.005 0.272 17 197403 -0.016 -0.030 -0.0218 -0.024 -0.115 0.021 18 197404 -0.008 -0.030 -0.0376 -0.016 0.011 -0.026 19 197405 0.012 0.007 -0.0269 -0.039 -0.068 -0.071 20 197406 0.000 -0.045 -0.0128 -0.030 0.124 -0.062 21 197407 0.001 -0.009 -0.0767 -0.058 0.238 0.049 22 197408 0.001 -0.025 -0.0822 -0.095 -0.049 0.008 23 197409 0.025 0.012 -0.1175 -0.092 0.121 -0.050 24 197410 0.012 0.073 0.1681 0.097 0.090 0.128 25 197411 0.020 -0.003 -0.0457 -0.014 0.019 0.094 26 197412 0.012 -0.008 -0.0180 -0.015 -0.083 0.030 27 197501 0.012 0.068 0.1236 0.147 -0.156 -0.060 28 197502 0.012 0.020 0.0675 0.090 -0.104 0.031 29 197503 -0.004 -0.032 0.0240 0.008 0.084 -0.022 30 197504 -0.014 -0.009 0.0494 0.043 -0.046 -0.058 31 197505 0.020 0.026 0.0512 0.025 -0.015 0.002 32 197506 0.004 0.027 0.0462 0.014 0.016 -0.010 33 197507 -0.003 -0.002 -0.0655 0.054 0.078 0.002 4 197508 0.004 -0.005 -0.0157 -0.014 0.096 -0.029 35 197509 -0.002 -0.012 -0.0323 -0.041 0.011 -0.144 36 197510 0.031 0.048 0.0649 0.070 -0.080 0.037 37 197511 -0.001 -0.005 0.0301 0.028 -0.012 -0.036 38 197512 0.019 0.035 -0.0105 0.002 -0.026 0.014 39 197601 0.010 0.029 0.1201 0.090 -0.048 -0.087 40 197602 0.002 0.010 -0.0058 -0.007 0.057 0.034 41 197603 0.010 0.015 0.0326 0.013 0.002 -0.021 42 197604 0.007 0.004 -0.0096 -0.006 0.038 -0.010 43 197605 -0.007 -0.009 -0.0081 -0.016 0.018 -0.023 44 197606 0.013 0.015 0.0440 0.032 -0.017 -0.012 45 197607 0.010 0.014 -0.0072 -0.008 -0.089 -0.092 46 197608 0.014 0.022 0.0016 -0.001 -0.028 -0.083 47 197609 0.009 0.017 0.0244 0.009 -0.099 0.127 48 197610 0.012 0.010 -0.0202 -0.034 -0.012 0.053 49 197611 0.023 0.025 -0.0010 -0.003 0.014 0.064 50 197612 0.009 0.028 0.0538 0.076 0.050 0.034\f\f\f201 198907 0.022 0.019 0.0901 0.113 -0.028 -0.006 202 198908 -0.017 -0.011 0.0199 -0.024 0.035 -0.026 203 198909 0.004 0.005 -0.0040 0.028 0.060 0.026 204 198910 0.027 0.023 -0.0236 -0.033 -0.007 0.019 205 198911 0.010 0.007 0.0205 0.040 0.016 0.082 206 198912 0.002 0.001 0.0227 0.032 0.091 -0.014 207 199001 -0.015 -0.013 -0.0677 -0.047 -0.004 0.041 208 199002 0.002 0.003 0.0134 -0.043 -0.003 -0.020 209 199003 0.000 0.001 0.0266 -0.060 0.007 -0.090 210 199004 -0.009 -0.010 -0.0245 -0.014 -0.010 -0.002 211 199005 0.028 0.032 0.0974 0.105 -0.007 -0.021 212 199006 0.016 0.017 -0.0068 -0.007 -0.016 -0.031 213 199007 0.013 0.011 -0.0045 0.009 0.083 0.053 214 199008 -0.014 -0.016 -0.0908 -0.093 0.166 0.046 215 199009 0.010 0.005 -0.0490 -0.105 0.229 0.046 216 199010 0.017 0.005 -0.0036 0.094 -0.061 -0.066 217 199011 0.022 0.021 0.0646 -0.016 -0.066 0.015 218 199012 0.016 0.014 0.0280 0.021 -0.020 0.016 219 199101 0.011 0.013 0.0450 0.037 -0.094 -0.055 220 199102 0.005 0.017 0.0716 0.093 0.014 -0.018 221 199103 0.005 0.012 0.0244 -0.029 0.038 -0.025 222 199104 0.011 0.013 0.0023 0.008 0.023 -0.002 223 199105 0.004 0.007 0.0429 0.023 -0.001 0.023 224 199106 -0.002 0.000 -0.0454 -0.062 -0.024 0.015 225 199107 0.012 0.014 0.0465 0.047 0.051 -0.009 226 199108 0.023 0.023 0.0239 -0.003 0.015 -0.046 227 199109 0.021 0.021 -0.0169 0.026 0.008 0.010 228 199110 0.009 0.010 0.0135 0.016 0.029 0.020 229 199111 0.010 0.010 -0.0402 -0.043 -0.040 0.026 230 199112 0.035 0.033 0.1141 0.073 -0.071 -0.037 231 199201 -0.016 -0.013 -0.0183 -0.018 0.027 0.002 232 199202 0.004 0.010 0.0129 -0.017 -0.011 -0.003 233 199203 -0.006 -0.004 -0.0195 -0.047 0.011 -0.033 234 199204 0.006 0.005 0.0286 0.014 0.030 -0.015 235 199205 0.018 0.022 0.0049 0.040 0.027 0.004 236 199206 0.015 0.016 -0.0150 -0.033 -0.006 0.017 237 199207 0.026 0.027 0.0409 0.003 -0.014 0.042 238 199208 0.010 0.008 -0.0206 0.025 0.001 -0.049 239 199209 0.015 0.012 0.0113 -0.009 0.011 0.025 240 199210 -0.015 -0.018 0.0048 -0.027 -0.022 -0.029 241 199211 -0.002 0.002 0.0338 0.018 -0.013 -0.015 242 199212 0.017 0.019 0.0134 0.008 0.002 -0.002 243 199301 0.022 0.023 0.0073 0.004 0.012 -0.006 244 199302 0.020 0.023 0.0135 0.024 0.012 -0.006 245 199303 0.003 0.004 0.0212 0.058 0.021 0.025 246 199304 0.008 0.008 -0.0245 0.047 -0.011 0.049 247 199305 -0.001 0.001 0.0263 0.023 -0.028 0.078 248 199306 0.022 0.024 0.0035 -0.008 -0.031 -0.005 249 199307 0.006 0.007 -0.0046 0.021 -0.009 0.065 250 199308 0.022 0.025 0.0374 0.046 0.008 -0.082\f301 199711 0.005 0.006 0.0463 0.018 -0.099 -0.043 302 199712 0.011 0.011 0.0171 0.012 -0.068 -0.026 303 199801 0.015 0.012 0.0120 0.028 -0.016 0.044 304 199802 -0.003 0.000 0.0720 0.068 -0.066 -0.017 305 199803 0.003 0.004 0.0513 0.042 -0.005 0.011 306 199804 0.005 0.006 0.0113 0.010 -0.027 0.036 307 199805 0.010 0.012 -0.0177 -0.012 -0.047 -0.059 308 199806 0.012 0.007 0.0410 0.024 -0.035 0.011 309 199807 0.002 -0.001 -0.0101 -0.001 -0.079 -0.021 310 199808 0.027 0.005 -0.1431 -0.133 -0.059 -0.055 311 199809 0.028 0.032 0.0632 0.018 0.102 0.076 312 199810 -0.003 -0.015 0.0801 0.091 -0.047 -0.003 313 199811 0.000 0.019 0.0622 0.060 -0.122 0.009 314 199812 0.002 0.003 0.0597 0.049 -0.017 -0.028 315 199901 0.006 0.010 0.0428 0.022 0.004 -0.006 316 199902 -0.026 -0.024 -0.0319 0.026 -0.046 0.004 317 199903 0.004 0.007 0.0390 0.042 0.169 -0.024 318 199904 0.002 0.003 0.0376 0.040 0.041 0.022 319 199905 -0.009 -0.013 -0.0232 -0.036 -0.055 -0.052 320 199906 -0.002 -0.005 0.0544 0.047 0.064 -0.036 321 199907 -0.001 -0.006 -0.0302 -0.003 0.036 -0.017 322 199908 0.000 -0.002 -0.0050 -0.002 0.070 -0.008 323 199909 0.008 0.011 -0.0281 -0.010 0.053 0.193 324 199910 0.001 0.005 0.0642 0.052 -0.052 -0.016 325 199911 -0.002 0.001 0.0208 0.028 0.040 -0.023 326 199912 -0.007 -0.005 0.0626 0.081 0.042 -0.004 327 200001 0.003 -0.004 -0.0496 0.057 0.072 -0.027 328 200002 0.015 0.009 -0.0175 0.003 0.062 0.039 329 200003 0.020 0.009 0.0985 0.069 -0.012 -0.062 330 200004 -0.003 -0.009 -0.0316 -0.042 -0.009 0.000 331 200005 0.002 -0.004 -0.0224 -0.025 0.112 -0.013 332 200006 0.017 0.025 0.0262 0.034 0.071 0.062 333 200007 0.010 0.012 -0.0120 -0.028 -0.077 -0.041 334 200008 0.015 0.013 0.0637 0.033 0.154 -0.009 335 200009 0.001 0.006 -0.0519 -0.053 -0.014 -0.003 336 200010 0.010 0.000 -0.0042 -0.017 0.002 -0.038 337 200011 0.021 0.012 -0.0783 -0.061 0.092 0.012 338 200012 0.019 0.019 0.0057 0.016 -0.021 0.021 339 200101 0.008 0.029 0.0323 0.019 -0.053 -0.024 340 200102 0.012 0.009 -0.0911 -0.084 -0.014 -0.005 341 200103 0.003 0.006 -0.0635 -0.065 -0.039 -0.022 342 200104 -0.012 -0.003 0.0778 0.074 0.054 0.017 343 200105 0.003 0.009 0.0070 -0.012 -0.028 0.010 344 200106 0.005 0.005 -0.0244 -0.031 -0.072 0.014 345 200107 0.025 0.027 -0.0093 0.013 0.002 -0.016 346 200108 0.013 0.013 -0.0634 0.048 0.010 0.037 347 200109 0.016 -0.003 -0.0804 0.088 -0.110 0.056 348 200110 0.028 0.025 0.0196 0.019 -0.050 -0.034 349 200111 -0.025 -0.009 0.0788 0.059 -0.054 -0.022 350 200112 -0.010 -0.007 0.0091 0.006 -0.013 0.007351 200201 0.007 0.009 -0.0143 -0.030 -0.031 0.018 352 200202 0.009 0.007 -0.0195 -0.008 0.044 0.053 353 200203 -0.024 -0.019 0.0376 0.044 0.135 0.022 354 200204 0.025 0.013 -0.0610 -0.034 0.011 0.021 355 200205 0.006 0.014 -0.0078 0.002 -0.044 0.058 356 200206 0.014 0.000 -0.0713 -0.060 0.034 -0.025 357 200207 0.024 -0.004 -0.0740 -0.084 0.006 -0.042 358 200208 0.022 0.027 0.0070 0.002 0.060 0.023 359 200209 0.027 0.019 -0.1090 -0.110 0.046 0.032 360 200210 -0.011 -0.013 0.0886 0.074 -0.047 -0.019 361 200211 -0.010 0.016 0.0590 0.054 -0.002 0.006 362 200212 0.026 0.031 -0.0588 -0.048 0.085 0.077 363 200301 -0.003 0.004 -0.0266 -0.030 0.090 0.081 364 200302 0.017 0.021 -0.0152 -0.017 0.121 -0.061 365 200303 -0.004 0.000 0.0103 -0.003 -0.144 -0.035 366 200304 0.005 0.020 0.0828 0.089 -0.061 0.002 367 200305 0.029 0.032 0.0533 0.058 0.096 0.089 368 200306 -0.006 -0.002 0.0128 0.018 0.002 -0.056 369 200307 -0.044 -0.043 0.0179 0.020 0.007 0.031 370 200308 0.006 0.008 0.0196 0.022 0.041 0.043 371 200309 0.030 0.036 -0.0107 0.006 -0.041 0.036 372 200310 -0.015 -0.011 0.0556 0.060 0.022 0.000 373 200311 0.001 0.005 0.0093 0.015 0.026 0.035 374 200312 0.009 0.011 0.0518 0.063 0.062 0.048 375 200401 0.009 0.011 0.0191 0.016 0.004 -0.038 376 200402 0.012 0.013 0.0144 0.017 0.074 -0.023 377 200403 0.009 0.009 -0.0150 -0.006 0.020 0.078 378 200404 -0.032 -0.031 -0.0156 -0.020 0.028 -0.084 379 200405 -0.003 -0.007 0.0137 0.010 0.046 0.017 380 200406 0.004 0.004 0.0195 0.021 -0.047 0.000 381 200407 0.010 0.012 -0.0329 -0.032 0.078 -0.011 382 200408 0.021 0.024 0.0038 0.005 -0.039 0.047 383 200409 0.003 0.006 0.0108 0.019 0.126 0.010 384 200410 0.008 0.010 0.0150 0.025 0.041 0.034 385 200411 -0.013 -0.010 0.0406 0.053 -0.048 0.061 386 200412 0.010 0.014 0.0337 0.038 -0.100 -0.031 387 200501 0.007 0.008 -0.0238 -0.022 0.068 -0.032 388 200502 -0.008 -0.006 0.0212 0.032 0.062 0.030 389 200503 -0.003 -0.013 -0.0172 -0.019 0.076 -0.021 390 200504 0.018 0.013 -0.0189 -0.021 -0.091 0.013 391 200505 0.012 0.014 0.0320 0.019 -0.007 -0.038 392 200506 0.006 0.008 0.0017 0.009 0.058 0.048 393 200507 -0.014 -0.010 0.0374 0.035 0.055 -0.022 394 200508 0.016 0.015 -0.0092 0.008 0.151 0.014 395 200509 -0.013 -0.016 0.0080 0.026 0.000 0.093 396 200510 -0.008 -0.012 -0.0156 -0.024 -0.103 -0.002 397 200511 0.005 0.006 0.0384 0.034 -0.038 0.045 398 200512 0.010 0.010 -0.0001 0.022 0.029 0.039 399 200601 -0.003 -0.002 0.0264 0.045 0.043 0.111 400 200602 0.002 0.005 0.0024 -0.001 -0.101 -0.023\f451 201005 0.017 -0.006 -0.0801 -0.095 -0.132 0.033 452 201006 0.019 0.021 -0.0535 -0.034 0.004 0.022 453 201007 0.007 0.020 0.0705 0.081 0.056 -0.058 454 201008 0.020 0.020 -0.0454 -0.037 -0.055 0.056 455 201009 0.000 0.007 0.0904 0.094 0.085 0.063 456 201010 -0.002 0.001 0.0387 0.037 0.026 0.020 457 201011 -0.007 -0.008 -0.0001 -0.021 0.011 0.029 458 201012 -0.018 -0.009 0.0671 0.074 0.094 0.026 459 201101 0.000 0.002 0.0233 0.023 0.031 -0.054 460 201102 -0.001 0.008 0.0325 0.035 0.037 0.057 461 201103 -0.001 -0.001 0.0006 -0.009 0.044 0.015 462 201104 0.012 0.017 0.0294 0.043 0.044 0.070 463 201105 0.016 0.014 -0.0113 -0.020 -0.069 0.004 464 201106 -0.003 -0.009 -0.0165 -0.015 -0.053 -0.019 465 201107 0.018 0.025 -0.0198 -0.018 0.024 0.070 466 201108 0.028 0.001 -0.0543 -0.070 -0.018 0.132 467 201109 0.018 0.003 -0.0702 -0.086 -0.122 -0.108 468 201110 -0.008 0.018 0.1090 0.104 0.097 0.055 469 201111 0.008 -0.020 -0.0027 -0.024 0.014 -0.008 470 201112 0.010 0.021 0.0094 0.000 -0.021 -0.076 471 201201 0.004 0.022 0.0452 0.050 0.022 0.104 472 201202 -0.007 0.008 0.0433 0.049 0.061 0.029 473 201203 -0.010 -0.010 0.0329 0.013 -0.024 -0.071 474 201204 0.015 0.014 -0.0060 -0.011 -0.005 0.001 475 201205 0.017 0.008 -0.0598 -0.084 -0.130 -0.057 476 201206 -0.004 0.004 0.0415 0.051 0.012 0.001 477 201207 0.010 0.029 0.0144 0.013 0.064 0.034 478 201208 -0.001 0.002 0.0227 0.026 0.064 0.022 479 201209 -0.003 0.007 0.0251 0.028 -0.014 0.074 480 201210 -0.002 0.013 -0.0178 -0.006 -0.041 -0.035 481 201211 0.005 -0.002 0.0052 0.013 0.015 0.006 482 201212 -0.004 -0.001 0.0082 0.019 -0.006 -0.037 483 201301 -0.008 -0.009 0.0522 0.051 0.044 0.006 484 201302 0.005 0.008 0.0132 0.002 -0.044 -0.050 485 201303 0.001 0.000 0.0375 0.024 0.008 0.007 486 201304 0.009 0.018 0.0198 0.032 -0.047 -0.081 487 201305 -0.017 -0.023 0.0229 0.001 -0.015 -0.042 488 201306 -0.011 -0.028 -0.0137 -0.024 0.002 -0.147 489 201307 -0.001 0.008 0.0507 0.053 0.049 0.107 490 201308 -0.005 -0.007 -0.0293 -0.021 0.034 0.046 491 201309 0.007 0.007 0.0317 0.050 -0.034 -0.041 492 201310 0.005 0.015 0.0463 0.039 -0.014 -0.001 493 201311 -0.003 -0.002 0.0308 0.018 -0.008 -0.066 494 201312 -0.009 -0.002 0.0258 0.022 0.019 -0.035 495 201401 0.014 0.018 -0.0346 -0.037 -0.016 0.037 496 201402 0.003 0.010 0.0457 0.051 0.045 0.065 497 201403 -0.003 0.001 0.0084 0.002 0.001 -0.025 498 201404 0.006 0.012 0.0074 0.011 0.007 -0.002 499 201405 0.009 0.014 0.0235 0.021 -0.002 -0.029 500 201406 -0.001 0.001 0.0207 0.018 0.021 0.047\f