Pythonを用いて，S&P500(米国優良企業約500社)の組合せの中から最適ポートフォリオを見つけてみました．
この記事には，そのコードの実行結果のみを書いています．
最適ポートフォリオを見つけるコードは，以下で解説しているので気になる方はご覧ください．
やったこと
・S&P500銘柄をこちらのCSVから取得し，pandas-datareaderを使って株価時系列データを取得
・取得した株価データから各銘柄の期待リターンとボラティリティ（リスク，共分散の平方根）を求め，効率的フロンティアを生成
・効率的フロンティアから，ボラティリティが最小になるポートフォリオとシャープレシオ（期待リターン/ボラティリティ）が最大になるポートフォリオを探索
・セクター別にまとめたものも出力
条件
2014年からの株価データで実行しました．そのため，2014年以降に上場した銘柄は含まれていません．
効率的フロンティア
最適ポートフォリオ
左がシャープレシオを最大，右がボラティリティを最小にするポートフォリオ
シャープレシオ最大ポートフォリオ
リターン 0.1850
ボラティリティ 0.1846
シャープレシオ 1.0018
| 0 | MMM | 0.001556 |
| 1 | AOS | 0.003068 |
| 2 | ABT | 0.002113 |
| 3 | ABBV | 0.004224 |
| 4 | ABMD | 0.000507 |
| 5 | ACN | 0.000816 |
| 6 | ATVI | 0.000815 |
| 7 | ADBE | 0.002034 |
| 8 | AAP | 0.000342 |
| 9 | AMD | 0.001637 |
| 10 | AES | 0.001607 |
| 11 | AFL | 0.001149 |
| 12 | A | 0.000501 |
| 13 | APD | 0.000122 |
| 14 | AKAM | 0.000744 |
| 15 | ALK | 0.002818 |
| 16 | ALB | 0.001625 |
| 17 | ARE | 0.003103 |
| 18 | ALXN | 0.001473 |
| 19 | ALGN | 0.002462 |
| 20 | ALLE | 0.001072 |
| 21 | LNT | 0.003484 |
| 22 | ALL | 0.00218 |
| 23 | GOOGL | 0.000584 |
| 24 | GOOG | 0.002793 |
| 25 | MO | 0.001948 |
| 26 | AMZN | 0.002873 |
| 27 | AMCR | 0.00076 |
| 28 | AEE | 0.000358 |
| 29 | AAL | 0.001607 |
| 30 | AEP | 0.003496 |
| 31 | AXP | 0.002364 |
| 32 | AIG | 0.003323 |
| 33 | AMT | 0.001969 |
| 34 | AWK | 0.002709 |
| 35 | AMP | 0.000841 |
| 36 | ABC | 0.001677 |
| 37 | AME | 0.00185 |
| 38 | AMGN | 0.001877 |
| 39 | APH | 0.00014 |
| 40 | ADI | 0.001526 |
| 41 | ANSS | 0.003541 |
| 42 | ANTM | 0.003514 |
| 43 | AON | 0.002561 |
| 44 | APA | 0.001469 |
| 45 | AAPL | 0.003683 |
| 46 | AMAT | 0.00438 |
| 47 | APTV | 0.002046 |
| 48 | ADM | 0.000528 |
| 49 | AJG | 0.001756 |
| 50 | AIZ | 0.001609 |
| 51 | T | 0.00181 |
| 52 | ATO | 0.002532 |
| 53 | ADSK | 0.00102 |
| 54 | ADP | 0.004231 |
| 55 | AZO | 0.003406 |
| 56 | AVB | 0.001023 |
| 57 | AVY | 0.003919 |
| 58 | BKR | 0.002553 |
| 59 | BLL | 0.003455 |
| 60 | BAC | 0.000849 |
| 61 | BAX | 0.004239 |
| 62 | BDX | 0.001088 |
| 63 | BBY | 0.003686 |
| 64 | BIO | 0.001262 |
| 65 | BIIB | 0.000633 |
| 66 | BLK | 0.001447 |
| 67 | BA | 0.001992 |
| 68 | BKNG | 0.000615 |
| 69 | BWA | 0.000595 |
| 70 | BXP | 0.00169 |
| 71 | BSX | 0.004203 |
| 72 | BMY | 0.000179 |
| 73 | AVGO | 0.002477 |
| 74 | BR | 0.003053 |
| 75 | CHRW | 0.003887 |
| 76 | COG | 0.003085 |
| 77 | CDNS | 0.001951 |
| 78 | CPB | 0.003925 |
| 79 | COF | 0.000789 |
| 80 | CAH | 0.002471 |
| 81 | KMX | 0.002217 |
| 82 | CCL | 4.28E-05 |
| 83 | CAT | 0.002233 |
| 84 | CBOE | 0.00406 |
| 85 | CBRE | 0.00032 |
| 86 | CDW | 0.001899 |
| 87 | CE | 0.004265 |
| 88 | CNC | 0.004323 |
| 89 | CNP | 0.00429 |
| 90 | CERN | 0.001175 |
| 91 | CF | 0.003116 |
| 92 | SCHW | 0.003537 |
| 93 | CHTR | 0.001109 |
| 94 | CVX | 0.002805 |
| 95 | CMG | 0.004334 |
| 96 | CB | 0.004004 |
| 97 | CHD | 0.002862 |
| 98 | CI | 0.00407 |
| 99 | CINF | 0.002421 |
| 100 | CTAS | 0.000582 |
| 101 | CSCO | 0.003652 |
| 102 | C | 0.002986 |
| 103 | CTXS | 0.002891 |
| 104 | CME | 0.002003 |
| 105 | CMS | 0.00289 |
| 106 | KO | 0.00197 |
| 107 | CTSH | 0.003769 |
| 108 | CL | 0.001071 |
| 109 | CMCSA | 0.00047 |
| 110 | CMA | 0.004167 |
| 111 | CAG | 0.00376 |
| 112 | COP | 0.002464 |
| 113 | ED | 0.003286 |
| 114 | STZ | 0.003693 |
| 115 | CPRT | 0.003543 |
| 116 | GLW | 0.002624 |
| 117 | COST | 0.001927 |
| 118 | CCI | 0.003222 |
| 119 | CSX | 0.003532 |
| 120 | CMI | 0.000712 |
| 121 | CVS | 0.000456 |
| 122 | DHI | 0.004238 |
| 123 | DHR | 0.000525 |
| 124 | DRI | 0.001384 |
| 125 | DVA | 0.003896 |
| 126 | DE | 8.07E-05 |
| 127 | DAL | 0.003044 |
| 128 | XRAY | 0.001999 |
| 129 | DVN | 0.000815 |
| 130 | DXCM | 0.002918 |
| 131 | FANG | 0.001972 |
| 132 | DLR | 0.000462 |
| 133 | DFS | 0.001756 |
| 134 | DISCA | 0.002908 |
| 135 | DISCK | 0.002019 |
| 136 | DISH | 0.004354 |
| 137 | DG | 0.002262 |
| 138 | DLTR | 0.003274 |
| 139 | D | 0.002299 |
| 140 | DPZ | 0.000336 |
| 141 | DOV | 0.001682 |
| 142 | DTE | 0.00063 |
| 143 | DUK | 0.001337 |
| 144 | DRE | 0.000277 |
| 145 | DD | 0.001515 |
| 146 | DXC | 5.80E-05 |
| 147 | EMN | 0.00325 |
| 148 | ETN | 0.00418 |
| 149 | EBAY | 0.000274 |
| 150 | ECL | 0.002474 |
| 151 | EIX | 0.000762 |
| 152 | EW | 0.000396 |
| 153 | EA | 0.004091 |
| 154 | EMR | 0.000801 |
| 155 | ENPH | 0.003513 |
| 156 | ETR | 0.000177 |
| 157 | EOG | 0.000262 |
| 158 | EFX | 0.000122 |
| 159 | EQIX | 0.003399 |
| 160 | EQR | 0.002442 |
| 161 | ESS | 0.004048 |
| 162 | EL | 0.004262 |
| 163 | RE | 0.002027 |
| 164 | EVRG | 0.001498 |
| 165 | ES | 0.001065 |
| 166 | EXC | 0.000979 |
| 167 | EXPE | 0.000745 |
| 168 | EXPD | 0.00131 |
| 169 | EXR | 0.003066 |
| 170 | XOM | 9.80E-05 |
| 171 | FFIV | 0.002664 |
| 172 | FB | 0.004414 |
| 173 | FAST | 0.001063 |
| 174 | FRT | 0.0002 |
| 175 | FDX | 0.001856 |
| 176 | FIS | 0.002155 |
| 177 | FITB | 0.000484 |
| 178 | FRC | 1.16E-05 |
| 179 | FE | 0.003954 |
| 180 | FISV | 0.001686 |
| 181 | FLT | 0.000597 |
| 182 | FLIR | 0.003762 |
| 183 | FMC | 0.000903 |
| 184 | F | 0.001881 |
| 185 | FTNT | 0.002509 |
| 186 | FBHS | 0.00399 |
| 187 | BEN | 0.001111 |
| 188 | FCX | 0.001853 |
| 189 | GPS | 0.00026 |
| 190 | GRMN | 0.002384 |
| 191 | IT | 0.004004 |
| 192 | GNRC | 0.00093 |
| 193 | GD | 0.000589 |
| 194 | GE | 0.00086 |
| 195 | GIS | 0.00064 |
| 196 | GM | 0.001713 |
| 197 | GPC | 0.001983 |
| 198 | GILD | 0.001495 |
| 199 | GPN | 0.001746 |
| 200 | GL | 0.002183 |
| 201 | GS | 0.000598 |
| 202 | GWW | 0.002425 |
| 203 | HAL | 0.000719 |
| 204 | HBI | 0.0015 |
| 205 | HIG | 2.20E-05 |
| 206 | HAS | 0.002993 |
| 207 | HCA | 0.00119 |
| 208 | PEAK | 0.000381 |
| 209 | HSIC | 0.0019 |
| 210 | HES | 0.004288 |
| 211 | HLT | 0.003415 |
| 212 | HFC | 0.003815 |
| 213 | HOLX | 0.002005 |
| 214 | HD | 0.003524 |
| 215 | HON | 0.002255 |
| 216 | HRL | 0.003015 |
| 217 | HST | 0.000502 |
| 218 | HPQ | 0.004393 |
| 219 | HUM | 0.003084 |
| 220 | HBAN | 0.004272 |
| 221 | HII | 0.00185 |
| 222 | IEX | 0.001409 |
| 223 | IDXX | 0.000724 |
| 224 | ITW | 0.002107 |
| 225 | ILMN | 0.003685 |
| 226 | INCY | 0.004037 |
| 227 | INTC | 0.00083 |
| 228 | ICE | 0.002565 |
| 229 | IBM | 0.001042 |
| 230 | IFF | 0.000451 |
| 231 | IP | 0.00193 |
| 232 | IPG | 0.004239 |
| 233 | INTU | 0.002344 |
| 234 | ISRG | 0.004355 |
| 235 | IVZ | 0.000966 |
| 236 | IPGP | 0.000872 |
| 237 | IQV | 0.001089 |
| 238 | IRM | 0.000822 |
| 239 | JBHT | 0.003782 |
| 240 | JKHY | 0.003435 |
| 241 | J | 0.001682 |
| 242 | SJM | 0.000311 |
| 243 | JNJ | 0.003771 |
| 244 | JCI | 0.000939 |
| 245 | JPM | 0.002937 |
| 246 | JNPR | 0.000615 |
| 247 | KSU | 0.003737 |
| 248 | K | 0.003308 |
| 249 | KEY | 0.002243 |
| 250 | KMB | 0.000917 |
| 251 | KIM | 0.001209 |
| 252 | KMI | 0.001916 |
| 253 | KLAC | 0.001403 |
| 254 | KR | 0.002807 |
| 255 | LB | 0.001545 |
| 256 | LHX | 0.004289 |
| 257 | LH | 0.003646 |
| 258 | LRCX | 0.003018 |
| 259 | LVS | 0.001964 |
| 260 | LEG | 6.11E-05 |
| 261 | LDOS | 0.000454 |
| 262 | LEN | 0.004406 |
| 263 | LLY | 0.003732 |
| 264 | LNC | 0.001283 |
| 265 | LIN | 0.003525 |
| 266 | LYV | 0.00151 |
| 267 | LKQ | 0.001402 |
| 268 | LMT | 0.003648 |
| 269 | L | 0.001538 |
| 270 | LOW | 0.000512 |
| 271 | LYB | 0.002385 |
| 272 | MTB | 9.60E-05 |
| 273 | MRO | 0.000886 |
| 274 | MPC | 0.00373 |
| 275 | MKTX | 0.000331 |
| 276 | MAR | 0.003508 |
| 277 | MMC | 0.001232 |
| 278 | MLM | 0.004144 |
| 279 | MAS | 0.001455 |
| 280 | MA | 0.001686 |
| 281 | MXIM | 0.001791 |
| 282 | MKC | 0.000329 |
| 283 | MCD | 0.00361 |
| 284 | MCK | 0.000309 |
| 285 | MDT | 0.000841 |
| 286 | MRK | 0.004368 |
| 287 | MET | 0.003403 |
| 288 | MTD | 0.002614 |
| 289 | MGM | 0.000284 |
| 290 | MCHP | 0.000627 |
| 291 | MU | 0.003925 |
| 292 | MSFT | 0.003874 |
| 293 | MAA | 0.001698 |
| 294 | MHK | 0.00202 |
| 295 | TAP | 0.001688 |
| 296 | MDLZ | 0.003509 |
| 297 | MPWR | 0.002057 |
| 298 | MNST | 0.002151 |
| 299 | MCO | 0.001742 |
| 300 | MS | 0.000289 |
| 301 | MSI | 0.003402 |
| 302 | MSCI | 0.003544 |
| 303 | NDAQ | 0.004258 |
| 304 | NTAP | 0.001293 |
| 305 | NFLX | 0.001439 |
| 306 | NWL | 0.002156 |
| 307 | NEM | 0.001923 |
| 308 | NWSA | 0.001168 |
| 309 | NWS | 0.003408 |
| 310 | NEE | 0.001181 |
| 311 | NLSN | 0.002508 |
| 312 | NKE | 0.002034 |
| 313 | NI | 0.002016 |
| 314 | NSC | 0.002265 |
| 315 | NTRS | 0.001135 |
| 316 | NOC | 0.000686 |
| 317 | NLOK | 0.00299 |
| 318 | NCLH | 0.001595 |
| 319 | NOV | 0.000133 |
| 320 | NRG | 0.003199 |
| 321 | NUE | 0.002911 |
| 322 | NVDA | 0.002614 |
| 323 | NVR | 7.73E-05 |
| 324 | NXPI | 0.003558 |
| 325 | ORLY | 0.00392 |
| 326 | OXY | 0.000724 |
| 327 | ODFL | 0.003476 |
| 328 | OMC | 0.001783 |
| 329 | OKE | 0.000899 |
| 330 | ORCL | 0.0031 |
| 331 | PCAR | 0.000365 |
| 332 | PKG | 0.00173 |
| 333 | PH | 0.001645 |
| 334 | PAYX | 0.001527 |
| 335 | PENN | 0.004407 |
| 336 | PNR | 0.000677 |
| 337 | PBCT | 0.002732 |
| 338 | PEP | 0.001101 |
| 339 | PKI | 0.001969 |
| 340 | PRGO | 0.00404 |
| 341 | PFE | 0.001199 |
| 342 | PM | 0.003007 |
| 343 | PSX | 0.000455 |
| 344 | PNW | 0.004281 |
| 345 | PXD | 0.003193 |
| 346 | PNC | 0.001003 |
| 347 | POOL | 0.003702 |
| 348 | PPG | 0.002053 |
| 349 | PPL | 0.001594 |
| 350 | PFG | 0.003429 |
| 351 | PG | 0.001222 |
| 352 | PGR | 0.00265 |
| 353 | PLD | 0.001635 |
| 354 | PRU | 0.003708 |
| 355 | PTC | 0.004267 |
| 356 | PEG | 0.004046 |
| 357 | PSA | 0.004177 |
| 358 | PHM | 0.003488 |
| 359 | PVH | 0.001622 |
| 360 | QCOM | 0.000271 |
| 361 | PWR | 0.001752 |
| 362 | DGX | 0.002721 |
| 363 | RL | 0.00208 |
| 364 | RJF | 0.002551 |
| 365 | RTX | 0.000691 |
| 366 | O | 0.004043 |
| 367 | REG | 0.00295 |
| 368 | REGN | 6.88E-05 |
| 369 | RF | 0.004377 |
| 370 | RSG | 0.002779 |
| 371 | RMD | 0.002018 |
| 372 | RHI | 0.002551 |
| 373 | ROK | 0.00047 |
| 374 | ROL | 0.004085 |
| 375 | ROP | 0.002218 |
| 376 | ROST | 0.003725 |
| 377 | RCL | 0.000462 |
| 378 | SPGI | 0.001234 |
| 379 | CRM | 0.003063 |
| 380 | SBAC | 0.002102 |
| 381 | SLB | 0.000148 |
| 382 | STX | 0.000671 |
| 383 | SEE | 4.72E-05 |
| 384 | SRE | 0.000603 |
| 385 | NOW | 0.003698 |
| 386 | SHW | 0.001931 |
| 387 | SPG | 0.000594 |
| 388 | SWKS | 0.001424 |
| 389 | SNA | 0.001067 |
| 390 | SO | 0.002533 |
| 391 | LUV | 0.004032 |
| 392 | SWK | 0.000284 |
| 393 | SBUX | 0.001928 |
| 394 | STT | 0.000656 |
| 395 | STE | 0.002567 |
| 396 | SYK | 0.0013 |
| 397 | SIVB | 0.001642 |
| 398 | SNPS | 0.001379 |
| 399 | SYY | 0.00254 |
| 400 | TMUS | 0.004058 |
| 401 | TROW | 0.000258 |
| 402 | TTWO | 0.000719 |
| 403 | TPR | 0.001083 |
| 404 | TGT | 0.003278 |
| 405 | TEL | 0.002221 |
| 406 | TDY | 0.004209 |
| 407 | TFX | 0.000492 |
| 408 | TER | 0.00349 |
| 409 | TSLA | 0.00302 |
| 410 | TXN | 0.001602 |
| 411 | TXT | 0.003345 |
| 412 | BK | 0.002906 |
| 413 | CLX | 0.002474 |
| 414 | COO | 0.003084 |
| 415 | HSY | 0.003822 |
| 416 | MOS | 0.000539 |
| 417 | TRV | 0.002999 |
| 418 | DIS | 0.000136 |
| 419 | TMO | 0.000837 |
| 420 | TJX | 0.002318 |
| 421 | TSCO | 0.00113 |
| 422 | TT | 0.002183 |
| 423 | TDG | 1.46E-05 |
| 424 | TRMB | 0.001709 |
| 425 | TFC | 0.001957 |
| 426 | TWTR | 0.000341 |
| 427 | TYL | 0.004396 |
| 428 | TSN | 0.003661 |
| 429 | USB | 0.002238 |
| 430 | UDR | 0.003922 |
| 431 | ULTA | 0.000737 |
| 432 | UAA | 0.000973 |
| 433 | UNP | 0.001491 |
| 434 | UAL | 0.003173 |
| 435 | UPS | 0.003035 |
| 436 | URI | 0.000525 |
| 437 | UNH | 0.002869 |
| 438 | UHS | 0.000752 |
| 439 | UNM | 0.001754 |
| 440 | VLO | 0.003912 |
| 441 | VTR | 0.000504 |
| 442 | VRSN | 0.001315 |
| 443 | VRSK | 0.000684 |
| 444 | VZ | 0.000375 |
| 445 | VRTX | 0.001287 |
| 446 | VFC | 0.002576 |
| 447 | VIAC | 7.38E-05 |
| 448 | VTRS | 0.001853 |
| 449 | V | 0.001623 |
| 450 | VNO | 2.88E-05 |
| 451 | VMC | 0.001422 |
| 452 | WRB | 0.003214 |
| 453 | WBA | 0.002848 |
| 454 | WMT | 0.000295 |
| 455 | WM | 0.003351 |
| 456 | WAT | 0.001492 |
| 457 | WEC | 6.29E-05 |
| 458 | WFC | 0.001794 |
| 459 | WELL | 0.000767 |
| 460 | WST | 0.000915 |
| 461 | WDC | 0.002171 |
| 462 | WU | 0.003933 |
| 463 | WAB | 0.000851 |
| 464 | WY | 0.001168 |
| 465 | WHR | 0.003239 |
| 466 | WMB | 0.003283 |
| 467 | WLTW | 0.003866 |
| 468 | WYNN | 0.004188 |
| 469 | XEL | 0.004295 |
| 470 | XLNX | 0.001685 |
| 471 | XYL | 0.000323 |
| 472 | YUM | 0.001529 |
| 473 | ZBRA | 0.001187 |
| 474 | ZBH | 0.003633 |
| 475 | ZION | 0.002556 |
| 476 | ZTS | 0.003414 |
ボラティリティ最小ポートフォリオ
リターン 0.1775
ボラティリティ 0.1821
シャープレシオ 0.9747
| 0 | MMM | 0.003041 |
| 1 | AOS | 0.001196 |
| 2 | ABT | 0.001024 |
| 3 | ABBV | 0.001947 |
| 4 | ABMD | 0.00166 |
| 5 | ACN | 0.004079 |
| 6 | ATVI | 0.000137 |
| 7 | ADBE | 0.001332 |
| 8 | AAP | 0.003516 |
| 9 | AMD | 0.000658 |
| 10 | AES | 0.001894 |
| 11 | AFL | 0.003172 |
| 12 | A | 0.00291 |
| 13 | APD | 0.000104 |
| 14 | AKAM | 0.001153 |
| 15 | ALK | 0.003417 |
| 16 | ALB | 0.00137 |
| 17 | ARE | 0.002833 |
| 18 | ALXN | 0.000738 |
| 19 | ALGN | 0.000135 |
| 20 | ALLE | 0.001342 |
| 21 | LNT | 0.002455 |
| 22 | ALL | 5.47E-05 |
| 23 | GOOGL | 0.003308 |
| 24 | GOOG | 0.001109 |
| 25 | MO | 0.000958 |
| 26 | AMZN | 0.003861 |
| 27 | AMCR | 0.002055 |
| 28 | AEE | 0.001187 |
| 29 | AAL | 0.002177 |
| 30 | AEP | 0.003851 |
| 31 | AXP | 0.003755 |
| 32 | AIG | 0.000528 |
| 33 | AMT | 0.00187 |
| 34 | AWK | 0.004095 |
| 35 | AMP | 0.001873 |
| 36 | ABC | 0.000453 |
| 37 | AME | 0.002474 |
| 38 | AMGN | 0.003098 |
| 39 | APH | 0.00213 |
| 40 | ADI | 0.001407 |
| 41 | ANSS | 0.001536 |
| 42 | ANTM | 0.001742 |
| 43 | AON | 0.001082 |
| 44 | APA | 0.001328 |
| 45 | AAPL | 0.003903 |
| 46 | AMAT | 0.000337 |
| 47 | APTV | 0.002937 |
| 48 | ADM | 0.000496 |
| 49 | AJG | 0.002914 |
| 50 | AIZ | 0.002282 |
| 51 | T | 0.001728 |
| 52 | ATO | 0.003316 |
| 53 | ADSK | 0.003947 |
| 54 | ADP | 0.001045 |
| 55 | AZO | 0.003622 |
| 56 | AVB | 0.00393 |
| 57 | AVY | 0.001864 |
| 58 | BKR | 0.002564 |
| 59 | BLL | 0.002271 |
| 60 | BAC | 0.002981 |
| 61 | BAX | 0.002603 |
| 62 | BDX | 0.002046 |
| 63 | BBY | 0.002842 |
| 64 | BIO | 0.000176 |
| 65 | BIIB | 0.003187 |
| 66 | BLK | 0.001546 |
| 67 | BA | 0.004273 |
| 68 | BKNG | 0.001948 |
| 69 | BWA | 0.004214 |
| 70 | BXP | 0.004292 |
| 71 | BSX | 0.003786 |
| 72 | BMY | 0.001718 |
| 73 | AVGO | 0.001187 |
| 74 | BR | 0.001221 |
| 75 | CHRW | 0.003163 |
| 76 | COG | 0.00311 |
| 77 | CDNS | 0.004167 |
| 78 | CPB | 0.001452 |
| 79 | COF | 0.000854 |
| 80 | CAH | 0.000253 |
| 81 | KMX | 0.001913 |
| 82 | CCL | 0.003719 |
| 83 | CAT | 0.00312 |
| 84 | CBOE | 0.004172 |
| 85 | CBRE | 0.002036 |
| 86 | CDW | 0.001401 |
| 87 | CE | 0.000151 |
| 88 | CNC | 0.003395 |
| 89 | CNP | 0.001863 |
| 90 | CERN | 0.000403 |
| 91 | CF | 9.95E-05 |
| 92 | SCHW | 0.002418 |
| 93 | CHTR | 0.001931 |
| 94 | CVX | 0.001959 |
| 95 | CMG | 0.003388 |
| 96 | CB | 0.002176 |
| 97 | CHD | 0.004153 |
| 98 | CI | 0.001417 |
| 99 | CINF | 2.36E-05 |
| 100 | CTAS | 0.000262 |
| 101 | CSCO | 0.003195 |
| 102 | C | 0.003684 |
| 103 | CTXS | 0.001514 |
| 104 | CME | 0.002548 |
| 105 | CMS | 0.000898 |
| 106 | KO | 0.002402 |
| 107 | CTSH | 0.001878 |
| 108 | CL | 0.000396 |
| 109 | CMCSA | 0.003671 |
| 110 | CMA | 0.000229 |
| 111 | CAG | 0.001676 |
| 112 | COP | 0.0024 |
| 113 | ED | 0.003513 |
| 114 | STZ | 0.00392 |
| 115 | CPRT | 3.61E-05 |
| 116 | GLW | 0.002612 |
| 117 | COST | 5.61E-05 |
| 118 | CCI | 0.003912 |
| 119 | CSX | 0.001116 |
| 120 | CMI | 0.000739 |
| 121 | CVS | 0.000489 |
| 122 | DHI | 0.002427 |
| 123 | DHR | 0.003892 |
| 124 | DRI | 0.000318 |
| 125 | DVA | 0.003535 |
| 126 | DE | 0.002717 |
| 127 | DAL | 0.000272 |
| 128 | XRAY | 0.00274 |
| 129 | DVN | 0.002708 |
| 130 | DXCM | 0.003378 |
| 131 | FANG | 0.002326 |
| 132 | DLR | 0.002648 |
| 133 | DFS | 0.00131 |
| 134 | DISCA | 0.000357 |
| 135 | DISCK | 0.002923 |
| 136 | DISH | 0.002152 |
| 137 | DG | 0.001601 |
| 138 | DLTR | 0.003678 |
| 139 | D | 0.003743 |
| 140 | DPZ | 0.003563 |
| 141 | DOV | 0.002452 |
| 142 | DTE | 0.001349 |
| 143 | DUK | 0.000629 |
| 144 | DRE | 0.000992 |
| 145 | DD | 0.001122 |
| 146 | DXC | 0.003641 |
| 147 | EMN | 0.000439 |
| 148 | ETN | 0.001211 |
| 149 | EBAY | 0.003739 |
| 150 | ECL | 0.004111 |
| 151 | EIX | 0.000716 |
| 152 | EW | 0.003407 |
| 153 | EA | 0.002959 |
| 154 | EMR | 0.001356 |
| 155 | ENPH | 0.000248 |
| 156 | ETR | 0.003195 |
| 157 | EOG | 0.002036 |
| 158 | EFX | 4.72E-05 |
| 159 | EQIX | 0.001039 |
| 160 | EQR | 0.003438 |
| 161 | ESS | 0.000937 |
| 162 | EL | 0.00244 |
| 163 | RE | 0.001121 |
| 164 | EVRG | 0.002806 |
| 165 | ES | 0.00222 |
| 166 | EXC | 0.000796 |
| 167 | EXPE | 0.003597 |
| 168 | EXPD | 0.001463 |
| 169 | EXR | 0.003255 |
| 170 | XOM | 0.000206 |
| 171 | FFIV | 0.001209 |
| 172 | FB | 0.001197 |
| 173 | FAST | 0.002339 |
| 174 | FRT | 0.002788 |
| 175 | FDX | 0.001294 |
| 176 | FIS | 0.003208 |
| 177 | FITB | 0.002849 |
| 178 | FRC | 0.003657 |
| 179 | FE | 0.004088 |
| 180 | FISV | 0.002754 |
| 181 | FLT | 0.002382 |
| 182 | FLIR | 0.003698 |
| 183 | FMC | 0.001434 |
| 184 | F | 0.000749 |
| 185 | FTNT | 0.003133 |
| 186 | FBHS | 0.000254 |
| 187 | BEN | 0.003961 |
| 188 | FCX | 0.001104 |
| 189 | GPS | 0.003488 |
| 190 | GRMN | 0.00113 |
| 191 | IT | 0.002694 |
| 192 | GNRC | 0.003475 |
| 193 | GD | 0.001084 |
| 194 | GE | 0.002365 |
| 195 | GIS | 0.002334 |
| 196 | GM | 0.000391 |
| 197 | GPC | 0.001395 |
| 198 | GILD | 0.003879 |
| 199 | GPN | 0.000603 |
| 200 | GL | 0.002161 |
| 201 | GS | 4.62E-05 |
| 202 | GWW | 0.000451 |
| 203 | HAL | 0.003127 |
| 204 | HBI | 0.001321 |
| 205 | HIG | 0.000437 |
| 206 | HAS | 0.001243 |
| 207 | HCA | 0.002368 |
| 208 | PEAK | 0.003152 |
| 209 | HSIC | 0.002162 |
| 210 | HES | 0.000396 |
| 211 | HLT | 0.004152 |
| 212 | HFC | 0.001797 |
| 213 | HOLX | 0.000126 |
| 214 | HD | 0.004017 |
| 215 | HON | 0.002355 |
| 216 | HRL | 0.003962 |
| 217 | HST | 0.001806 |
| 218 | HPQ | 0.000721 |
| 219 | HUM | 0.000523 |
| 220 | HBAN | 0.002971 |
| 221 | HII | 0.001182 |
| 222 | IEX | 0.002822 |
| 223 | IDXX | 0.002022 |
| 224 | ITW | 0.001697 |
| 225 | ILMN | 0.001183 |
| 226 | INCY | 0.004116 |
| 227 | INTC | 0.000467 |
| 228 | ICE | 0.004028 |
| 229 | IBM | 0.000376 |
| 230 | IFF | 0.004118 |
| 231 | IP | 0.002543 |
| 232 | IPG | 0.002501 |
| 233 | INTU | 0.003726 |
| 234 | ISRG | 0.000235 |
| 235 | IVZ | 0.000836 |
| 236 | IPGP | 0.001006 |
| 237 | IQV | 0.001185 |
| 238 | IRM | 0.000917 |
| 239 | JBHT | 0.001146 |
| 240 | JKHY | 0.002873 |
| 241 | J | 0.001034 |
| 242 | SJM | 0.003202 |
| 243 | JNJ | 0.000898 |
| 244 | JCI | 0.004197 |
| 245 | JPM | 0.000727 |
| 246 | JNPR | 0.001906 |
| 247 | KSU | 0.003265 |
| 248 | K | 0.002507 |
| 249 | KEY | 0.002985 |
| 250 | KMB | 0.000622 |
| 251 | KIM | 0.002884 |
| 252 | KMI | 0.000336 |
| 253 | KLAC | 0.002735 |
| 254 | KR | 0.004177 |
| 255 | LB | 0.000804 |
| 256 | LHX | 0.003238 |
| 257 | LH | 0.001749 |
| 258 | LRCX | 0.001948 |
| 259 | LVS | 0.001774 |
| 260 | LEG | 0.000746 |
| 261 | LDOS | 0.000934 |
| 262 | LEN | 0.001673 |
| 263 | LLY | 0.00277 |
| 264 | LNC | 0.001156 |
| 265 | LIN | 0.004247 |
| 266 | LYV | 0.002336 |
| 267 | LKQ | 0.001788 |
| 268 | LMT | 0.001301 |
| 269 | L | 0.000226 |
| 270 | LOW | 0.003878 |
| 271 | LYB | 0.002127 |
| 272 | MTB | 0.00156 |
| 273 | MRO | 0.001003 |
| 274 | MPC | 0.000496 |
| 275 | MKTX | 0.001202 |
| 276 | MAR | 0.002348 |
| 277 | MMC | 0.000481 |
| 278 | MLM | 0.00016 |
| 279 | MAS | 0.001216 |
| 280 | MA | 0.001759 |
| 281 | MXIM | 0.001049 |
| 282 | MKC | 0.003484 |
| 283 | MCD | 0.002914 |
| 284 | MCK | 0.000664 |
| 285 | MDT | 0.000355 |
| 286 | MRK | 0.00396 |
| 287 | MET | 0.002495 |
| 288 | MTD | 0.001589 |
| 289 | MGM | 0.000601 |
| 290 | MCHP | 0.004032 |
| 291 | MU | 0.000962 |
| 292 | MSFT | 0.001715 |
| 293 | MAA | 0.002443 |
| 294 | MHK | 0.001202 |
| 295 | TAP | 0.002317 |
| 296 | MDLZ | 0.002658 |
| 297 | MPWR | 0.001229 |
| 298 | MNST | 0.002344 |
| 299 | MCO | 0.001322 |
| 300 | MS | 0.000406 |
| 301 | MSI | 0.002683 |
| 302 | MSCI | 0.000123 |
| 303 | NDAQ | 0.003056 |
| 304 | NTAP | 0.00392 |
| 305 | NFLX | 0.004047 |
| 306 | NWL | 0.001139 |
| 307 | NEM | 0.002566 |
| 308 | NWSA | 0.001357 |
| 309 | NWS | 0.001148 |
| 310 | NEE | 0.004006 |
| 311 | NLSN | 0.001363 |
| 312 | NKE | 0.000641 |
| 313 | NI | 0.003075 |
| 314 | NSC | 0.001187 |
| 315 | NTRS | 0.004012 |
| 316 | NOC | 0.003632 |
| 317 | NLOK | 0.000383 |
| 318 | NCLH | 0.001678 |
| 319 | NOV | 0.001471 |
| 320 | NRG | 0.00145 |
| 321 | NUE | 0.003863 |
| 322 | NVDA | 0.003912 |
| 323 | NVR | 0.003362 |
| 324 | NXPI | 0.000851 |
| 325 | ORLY | 0.000324 |
| 326 | OXY | 0.00394 |
| 327 | ODFL | 0.003387 |
| 328 | OMC | 0.000829 |
| 329 | OKE | 0.0038 |
| 330 | ORCL | 0.003259 |
| 331 | PCAR | 0.002023 |
| 332 | PKG | 0.001394 |
| 333 | PH | 0.003663 |
| 334 | PAYX | 0.004222 |
| 335 | PENN | 0.003164 |
| 336 | PNR | 0.00291 |
| 337 | PBCT | 0.000121 |
| 338 | PEP | 0.002954 |
| 339 | PKI | 0.000521 |
| 340 | PRGO | 0.002758 |
| 341 | PFE | 1.75E-05 |
| 342 | PM | 0.000267 |
| 343 | PSX | 0.002731 |
| 344 | PNW | 0.003972 |
| 345 | PXD | 0.002428 |
| 346 | PNC | 0.002099 |
| 347 | POOL | 0.004244 |
| 348 | PPG | 0.003508 |
| 349 | PPL | 0.003425 |
| 350 | PFG | 0.002967 |
| 351 | PG | 0.003946 |
| 352 | PGR | 0.00376 |
| 353 | PLD | 0.002409 |
| 354 | PRU | 0.001192 |
| 355 | PTC | 0.001369 |
| 356 | PEG | 0.002051 |
| 357 | PSA | 0.003317 |
| 358 | PHM | 0.004215 |
| 359 | PVH | 0.002402 |
| 360 | QCOM | 0.001483 |
| 361 | PWR | 0.001642 |
| 362 | DGX | 0.00046 |
| 363 | RL | 0.002819 |
| 364 | RJF | 0.000161 |
| 365 | RTX | 0.003576 |
| 366 | O | 5.34E-05 |
| 367 | REG | 0.001276 |
| 368 | REGN | 0.003749 |
| 369 | RF | 0.001673 |
| 370 | RSG | 0.004284 |
| 371 | RMD | 0.002423 |
| 372 | RHI | 0.003589 |
| 373 | ROK | 0.002425 |
| 374 | ROL | 0.000422 |
| 375 | ROP | 0.001174 |
| 376 | ROST | 0.000346 |
| 377 | RCL | 0.002842 |
| 378 | SPGI | 0.000658 |
| 379 | CRM | 0.003063 |
| 380 | SBAC | 0.003241 |
| 381 | SLB | 0.00188 |
| 382 | STX | 0.001893 |
| 383 | SEE | 0.001153 |
| 384 | SRE | 0.003075 |
| 385 | NOW | 0.002162 |
| 386 | SHW | 0.002804 |
| 387 | SPG | 1.84E-05 |
| 388 | SWKS | 0.003023 |
| 389 | SNA | 0.002382 |
| 390 | SO | 0.004262 |
| 391 | LUV | 0.001783 |
| 392 | SWK | 0.002373 |
| 393 | SBUX | 0.000681 |
| 394 | STT | 0.002469 |
| 395 | STE | 0.002366 |
| 396 | SYK | 0.001516 |
| 397 | SIVB | 0.003039 |
| 398 | SNPS | 0.002491 |
| 399 | SYY | 0.000659 |
| 400 | TMUS | 0.003333 |
| 401 | TROW | 0.003474 |
| 402 | TTWO | 0.004106 |
| 403 | TPR | 0.001784 |
| 404 | TGT | 0.00141 |
| 405 | TEL | 0.000943 |
| 406 | TDY | 0.002435 |
| 407 | TFX | 0.004011 |
| 408 | TER | 0.001664 |
| 409 | TSLA | 0.00104 |
| 410 | TXN | 0.00061 |
| 411 | TXT | 0.000423 |
| 412 | BK | 5.63E-05 |
| 413 | CLX | 0.003706 |
| 414 | COO | 0.002855 |
| 415 | HSY | 0.00224 |
| 416 | MOS | 0.00117 |
| 417 | TRV | 0.001742 |
| 418 | DIS | 0.003391 |
| 419 | TMO | 0.002421 |
| 420 | TJX | 0.003475 |
| 421 | TSCO | 0.001356 |
| 422 | TT | 0.000656 |
| 423 | TDG | 0.002472 |
| 424 | TRMB | 0.001991 |
| 425 | TFC | 0.000603 |
| 426 | TWTR | 0.000801 |
| 427 | TYL | 0.003743 |
| 428 | TSN | 0.00376 |
| 429 | USB | 0.000155 |
| 430 | UDR | 0.003759 |
| 431 | ULTA | 0.000646 |
| 432 | UAA | 0.000373 |
| 433 | UNP | 0.004107 |
| 434 | UAL | 0.001074 |
| 435 | UPS | 0.004319 |
| 436 | URI | 0.000531 |
| 437 | UNH | 0.001881 |
| 438 | UHS | 0.003957 |
| 439 | UNM | 7.63E-05 |
| 440 | VLO | 0.003264 |
| 441 | VTR | 0.001758 |
| 442 | VRSN | 0.003821 |
| 443 | VRSK | 0.001043 |
| 444 | VZ | 0.003556 |
| 445 | VRTX | 0.002321 |
| 446 | VFC | 9.45E-05 |
| 447 | VIAC | 0.00092 |
| 448 | VTRS | 0.001684 |
| 449 | V | 0.0021 |
| 450 | VNO | 0.00304 |
| 451 | VMC | 0.003051 |
| 452 | WRB | 0.002426 |
| 453 | WBA | 0.00039 |
| 454 | WMT | 0.004024 |
| 455 | WM | 0.00423 |
| 456 | WAT | 0.002448 |
| 457 | WEC | 0.00111 |
| 458 | WFC | 0.003707 |
| 459 | WELL | 0.001077 |
| 460 | WST | 0.002261 |
| 461 | WDC | 0.00194 |
| 462 | WU | 0.003893 |
| 463 | WAB | 0.004237 |
| 464 | WY | 0.000637 |
| 465 | WHR | 0.000878 |
| 466 | WMB | 0.001058 |
| 467 | WLTW | 0.003424 |
| 468 | WYNN | 0.001837 |
| 469 | XEL | 0.000269 |
| 470 | XLNX | 0.001201 |
| 471 | XYL | 0.000513 |
| 472 | YUM | 0.000105 |
| 473 | ZBRA | 0.003757 |
| 474 | ZBH | 0.001905 |
| 475 | ZION | 0.001155 |
| 476 | ZTS | 0.002688 |
セクター別最適ポートフォリオ
上の最適ポートフォリオをセクター別にまとめたものです．
シャープレシオ最大
セクター 割合
0 Industrials 0.133726
1 Health Care 0.131538
2 Information Technology 0.159262
3 Communication Services 0.044618
4 Consumer Discretionary 0.126905
5 Utilities 0.061165
6 Financials 0.129596
7 Materials 0.052247
8 Real Estate 0.051724
9 Consumer Staples 0.065592
10 Energy 0.043626ボラティリティ最小
セクター 割合
0 Industrials 0.139383
1 Health Care 0.122160
2 Information Technology 0.149156
3 Communication Services 0.049797
4 Consumer Discretionary 0.127357
5 Utilities 0.069310
6 Financials 0.114380
7 Materials 0.048829
8 Real Estate 0.065760
9 Consumer Staples 0.067503
10 Energy 0.046365この結果を出力するコードについては以下の記事をご覧ください．
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