Answer
There are three steps to calculating equity risk premia.
Step 1: Get the risk premia 𝛾𝑗,𝑡 from market prices:
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101 286T105 299Q126 348 164 391T252 441Q253 441 260 441T272 442Q296 441 316 432Q341 418 354 401T367 348V332L318 133Q267 -67 264 -75Q246 -125 194 -164T75 -204Q25 -204 7 -183T-12 -137Q-12 -110 7 -91T53 -71Q70 -71 82 -81T95 -112Q95 -148 63 -167Q69 -168 77 -168Q111 -168 139 -140T182 -74L193 -32Q204 11 219 72T251 197T278 308T289 365Q289 372 288 376Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-2C' d='M78 35T78 60T94 103T137 121Q165 121 187 96T210 8Q210 -27 201 -60T180 -117T154 -158T130 -185T117 -194Q113 -194 104 -185T95 -172Q95 -168 106 -156T131 -126T157 -76T173 -3V9L172 8Q170 7 167 6T161 3T152 1T140 0Q113 0 96 17Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-74' d='M26 385Q19 392 19 395Q19 399 22 411T27 425Q29 430 36 430T87 431H140L159 511Q162 522 166 540T173 566T179 586T187 603T197 615T211 624T229 626Q247 625 254 615T261 596Q261 589 252 549T232 470L222 433Q222 431 272 431H323Q330 424 330 420Q330 398 317 385H210L174 240Q135 80 135 68Q135 26 162 26Q197 26 230 60T283 144Q285 150 288 151T303 153H307Q322 153 322 145Q322 142 319 133Q314 117 301 95T267 48T216 6T155 -11Q125 -11 98 4T59 56Q57 64 57 83V101L92 241Q127 382 128 383Q128 385 77 385H26Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-3D' d='M56 347Q56 360 70 367H707Q722 359 722 347Q722 336 708 328L390 327H72Q56 332 56 347ZM56 153Q56 168 72 173H708Q722 163 722 153Q722 140 707 133H70Q56 140 56 153Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJSZ1-2211' d='M61 748Q64 750 489 750H913L954 640Q965 609 976 579T993 533T999 516H979L959 517Q936 579 886 621T777 682Q724 700 655 705T436 710H319Q183 710 183 709Q186 706 348 484T511 259Q517 250 513 244L490 216Q466 188 420 134T330 27L149 -187Q149 -188 362 -188Q388 -188 436 -188T506 -189Q679 -189 778 -162T936 -43Q946 -27 959 6H999L913 -249L489 -250Q65 -250 62 -248Q56 -246 56 -239Q56 -234 118 -161Q186 -81 245 -11L428 206Q428 207 242 462L57 717L56 728Q56 744 61 748Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-54' d='M40 437Q21 437 21 445Q21 450 37 501T71 602L88 651Q93 669 101 677H569H659Q691 677 697 676T704 667Q704 661 687 553T668 444Q668 437 649 437Q640 437 637 437T631 442L629 445Q629 451 635 490T641 551Q641 586 628 604T573 629Q568 630 515 631Q469 631 457 630T439 622Q438 621 368 343T298 60Q298 48 386 46Q418 46 427 45T436 36Q436 31 433 22Q429 4 424 1L422 0Q419 0 415 0Q410 0 363 1T228 2Q99 2 64 0H49Q43 6 43 9T45 27Q49 40 55 46H83H94Q174 46 189 55Q190 56 191 56Q196 59 201 76T241 233Q258 301 269 344Q339 619 339 625Q339 630 310 630H279Q212 630 191 624Q146 614 121 583T67 467Q60 445 57 441T43 437H40Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-31' d='M213 578L200 573Q186 568 160 563T102 556H83V602H102Q149 604 189 617T245 641T273 663Q275 666 285 666Q294 666 302 660V361L303 61Q310 54 315 52T339 48T401 46H427V0H416Q395 3 257 3Q121 3 100 0H88V46H114Q136 46 152 46T177 47T193 50T201 52T207 57T213 61V578Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-44' d='M287 628Q287 635 230 637Q207 637 200 638T193 647Q193 655 197 667T204 682Q206 683 403 683Q570 682 590 682T630 676Q702 659 752 597T803 431Q803 275 696 151T444 3L430 1L236 0H125H72Q48 0 41 2T33 11Q33 13 36 25Q40 41 44 43T67 46Q94 46 127 49Q141 52 146 61Q149 65 218 339T287 628ZM703 469Q703 507 692 537T666 584T629 613T590 629T555 636Q553 636 541 636T512 636T479 637H436Q392 637 386 627Q384 623 313 339T242 52Q242 48 253 48T330 47Q335 47 349 47T373 46Q499 46 581 128Q617 164 640 212T683 339T703 469Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-28' d='M94 250Q94 319 104 381T127 488T164 576T202 643T244 695T277 729T302 750H315H319Q333 750 333 741Q333 738 316 720T275 667T226 581T184 443T167 250T184 58T225 -81T274 -167T316 -220T333 -241Q333 -250 318 -250H315H302L274 -226Q180 -141 137 -14T94 250Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-2B' d='M56 237T56 250T70 270H369V420L370 570Q380 583 389 583Q402 583 409 568V270H707Q722 262 722 250T707 230H409V-68Q401 -82 391 -82H389H387Q375 -82 369 -68V230H70Q56 237 56 250Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-72' d='M21 287Q22 290 23 295T28 317T38 348T53 381T73 411T99 433T132 442Q161 442 183 430T214 408T225 388Q227 382 228 382T236 389Q284 441 347 441H350Q398 441 422 400Q430 381 430 363Q430 333 417 315T391 292T366 288Q346 288 334 299T322 328Q322 376 378 392Q356 405 342 405Q286 405 239 331Q229 315 224 298T190 165Q156 25 151 16Q138 -11 108 -11Q95 -11 87 -5T76 7T74 17Q74 30 114 189T154 366Q154 405 128 405Q107 405 92 377T68 316T57 280Q55 278 41 278H27Q21 284 21 287Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMATHI-3B3' d='M31 249Q11 249 11 258Q11 275 26 304T66 365T129 418T206 441Q233 441 239 440Q287 429 318 386T371 255Q385 195 385 170Q385 166 386 166L398 193Q418 244 443 300T486 391T508 430Q510 431 524 431H537Q543 425 543 422Q543 418 522 378T463 251T391 71Q385 55 378 6T357 -100Q341 -165 330 -190T303 -216Q286 -216 286 -188Q286 -138 340 32L346 51L347 69Q348 79 348 100Q348 257 291 317Q251 355 196 355Q148 355 108 329T51 260Q49 251 47 251Q45 249 31 249Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJMAIN-29' d='M60 749L64 750Q69 750 74 750H86L114 726Q208 641 251 514T294 250Q294 182 284 119T261 12T224 -76T186 -143T145 -194T113 -227T90 -246Q87 -249 86 -250H74Q66 -250 63 -250T58 -247T55 -238Q56 -237 66 -225Q221 -64 221 250T66 725Q56 737 55 738Q55 746 60 749Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJSZ1-28' d='M152 251Q152 646 388 850H416Q422 844 422 841Q422 837 403 816T357 753T302 649T255 482T236 250Q236 124 255 19T301 -147T356 -251T403 -315T422 -340Q422 -343 416 -349H388Q359 -325 332 -296T271 -213T212 -97T170 56T152 251Z'%3e%3c/path%3e %3cpath stroke-width='1' id='E1-MJSZ1-29' d='M305 251Q305 -145 69 -349H56Q43 -349 39 -347T35 -338Q37 -333 60 -307T108 -239T160 -136T204 27T221 250T204 473T160 636T108 740T60 807T35 839Q35 850 50 850H56H69Q197 743 256 566Q305 425 305 251Z'%3e%3c/path%3e %3c/defs%3e %3cg stroke='currentColor' fill='currentColor' stroke-width='0' transform='matrix(1 0 0 -1 0 0)' aria-hidden='true'%3e %3cg 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Step 2: Estimate the price 𝜆𝑘,,𝑡 of each risk factor given the factor exposures 𝛽𝑗,𝑘,𝑡 of each transaction.
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y='488'%3e%3c/use%3e %3cg transform='translate(878%2c-327)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-6B' x='0' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-3D' x='521' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-31' x='1300' y='0'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3cuse xlink:href='%23E1-MJMAIN-3D' x='4627' y='0'%3e%3c/use%3e %3cg transform='translate(5683%2c0)'%3e %3cuse xlink:href='%23E1-MJMATHI-3B2' x='0' y='0'%3e%3c/use%3e %3cg transform='translate(566%2c-150)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-6A' x='0' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-2C' x='412' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-6B' x='691' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-2C' x='1212' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-74' x='1491' y='0'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3cg transform='translate(7660%2c0)'%3e %3cuse xlink:href='%23E1-MJMATHI-3BB' x='0' y='0'%3e%3c/use%3e %3cg transform='translate(583%2c-150)'%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-6B' x='0' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMAIN-2C' x='521' y='0'%3e%3c/use%3e %3cuse transform='scale(0.707)' xlink:href='%23E1-MJMATHI-74' x='800' y='0'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3cuse xlink:href='%23E1-MJMAIN-2B' x='9387' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMATHI-3C9' x='10388' y='0'%3e%3c/use%3e %3cuse xlink:href='%23E1-MJMAIN-2C' x='11010' y='0'%3e%3c/use%3e %3c/g%3e %3c/g%3e %3c/g%3e %3c/g%3e %3c/svg%3e)
Step 3: Apply factor prices (lambdas) to new assets to compute their risk premia given their factor exposures.