713:) one could ascertain a 4-factor alpha, and so on. If Jensen's alpha is significant and positive, then the strategy being considered has a history of generating returns on top of what would be expected based on other factors alone. For example, in the 3-factor case, we may regress momentum factor returns on 3-factor returns to find that momentum generates a significant premium on top of size, value, and market returns.
73:
This is based on the concept that riskier assets should have higher expected returns than less risky assets. If an asset's return is even higher than the risk adjusted return, that asset is said to have "positive alpha" or "abnormal returns". Investors are constantly seeking investments that have
701:
Jensen's alpha is a statistic that is commonly used in empirical finance to assess the marginal return associated with unit exposure to a given strategy. Generalizing the above definition to the multifactor setting, Jensen's alpha is a measure of the marginal return associated with an additional
248:
501:
691:
85:
to allow for repeatedly earning positive Alpha, unless by chance. Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the
622:
563:
104:
383:
347:
314:
281:
867:
46:
The security could be any asset, such as stocks, bonds, or derivatives. The theoretical return is predicted by a market model, most commonly the
399:
50:(CAPM). The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses
860:
630:
70:
in 1968. The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset.
853:
1098:
727:
813:
797:
706:
568:
509:
1123:
784:
Jensen, M.C., "The
Performance of Mutual Funds in the Period 1945-1964," Journal of Finance 23, 1968, pp. 389-416.
1651:
1656:
1117:
243:{\displaystyle {\overset {\text{Jensen's alpha}}{\alpha _{J}}}={\overset {\text{portfolio return}}{R_{i}}}-}
1600:
1540:
1336:
1242:
709:
factors (of size and value), we obtain the 3-factor alpha. If additional factors were to be added (such as
1661:
1326:
1294:
1198:
1152:
1135:
1088:
82:
47:
1646:
1111:
1105:
1500:
1175:
705:
We obtain the CAPM alpha if we consider excess market returns as the only factor. If we add in the
1454:
1315:
1210:
1093:
837:
764:
358:
1342:
752:
1480:
1289:
1615:
1535:
1300:
1284:
1247:
1129:
1072:
1040:
325:
292:
259:
8:
1545:
1490:
1414:
1274:
1204:
1033:
1006:
32:
1585:
1560:
1520:
1505:
1424:
1394:
1363:
1321:
1065:
975:
965:
722:
710:
40:
393:
An additional way of understanding the definition can be obtained by rewriting it as:
1449:
1434:
1186:
67:
1550:
1470:
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1147:
1023:
942:
898:
876:
386:
317:
284:
51:
1625:
1620:
1555:
1530:
1465:
1439:
1419:
1378:
1373:
1368:
1353:
1348:
1236:
1170:
1162:
1050:
937:
801:
506:
If we define the excess return of the fund (market) over the risk free return as
36:
1580:
1575:
1475:
1460:
1221:
1216:
1181:
980:
947:
893:
885:
817:
350:
794:
1640:
1444:
1429:
1404:
1358:
1310:
1013:
970:
957:
908:
747:
742:
90:
1605:
1525:
1495:
1485:
1305:
1279:
1028:
1018:
1001:
932:
927:
903:
737:
86:
35:
of securities over the theoretical expected return. It is a version of the
1610:
1590:
1570:
1565:
1510:
1399:
1331:
732:
253:
In the context of CAPM, calculating alpha requires the following inputs:
78:
63:
496:{\displaystyle \alpha _{J}=(R_{i}-R_{f})-\beta _{iM}\cdot (R_{M}-R_{f})}
1595:
1515:
1192:
1055:
1231:
1226:
1141:
1060:
845:
1409:
1045:
783:
1253:
62:
Jensen's alpha was first used as a measure in the evaluation of
996:
686:{\displaystyle \alpha _{J}=\Delta _{R}-\beta _{iM}\Delta _{M}}
919:
31:) is used to determine the abnormal return of a security or
633:
571:
512:
402:
361:
328:
295:
262:
107:
702:
strategy that is not explained by existing factors.
81:, many academics believe financial markets are too
685:
616:
557:
495:
377:
341:
308:
275:
242:
1638:
838:Addendum, Jensen's Alpha in Quantitative Finance
39:based on a theoretical performance instead of a
617:{\displaystyle \Delta _{M}\equiv (R_{M}-R_{f})}
558:{\displaystyle \Delta _{R}\equiv (R_{i}-R_{f})}
696:
861:
868:
854:
624:then Jensen's alpha can be expressed as:
814:"Jensen's Alpha in Quantitative Finance"
1639:
875:
849:
728:Modigliani risk-adjusted performance
13:
765:Evaluating Mutual Fund Performance
674:
648:
573:
514:
14:
1673:
758:
1124:Electronic communication network
831:
806:
788:
777:
611:
585:
552:
526:
490:
464:
442:
416:
237:
234:
194:
148:
96:
1:
1118:Multilateral trading facility
770:
1541:Returns-based style analysis
1337:Post-modern portfolio theory
1243:Security characteristic line
7:
1295:Efficient-market hypothesis
1199:Capital asset pricing model
1136:Straight-through processing
716:
697:Use in quantitative finance
378:{\displaystyle \beta _{iM}}
48:capital asset pricing model
10:
1678:
1112:Alternative Trading System
795:"Alpha", Risk Encyclopedia
57:
25:Jensen's Performance Index
1387:
1262:
1161:
1081:
989:
956:
917:
883:
1176:Arbitrage pricing theory
1455:Initial public offering
1316:Modern portfolio theory
1211:Dividend discount model
1094:List of stock exchanges
1343:Random walk hypothesis
753:Upside potential ratio
687:
618:
559:
497:
379:
343:
310:
277:
244:
1652:Investment indicators
1481:Market capitalization
1290:Dollar cost averaging
688:
619:
560:
498:
380:
344:
342:{\displaystyle R_{f}}
311:
309:{\displaystyle R_{M}}
278:
276:{\displaystyle R_{i}}
245:
16:Financial calculation
1657:Mathematical finance
1301:Fundamental analysis
1285:Contrarian investing
1248:Security market line
1153:Liquidity aggregator
1130:Direct market access
1041:Quantitative analyst
631:
569:
510:
400:
359:
326:
293:
260:
105:
1546:Reverse stock split
1491:Market manipulation
1415:Dual-listed company
1275:Algorithmic trading
1205:Capital market line
1007:Inter-dealer broker
287:(on the portfolio),
1662:Portfolio theories
1586:Stock market index
1425:Efficient frontier
1364:Technical analysis
1322:Momentum investing
1144:(private exchange)
1034:Proprietary trader
976:Shares outstanding
966:Authorised capital
800:2013-10-04 at the
723:Alpha (investment)
683:
614:
555:
493:
375:
339:
306:
273:
240:
1647:Financial markets
1634:
1633:
1435:Flight-to-quality
1187:Buffett indicator
877:Financial markets
389:of the portfolio.
232:
231:
212:
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189:
188:
166:
165:
143:
142:
123:
122:
54:as a multiplier.
1669:
1551:Share repurchase
1263:Trading theories
1148:Crossing network
1106:Over-the-counter
943:Restricted stock
899:Secondary market
870:
863:
856:
847:
846:
840:
835:
829:
828:
826:
825:
816:. Archived from
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172:
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141:portfolio return
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129:
124:
120:
119:
118:
109:
1677:
1676:
1672:
1671:
1670:
1668:
1667:
1666:
1637:
1636:
1635:
1630:
1621:Voting interest
1531:Public offering
1466:Mandatory offer
1440:Government bond
1420:DuPont analysis
1383:
1379:Value investing
1374:Value averaging
1369:Trend following
1354:Style investing
1349:Sector rotation
1264:
1258:
1237:Net asset value
1163:Stock valuation
1157:
1077:
985:
952:
938:Preferred stock
913:
879:
874:
844:
843:
836:
832:
823:
821:
812:
811:
807:
802:Wayback Machine
793:
789:
782:
778:
773:
761:
719:
699:
677:
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664:
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629:
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592:
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576:
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566:
546:
542:
533:
529:
517:
513:
511:
508:
507:
484:
480:
471:
467:
452:
448:
436:
432:
423:
419:
407:
403:
401:
398:
397:
366:
362:
360:
357:
356:
333:
329:
327:
324:
323:
300:
296:
294:
291:
290:
285:realized return
267:
263:
261:
258:
257:
223:
219:
217:
203:
199:
197:
177:
173:
171:
157:
153:
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134:
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114:
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102:
99:
60:
17:
12:
11:
5:
1675:
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1623:
1618:
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1603:
1598:
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1588:
1583:
1581:Stock exchange
1578:
1576:Stock dilution
1573:
1568:
1563:
1558:
1553:
1548:
1543:
1538:
1533:
1528:
1523:
1518:
1513:
1508:
1503:
1501:Mean reversion
1498:
1493:
1488:
1483:
1478:
1476:Market anomaly
1473:
1468:
1463:
1458:
1452:
1447:
1442:
1437:
1432:
1427:
1422:
1417:
1412:
1407:
1402:
1397:
1395:Bid–ask spread
1391:
1389:
1385:
1384:
1382:
1381:
1376:
1371:
1366:
1361:
1356:
1351:
1346:
1340:
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1329:
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1229:
1224:
1222:Earnings yield
1219:
1217:Dividend yield
1214:
1208:
1202:
1196:
1190:
1184:
1179:
1173:
1167:
1165:
1159:
1158:
1156:
1155:
1150:
1145:
1139:
1133:
1127:
1121:
1115:
1109:
1108:(off-exchange)
1103:
1102:
1101:
1096:
1085:
1083:
1082:Trading venues
1079:
1078:
1076:
1075:
1070:
1069:
1068:
1058:
1053:
1048:
1043:
1038:
1037:
1036:
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1021:
1016:
1011:
1010:
1009:
1004:
993:
991:
987:
986:
984:
983:
981:Treasury stock
978:
973:
968:
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960:
954:
953:
951:
950:
948:Tracking stock
945:
940:
935:
930:
924:
922:
915:
914:
912:
911:
906:
901:
896:
894:Primary market
890:
888:
881:
880:
873:
872:
865:
858:
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842:
841:
830:
805:
787:
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759:External links
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406:
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372:
369:
365:
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353:of return, and
351:risk-free rate
336:
332:
321:
303:
299:
288:
270:
266:
251:
250:
239:
236:
230:risk free rate
226:
222:
216:
206:
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196:
193:
187:portfolio beta
183:
180:
176:
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164:risk free rate
160:
156:
150:
147:
137:
133:
127:
121:Jensen's alpha
117:
113:
98:
95:
74:higher alpha.
68:Michael Jensen
59:
56:
37:standard alpha
21:Jensen's alpha
15:
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6:
4:
3:
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1559:
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1556:Short selling
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1445:Greenspan put
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1431:
1430:Financial law
1428:
1426:
1423:
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1408:
1406:
1405:Cross listing
1403:
1401:
1398:
1396:
1393:
1392:
1390:
1388:Related terms
1386:
1380:
1377:
1375:
1372:
1370:
1367:
1365:
1362:
1360:
1359:Swing trading
1357:
1355:
1352:
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1347:
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1341:
1338:
1335:
1333:
1330:
1328:
1327:Mosaic theory
1325:
1323:
1320:
1317:
1314:
1312:
1311:Market timing
1309:
1307:
1304:
1302:
1299:
1296:
1293:
1291:
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1283:
1281:
1278:
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1252:
1249:
1246:
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1228:
1225:
1223:
1220:
1218:
1215:
1212:
1209:
1206:
1203:
1200:
1197:
1194:
1191:
1188:
1185:
1183:
1180:
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1174:
1172:
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1160:
1154:
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1134:
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1128:
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1119:
1116:
1113:
1110:
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1104:
1100:
1099:Trading hours
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1095:
1092:
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1090:
1087:
1086:
1084:
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1074:
1071:
1067:
1064:
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1062:
1059:
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1042:
1039:
1035:
1032:
1030:
1027:
1026:
1025:
1022:
1020:
1017:
1015:
1014:Broker-dealer
1012:
1008:
1005:
1003:
1000:
999:
998:
995:
994:
992:
988:
982:
979:
977:
974:
972:
971:Issued shares
969:
967:
964:
963:
961:
959:
958:Share capital
955:
949:
946:
944:
941:
939:
936:
934:
931:
929:
926:
925:
923:
921:
916:
910:
909:Fourth market
907:
905:
902:
900:
897:
895:
892:
891:
889:
887:
882:
878:
871:
866:
864:
859:
857:
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851:
848:
839:
834:
820:on 2016-03-04
819:
815:
809:
803:
799:
796:
791:
785:
780:
776:
766:
763:
762:
754:
751:
749:
748:Treynor ratio
746:
744:
743:Sortino ratio
741:
739:
736:
734:
731:
729:
726:
724:
721:
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703:
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318:market return
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210:market return
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91:Treynor ratio
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75:
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65:
55:
53:
49:
44:
42:
38:
34:
30:
29:ex-post alpha
26:
22:
1606:Tender offer
1526:Public float
1496:Market trend
1486:Market depth
1306:Growth stock
1280:Buy and hold
1189:(Cap-to-GDP)
1029:Floor trader
1019:Market maker
1002:Floor broker
990:Participants
933:Golden share
928:Common stock
904:Third market
833:
822:. Retrieved
818:the original
808:
790:
779:
738:Sharpe ratio
704:
700:
505:
392:
252:
87:Sharpe ratio
76:
72:
66:managers by
61:
45:
41:market index
28:
24:
20:
19:In finance,
18:
1611:Uptick rule
1591:Stock split
1571:Squeeze-out
1566:Speculation
1511:Open outcry
1400:Block trade
1332:Pairs trade
733:Omega ratio
707:Fama-French
97:Calculation
79:Eugene Fama
64:mutual fund
1641:Categories
1616:Volatility
1596:Stock swap
1516:Order book
1267:strategies
1193:Book value
1061:Arbitrager
1056:Speculator
824:2015-10-17
771:References
1232:Fed model
1227:EV/EBITDA
1142:Dark pool
1073:Regulator
918:Types of
884:Types of
675:Δ
662:β
658:−
649:Δ
636:α
599:−
583:≡
574:Δ
540:−
524:≡
515:Δ
478:−
462:⋅
450:β
446:−
430:−
405:α
364:β
215:−
192:⋅
175:β
146:−
112:α
83:efficient
33:portfolio
1561:Slippage
1521:Position
1506:Momentum
1410:Dividend
1089:Exchange
1046:Investor
798:Archived
717:See also
711:momentum
89:and the
1450:Haircut
1254:T-model
1066:Scalper
886:markets
58:History
1471:Margin
1339:(PMPT)
1201:(CAPM)
1051:Hedger
1024:Trader
997:Broker
920:stocks
385:: the
349:: the
316:: the
283:: the
77:Since
1626:Yield
1601:Trade
1536:Rally
1457:(IPO)
1345:(RMH)
1318:(MPT)
1297:(EMH)
1250:(SML)
1239:(NAV)
1213:(DDM)
1207:(CML)
1178:(APT)
1171:Alpha
1138:(STP)
1132:(DMA)
1126:(ECN)
1120:(MTF)
1114:(ATS)
1461:Long
1265:and
1195:(BV)
1182:Beta
565:and
387:beta
52:beta
23:(or
1643::
93:.
43:.
27:,
869:e
862:t
855:v
827:.
679:M
669:M
666:i
653:R
645:=
640:J
612:)
607:f
603:R
594:M
590:R
586:(
578:M
553:)
548:f
544:R
535:i
531:R
527:(
519:R
491:)
486:f
482:R
473:M
469:R
465:(
457:M
454:i
443:)
438:f
434:R
425:i
421:R
417:(
414:=
409:J
371:M
368:i
335:f
331:R
320:,
302:M
298:R
269:i
265:R
238:]
235:)
225:f
221:R
205:M
201:R
195:(
182:M
179:i
169:+
159:f
155:R
149:[
136:i
132:R
126:=
116:J
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