We now move to examine performance consequences of both the segment and family tournaments. As a first step, in this section we analyse funds’ rank transitions. Table 3.10 reports the transition probability of funds’ segment ranks. In the first column, we sort all the funds into 10 deciles in ascending order according to their segment ranks. As such, the 1st decile includes bottom ranked
funds while the 10th decile contains top ranked funds. The remaining columns
present the probability of funds ranked in each of the deciles moving to the other deciles.
We find that the performance of top ranked funds persists for the ranking period and the post-ranking period. The transition probability of staying in the 10th decile
is the highest, with a probability of 28.69% of the funds remaining in the same decile in the second half of the year. The transition probability of remaining in the 1st decile is the second highest value. Thus, the very best and worst-performing
funds seem to show performance persistency throughout the sample period. It is also the case that the probability for top ranked funds to have extremely bad performance in the second half of the year increases, particularly when their ranks are higher in the first half of the year. That is, funds located in the 10th, 9th, 8th and
7th deciles have a cumulative probability of being demoted to a decile lower than
or equal to the 3rd decile of 21.54%, 26.34%, 23%, and 27.73%, respectively. Top
performing managers, therefore, are capable of retaining their positions. On the other hand, bottom ranked funds seem to have more difficulty in being promoted to higher ranking groups.
Table 3.10 Segment rank transition matrix Panel A Current Decile 1 2 3 4 5 6 7 8 9 10 1 0.1930 0.1004 0.1471 0.0786 0.1085 0.0639 0.1239 0.0643 0.0497 0.0710 2 0.1012 0.1513 0.1059 0.1329 0.0911 0.0856 0.0826 0.1078 0.0744 0.0678 3 0.1342 0.1083 0.0764 0.1333 0.1152 0.1394 0.0982 0.0721 0.0712 0.0510 4 0.0807 0.0863 0.1152 0.1275 0.1378 0.1137 0.1051 0.0957 0.0832 0.0547 5 0.0834 0.1365 0.1219 0.1113 0.0727 0.1170 0.1200 0.0927 0.0660 0.0787 6 0.0940 0.1115 0.0940 0.0782 0.1169 0.0971 0.1173 0.1257 0.0838 0.0814 7 0.0673 0.0949 0.1151 0.0799 0.1339 0.0847 0.1099 0.1108 0.1151 0.0887 8 0.0990 0.0528 0.0782 0.0961 0.0965 0.0864 0.0814 0.1158 0.1623 0.1313 9 0.0999 0.0984 0.0651 0.0733 0.0948 0.1187 0.0736 0.1034 0.1370 0.1362 10 0.1021 0.0566 0.0567 0.0746 0.0486 0.0670 0.0635 0.1027 0.1417 0.2869 Panel B Current Decile 1 2 3 4 5 6 7 8 9 10 1 0.1806 0.1055 0.1415 0.0992 0.0831 0.1071 0.0874 0.0601 0.0646 0.0711 2 0.1002 0.1512 0.0740 0.0941 0.1477 0.0991 0.0879 0.105 0.0859 0.0548 3 0.1071 0.115 0.1571 0.0796 0.1138 0.0809 0.1096 0.0852 0.0686 0.0829 4 0.0814 0.0952 0.0908 0.1684 0.0837 0.1543 0.1137 0.0729 0.0778 0.0618 5 0.1030 0.1152 0.1339 0.1323 0.1083 0.0854 0.0786 0.1055 0.0845 0.0531 6 0.1110 0.1262 0.1018 0.0745 0.1171 0.0724 0.1057 0.1047 0.1023 0.0844 7 0.0753 0.0641 0.0718 0.1073 0.1259 0.0959 0.1231 0.1177 0.1216 0.0971 8 0.1216 0.0970 0.0610 0.1109 0.0755 0.1111 0.0843 0.1204 0.0986 0.1196 9 0.0843 0.0667 0.0592 0.0633 0.0814 0.1021 0.1115 0.1072 0.1261 0.1989 10 0.0927 0.0617 0.0822 0.0544 0.0782 0.0638 0.0744 0.1112 0.1528 0.2289 Notes: This table reports the transition probability of the return ranks between the ranking and post-ranking periods. Funds are
ranked in ascending order into 10 deciles compared with the mean returns from other funds in the same segment during the ranking period. Columns 2 to 11 report the transition probability of rank shifting for funds in each decile from the ranking period to the post-ranking period. Panel A reports the transition probability on a mid-year basis while Panel B considers a 7-month ranking period. All the figures reported here are in percentage value.
We then switch our attention to the transition probability of the family ranks. A transition matrix similar to that in Table 3.10 is developed in Table 3.11. However, instead of using the segment ranks, in the first column of Table 3.11 we group all the sample funds into 5 percentiles according to their family ranks. For example, the 1st percentile group contains all funds that are ranked in the bottom 20%
within their affiliated families, while funds within the 5th percentile group are
ranked in the top 20% by their average returns. The results are found to be similar to those in the transition matrix of the segment ranks. Performance of the top and bottom ranked funds persists over time. Funds in the 1st percentile group have a
32.04% probability of staying in the same group and 32.44% of the funds in the 5th percentile group will keep performing at the high level. Panel B of Table 3.11
confirms a similar outcome.
As shown in Tables 3.10 and 3.11, we use the transition probability to provide a general picture of funds’ performance persistence over the sample interval. Evidence shows that both the leading funds and the losing funds have higher probability to retain their positions. However, the analytics in Tables 3.10 and 3.11 take no consideration of managers’ possible risk shifting. HSZ argue that if risk taking brings no improvement to funds’ performance, the motivation left could be driven by either inferior ability or the agency problem. But, compared with the segment tournament, funds in family tournament can win the opportunity to gain benefits from family favouritism. Therefore, the motivation behind risk taking in family tournament is in line with investors’ interests. This prompts us to
further examine how funds’ performance responds to managers’ risk taking in family tournaments.
Table 3.12 presents examination results of the transition probability of family ranks under various levels of risk shifting. In the first column we create 5 groups by ranking funds in ascending order according to their levels of risk shifting between the ranking and post-ranking periods. In the second column we further sort all funds by their performance into 3 percentile groups; i.e., funds in the 1st group have
performance ranked within the bottom 33% percentile, and so on. For each risk shifting group Table 3.12 reports the transition probability of moving from one percentile to another. We use both the mean returns and the 4-factor model alphas
Table 3.11 Family rank transition matrix
Panel A Current Percentile 1 2 3 4 5 1 0.3204 0.2262 0.1792 0.1521 0.1223 2 0.2117 0.2622 0.2615 0.1371 0.1277 3 0.2078 0.1499 0.1793 0.1813 0.2820 4 0.1602 0.2189 0.2349 0.2257 0.1602 5 0.1327 0.1272 0.1271 0.2891 0.3244 Panel B Current Percentile 1 2 3 4 5 1 0.3319 0.2284 0.1277 0.136 0.1763 2 0.2055 0.2352 0.2733 0.1778 0.1082 3 0.1854 0.1873 0.2282 0.2342 0.1653 4 0.1993 0.1889 0.1584 0.2184 0.2352 5 0.115 0.1431 0.1947 0.222 0.3255
Notes: This table reports the probability of return rank transition between the ranking and
post-ranking periods. Fund families are ranked in ascending order into 5 deciles according to their value weighted family returns during the ranking period. Columns 2 to 6 report the transition probability of rank shifting in each decile from the ranking period to the post-ranking period. Panel A reports the transition probability on a middle year basis while in Panel B a 7 month period is considered for the ranking period. All values reported in the table are in percentage.
to evaluate funds’ performance. It comes as no surprise that, once again, relative performance of the top and bottom ranked funds in the same family persists over time.
Moreover, Table 3.12 suggests that the transition probability of top ranked funds reduces with the increase in risk altering. Of the sample funds, 58.5% of the top funds stay in the same percentile group when the magnitude of changes in the risk taking level is low. This percentage value decreases to 50% when risk changes are more substantial. However, the opposite result is found when performance is estimated with the 4-factor model alpha. In the last column of Table 3.12 the transition probability in the 1st RS group increases from 48% to 58.7%, an increase of 10%. This gives some supportive evidence that risk shifting can lead to the promotion/demotion of family ranks.
Taking Jensen alphas as indication of managers’ stock selection ability, the raw returns contain information about the performance that certain funds may deliver. Unlike the risk taking in segment tournaments, in family tournaments none of the performance measures show any improvement after altering the risk exposure. We believe that risk shifting could be an indication of managers’ superior ability. Since top managers may already be rewarded by the fund company after mid-year ranking, funds may therefore profitably utilise the information advantage to purchase more under-priced stocks or increase portfolio concentration.
Equities that may have helped funds gain a top ranking are normally funds’ major holdings, although they could experience mean reversion in their returns during the second half of the year. It is then expensive for the funds to ditch these holdings, and this is especially so for large funds, as they are more likely to engage in family tournaments. In addition, the agency problem could be another reason for funds to close those long positions. On the other hand, no clear trend is detected in our empirical investigation of bottom ranked funds improving their ranking by increasing the risk taking, consistent with our earlier analysis showing that mid-year losers are not actively involved in family tournaments.
Table 3.12 Risk shifting and post-ranking performance transition
RS
ranking percentile Current Raw returns 4-factor alphas
1 2 3 1 2 3 1 1 0.4824 0.3978 0.1193 0.5779 0.3201 0.1021 2 0.2443 0.6279 0.1281 0.2668 0.6340 0.0999 3 0.1375 0.2763 0.5849 0.1634 0.3576 0.4800 2 1 0.4021 0.4543 0.1444 0.4582 0.3754 0.1671 2 0.1855 0.6687 0.1442 0.1500 0.6957 0.1543 3 0.1500 0.3421 0.5079 0.1825 0.3459 0.4712 3 1 0.4642 0.4113 0.1253 0.4453 0.4374 0.1182 2 0.1411 0.7214 0.1379 0.1258 0.7174 0.1561 3 0.1787 0.2737 0.5474 0.1467 0.2947 0.5579 4 1 0.3821 0.4406 0.1762 0.3813 0.4432 0.1752 2 0.1342 0.6945 0.1713 0.1314 0.7121 0.1565 3 0.1834 0.3755 0.4400 0.1287 0.4048 0.4656 5 1 0.4600 0.4442 0.0969 0.5086 0.3624 0.1292 2 0.1921 0.6637 0.1464 0.1553 0.6816 0.1628 3 0.1733 0.3268 0.5000 0.1382 0.2748 0.5873
Notes: This table shows mean performance of the funds subsequent to risk shifting. In Column 1, all sample funds are ranked in
ascending order in terms of the magnitude of risk shifting, leading to the formation of 5 groups. In Column 2, funds in each of the risk shifting groups are further ranked into 3 groups in ascending order based on their mean returns in the first half of the year. The subsequent family performance is then calculated for each of the risk shifting groups and for the corresponding return ranking groups. Columns 3 to 8 report the transition probability of each percentile’s rank shifting between the ranking period and the post-ranking period. The post-ranking performance is measured by funds’ mean returns and funds’ alphas estimated from the Carhart 4 factors model.