ANEXOS

We now apply the bootstrapping procedure to separate the effect of skills from that of luck in the performance of replaced funds, and the good and bad skills among skilful managers. We assume that the probability of top management replacement is negatively correlated to stock selection skills and that lucky managers are more likely to be replaced.

Figures 2 and 3 show the comparison between the funds’ actual alphas and t ratios and their corresponding bootstrapped ones, respectively. As suggested previously, the funds included in the bootstrapping simulation are all from the NG group. Given that previous underperformance is a good indicator of possible replacement, most of the replaced funds are expected to lie in the left tail of the cross-sectional distribution of alphas. However, due to non-normal distribution of idiosyncratic risks across the funds in both tails, conventional alphas might be misleading. For example, Panel C2 of Figure 2 signifies a performance that may be due to luck as actual alphas of these funds lie close to the ‘luck distribution’. But after the replacement, the rank of the funds experiences a remarkable increase as the incoming new managers are more capable of selecting stocks. (See Panel A1 of Figure 2). The replacement of such managers by the fund companies implies effective internal controls within the fund companies.

Figure 2 Histogram of Actual Alpha against Matching Bootstrapped Alpha around Replacement Period

Panel B1: Top one

Panel A1: Top one Panel A2: Bottom 0.3% Panel B2: Bottom 0.4%

Panel C1: Bottom 40.9% Panel C2: Top 65.5%

Figure 2 shows the histogram of the funds’ actual alphas against their matching bootstrapped alphas around the replacement time. The vertical line gives the actual alphas obtained from estimation of the three factor model on funds with negative ORA. The selection of the funds to form bootstrapped alphas is based on their matching counterparts in the replacement group.

Figure 3 Histogram of Actual T Ratio against Matching Bootstrapped T Ratio around Replacement Period

Panel A1: Top one Panel A2: Bottom 0.3% Panel B1: Top one

Panel C1: Bottom 40.9%

Panel B2: Bottom 0.4%

Panel C2: Top 65.5% Panel D1: Bottom 25.4% Panel D2: Top 70.1%

Figure 3 shows the histogram of the funds’ actual t ratios against their matching bootstrapped ones around the replacement period. The vertical line gives the actual t ratios obtained from estimation of the three factor model on funds with negative ORA. The funds selected to form the bootstrapped t ratios are based on the matching sample of each fund in the replacement group.

Panels B2 and D2 show the performance generated by poor stock selection skills. It comes as no surprise that, while the managers with bad skills are replaced by fund companies, some of the better-skilled managers are also dismissed. A possible reason for this is investors’ high demand for redemption, which decreases the net cash flow because the funds’ returns and alphas are more visible for investors.

In Figure 3, we display the comparison between actual t ratios of sample alphas and the bootstrapped ones. Panel C2 of Figure 3 presents the case where the performance of the funds is triggered by lucky managers (sample variation) rather than by those with genuine skills. The outcome of Panel C2 of Figure 2 is consistent with that in C2 of Figure 2. But, due to lack of precision in forming confidence internals, we will look more closely at the results by comparing actual and bootstrapped t values (Kosowski, 2006).

Table 8 reports the bootstrapping results for those funds whose managers are to be replaced. Funds with performance in the extreme left tail are of great concern to fund companies. In the group that falls below a min of 1%, 2 out of 6 funds which have recorded inferior performance can be regarded as being operated by “lucky” managers. A straight count of all the bootstrapping results in the pre-replacement period reveals that, among the 68 funds whose managers are outgoing and whose performance lies in the bottom 40% of their matching samples, 47 are managed by “lucky” managers. But the number drops to 28 after a top management turnover.

Table 8 Bootstrapping Results for Funds with Top Management Turnover

Table 8 reports the bootstrapping results for all the replaced funds with negative OAR in the pre-replacement period. Funds have been sorted into 6 groups by their percentage ranking before replacement, e.g. the group of below min 1% includes funds that lie below the bottom 1% of the performance ranking in their own matching sample. The first and second rows give the abnormal performance within pre- and post-replacement periods. The 3rd row indicates the percentage ranking in the post-replacement period. The 4th and 5th rows report the p value of the bootstrapped t ratios in both the pre- and post-replacement periods.

Percentage

Ranking Below min 1%

Min 1% to 2% Min 3% to 6% Min 6% to 10% Min 10% to 40% Over 50% Pre alpha -0.0042 -0.0199 -0.0096 -0.0088 -0.0085 -0.0056 -0.0048 -0.0041 -0.0037 -0.0017 0.0003 0.0012 0.0006 0.0005 Post alpha 0.0354 0.0078 0.0031 0.0018 0.0022 0.0015 0.0015 0.0037 0.0019 0.0019 -0.0002 -0.0020 0.0005 -0.0012 Post Rank 1.0000 1.0000 0.9360 0.8400 0.8890 0.6210 0.5878 0.7251 0.7467 0.5507 0.2800 0.1860 0.4090 0.2540 Bootstrapped pre p value 0.0000 0.2840 0.0040 0.0020 0.0050 0.5320 0.4690 0.2878 0.2440 0.5766 0.5600 0.1830 0.6960 0.9580 Bootstrapped post p value 0.0000 0.8860 0.2430 0.5330 0.4610 0.0350 0.0230 0.1997 0.7830 0.1980 0.0000 0.6230 0.0000 0.4810

To further investigate the relation between managerial skills and managers’ dismissal, we compute all alphas of the funds in NG and draw the distribution of bootstrapped alphas for each replaced NG fund. The results are displayed in Figure 4.

Figure 4 demonstrates the proportions of managers who are dismissed on the basis of their having bad skills, good skills, or luck. The separation of skills from luck is according to the bootstrapping simulation for replaced funds with negative OAR in the pre-replacement period. It can be seen from Figure 4 that, among the funds in the bottom 5% of the cross-section of all funds, almost 80% of the managers being replaced are the “lucky” ones. This proportion approaches 85% for the funds ranked in the bottom 30% to 50%. Since the funds that are subject to bootstrapping estimation are from the NG group, most of these funds are ranked in the bottom 30%. Therefore, the bootstrapping technique is able to identify lucky managers whose performance falls in the extreme tails of the cross-sectional distribution. With the finding that “lucky” managers are more likely to be dismissed, as shown in Figure 4, one may conclude that stock selection skills

0% 20% 40% 60% 80% 100%

<bottom 5% <bottom 30% bottom 30% to 50% >50%

Figure 4 Dismissal of Managers

have a significant impact on the probability of management turnover in the UK fund industry.

Next, we consider the case in the post replacement period. Figure 5 below shows the extent to which managers of underperforming funds are replaced by skilled ones.

As shown in Figure 5, for the funds located in the bottom 5% of the cross-sectional distribution, 65% of them have replaced their managers with better skilled ones. This proportion approaches to 70% when funds in the bottom 30% are included.

An alternative approach to explaining the bootstrapping simulation is to compare the true and bootstrapped alphas of the entire replacement group. Thus in Figures 6 and 7 we apply the kernel density estimation to see how many replaced funds are able to achieve superior performance through genuine stock-picking skill. Figure 6 compares the distribution of true (the solid line) and simulated alphas (the dashed line) in the pre replacement period. It shows that the solid line almost matches the dashed line,

0% 20% 40% 60% 80% 100%

<bottom 5% <bottom 30% bottom30% to top 50% >50%

Figure 5 Managers in Post Replacement Period

suggesting that those replaced managers cannot attribute their inferior performance to poor skill but to their ‘bad luck’. In contrast, in the post replacement period (Figure 7), the dashed line largely deviates from the solid one. This means that many of the incoming managers achieve their outperformance through genuine stock-picking skill. Such findings are consistent with the results given by Figures 4 and 5.

0 100 200 300 400 -.025 -.02 -.015 -.01 -.005 0 alpha

true alpha bootstrapped alpha Figure 6 Kernel Density Estimate of Pre-Alpha

0 50 100 150 200 250 -.04 -.02 0 .02 .04 alpha

true alpha bootstrapped alpha Figure 7 Kernel Density Estimate of Post-Alpha

Combining the above results, Figure 6 shows that more than 60% of the manager-replaced NG funds have replaced their “lucky” managers with more skilful ones, while only 15% of the funds fail to do so (12% of the funds have replaced skilful managers with ‘lucky’ ones and 3% of the funds have replaced poor skill managers with ‘lucky’ ones). It is worth noting that, among the funds whose managers have good stock selection skills, 15% of them have replaced these managers with other skilled managers. This is likely to be a result of the whims of unit holders, since evaluation results can sometimes mislead investors. Although a better successor might not negatively affect the fund’s performance, the replacement can still be regarded as a ‘costly firing’.

Poor to good skill 6%

Good to good skill 15%

Poor skill to lucky 3% Good skill to lucky 12% Lucky to good skill 64%

Figure 8 Proportion of Fund Performance Driven by Skills in Pre/Post Replacement Periods