de Mauroa church, Venezuela
2.2. Vulnerabilidad del área a desastres naturales
Figure 8.3 shows that large GSET algo parent orders have high Alpha. Tables 8.2 and 8.3 suggest that when GSET algos slice up these large parent orders into small child orders, mix them with small low-Alpha orders and execute them over time the high Alpha disappears. But can BadMax identify the large high-Alpha algo par- ent orders from clusters of small algo executions? To answer this question we examine sequences of GSET algo executions, identify clusters and measure their Alpha signal.
We tested many clustering definitions. We present the results for the following definition: executions form a cluster if they are less than 60 seconds apart, have the same symbol, the same side and
originate from marketable GSET algo child orders.20Using this def-
inition, the first three executions in Table 8.1 form a three-execution cluster of marketable GSET algo buy executions in symbol A. The ninth execution in Table 8.1 stands alone with no same symbol and no same-side marketable GSET algo execution within 60 seconds
and so forms a one-execution non-cluster.21
Using our clustering definition, we constructed 703,765 clusters of marketable GSET algo executions. The average cluster has six execu- tions with five seconds between executions. In Table 8.4, we arrange the 703,765 clusters into 10 groups: one-execution non-clusters, two- execution clusters, etc, all the way to extreme clusters with more than 100 executions. The one-execution non-clusters account for 44% of all clusters but include only 7% of all executions; the extreme clusters account for only 1% of all clusters but include 26% of all
Table 8.4 Clusters of marketable GSET algo executions Cluster group A B C D E F 1 1 311,130 311,130 44 7 NA 2 2 127,004 254,008 18 6 9 3 3 368,066 204,198 10 5 9 4 4–5 67,322 296,317 10 7 9 5 6–10 61,469 461,707 9 11 8 6 11–15 22,486 285,176 3 7 8 7 16–25 18,921 372,819 3 9 7 8 26–50 14,745 520,084 2 12 5 9 51–100 7,508 520,926 1 12 4 10 >100 5,114 1,143,995 1 26 3 All All 703,765 4,370,360 100 100 5
The sample is 4,370,360 marketable GSET algo executions, October 3–28, 2011. A, Executions in cluster; B, number of clusters; C, number of executions; D, percentage of clusters; E, percentage of executions; F, execution gap (in seconds).
executions. The average time between executions is nine seconds on
two-execution clusters and only three seconds on extreme clusters.22
Part (a) of Figure 8.5 shows the five-minute net Alpha of differ- ent size clusters. To calculate this net Alpha we first calculate the gross Alpha for each cluster group. To calculate the five-minute gross Alpha of three-execution clusters, for example, we focus on the three- execution clusters in our sample and calculate the mid-quote move from first execution in each three-execution cluster to five minutes
later.23 To calculate the five-minute net Alpha we subtract the half-
spread at trade-out from gross Alpha. The graph shows that the five-minute net Alpha increases with cluster size. The five-minute
net Alpha, which averaged−0.7bp across all marketable GSET algo
executions (Table 8.3), is−3.3bp for two-execution clusters, increases
to 2.7bp for clusters with 16–25 executions and is a spectacular 13.1bp on extreme clusters.
BadMax wants to identify the large clusters and capture their high Alpha. To capture this high Alpha BadMax must identify large clus- ters and trade in at the first clustered execution. GSET algos, how- ever, generate many small clusters and few large clusters. Our sam- ple contains 506,000 clusters with less than four executions (gross
Figure 8.5 The Alpha signal from clusters of marketable GSET algo executions 1 2 3 4–5 6–10 11–15 16–25 26–50 51–100 1.5 2.7 6.4 8.8 13.1 Large clusters of marketable GSET
algo executions have high Alpha ...
... but BadMax can extract little, if any, Alpha from these large high-Alpha clusters
>100
1st 2nd 3rd 5th 10th 15th 25th 50th 100th 200th
Number of executions in cluster
Execution position in cluster bp bp (3.7) (3.3) (2.9) (2.0) (0.9) (2.3) (1.7) (1.4) (0.7) 0.0 0.5 0.8 0.0 0.0 0.0 (b) (a)
The sample is 4,370,360 marketable GSET algo executions, October 3–28, 2011; net Alpha not significantly different from zero is shown as zero. (a) Five-minute net Alpha from first execution in clusters of marketable GSET algo executions. (b) Five- minute BadMax net Alpha from different positions in clusters of marketable GSET algo executions.
Alpha less than 2.3bp) but only 27,000 clusters with more than 25 exe- cutions (gross Alpha more than 11.2bp). Because BadMax observes executions as they occur over time, at the first clustered execution BadMax cannot distinguish between the many small low-Alpha clusters and the few large high-Alpha clusters.
To identify large high-Alpha clusters, BadMax must count clus- tered executions sequentially as they occur over time. On observing a second clustered execution, for example, BadMax filters out all one-execution low-Alpha non-clusters. On observing a third clus- tered execution, BadMax also filters out all two-execution low-Alpha clusters, and so on. As BadMax waits for each successive clustered execution, however, BadMax loses Alpha. BadMax, therefore, faces
a trade-off:
• as BadMax waits longer to observe more clustered executions,
it filters out more of the small low-Alpha clusters and buys into the larger higher-Alpha clusters;
• but as BadMax waits longer, BadMax loses more Alpha.
To quantify this trade-off and choose the wait time that maximises BadMax net Alpha, we calculate BadMax net Alpha from each suc- cessive execution in a sequence of clustered executions. At the second clustered execution we calculate BadMax net Alpha relative to mid
at second execution.24At the third clustered execution we calculate
BadMax net Alpha relative to mid at third execution, and so on. Part (b) of Figure 8.5 shows the five-minute BadMax net Alpha at ten different positions in a sequence of clustered executions. BadMax
net Alpha at the second clustered execution, for example, is−1.7bp,
at the tenth clustered execution is zero and peaks at a mere 0.8bp at
the twenty-fifth clustered execution.25The BadMax optimal strategy,
therefore, is to wait for the twenty-fifth clustered execution. Comparing the graphs in Figure 8.5, we see that the high Alpha of large clusters in part (a) disappears when BadMax tries to iden- tify the large clusters and capture their high Alpha (part (b)). Fig- ure 8.5, therefore, highlights our most striking finding: large clusters of marketable GSET algo executions have high Alpha, but BadMax can extract little if any Alpha from these large high-Alpha clusters.
We next focus on clusters with 26–50 executions and show why even though these clusters have high-Alpha BadMax cannot capture it. In Figure 8.5 the five-minute net Alpha from the first execution in clusters with 26–50 executions is 6.4bp, but when BadMax optimally trades in at the twenty-fifth clustered execution the net Alpha is only 0.8bp. Figure 8.6 plots the intra-cluster Alpha for clusters with 26–50 executions and shows that BadMax loses 9.9bp Alpha waiting for
the twenty-fifth clustered execution.26
BadMax also loses Alpha by trading-out after the Alpha peaked. Figure 8.6 shows that large clusters of GSET algo executions are asso- ciated with high impact and reversal (from 12.6bp at last execution to 9.0bp to the close). With a five-minute holding period, BadMax will trade out well after the Alpha peaked. At the twenty-fifth clustered execution, BadMax buys into many 25-execution clusters where the price is about to revert and buys into few 100-execution clusters where the price will continue rising.
Figure 8.6 Intra-cluster Alpha and reversal for clusters with 26–50 executions 2 4 6 8 10 12 14 16 18 20 22 25 Last Close 0 0.81.2 1.62.1 3.1 3.5 4.04.5 4.95.3 5.76.1 6.56.9 7.47.7 8.08.4 8.79.0 9.4 9.6 9.9 2.6 Average time gap between executions: 5 sec
Execution position in cluster
9.0
2 min to 25th execution
Alpha peaks at last execution 12.6
Reversal last exec to close 25th clustered exec BadMax
trigger to buy
BadMax lost 9.9bp Alpha
Clusters with 25–50 executions consist of 520,084 GSET algo marketable executions, October 3–28, 2011.
Figure 8.7 Tape footprint of marketable GSET algo execution
All >25 exec clusters >100 exec clusters
100-shares marketable GSET algo prints relative to all 100-shares
marketable Tape prints
0 10 20 30 40 50 60 70 80 90 100
% 0.7%
13% 14%
October 3, 2011; 30 DJIA stocks.