A benchmark and two active funds hold six stocks with weights:
| Stock | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Benchmark | 0.30 | 0.25 | 0.20 | 0.15 | 0.10 | 0.00 |
| Fund X | 0.28 | 0.22 | 0.10 | 0.15 | 0.05 | 0.20 |
| Fund Y | 0.32 | 0.20 | 0.25 | 0.05 | 0.10 | 0.08 |
(a) Compute the overlap (6B.32) between X and Y, and verify that it equals one minus half the sum of absolute weight differences. (b) Compute the active share of each fund against the benchmark. (c) X charges 1.05% and Y 0.95%; an index fund costs 0.20%. Compute each fund's active expense ratio (6B.33). (d) An investor holds X and Y in equal amounts. Compute the blend's active share and its active expense ratio, taking its expense ratio as 1.00%. What does this say about holding several active funds in one category?