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Wasn't the regression beta greater than 1?

I believe while your example captures the spirit of OC it's oversimplified. OC test is done on tranche level. As that 1 mil is being chewed through most likely the senior tranche would breach the OC threshold first (since it has the smallest denominator) and trigger OC protection. Only at...

Waterfall is simply the order of payment and loss absorption, like someone mentioned before it's just a feature of securitization. The credit risk book has several sections on OC. It should be clear that it's there to protect senior tranche, often at the cost of the equity tranche.

I'm genuinely curious now that quite a few people mention OC protects equity tranche. From my limited exposure to the relevant products, OC kicks in when senior tranches's OC ratio (aka principal coverage) falls below a certain threshold, at which point the payout to equity tranche gets...

OC protects senior tranche, not so much the equity tranche.

I believe the question asked about "asset allocation", which means you assume benchmark return and multiply that with the difference in allocation weights achieve returns are used in "selection"