Reverse diversification when one winner enters a quiet book

A ten-sleeve compound average

A ten-sleeve illustration presented nine outcomes of 2% plus one outcome of 30% as a compound-style average of 4.504%. The 30% outcome was the single large result beside nine quiet 2% sleeves.

That presentation treated the ten printed rates as if they already belonged in one book average. The later exchange asked what kind of average that figure was, and what kind of diversification story the extra sleeve was being asked to tell.

Why the attributed lift did not match

A challenge to that illustration said a 1.15% lift attributed to the single 30% outcome does not match the move from 2% to 4.504%. The claimed increment and the printed change in the average were not the same arithmetic.

The 1.15% increment was later withdrawn as leftover arithmetic from an earlier version of the example. After that withdrawal, the remaining dispute was about how the ten outcomes should be averaged, not about keeping the withdrawn lift.

Sequential compounding is not a concurrent average

Under sequential-compounding, later gains apply to an already-grown stake. Nine 2% outcomes produce 19.5 cents of gain on a unit stake, while inserting the 30% outcome produces 55.4 cents, a multiple of 2.84.

If the same ten outcomes are treated as concurrent equal weights, the concurrent-book-average, the simple mean of sleeves held at the same time, is 4.8% rather than the 4.504% compound figure.

Reverse diversification and the opposite spread

Adding a 30% sleeve to nine 2% sleeves was recast as reverse-diversification because average return can rise while volatility also rises. The quiet book is not being protected. Its average is being lifted by a louder sleeve.

Risk-reducing diversification was defined in the opposite direction as a risk-reducing-spread: pair lower-return, lower-risk sleeves with a high-return sleeve to dampen that sleeve’s implied risk.

Spreading one 30% position into 2% sleeves was said to cut the standalone 30% average to about 4.8% if positions are concurrent, or about 4.5% if returns are compounded. That gap was treated as secondary to the risk point.

An already-known winner is not a risk plan

The attached caution is that winners are identified only after they have already won. An ex-post-winner is a sleeve whose large gain is already known and therefore cannot be treated as if future winners were equally visible.

Recycling a known winner into many new sleeves was described as a fragile habit rather than a risk plan. The archive caution sits on that timing problem, not on a claim that the next quiet book will contain another visible 30% sleeve.