Why a hedge and a holding can correlate positively at the worst moment

A hedge is a position whose correlation with the thing it hedges is negative. That is a statement about a measured number, and lessons 10 through 16 were about what measured numbers do.

A concentrated holding with 38 percent annualised volatility at a weight of 0.75, alongside a hedging instrument with 22 percent volatility at 0.25. The two squared terms sum to 0.08425 regardless of the correlation. At minus 0.55 the cross term is minus 0.0172425, giving a variance of 0.0670075 and a volatility of 25.89 percent. At zero it is 29.03 percent. At plus 0.30 the cross term is plus 0.009405 and the volatility is 30.60 percent. The unhedged holding on its own is 38 percent.

Read the honest version of that. The pairing still reduced risk in both cases — 12.11 points at minus 0.55 and 7.40 points at plus 0.30. The hedge did not stop working; it worked 39 percent less well, which is a different and more accurate claim. The 4.72 points between the two columns is what a sign flip in the hedge relationship costs.

Two mechanisms produce the flip, and neither requires the hedging relationship to have been misunderstood. The first is forced selling: when participants need cash they sell what can be sold, and a liquid hedging instrument is by construction easy to sell, so its price reflects the seller's need rather than its own exposure. The second is a funding event, in which the cost of holding any position rises for everyone at once. Both are lesson 14's mechanism with a new factor — the demand for cash — that many instruments load on positively at the same moment.

Track 7 covers what specific hedging structures do to the figure a lender computes. The point here sits underneath all of them: whatever credit a schedule extends for a hedge is credit extended for a correlation, and that correlation was measured in a window.