Case analysis: testing whether a merger broke a pair

You suspect that the HDFC merger (effective 1 Jul 2023) broke the relationship between HDFC Bank and ICICI Bank. (a) Design a test, stating the null and alternative, whether you work in levels or returns, and which critical values apply. Consider Gregory–Hansen. (b) 13A.10.5 finds no break in the return regression. 13A.12.1 finds no cointegration before or after. Reconcile these with the observed price relatives (0.95 and 1.98 from 4 Apr 2022 to 4 Nov 2026). (c) What would a trader have needed to see before 2022 to justify trading the pair, and what event-driven rule would have protected the position?