Convergence trading

In economics, there was a widely accepted theory named the Law of one price, whereby the same good should be sold at the same prices, if you remove the transportation, for-ex and other administrative and misc costs. The popular Big Mac index is a popular illustration of this concept although its credibility is also disputed
https://en.wikipedia.org/wiki/Law_of_one_price
https://en.wikipedia.org/wiki/Big_Mac_Index is a so called popular

Surprisingly, there is little documentation about convergence trades in academia finance, despite sharing common roots. Economics explaining why money functions and how it flows, and finance tracking its actual movements and on the practical applications. My curiosity is piqued when I was made aware of HSBC HK/ HSBC UK, TJZX China A and TJZX SG, and this recent discovery, HKL USD and HKL GBP. Theoretically, in efficient financial markets, the law of one price should hold, and triangular arbitrage should eliminate pricing anomaly. In actuality, the gap is present in the mentioned cross listed securities. Granted, settlements timings and risks, length of cross border transfers and for-ex risks made it impossible to conduct a completely risk free arbitrage profit. But is this sufficient to explain this pricing anomaly?

Through a quick search on google, there is little or almost no empirical evidence related to the reliability of profitability in the arbitrage of convergence trade, despite the widespread belief in the law of one price in Economics theory. Theoretically, it works. Nonetheless, top academics and scholars whom used convergence trades with leverage, short-selling  and betting in certain direction of markets, had their investments went south and incurring almost infinite liability. Long term capital management, whom marketed themselves as investing for the long term, lost it all and failed after a few years although their calls turned out to be right in the long run, when they are all dead (Quote John Keynes)
https://en.wikipedia.org/wiki/Long-Term_Capital_Management

I am not smart enough to make such risky arbitrage calls. I am armed with only a spreadsheet and online financial data providers, compared to the Nobel Award winners and investment banks, whom had the capacity to monitor and hire PHDs to research pricing anomalies. Arbitrage theory is also not within my circle of competence, financial statement analysis and fundamental analysis are. Nonetheless, these TJZX SG and HKL SG USD do seemed to be undervalued in SG market at the moment. TJZX CN belongs to the China A market and there might be capital restrictions that prop up its share price for an unusually long time. HKL GBP should have no restraint, but this anomaly persists. If I were to start accumulating / buying these holdings, the basis is on the fundamental soundness and financial health of these companies, and not on the illusion of arbitrage profit.