A Pepsi and Coca-Cola pairs trade stops working after 2022

In September, Davide Graziano published a case study of one of the oldest pairs in quantitative trading: PepsiCo and Coca-Cola. The two stocks moved together from 2013 to 2017, and a spread between them pulled back to its average. A rule that traded that pull made money from 2018 to 2022. The study then froze the rule and ran it on 2023 to 2026, and it lost money.

A loss is a useful claim to test, because a careless rebuild tends to find one. I wanted to know whether the rule, written from the paper’s text alone, gives the same loss, and the same profit before it.

The method

I fixed every test and tolerance before I read a price. The rule regresses PepsiCo’s log price on Coca-Cola’s over 2013 to 2017, and measures how far the spread is from its average in standard deviations. It sells the spread above 2.15, buys it below −2.15, and closes the trade when the spread comes back within 0.50. It sizes each trade by the spread’s recent volatility and charges 0.20 percent of each leg on entry and exit. It starts with $100,000.

The text leaves some choices open: the exact dates, how the fills work, when an open trade closes at the end. I wrote each choice down before the run. The prices are Yahoo’s adjusted daily closes. I did not open the author’s code before the result.

The result

The rebuild had to match the paper’s own statistics and its profit before 2023 first. If it missed, the loss after 2023 would say nothing about the paper.

Check	Paper	This run
Hedge ratio, 2013 to 2017	1.6618	1.6618
Half-life of the spread	31.9 days	31.9 days
Trades, 2018 to 2022	9	9
Sharpe ratio, 2018 to 2022	0.67	0.67
Net profit, 2018 to 2022	$16,941	$16,891
Trades, 2023 to September 2026	1	1
Net profit, 2023 to September 2026	−$28,131	−$28,022
Sharpe ratio, 2023 to September 2026	−1.19	−1.17

Every check before 2023 holds, so the rebuild is the paper’s rule. After 2023, the frozen rule takes one trade and loses about 28 percent of its capital. That is consistent with the paper’s claim.

The study gives a reason: after 2022 the two stocks stop moving together. On 2023 to 2026, the hedge ratio between them is −0.24, not 1.66, and a test for a stable relation no longer passes at the 5 percent level. My run gives a p-value of 0.129, against the paper’s 0.12.

I ran the result again on new downloads on 3 November, and the loss repeated to within one cent.

What failed

• The author’s code did not run. The session that ran the test was not allowed to execute code from an outside repository. The result rests on my rebuild from the text.
• The checks cannot tell neighbouring exits apart. An exit at 0.55 instead of 0.50 also passes every check before 2023. So the checks prove the rule’s shape, not each of its settings.
• The end date is my choice. The paper says “2023 to present” and gives no end. I used the last trading day before the paper’s release. The author’s own end date gives −$28,169.
• The grid has a different size. The paper picks its entry and exit bands as the best of 901 pairs on 2018 to 2022. My grid of the same bands has 895. Its best pair is the paper’s.

What was not tested

• One trade decides the result. A single losing trade cannot separate a broken relation from bad luck. The paper’s argument rests on its cointegration test as much as on the loss.
• The choice of the best bands from 895. The best rule out of many is too good by chance, as the 1992 trading-rule test on this site shows. I did not adjust for the search.
• A second price source. Only Yahoo’s closes were tried.
• The paper’s other hedge ratios and folds: its rolling and Kalman hedges, its walk-forward tests and its COVID-19 exclusion.

What happens next

On 3 November I froze the rule, every parameter included, and sealed it with a hash. From 5 December I will read it once a month for twelve months, on prices that did not exist when it was sealed. The paper predicts that the rule keeps losing. That test cannot be tuned after the fact.

This page reports a test of a published study. It is not investment advice.