Berenberg analyst William Howard had previously rated both companies hold.
At last check shares of FedEx, Memphis, fell 2% to $222.69 while UPS, Atlanta, dropped 3.6% to $159.86.
Fedex shares dipped even as the company said it would be expanding its Sunday delivery service to nearly 95% of the U.S. population.
An "unprecedented peak holiday shopping season" necessitates the move, which will become official on Sept. 13, FedEx said. It began seven-day shipping full time at the beginning of the year.
A pair trade is a situation when an investor goes long with one stock and short for another, usually in the same sector.
"All three global integrators - Deutsche Post, FedEx and UPS - have had a pretty good pandemic so far. The market has got overexuberant about e-commerce growth," Howard said.
The firm expects business-to-consumer shipping to grow about 20% in 2020 thanks to the coronavirus pandemic. The firm says that's already reflected in FedEx's 51% year-to-date share-price increase and UPS' 42% year to date rise.
UPS is trading, however, at 21 times estimated 2021 earnings, a 32% premium over its 10-year trading history.
For FedEx, Berenberg sees a wider profit margin relative to UPS.
The firm set a price target of $280 for FedEx, representing 23% potential upside. He set a price target of $130 for UPS, a potential 22% downside from its Wednesday close.