Sterling's losses since Britain's vote to leave the European Union have been the blue-chip FTSE 100 <.FTSE> index's gain, with every fall in the pound -- down more than 10 percent since the June 2016 poll -- pushing stocks higher.

The argument is straightforward. With around 75 percent of FTSE 100 firms' revenue generated overseas, the weaker currency supported sterling-denominated earnings projections while boosting export competitiveness. It also cheapened the stock price of UK-listed multinationals for overseas investors.

But as inflation eats into domestic demand, forcing the Bank of England to raise interest rates last week for the first time in over a decade, some strategists argue that relationship is set to break down, removing a key support for British stocks.

"That negative correlation tends to exist typically when you don't have inflation pressures, when no one is hiking rates and when you don't have too much depreciation going on," said Yianos Kontopoulos, head of macro strategy at UBS.

A hawkish central bank could disrupt the negative correlation, he said -- even though most economists in a Reuters poll saw last week's rate rise as "one and done", with no further increases to come until 2019.

"While it's not necessarily going to change the relationship in the first days, and we won't know because correlation is a little bit more elusive than that, it will over the next year if you have inflationary pressures too," said Kontopoulos.

Inflation jumped to its highest in more than five years in September, largely as a result of sterling's post-Brexit decline, all but sealing the Bank's decision to raise rates.

British-based equity investors have been reaping the benefits of the depreciation, which effectively boosts earnings for companies that do the bulk of their business abroad once converted into sterling. They stand to lose should that relationship loosen.

Sterling's weakness has boosted FTSE earnings by up to double digits for some quarters, but its effect is likely to fade to having no impact at all on stocks in the fourth quarter, said Caroline Simmons, deputy head of UK investment office at UBS Wealth Management.

Earnings for MSCI's index of all UK stocks are expected to grow 20 percent for the year in sterling terms, compared with 10.4 percent in euro terms for MSCI EMU, according to Thomson Reuters data, largely thanks to currency translation and a high weighting for energy stocks.

While domestic investors enjoy that outperformance, the negative currency translation blunts the benefits for foreign investors in the market.

After a sharp depreciation, the currency is now relatively rangebound, making its effect more negligible. And according to UBS analysis, periods of negative correlation have historically been short-lived.

"Unless one is very bearish around one's sterling forecasts, it's definitely going to be a fading factor in UK profitability," said Matthew Garman, equity strategist at Morgan Stanley.

  

NOT A GIFT THAT KEEPS ON GIVING

Options markets indicate investors are still pricing in a negative relationship between sterling and the FTSE 100.

It would be cheaper for an investor seeking to short FTSE and short sterling to buy those two options jointly, Kontopoulos said, indicating a strong negative correlation is priced in.

Some investors could therefore get a nasty surprise when the carpet is pulled from under them.

"It's something that people might be banking on," said Kontopoulos. "It has been the case historically but this is not the gift that keeps on giving under any and all circumstances."

The currency effect will not insulate or help diversify away from domestic risks as it has done thus far -- and multiplying profit warnings recently suggest slower economic growth is beginning to be felt at company level.

"The net earnings surprise -- when I look at the breadth of companies in the UK -- is better than the euro zone, which I think comes down to the currency," said Matthew Garman, European equity strategist at Morgan Stanley.

"But I don't think the euro zone has had anywhere near the same degree of profit warnings or earnings surprises to the downside that you've seen during the last quarter in the UK."

But equally, a diminishing currency translation also means that a rising pound won't hurt the index anymore.

Most banks predict the pound will fall, not rise, in the next year as Brexit negotiations inch closer to the divorce date. UBS sees the pound weakening, but does not expect that to support the equity market.

JP Morgan analysts on the other hand expressed concern the FX backdrop could turn into a "lose-lose" for UK stocks. They see the pound appreciating -- a (presumed) negative for equities -- and say any major Brexit fallout would cause stocks to fall as well, flipping the correlation to positive.

Investors wary of predicting the direction of either stocks or the currency have been moving into volatility trades -- where the bet is on price fluctuations rather than price direction.

A short FTSE volatility, long EUR/GBP volatility trade is one of Societe Generale's best-performing this year, said the bank's head of equity derivatives Vincent Cassot.

"A lot will be dependent on Brexit negotiations," he said. "It's hard to have a view of where it's going to go, but we do know it's going to be volatile."

(Reporting by Helen Reid and Kit Rees Additional reporting by Saikat Chatterjee and Jemima Kelly; Editing by Catherine Evans)

By Kit Rees and Helen Reid