By John Miller and Oliver Hirt

ZURICH (Reuters) - Top shareholders in LafargeHolcim <LHN.S> are backing Chief Executive Eric Olsen despite a share plunge of nearly half since France's Lafarge and Switzerland's Holcim merged last July to create the world's biggest cement maker.

The stock has shed around 20 billion Swiss francs ($21 billion), hitting its biggest investors, Swiss billionaire Thomas Schmidheiny and investment holding Groupe Bruxelles Lambert (GBL).

Both have defended a merger they helped engineer, arguing its span across 90 countries will help the company ride out regional slowdowns while combining their networks will allow it to return cash to shareholders.

Schmidheiny once predicted the shares, post-merger, would top 100 francs; they now trade just above 40, off a record low of 33.29 francs hit in February.

"Despite all the difficulties, I am convinced that Eric Olsen and his team will reach the ambitious targets," Schmidheiny, who holds 11 percent of shares, told Reuters.

GBL managing director Gerard Lamarche said he does not let share volatility dictate how he manages the nearly 10 percent LafargeHolcim stake owned by the fund of the billionaire Frere and Desmarais families. He urges patience.

"It is evident that a merger of that scale is not completed in one year," Lamarche said.

Convincing skeptics has been difficult, especially with rivals on the upswing.

As LafargeHolcim posted losses in two consecutive quarters, blaming tough markets in China, India and Russia, Mexico's Cemex <CMXCPO.MX> reported in April a surprise profit and its best quarterly core profit since 2009.

Germany's Heidelberg <HEIG.DE> upgraded its 2016 outlook to high single- to double-digit profit growth.

Ireland's CRH <CRH.I> in March reported 2015 operating profit rose by 35 percent as it benefits from assets in North America that competition regulators forced LafargeHolcim to unload.

"They had to sell lots of businesses where synergies would have existed," said David Moss, a BMO Global Asset Management fund manager. Moss has shunned LafargeHolcim shares.

Olsen, 52, insisted in an interview last week he is on track to boost underlying 2016 earnings before interest, taxes, depreciation and amortization by "at least high single-digit percentages", despite a 17 percent first-quarter slide.

His goal of 8 billion Swiss francs in operating EBITDA by 2018 -- from 5.7 billion in 2015 -- is also well within reach, he said.

Phil Roseberg, a Bernstein analyst who once worked for Lafarge, is dubious, citing his own calculations that LafargeHolcim must achieve unprecedented rest-of-year performance to hit its targets. He says the second-quarter report, due Aug. 5, could be a make-or-break moment for Olsen.

DAY OF RECKONING

"That for me will be the day of reckoning, on 2016 guidance and therefore on the targets they've been setting for 2018 ... That will be quite critical," Roseberg said.

"I would expect the board to have to react and do something quite soon. It's not possible to keep a situation where the management is in denial, and investors don't see where to set the baseline."

The union has been bumpy since before LafargeHolcim's share plunge.

In 2015 Holcim demanded better terms after the companies' performance diverged, briefly putting the tie-up in doubt. http://reut.rs/28ItV99

The initial CEO pick, ex-Lafarge head Bruno Lafont, was relegated to non-executive chairman as Swiss and French sides squabbled over his leadership style, according to people familiar with the matter.

Although Olsen had never led a company, his U.S. roots were seen as balm for Franco-Swiss friction.

But the first chairman, Wolfgang Reitzle, lasted just one year before being replaced by Beat Hess, once Royal Dutch Shell's <RDSa.L> top lawyer.

A former Holcim director, Hess has neither sought strategy changes nor wavered on targets since taking over in May, Olsen said. The board is behind him, he said.

While some see his "day of reckoning" approaching, Olsen said he and Hess would meet soon to focus on the company's future.

"We'll have dinner together and share our plans for the year and plans for the next couple of years," he said.

($1 = 0.9596 Swiss francs)

(Editing by Ruth Pitchford)