That's all for today, folks. See you tomorrow at 6am for all the latest business news, views and analysis.
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- US markets fall
- Inflation rises higher than expected to 1.6%
- China's president addresses WEF on trade
- Greggs cautious despite profit rise
Wall Street markets closed lower on Tuesday as banks and financial stocks weighed on the major indexes.
The Dow Jones shed 0.3% to 19,826.77, the S&P 500 closed 0.3% lower at 2,267.89, and the Nasdaq lost 0.63% to 5,538.73.
Biotech and pharma stocks slipped after Donald Trump said in an interview that he would target companies over drug pricing and that he was ready to unveil a plan to replace Obamacare.
Bank stocks - which have rallied since Mr Trump's surprise victory in November - also slipped back, with the S&P 500 financial index down 2.3%.
Rick Meckler, president of Liberty View Capital Management, told Reuters: "You're getting some giveback to the areas that have really done well with the Trump election. Some of that is a feeling he's starting to take on a lot of targets."
Theresa May's Brexit speech was broadly welcomed by UK business and finance for adding clarity.
But the widespread reaction was that it's the final detail of the EU exit terms that matter, not laying out the direction of travel. Here are some responses from business leaders.
A plan to save a subsidiary of Caesars Entertainment Corp, the casino group, from bankruptcy has been approved by a US judge.
It clears the way for the division - called Caesars Entertainment Operating Co - to escape insolvency after filing for Chapter 11 protection with $18bn in debt.
Under the plan, which is yet to be approved by regulators, Caesars Entertainment Operating Co would have its property assets and gaming operations separated.
Caesars Entertainment Corp owns the famous Caesars Palace casino in Las Vegas, and is one of the largest gaming companies in the world.
2016. The year in which populist forces across the developed world gained momentum, sowing the seeds of nationalism, protesting against mass immigration and rolling back the tide of globalisation.
Well, perhaps not if you lived in a major city.
In the UK, for example, London and many other cities voted to remain in the EU, while Hillary Clinton won most of urban America on 8 November.
In France, Germany and the Netherlands, far-right movements are weaker in capital cities than they are in many rural areas.
BBC World Service
The chief executive of Boeing, Dennis Muilenburg, has said he's had a very productive meeting with President-elect Donald Trump and agreed to provide a cheaper version of Air Force One, BBC World Service reports.
In December, Mr Trump said the government should cancel plans for two new presidential planes, describing them as ridiculously expensive.
Boeing's share price dipped on the news. Mr Muilenburg said that he and Mr Trump had agreed to simplify the requirements, which would result in a better plane for a lower cost.
Saudi Arabia has opened its first wind turbine as part of a renewable energy drive.
The turbine, operated by state oil giant Saudi Aramco, will power a refining plant in Turaif, near Jordan. The firm said it would create enough power to supply 250 homes, displacing the equivalent of 19,000 barrels of oil.
Almost all of the kingdom's power currently comes from oil or natural gas, but it aims to achieve 9.5 gigawatts of renewable energy production by 2030 - around a 12th of total supply.
One of Donald Trump's closest advisers has told the BBC the US president-elect's criticism of German Chancellor Angela Merkel has been misinterpreted.
In an interview on Monday, Mr Trump had said Mrs Merkel had made an "utterly catastrophic mistake by letting all these illegals into the country".
But Anthony Scaramucci said the incoming president had an "enormous amount of respect for her".
Mr Scaramucci also told the BBC the US would win a trade war with China.
Jeremy McKenzie - I'm not sure how Teresa May can say on the one hand that staying in the single market is incompatible with Brexit, yet on the other hand ask for tariff free trade, no eu contributions, control of immigration etc which is incompatible with eu principles. It's obvious which is more certain. Reality will be much worse than Brexiteers hope.
Gordon Phillips - We are leaving and have been since the vote… A bad deal for UK plc is a bad deal for Europe. The devil is in the detail and we have plenty to offer our European partners such as security in an evermore uncertain and threatening world.
Geoff Lofthouse - Shortly after Mrs May became Prime Minister she stated that "while the UK voted to leave the EU, voters did not vote to become poorer". I would suggest that with rising inflation and the falling pound she seems to have forgotten this promise. It's time she took action to protect standard of living for all voters, especially pensioners and other vulnerable groups, where rpi and cpi do not reflect... living costs.
Prime Minister Theresa May's Brexit speech is being seen in Europe as the "hard" option of full UK withdrawal - and there is some relief that the British position is clearer now.
"Finally we have a little more clarity re the British plans," German Foreign Minister Frank-Walter Steinmeier said.
Germany also wanted a "close and trusting relationship", he said.
The Czech Europe Minister, Tomas Prouza, tweeted: "UK's plan seems a bit ambitious".
As we reported earlier, authorities have confirmed Rolls Royce will pay £497m to settle bribery claims in the UK (and make further payments overseas).
In a court hearing today, chief executive Warren East said: "The behaviour uncovered in the course of the investigations by the Serious Fraud Office and other authorities is completely unacceptable and we apologise unreservedly for it.
"This was unworthy of everything which Rolls-Royce stands for, and that our people, customers, investors and partners rightly expect from us.
“The past practices that have been uncovered do not reflect the manner in which Rolls-Royce does business today. We now conduct ourselves in a fundamentally different way."
"Embrace your inner girl" is not a phrase you'll hear very often, particularly in the macho world of business where "manning up" is more de rigueur.
Yet if you attend any major business conference this year, then you're likely to come across "The Girls' Lounge".
It might sound like a name dreamt up by an unimaginative spa owner or an all-female pop-band, but in reality it's a professional networking space for women.
On the eve of the World Economic Forum in Davos - a place where male attendees outnumber females five to one, the space is just being prepared.
US stocks are still down in early afternoon trade, with banks and healthcare firms holding back the main indexes.
The Dow Jones has lost 0.2% to 19,845.04, the S&P 500 is down 0.23% at 2,269.39, and the Nasdaq is off by 0.5%, at 5,545.13.
Biotechnology and pharmaceutical stocks came under pressure after Donald Trump told the Washington Post that he would target drug companies over pricing and that he was ready to unveil a plan to replace Obamacare.
Financial stocks are thought to be losing steam after a huge rally in November and December.
Ratings agency Moody’s has downgraded British American Tobacco’s credit outlook from A3 to Baa2, hours after BAT said it would buy rival firm Reynolds (maker of Pall Mall cigarettes among other brands) for $49bn.
Moody's analyst Ernesto Bisagno said: "BAT's two-notch downgrade to Baa2 reflects the significant debt and resulting high leverage that it will incur to fund the Reynolds deal."
However, he said, despite the weakened score BAT's outlook remained stable and would "progressively improve" after the acquisition.
The investigation into Rolls Royce was the largest ever carried out by the SFO, costing £13m and involving some 70 SFO personnel.
And this is the third use of a so called deferred prosecution agreement since the power became available to prosecutors in 2014.
Rolls Royce's penalty is the highest ever enforcement action against company in the UK for criminal conduct. And don't forget, it will pay about $170m more to settle the same bribery claims in the US and Brazil.
According to the SFO, as part of the agreement, if the company does not honour certain conditions, the prosecution may resume.
The SFO's director, David Green CB QC, said: “Bribery harms the reputation of the UK as a safe place to do business."
After an announcement yesterday, authorities have confirmed that Rolls Royce will pay £497.25m (plus interest and costs of £13m) in the UK to settle bribery claims. This allows the company to avoid prosecution.
In a statement, the Serious Fraud Office said the manufacturing giant had been accused of 12 counts of conspiracy to corrupt, false accounting and failure to prevent bribery.
"The conduct spans three decades and involves Rolls-Royce’s Civil Aerospace and Defence Aerospace businesses and its former Energy business and relates to the sale of aero engines, energy systems and related services," it said.
"The conduct covered by the UK DPA took place across seven jurisdictions: Indonesia, Thailand, India, Russia, Nigeria, China and Malaysia."
Economics and Business analyst, BBC News
The BBC business team has been in the City today, gauging reactions to Theresa May's speech.
Here is presenter Vishala Sri-Pathma talking to Steven Fine from the stockbroking firm Peel Hunt.
We've seen the pound rise almost 3% against the dollar, it's best day since 2008.
Steven told us this was because of the additional certainty that the PM's speech gave us - and that the pound might be seen as a good commercial bet.
As expected the FTSE 100 closed lower today, in large part due to an almost 3% jump in the pound following Theresa May's Brexit speech.
The index lost 1.46%, or 106.75 points, to 7,220.38 points.
The biggest faller was British American Tobacco, which shed nearly 4% after announcing a $49bn deal to buy rival Reynolds.
Holiday operator Carnival, product testing business Intertek and plumbing giant Wolseley UK - all off which lost more than 3% - also did badly.
A strong pound tends to reduce London-listed firms' profits, a large proportion of which are generated overseas in dollars.
Morgan Stanley's profits jumped 83% in the fourth quarter, thanks in large part to a recent rally on US stock markets.
The firm said it earned $1.67bn in the period, compared with $908m a year ago - easily beating analysts' expectations.
The Wall Street bank's trading desks benefited heavily from the rally that began straight after the US presidential election and has only recently lost steam.
Investors had been inspired by Donald Trump's surprise victory, believing it would mean greater government spending and economic growth in the US.
Financier Anthony Scaramucci, an adviser to Donald Trump, has been speaking at the World Economic Forum in Davos, Switzerland.
He said president-elect Trump is likely to tear up the old rulebook of how trade deals are done and although he wants a strong relationship with countries like China, is seeking changes to what he called "asymmetrical deals" that have been struck in recent decades.
The BBC's Joe Miller caught up with Mr Scaramucci and asked him to explain Mr Trump's stance.
The TheCityUK, the financial sector's industry body, has welcomed the key promises of Mrs May's speech.
Chief executive Miles Celic said the Prime Minister was right to emphasise the need for a "bespoke agreement". He also welcomed her support for a transitional approach to Brexit that allows businesses time to adjust.
“The Prime Minister’s commitment to ensuring the UK will be able to continue to attract the best domestic, EU and global talent is welcome," he added.
The pound's strong performance today will not last, says Richard Falkenhall of Nordic bank SEB.
"The UK’s position in negotiations will be very weak once exit negotiations under the treaty starts. There is only a two-year period and the UK has the most to lose if negotiations fail," he says.
"The two-year period will create a lot of uncertainty which is likely to harm the British economy and in particular the important British financial industry," he adds.
“We view today’s GBP rally as temporary and expect the sterling to weaken again."
The European Union president Donald Tusk has said Theresa May's speech provided a "more realistic" picture of what she wanted from Brexit. He tweeted:
German firms will scale back investment in the UK as it heads for a 'hard brexit', Germany's Chamber of Commerce and Industry (DIHK) has said.
It follows a speech in which Theresa May confirmed Britain intended to quit the single market.
"There now will be less investment from German companies in Britain," Volker Treier, head of the DIHK's trade division, told Reuters.
He also said that a hard Brexit would impair growth both in Britain and the rest of Europe, and that the UK would probably become less important for Germany as export destination.
General Motors and Walmart have both promised to create more jobs in the US, following in the footsteps of Ford and Amazon.
GM said it would invest an additional $1bn in US manufacturing operations and create up to 5,000 jobs in the coming years.
Walmart said it would invest $6.8bn and create 10,000 jobs.
Donald Trump has been pressuring US firms to manufacture more of their goods onshore or face stiff border taxes.
Shortly after the announcements, the President-elect took credit for the news on Twitter:
Sterling is now 2.82% higher against the dollar at $1.24 as investors continue to react positively to Theresa May's Brexit speech.
Carlo Alberto De Casa, of online broker ActivTrades, said: “The market reaction to Theresa May’s big moment was quite clear – investors began buying the pound.
However, he added: "It looks like the UK will try to get the best of things from the EU, opting to go for a kind of cherry-picking that has already been excluded by Angela Merkel and other European politicians. It will be an interesting challenge."
Business will have a "clearer sense" of the Prime Minister's top-line priorities after her speech, says Adam Marshall of the British Chambers of Commerce .
But, he adds, it will come away knowing "little more about the likely outcome of the Brexit negotiations than it did yesterday".
"The simple fact is that businesses all across the UK are carrying on. Directly-affected companies are being pragmatic, and are preparing for a range of possible outcomes."
Investors have welcomed news that Rolls Royce will pay £671m to US, UK and Brazilian authorities to settle bribery claims.
Shares in the manufacturing giant are up almost 6% today, at 702 pence.
Nicholas Hyett, equity analyst at Hargreaves Lansdown, says: "The group’s comments that profit and cash flow are set to be ahead of prior expectations have overshadowed the bad news."
US stocks have opened lower on Tuesday after the long bank holiday weekend.
The Dow Jones index is down 0.21% at 19,843.24 points, the S&P 500 has lost 0.34% to 2,267.09, and the Nasdaq is 0.56% lower at 5,545.00.
Ibec, the leading trade group for Irish business, says it is "deeply concerned" by the UK government's "increasingly hardline" stance over Brexit.
In a statement published after the Prime Minister's speech, Ibec boss Danny McCoy said: “The possibility of the UK leaving both the single market and the customs union raises fundamental questions about Ireland's future trading relations with the UK.
"A return to WTO rules would be a significant economic shock to the [Irish] economy and would hit Irish exporters hard. It would also set the UK and Ireland on very different economic trajectories."
Others have praised the Prime Minister following her landmark speech:
The Labour leader, Jeremy Corbyn has called on the Prime Minister to "be clearer" about what her long-term objectives are on the UK's withdrawal from EU and that she seems to be wanting to "have her cake and eat it" when it comes to the single market.
He said he wasn't sure how Theresa May's comments on the single market "would go down in Europe" because she wants to leave the single market at the same time as having access to the single market.
Mr Corbyn warned that there are "enormous dangers" in what Theresa May said.
Some of the headlines from Theresa May's vision for future UK-EU relations.
Matina Stevis is the Africa correspondent for the Wall Street Journal.
She puts Brexit worries into perspective.
Neil Wilson, senior market analyst at ETX Capital writes:
“The pound took off like a rocket today on what amounts to a far less hawkish Brexit speech from Theresa May than many had feared.
"Some judicious leaks in the last couple of days had primed investors for the UK to be leaving the single market. Many expected a tough sounding speech that would send the pound lower – that could yet happen as we progress towards invoking Article 50.
"We’re definitely not out of the woods. It could take time for it to really sink in and hit home that Britain is leaving the single market
"The facts are this – we are leaving the single market and the customs union. We will try to strike a trade deal with the EU. Only the first is a certainty so this heavy bid for the pound looks risky."