So ends one version of the Iliad, as the Amazon queen Penthesilea arrives to do battle with the Greeks. The Amazons of ancient myth were fearsome female warriors from Scythia. The modern incarnation is an e-commerce behemoth that’s been scything all before it in the stock market. This week, shares in Amazon.com reached another all-time high, helping to propel the Nasdaq to a fresh record of its own.

But Penthesilea came a cropper when she encountered an angry Achilles on the plains of Troy. For Amazon.com, the perceived Achilles heel has been its profitability. Although the company has enjoyed spectacular increases in sales, it has been far less profitable than many conventional retailers. In its third-quarter earnings, however, the company outstripped expectations in its revenues and net income, encouraging investors to overlook a significant decline in operating profit. Its shares have been soaring ever since. This week’s all-time high took them above a 50% gain for the year to date.

Still, doubts remain. Amazon’s profit margins are wafer-thin, and it continues to burn through cash as it ventures into an ever-widening array of markets. This week, it announced the launch of two new furniture brands: Stone & Beam and Rivet. The Nasdaq champion’s shares now trade on around 264 times its estimated 2017 earnings. Will that prove sustainable? Many stocks were trading on eye-watering valuations before the tech bubble burst in 2000. And plenty of Trojan champions thought that it was “different this time” when they came up against Achilles …

Coming up Trumps?

The strong performance of tech stocks helped the S&P 500 reach a record high of its own on Wednesday, with the likes of Amazon and Apple to the fore. But the index sold off sharply on Thursday, leaving it down 0.1% for the first four days of the week.

This sell-off was sparked by renewed doubts about the Republicans’ ability to pass Donald Trump’s much-heralded tax reforms. A year on from Donald Trump’s election victory, the S&P is up almost 24%. But doubts persist as to whether the Republicans will be able to push through the programme of tax reforms that they announced last week.

Dax down

European investors were in a less-than-ebullient mood this week. The FTSE World Europe ex UK index had fallen by 1.8% by Thursday’s close. The declines were led by Germany’s DAX index, as investors reacted to disappointing earnings updates from companies such as Siemens. Shares in Infineon, Adidas and ProSiebenSat.1 all registered significant declines.

Priti upset

Political turmoil was the keynote of the week in the UK, where Priti Patel was forced to resign as Secretary of State for International Development, after it was disclosed that she had held unauthorised meetings with Israeli officials while on holiday. She was replaced by Penny Mordaunt, previously minister for disabled people. Many observers noting that the replacement of one ardent Brexiteer with another was necessary to preserve the delicate balance of the Cabinet. The stability of the government is a growing concern for investors, given its implications for progress in the Brexit negotiations.

A chequered future?

Shares in UK companies declined over the week. The FTSE 100 had lost 0.9% by Thursday’s close, as it drifted down from last week’s all-time high. Fashion house Burberry, known for its distinctive chequered patterns, was among the biggest fallers. Although the company announced an increase in profits for the six months to the end of September, investors took fright at the new chief executive’s plan to refocus the brand on the luxury market.

And finally …

If you’ve always assumed that sheep aren’t the sharpest tools in the box, you may need to rethink your assessment of ovine intelligence. Far from being woolly thinkers, sheep have similar face-recognition abilities to humans and monkeys, according to researchers at the University of Cambridge. A team led by Professor Henny Morton trained eight even-toed ungulates to recognise the faces of broadcaster Fiona Bruce, actors Emma Watson and Jake Gyllenhaal and Barack Obama, the former US president.

Nor were the sheep merely star-struck. They also proved able to recognise photographs of the people who looked after them. Their ability to separate the sheep from the goats has yet to be tested.