A look at the day ahead in U.S. and global markets from Mike Dolan

Big Tech heavyweights Microsoft and Alphabet are set to switch global investors' focus from Monday's bond market bounce, although the latter has improved the market mood considerably ahead of the week's big earnings reports.

The two tech giants report after the bell on Tuesday, with Meta following on Wednesday and Amazon on Thursday. These four stocks combined account for a whopping 23.4% weighting in the S&P500 - just shy of their 24% pandemic peak and twice the share they held just six years ago.

Partly lifted by the year's artificial intelligence craze, the tech behemoths have clearly flattered year-to-date gains of 10% in the overall S&P500. And on an equal-weighted basis, the index is actually down 3.6% for 2023 so far.

And yet the seemingly endless squeeze in bond markets since midyear has seen megacap indexes retreat some 12% from their highs for the year.

The sight of 10-year Treasury yields topping 5% for the first time in 16 years early on Monday underscored that angst - but the pressure eased significantly during the session as some bond buyers emerged above to lock in yields above that threshold.

The reason for the rather sudden 10-year recoil on Monday were sketchy beyond the breach of the milestone, though it coincided with some major investors claiming it was time to close short positions on Treasuries.

Billionaire investor Bill Ackman said the covered his previous bets against Treasuries on an expectation U.S. economic numbers would deteriorate from here and the Gaza war would push more investor dollars towards U.S. government bonds.

Perhaps ironically, it was also an ebbing oil price after the weekend - amid hostage releases and aid convoys that stirred some hope for a temporary ceasefire in Israel's military retaliation in Gaza - that helped bonds bounce on the day.

More broadly, sovereign debt prices were also helped on Tuesday by signs of mounting pressure on business activity around the world from spiralling borrowing costs, anxious geopolitics and China's economic problems.

Euro zone business activity took a surprise turn for the worse this month as demand fell in a broad-based downturn across the region, early "flash" surveys for October showed. The euro fell back sharply from one-month highs.

Sister surveys for the United States are due out later by contrast.

Britain's labour market also lost more of its inflationary heat in the three months to August, according to new data, potentially helping the Bank of England to keep interest rates on hold next week and dragging down gilt yields.

The upshot of the whole picture is to give U.S. stock futures a lift ahead of the open on Tuesday - with Asia and European bourses in positive territory too as bond markets stabilised. The Vix volatility gauge fell back below 20 from seven-month highs of 23 hit in the previous session.

Ten-year U.S. Treasury yields held about 4.83% - some 19 basis points below Monday's peak at 5.02%. The dollar bounced from one-month lows to trade higher on the day.

Treasury auctions this week will again test demand for U.S. government paper, with $51 billion of 2-year notes up for sale on Tuesday, $52 billion in 5-year notes due on Wednesday and $38 billion in 7-year notes on Thursday.

Elsewhere, Britain's FTSE 100 underperformed due to a near 7% drop in shares of Barclays after the UK lender cut its full-year guidance on net interest margins despite beating quarterly profit forecast.

In euro zone banking, UniCredit climbed 1.8% as the Italian bank posted a bigger-than-expected annual rise of 36% in its third-quarter profit.

Key developments that should provide more direction to U.S. markets later on Tuesday: * Flash October business surveys from United States and around the world via S&P Global; Richmond Fed Oct manufacturing survey, Philadelphia Fed Oct service sector survey * U.S. corporate earnings: Microsoft, Alphabet, Visa, Coca-Cola, Danaher, Texas Instruments, Verizon, General Electric, NextEra Energy, Invesco, Fiserv, HCA Healthcare, General Motors, Halliburton, Dow, Kimberly-Clark, Spotify, Dover, Nucor, Waste Management, CoStar, 3M, F5, Chubb, Paccar, Centene, Sherwin-Williams, Archer-Daniels-Midland, RTX, Quest, Pentair, Synchrony * U.S. Treasury auctions 2-year notes

(By Mike Dolan, editing by David Evans mike.dolan@thomsonreuters.com. Twitter: @reutersMikeD)