* Asian stock markets : tmsnrt.rs/2zpUAr4
* Trump menaces Mexico with tariffs in surprise tweet
* Markets see recession risk, price in deeper Fed rate cuts
* China PMI disappoints with drop to 49.4 in May
* S&P 500, European stock futures in the red
* Asia shares draw month-end demand in wake of steep losses
* Bonds jump on safe-haven rush, U.S. yields at fresh lows
By Wayne Cole
SYDNEY, May 31 (Reuters) - U.S. stock futures slid and sovereign bonds surged on Friday as investors feared President Donald Trump's shock threat of tariffs on Mexico risked tipping the United States, and maybe the whole world, into recession.
The investor mood darkened further when a key measure of Chinese manufacturing activity for May disappointed, raising questions about the effectiveness of Beijing's stimulus steps.
Markets moved aggressively to price in deeper rate cuts by the Federal Reserve this year, while bond yields touched fresh lows and curves inverted further in a warning of recession.
Washington will impose a 5% tariff from June 10, which would then rise steadily to 25% until illegal immigration across the southern border was stopped.
Trump announced the decision on Twitter late Thursday, catching markets completely by surprise.
"The mercurial President Trump has signalled via Twitter this morning that his mindset is shifting ever farther from reaching trade deals," warned Eleanor Creagh, a strategist at Saxo Capital Markets Australia.
"It seems now that market participants are finally realising that the narrative of an H2/19 recovery is fast dissipating," she added. "As escalating trade tensions across the globe cause growth expectations to be recalibrated, risk off sentiment will remain and volatility will increase."
Yields on the 10-year Treasury note quickly fell to a fresh 20-month low of 2.17%, while the dollar jumped 1.7% on the Mexican peso.
E-Mini futures for the S&P 500 slid 0.8% and FTSE futures 0.4%. Germany's DAX shed 0.7%.
Asian shares fell at first, only to draw month-end bargain hunting having endured a torrid few weeks. MSCI's broadest index of Asia-Pacific shares outside Japan edged up 0.3%, though it was still down a whopping 7.3% for the month.
China's blue chip index held steady, partly on talk Beijing would now have to ramp up its stimulus, but again was nursing loses of 6.8% for May. Japan's Nikkei fell 1.3%, dragged down by big falls in car makers, which left it off 7.1% for the month. Investors clearly reckoned that opening a new front in the trade wars would pressure central banks everywhere to consider new stimulus.
On Thursday, Federal Reserve Board of Governors Vice Chair Richard Clarida had said the central bank would act if inflation stays too low or global and financial risks endanger the economic outlook.
"What the Clarida's comments have done is clarify in many people's minds the answer to the questions of whether low inflation proving more than transitory would itself be enough to get the Fed to ease – the answer appears to be 'yes'," said Ray Attrill, head of FX strategy at National Australia Bank.
"That served to reinforce prevailing market expectations that the Fed will be easing in the second half of this year."
Indeed, the case that the inflation slowdown was temporary took a blow when the core personal consumption expenditures index, the Fed's favoured measure of inflation, was revised down to 1% for the first quarter, from 1.3%.
Trump's tariff threat only added to the dangers and the market further narrowed the odds on Fed easing this year and next. Futures imply no less than 44 basis points of cuts by year end in the current effective funds rate of 2.38%.
Bonds extended their bull run with 10-year Treasury yields now down a steep 33 basis points for the month and decisively below the overnight funds rate.
Such an inversion of the yield curve has presaged enough recessions in the past that investors are wagering the Fed will be forced to ease policy just as "insurance".
Yet Treasuries are hardly alone in rallying, with bond yields across Europe either at or near record lows. Yields in Australia and New Zealand have also hit an all-time trough on expectations of rate cuts there.
Those declines have kept the U.S. dollar relatively attractive from a yield point of view and it was trading near a two-year high against a basket of currencies at 98.115.
The euro was huddled at $1.1129, having shed 0.7% for the month. The safe-haven yen fared better as the dollar lost 0.6% on the day to a three-month low of 108.94.
Sterling was poised for the biggest monthly drop in a year as the imminent departure of Theresa May as prime minister deepened fears about a chaotic divorce from the European Union.
The pound was last at $1.2611 and nursing a 3.2% loss for the month so far.
In commodity markets, spot gold firmed 0.4% to $1,293.33 per ounce.
Oil prices fell to their lowest in almost three months on fears a global economic slowdown would crimp demand.
U.S. crude was last down 55 cents at $56.04 a barrel, while Brent crude futures lost 91 cents to $65.96.
Editing by Sam Holmes & Shri Navaratnam