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* Futures up: Dow 0.09%, S&P 0.06%, Nasdaq 0.11%

Jan 4 (Reuters) - U.S. stock index futures ticked up on Thursday, recovering from a grim start to the new year, as investors awaited more economic data for cues on the Federal Reserve's monetary easing path, while Apple slipped following a rating downgrade.

Wall Street stumbled in the first two sessions of 2024, with the benchmark S&P 500 notching its worst two-day performance since late-October as investors booked profits after a blistering rally last year.

Hopes that the Fed could start interest rate cuts this year had driven much of the gains towards the end of 2023, though the latest minutes from the central bank's December policy meeting did not offer many clues on when the easing might commence.

Traders now see a 72.6% chance for at least a 25 basis points (bps) rate cut in March and a near 96% probability for May.

Yields on U.S. Treasury tenors, an indicator of interest rate expectations, edged up, with the yield on the benchmark 10-year note climbing to 3.955%.

Investors now await the ADP National Employment Report due at 8:15 a.m. ET, ahead of a key jobs report on Friday, both of which could shed some light on the health of the labor market and influence expectations on the rate trajectory.

Economists polled by Reuters expect private payrolls to have increased by 115,000 in December, from a 103,000 rise the month before.

Also on tap are initial jobless claims data for the week ended Dec. 30 and December S&P services sector activity data.

Apple was the only megacap stock in the red, down 0.9% in trading before the bell, after brokerage Piper Sandler downgraded the iPhone maker to "neutral" from "overweight".

Micron Technology rose 2.1% after brokerage Piper Sandler upgraded its recommendation on the chipmaker to "overweight" from "neutral".

Other semiconductor stocks such as Advanced Micro Devices and Broadcom also gained 0.7% and 0.8%, respectively, recovering from a recent downturn.

At 5:52 a.m. ET, Dow e-minis were up 35 points, or 0.09%, S&P 500 e-minis were up 3 points, or 0.06%, and Nasdaq 100 e-minis were up 17.75 points, or 0.11%.

Among other movers, sportswear makers Nike and Foot Locker shed 1.4% and 1.4% after UK retailer JD Sports lowered its annual profit forecast.

Mattel dropped 2.6% after brokerage Roth MKM downgraded the Barbie doll maker to "neutral".

Fubotv gained 4.8% after the sports TV streaming platform and Nexstar Media reached a new multi-year distribution agreement.

(Reporting by Johann M Cherian in Bengaluru; Editing by Devika Syamnath)