GLOBAL MARKETS-Dollar falls, US bond prices rise as Fed tone mildly dovish

* Dollar dips after Fed statement

* U.S. companies report more upbeat earnings

* Copper prices rise for 4th session (Updates with closing U.S. market levels)

By Caroline Valetkevitch

NEW YORK, July 26 (Reuters) - The dollar touched its lowest in more than a year and U.S. Treasury prices rose on Wednesday after the Federal Reserve left interest rates unchanged and signaled it could begin to cut its massive bond portfolio in the coming months.

U.S. stocks held their gains after the statement, hitting record closing highs on another day of strong earnings reports from companies including Boeing (NYSE: BA - news) and AT&T (Sao Paolo: ATTB34.SA - news) .

In its statement following a two-day policy meeting, the U.S. central bank said it expected to start winding down its bond holdings "relatively soon." It noted that overall inflation and a measure of underlying price gains had both declined and said it would "carefully monitor" price trends. [

Strategists said bond prices and the dollar reacted to the statement's slightly more dovish tone.

"The statement was mildly more dovish than expected. The Fed's assessment of the inflation backdrop amounted to a very modest downgrade of the overall inflation situation and could signal slightly more concern on the part of the Fed with respect to their forecast for inflation," said Omer Esiner, chief market analyst at Commonwealth FX in Washington.

Benchmark 10-year notes gained 11/32 in price to yield 2.29 percent, down from 2.33 percent on Tuesday.

The U.S. Treasury yield curve also marked a milestone not seen since the onset of the financial crisis, with all maturities comprising the curve sporting a yield of at least 1 percent for the first time in nearly nine years.

The dollar index, which measures the greenback against six major currencies, reversed course after the statement and fell to 93.396, its lowest since June 23, 2016. It was last down 0.6 percent at 93.459.

Futures traders are pricing in a 50-percent chance that the Fed will raise rates at its December meeting, down from 52 percent before the statement, according to the CME Group (Kuala Lumpur: 7018.KL - news) 's FedWatch Tool.

The U.S. central bank's statement did not dramatically sway Wall Street's major indexes, but a 0.6 percent decline in S&P financials limited gains in the benchmark S&P index.

The Dow Jones Industrial Average rose 97.58 points, or 0.45 percent, to end at 21,711.01, the S&P 500 gained 0.7 point, or 0.03 percent, to 2,477.83 and the Nasdaq Composite added 10.57 points, or 0.16 percent, to 6,422.75.

MSCI (Frankfurt: 3HM.F - news) 's index of stock markets across the world was up 0.1 percent, while European shares ended up 0.5 percent.

Oil prices rose, with Brent futures gaining 1.5 percent to settle at $50.97 a barrel, after data showing a much-steeper-than-expected decline in U.S. inventories.

U.S. West Texas Intermediate futures rose 86 cents or 1.8 percent to settle at $48.75.

Copper rose for a fourth day to the highest in more than two years, helped by expectations of solid Chinese economic growth, closing in London up 1.7 percent at $6,330 a tonne after touching $6,400, its highest since May 2015.

For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets

(Additional reporting by Saqib Ahmed and Karen Brettell in New (KOSDAQ: 160550.KQ - news) York and Patrick Graham in London; Editing by Mark Trevelyan and James Dalgleish)