* Rates won't have to rise too much to reach neutral level -Yellen
* Temporary factors appear to be holding down inflation -Yellen
* Fed's Beige Book shows moderate economic growth
* Indexes up: Dow 0.6 pct, S&P 0.8 pct, Nasdaq 1.1 pct (Updates to late afternoon)
By Kimberly Chin
July 12 (Reuters) - U.S. stocks rose on Wednesday afternoon after Federal Reserve Chair Janet Yellen said interest rates hikes would be gradual and rates will not have to rise much further to reach a neutral level.
Yellen, in testimony to Congress, said the Fed will continue to gradually tighten policy and gradually unwind its massive balance sheet. A neutral interest rate level refers to one that neither encourages nor discourages economic activity.
Investors cheered Yellen's dovish tone. Investors and some Fed officials have been concerned with the recent dip in inflation.
"People were worried about her coming out more hawkish. She said exactly what the market expected and that's why the market was happy with it," said Chris Zaccarelli, chief investment officer at Cornerstone Financial Partners based in Charlotte, South Carolina.
The rate-sensitive S&P 500 real estate index rose 1.3 percent and was on track for its biggest one-day percentage gain in four months. It was the strongest sector of the day.
The dovish sentiment from the Fed put the S&P 500 financials , which tend to benefit from higher rates, last among sectors, with just a gain of 0.1 percent.
The Dow Jones Industrial Average was up 135.79 points, or 0.63 percent, to 21,544.86, the S&P 500 had gained 19.15 points, or 0.79 percent, to 2,444.68, and the Nasdaq Composite had added 65.45 points, or 1.06 percent, to 6,258.75.
The Dow reached a record intraday high.
An index of airline stocks was up 2.2 percent after the No. 1 U.S. airline, American Airlines Group Inc, reported quarterly results that beat expectations and its shares rose 3.8 percent.
Delta Air Lines Inc, United Continental Holdings Inc , Alaska Air Group Inc, Spirit Airlines Inc and JetBlue Airways Corp shares were up between 1 to 4 percent.
Stocks held their gains after the Fed's latest Beige Book report showed that the U.S. economy grew at a "slight to moderate" pace over the last several weeks across all regions of the country.
Investors will be keeping an eye on second-quarter earnings reports on Friday from big U.S. banks including JPMorgan Chase , Wells Fargo and Citigroup.
Advancing issues outnumbered declining ones on the NYSE on Wednesday by a 3.52-to-1 ratio; on Nasdaq, a 2.23-to-1 ratio favored advancers. (Reporting by Kimberly Chin; Additional reporting by Sweta Singh and Tanya Agrawal in Bengaluru; Editing by Leslie Adler)