FOREX-Dollar rises; investors remain wary of too much risk

* Dollar posts modest gains but ends off session highs

* Late afternoon stock rally limits dollar strength

* U.S. capital inflows surge to near 3-year highs

* Weak US data stokes concern; investors watch automakers

* For up-to-the-minute market news, click on FXNEWS (Recasts; adds comment, details; changes byline)

By Steven C. Johnson

NEW YORK, Nov 18 (Reuters) - The dollar strengthened on Tuesday as a batch of grim U.S. economic data pushed nervous investors to seek safety in the greenback.

A late rally on Wall Street limited dollar gains against the euro and sterling and boosted it against the yen on hopes that financial market turmoil may be starting to ease.

But with the euro zone and Japan already falling into recession in the third quarter, investors remained skittish, and U.S. data showing a sharp slide in home prices in the third quarter and a record decline in producer prices last month added to their unease. For full story, see [ID:nN18202597]