* Dollar up versus yen and the euro as Q2 ends * Investors square positions on quarter's last trading day * Fed's Stein sees September as possibility for QE reduction NEW YORK, June 28 (Reuters) - The dollar rose against the yen and euro on Friday, as investors again began pricing in the possibility that the U.S. Federal Reserve will begin to downsize its bond-buying program as soon as the September policy meeting. Fed Governor Jeremy Stein highlighted September as a possible time when the U.S. central bank will need to consider reducing the quantitative easing program while speaking on Friday in New York. Stein said the Fed's eventual decision to scale back its asset purchases must be based on the overall economic progress since it launched the stimulus and not be "excessively sensitive" to the most recent economic data. "This specific comment about September sparked speculation that this will be the month when the Fed starts tapering, which we also believe is likely because the central bank will not want to suddenly reduce stimulus right before the holidays," said Kathy Lien, managing director at BK Asset Management in New York. The dollar got an added boost when a report showed U.S. consumer sentiment improved in late June, ending the month close to a near six-year high set in May, as optimism among higher-income families rose to its strongest level in six years, a Thomson Reuters/University of Michigan survey released on Friday showed.. The euro was last down 0.3 percent at $1.3000 with the session low at $1.2990. Against the yen, the dollar was up 0.9 percent on Friday at 99.25 yen. For June, the dollar fell 1.2 percent against the yen, snapping eight straight months of gains against the Japanese currency, while the euro was little changed against the dollar. "We are settling into the bottom of the recent range (on euro/dollar) at around $1.3000," said Andrew Dilz, foreign currency trader at Tempus Inc in Washington. "But there is no reason not to be trading at $1.3000." Richmond Fed President Jeffrey Lacker said from West Virginia on Friday that financial markets should brace for more volatility as they digest news that the Federal Reserve will scale back bond buying later this year, but added it was was an understandable adjustment and will not derail growth. . Investors were also beginning to speculate about what announcements may come from the European Central Bank policy meeting next Thursday. Analysts said growing worries about the euro zone's faltering economy, in contrast to the relative optimism around the U.S. economy, could hurt the single currency. This week European Central Bank President Mario Draghi pointed out downside risks to growth and said the ECB was nowhere near exiting its accommodative monetary policy. "There is speculation that the ECB may do outright quantitative easing," said David Song, currency analyst at DailyFX in New York. While the Fed's asset purchases have weighed on the dollar, Song said investors would take it as a positive sign if the ECB ramped up efforts to stoke growth in Europe. "There is a little bit of a different dynamic on the two currencies," Song said. Other analysts cautioned that quarter-end flows were creating some distortion in market sentiment. "Today is dominated by quarter-end flows and one should not be reading too much into the price moves," said Chris Walker, currency strategist at Barclays in London. Large funds rebalance their investment portfolios at the end of the month and the quarter. Their flows and requirements to square positions often dominate trade on the last trading day. "The dollar's uptrend remains intact going into next quarter as we are expecting Fed tapering to start in September," Walker added. "We forecast euro/dollar to fall to $1.26 in six months and the dollar to rise to 103 yen in the next three months." The Australian dollar was last down 0.6 percent against the Canadian dollar at C$0.9644 and touched a session low of C$0.9607 after the release of IMF data on central bank holdings, which for the first time separated reserves in the two commodity bloc currencies as individual line items. . Central Bank reserves in the Australian dollar totaled US$98.66 billion, or 0.9 percent of the total reserves of US$11.09 trillion in the first quarter, slightly more than the US$94.93 billion, or 0.9 percent, in Canadian dollars. Some of the selling in the aussie against the loonie may have come from speculators betting that the aussie's percentage would have been higher. There was a spike in Australian dollar volume to AUD$2.1 billion. Volume in the yen also surged to US$3.94 billion around midday in New York.