* Mexican peso leads gains * Brazil's real rises on speculation over local reforms * Rising copper prices help Chile's peso (Adds details, updates prices) By Susan Mathew and Ambar Warrick Sept 9 (Reuters) - Mexico's peso hit a six-month high on Wednesday after the government unveiled a lean 2021 budget, while other Latin American currencies recovered from recent losses after a U.S. technology stock rout appeared to have stabilized. Mexico's peso jumped about 1.5% to its highest since early-March after the government unveiled a 2021 budget with limited infrastructure spending and tight debt targets. Data showed Mexican consumer price inflation in August rose above the central bank's target of 3%, owing to low interest rates in the country after an easing cycle that began last year. "The data might reinforce Bank of Mexico's increasingly cautious stance, but we still expect further monetary easing, including a 25 basis point cut at its meeting later this month," said William Jackson, chief emerging markets economist at Capital Economics. Similar data from Brazil showed inflation hit its highest in four years last month, although the pace slowed from July and overall inflation remained well below the central bank's goal. The real currency rose more than 1% as markets watched for progress in the country's administrative reform proposals, which are expected to generate at least 300 billion reais ($57 billion) of savings over the next decade. "They'll push the limits of what can be done within the current framework but won't break it. My sense is that they understand the risks of doing so well, even in Congress," Daniel Kerner, Eurasia Group managing director of Latin America told the Reuters Global Markets Forum on Tuesday. As oil prices rose, crude exporter Colombia's currency broke a four-session losing run, while Chile's peso tracked a rise in copper prices. Barring a few outperformers, regional currencies still have a long road to pre-pandemic levels, as uncertainty over the virus' economic impact persists. Latin American stocks rose as Wall Street recovered from a technology-related rout. Brazil's Bovespa rose 0.8%, while Colombia's COCLAP was set for its best session in more than a week. MSCI's index of Latam stocks jumped 2.3%. A Vontobel Asset Management survey of 300 institutional investors and discretionary wealth managers showed that a majority of investors are planning to increase their emerging markets exposure over the next five years, even as concerns over the impact of the COVID-19 pandemic are limiting the short-term flow of investments to those economies. Key Latin American stock indexes and currencies: Stock indexes Latest Daily % change MSCI Emerging Markets 1086.71 -0.07 MSCI LatAm 2009.56 2.27 Brazil Bovespa 100871.98 0.82 Mexico IPC 36237.52 0.46 Chile IPSA 3782.13 -1.15 Argentina MerVal 46295.23 1.789 Colombia COLCAP 1242.66 0.84 Currencies Latest Daily % change Brazil real 5.2893 1.43 Mexico peso 21.4255 1.56 Chile peso 766.2 0.80 Colombia peso 3712.77 0.65 Peru sol 3.5368 0.11 Argentina peso 74.7600 -0.07 (interbank) (Reporting by Susan Mathew and graphic by Aaron Saldanha in Bengaluru; Additional reporting by Lisa Puline Mattackal; Editing by Aurora Ellis)