This summer's stock market rally has helped wealth manager Hargreaves Lansdown boost assets under administration by 14% during its first quarter.In what has historically tended to be the company's quietest period, assets under administration grew to £19.9bn on 30 September from £17.5bn at the end of June.Assets held within the Vantage service, its direct-to-private investor platform, rose 13% in three months, with net new business inflow of £0.55bn in line with the same time last year despite fears of a double dip recession. There was also the £1.71bn positive impact of the market and other growth factors.Equity deal volumes have also been consistent with the first quarter of 2009."The rise in stock markets during the first quarter (FTSE All-Share index increased by 12.7% from 2543.47 to 2867.58) has helped increase the value of assets under our administration," explained boss Ian Gorham."Both the rising stock markets and net new business have helped to drive up operating revenue. Future stock market levels and investor confidence will have a significant part to play during the remainder of our financial year."Operating revenue for the first quarter is 25% higher than the last time at £45.2bn.Hargreaves welcomed clarity over pension rules, which it thinks should remove current uncertainties and retain "effective levels of tax relief for private pensions saving". The government yesterday announced a reduction in the annual tax-free pension allowance from £255,000 to £50,000, which it estimates will save £4bn a year.