Commonwealth Bank's execution only share-broking business CommSec lost seven percentage points of market share during the second half of last year, according to researcher Investment Trends.In a report issued yesterday, Investment Trends said CommSec's primary share (customers who see the organisation as their main broker) fell from 51 per cent to 44 per cent in the December half last year.The proportion of all online share investors holding an account with CommSec (main broker or otherwise) fell two percentage points to 59 per cent.ANZ's E*Trade also lost share - down two percentage points to 15 per cent in primary share, and down four percentage points to 25 per cent in total share.The winners were Westpac Online Investing, nabtrade and CMC Markets Stockbroking.Westpac Online increased its primary share by three percentage points to 10 per cent. Its total share was steady at 12 per cent.nabtrade increased its primary share by three percentage points to eight per cent and its total share by two percentage points to 11 per cent.CMC increased its primary share by three percentage points to six percent and its total share by two percentage points to seven per cent.Investment Trends' analyst, Pawel Rokicki, said the main reason investors changed primary brokers was cost.Rokicki said: "People have modest expectations for the returns they will make from shares now - about six or seven per cent a year. When their return expectations are low they are more conscious of costs."nabtrade and CMC have been marketing aggressively on price and that has had an impact."Another factor is that share investors are tending to trade more, and this also makes them more sensitive to transaction costs."Some good news for brokers is that the number of online investors grew last year, for the first time since 2011. Investment Trends said the number of online investors grew by 10 per cent, to 585,000, in the December half.