* SSEC -0.3 pct, CSI300 -0.4 pct, HSI flat
* China insurance regulator punishes two more insurers
* U.S. posts upbeat economic data overnight
SHANGHAI, Dec 28 (Reuters) - China stocks fell on Wednesday morning, with any optimism generated by strength in commodities overshadowed by the regulator's latest measures to rein in aggressive stock investments by insurance companies.
Hong Kong stocks held their ground on the first trading day following the Christmas break, but trade was thin and many operators were not yet back from holiday.
The CSI300 index fell 0.4 percent to 3,303.16 points at the end of the morning session, while the Shanghai Composite Index lost 0.3 percent, to 3,106.24.
The Hang Seng index was unchanged at 21,568.05 points, while the Hong Kong China Enterprises Index gained 0.5 percent, to 9,230.99 points.
Sentiment soured on Wednesday following media reports that the vice chairman of China's insurance regulator said insurers were not platforms to enrich speculators.
Also on Wednesday, the regulator said it had suspended two insurers from online insurance business and ordered them not to apply for new product approvals for three months - the latest move to put insurers under stricter supervision.
Investors were unimpressed by the strong fourth quarter performance among Chinese firms as cash flow remained weak and inventories rose at a record pace in late 2016.
Some analysts questioned whether solid profits from the rising prices of coal, steel and some building materials were driven by price speculation or genuine demand.
All sectors in China stepped back at the lunch break, with the biggest declines seen in infrastructure shares, downed nearly 1 percent.
Energy shares steadied in the morning session from a three-day losing streak, thanks to a bounce in commodity prices. The coking coal futures contract surged around 7 percent at some point, after hitting a nearly 8-week low in the previous session.
Commodity strength also helped offset bearish sentiment among raw materials shares, with rebar gaining nearly 4 percent by midday.
In Hong Kong, most sectors advanced modestly, with energy leading the gains, up more than 1.3 percent.
Investors were sitting on their hands as the U.S. dollar had hovered near a 13-year high for two weeks, with yet more upbeat economic data released overnight, potentially luring even more capital out of emerging markets.
Reporting by Jackie Cai and John Ruwitch; Editing by Eric Meijer