NEW YORK, July 12 (Reuters) - Cryptocurrency investment products and funds posted outflows to start the second half of the year, as cautious sentiment persisted in the midst of a summer lull, according to data from digital asset manager CoinShares released on Monday. Crypto outflows were $4 million in the week ended July 9, with bitcoin products showing the most outflows of nearly $7 million in what was the quietest trading week since October 2020. The outflows came after a two-week run of inflows, CoinShares said in its report. Still, bitcoin showed net inflows of $4.2 billion so far this year. Blockchain data provider Glassnode said in a report on Monday that there are signs of recovery in bitcoin mining, a sector that has been hit hard recently due to China"s restrictions. Data showed that hash-rate, a gauge of mining activity, has recovered from the peak-to-trough decline of 55% to just a 39% fall. If this holds, Glassnode said this would suggest that about a hash power equivalent of roughly 29% has come back online. Despite bitcoin"s struggles this year, the world"s most popular cryptocurrency was up about 14% in price in 2021. Ether, the token used in the Ethereum blockchain, posted a minor outflow of $800,000 the last week. So far this year, ether"s net inflows totaled $961 million. Multi-asset investment products were the most popular last week, with inflows of $1.2 million. In 2021, these products showed inflows of $362 million or 16.5% of total crypto assets under management of $39.2 billion, which implied that investors are looking to diversify their digital asset holdings. Grayscale remains the largest crypto asset manager, but has seen its assets under supervision decline further to $29.3 billion as crypto prices slumped. CoinShares, the second biggest digital asset manager, saw AUM slip to $3.3 billion, little changed from the previous week.