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* Pan-European STOXX 600 index rises 0.8 pct
* UK mid-cap index hits record high as sterling slumps
* Deutsche Bank bounces back to touch 2-week high
* Randgold, Fresnillo drop on weaker gold prices
By Atul Prakash
LONDON, Oct 4 (Reuters) - European shares advanced on Tuesday, with Germany's Deutsche Bank hitting a two-week high following steep losses and the world's biggest education company Pearson gaining after encouraging comments by Morgan Stanley.
Pearson rose 5.2 percent, among the top gainers in the pan-European STOXX 600 index, after Morgan Stanley said the company was unlikely to issue a profit warning, "meaning the shares could recover sharply on the Q3 results".
Deutsche Bank rose as much as 3.5 percent to a two-week high. Its shares had slumped to a record low on Friday before bouncing back on expectations of a swift deal with U.S. authorities over a multi-billion dollar penalty.
HSBC said that despite Deutsche Bank's obvious operational shortcomings, fears over the bank's solvency were overdone. However, HSBC cut its target price for the bank, forecasting challenging conditions for the banking environment.
"Deutsche Bank should be well equipped to deal with this short-term lack of confidence," HSBC analysts said. "We maintain our 'hold' rating despite the selling pressure on the market as we believe the fundamentals of the company have not changed."
Its shares ended up 1.5 percent.
The STOXX Europe 600 index rose 0.8 percent, while Germany's DAX, which resumed trading after a holiday on Monday, added 1 percent.
Britain's domestically-focused mid-cap FTSE 250 rose 0.8 percent to a record high, while the FTSE 100 index, dominated by international firms, gained 1.3 percent to 7,074 points - the first time since the mid-2015 it breached the 7,000 mark - as the pound slid to its lowest in more than three decades on fears of a "hard Brexit" from the European Union and its single market that could hurt the economy.
Among sector movers, BMW rose 3.3 percent and helped the European auto and parts index to gain 2 percent after Exane BNP Paribas raised its target price for the automaker to 87 euros from 70 euros.
Shares in Intertek rose 5.2 percent after Jefferies raised its stance on the stock to "buy" from "underperform" and lifted its target price to 4,300 pence from 3,000 pence.
Precious metal stocks Randgold and Fresnillo both fell more than 5 percent, leading losers on the STOXX index, as gold prices fell to their lowest since Britain's Brexit vote in June, as a bounce in the dollar after upbeat U.S. data triggered a break of key support at $1,300 an ounce. (Additional reporting by Danilo Masoni in Milan; Editing by Richard Balmforth)