* Portugal's BES says not at risk of running short of capital
* Greek, other peripheral euro zone bond yields fall
* Italy tests demand with up to 7.5 bln euro bond sale
By Emelia Sithole-Matarise
LONDON, July 11 (Reuters) - Portuguese bond yields fell on Friday as the country's biggest bank sought to reassure investors about its financial stability after concerns over the health of its parent company rattled financial markets this week.
Investor worries about losses on loans to the parent company of Banco Espirito Santo accelerated a sell-off in Portuguese assets this week that triggered the first significant episode of contagion this year in peripheral euro zone bonds.
Euro zone bonds recovered some poise after Banco Espirito Santo said on Thursday night that losses on loans to the troubled business empire of its founding family will not put BES at risk of running short of capital.
Yields on Portuguese 10-year bonds were down 10 basis points at 3.92 percent. They had risen about 40 bps this week, their biggest weekly increase this year.
"It (the sell-off) was a bit overblown. After the huge rally behind us in non-core bonds as well as equities, we've had a multitude of bad news ... and so the market clearly needed a trigger for profit-taking and that's what happened," said Jan von Gerich, chief fixed income analyst at Nordea.
"For now at least, the sentiment will remain nervous but I don't think its something that will reverse the general downward trend in peripheral bond yields."
Yields on bonds issued by bailed-out Greece, whose three-year debt sale on Thursday was undermined by the fallout from Portugal, were 4 bps lower at 6.28 percent.
Italy will provide a further test of investor appetite for peripheral bonds later in the day, when it auctions up to 7.5 billion euros of short- and long-term bonds later in the day. Many in the market expect Rome to sell the maximum amount it is targeting, noting that this week's rise in yields might attract buyers to the larger, more liquid peripheral bond markets.
Italian 10-year yields were 3 bps down at 2.91 percent. Spanish equivalents were 2 bps lower at 2.80 percent.
"The sell-off may provide some attractive entry levels into the periphery, which still offers some yield pickup in an environment of even lower core rates," one trader said. (Editing by Larry King)