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* Average German bond bought in May is loss making
* To see a chart:
* tmsnrt.rs/2mwLWBd (Writes through)
By Francesco Canepa and Balazs Koranyi
FRANKFURT, June 6 (Reuters) - The European Central Bank bought a record proportion of loss-making German government bonds last month, data showed on Tuesday, in a sign it may be running out of positive-yielding paper to buy for its massive stimulus programme.
The threat of losses is likely to strengthen German calls to wind down the ECB's 2.3 trillion euro purchase programme, aimed at boosting the euro zone's economy, ahead of general elections in September.
The ECB will hold its policy meeting on Thursday and is expected to reiterate its plan to extend the money-printing scheme at least until the end of the year despite a recent rebound in inflation.
ECB purchases have depleted the German government debt market, forcing it and the Bundesbank, which carries out the bulk of the purchases in Germany, to buy short-dated, loss-making paper to meet their monthly purchase target.
The average German public sector bond bought by the two central banks in May had a maturity of just four years -- the shortest since the scheme was launched in March 2015.
This means it was likely to yield around -0.58 percent at Tuesday's prices, a guaranteed loss for the ECB and Bundesbank that will not be fully compensated by the 0.4 percent charge that they impose on banks for storing their excess cash overnight.
The Bundesbank has been setting aside money for potential losses on bonds bought under the scheme. But if it were to need capital as a result of even larger losses, this would fall upon the taxpayer.
On top of market constraints, the ECB is running against many of its self-imposed limits.
Its purchases of Portuguese bonds dwindled to a record low of 504 million euros, less than half what its rule would dictate, in May as the ECB tried to avoid hitting a limit on how many bonds it can own from each country. (Reporting by Francesco Canepa; Editing by Adrian Croft)