Has Donald Trump really wiped out the Barack Obama administration’s debt?

In an interview with Fox News on Wednesday, Donald Trump seemed to suggest that his administration has already wiped out all the government debt incurred by the US under the Obama presidency.

He said: “In eight years they [the Obama administration] borrowed more than it [the government] did in the whole history of our country. They borrowed more than $10 trillion, right? And yet we picked up $5 trillion just in the stock market, possibly the whole thing in terms of the first nine months [of my presidency] in terms of values. So in one sense you could say we’re really increasing values and maybe in a sense we’re reducing debt.”

Are these figures true? Does the value of the of the stock market have anything to do with government borrowing? And is the Trump administration really ‘reducing’ American debt?
Did the US national debt really rise by $10 trillion under Obama?

In January 2009, when Obama took office the value of the US public debt was $10.6 trillion. When he left office in January 2017 it was $19.9 trillion.

But this measure includes liabilities owed to the arm of the US government that administers state pension payments. This arm of the state has built up cash surpluses over the years, as incoming social security payments from the working public have outstripped payments to the retired. It has invested these surpluses in special non-marketable US Treasury bonds.