No one knows exactly how much of Safe's US$3.2 trillion stash of foreign currency is denominated in US dollars. But if China's holdings are in line with other countries', the proportion is at least 60 per cent. And given that the bulk of China's trade is denominated in US dollars and that Beijing has long managed the yuan against the US currency, it is very likely the figure is higher.

Similarly, no one knows precisely how many of those US dollars are invested in US Treasury debt.

According to the Treasury's own data, at the end of May China held US$1.16 trillion-worth of US Treasury bills and notes.

But that figure certainly understates the true extent of China's position in US government debt. Safe makes many of its purchases through banks based in London, which means they show up as British rather than Chinese in the Treasury data.

Looking at how these 'British' holdings have grown, we can estimate that Safe has bought around US$250 billion-worth of Treasury debt through London in the last year, bringing its total holdings to at least US$1.4 trillion.

That means Safe stands to suffer enormous losses on its portfolio should the US government lose its AAA credit rating or, in the worst case, default on its obligations.

It would be a double hit. Not only would Safe take heavy mark-to-market losses from the inevitable slide in US Treasury, agency and corporate bond prices. China's reserve managers would also risk massive losses if the blow to US credibility caused the US dollar to weaken against the yuan, which would hammer the yuan value of their US dollar holdings.

Of course, China's authorities could seek to avoid this valuation loss by stepping up their intervention in the foreign exchange market to hold the yuan steady against the US currency.

But that would mean buying more US dollars and accumulating even more US dollar-denominated assets, which would mean piling up an even greater risk of loss in the future. No wonder Safe's officials are nervous.

That nervousness is clearly prompting them to make some ill-considered remarks.

In further comments, Safe claimed that the yuan's appreciation - the currency hit a 17-year high against the US dollar yesterday - won't cause valuation losses on China's holdings of foreign reserves.

'The changes in the yuan's exchange rate against the US dollar causes changes in the paper value of the reserves when valued in yuan,' Safe declared. 'This is not a real loss.'

Well, if you insist on reporting your foreign reserves in US dollars rather than in your home currency, then I suppose you can pretend you don't take a loss when your own currency strengthens.

But you'd be deceiving yourself. As far as China's central bank is concerned, there is a very clear cost to yuan strength.

China's accumulation of foreign reserves doesn't occur in a vacuum. When the central bank steps into the foreign exchange market to buy US dollars, it has to fund those purchases.

It does this by borrowing yuan from China's banks. Either it issues short-term bills, which the banks buy, or it orders them to lodge more of their deposits at the central bank as statutory reserves, in effect commanding them to lend to the central bank.

As a result, China's foreign reserves make up assets on one side of the central bank's balance sheet, offset by its liabilities to the banking system on the other side.

The trouble is that these assets are denominated in foreign currencies, largely US dollars, while the liabilities are in yuan.

That means if the yuan appreciates against the US dollar, the central bank's liabilities grow relative to its assets.

According to its balance sheet, at the end of last year the central bank had foreign currency assets of 21 trillion yuan, offset by its domestic liabilities and just 220 billion yuan of capital.

If we assume 60 per cent of the foreign currency assets are denominated in US dollars, it would only take a yuan appreciation of 0.2 per cent against the US dollar for the central bank's liabilities to exceed its assets, wiping out its capital base and leaving the People's Bank of China insolvent.

Given that the yuan has appreciated 2.2 per cent against the US dollar since December, it is a fair bet that that has already happened.

Of course, you can argue that it doesn't much matter if the People's Bank of China is technically insolvent.

And you'd have a point. But to claim that the institution suffers no loss if the yuan appreciates is clearly nonsense.