Bloomberg reports,

“On any measure, Japan is the most indebted sovereign rated by Fitch,” Colquhoun, Hong Kong-based director at the company’s Asia-Pacific sovereign group, said in a conference call today.

…The yield on Japan’s 10-year bond was unchanged at 1.315 percent

The Congressional Budget Office now forecasts that the U.S. will have a ratio of government debt to GDP of 90 percent by 2020. However, that seems low relative to Japan, which already has a ratio of close to 200 percent. How does Japan do it? Some thoughts below.Imagine that you have an investment in a rental property financed in part by a loan. Suppose that you have an operating loss (the rent on the property is less than the expenses). How can you hold onto the property? There are three issues:

1. The size of the loan. If it were small, you could perhaps continue to borrow in order to hold onto the property, with the lender hoping that you can eventually turn the operating loss into a profit.

2. The size of the operating loss. if it is small, then your debt may not grow terribly quickly. Again, the lender may be willing to extend the loan in the hope of a turnaround.

3. The interest rate on the debt minus the rate of price appreciation of the property. Call this the erosion factor. If the erosion factor is low, then it will take a long time before the debt burden becomes unbearable. If the erosion factor is negative, then you may actually have a sustainable investment.

These are also the three factors at work in the world of sovereign debt. The amount of outstanding debt matters. The “operating loss” is what is known as the primary deficit, meaning government revenue minus spending other than interest. The erosion factor is the interest rate minus the growth rate of GDP. Now, the government does not have an ownership stake in GDP in quite the same way that a landlord has an ownership stake in a rental property, but the arithmetic of government debt is such that the analogy holds fairly well.

The erosion factor can be negative for government debt. That is, the nominal interest rate may be less than the rate of GDP growth. That is in fact what happened in the United States after World War II. Nominal interest rates were low. Ex post, investors who bought U.S. government debt from 1945 through about 1975 suffered negative inflation-adjusted returns.

Which brings us to Japan. The size of the loan is high–200 percent of GDP, the highest in the industrialized world. The size of the operating loss is also high. According to the Wall Street Journal,

Another idea is to aim to cut the ratio of Japan’s overall deficit to about 6% of GDP by the year ending in 2016, then to 3% or below five years later, the officials said. The figures compare with 9.4%, or 44.8 trillion yen, expected by the cabinet office for the current fiscal year.

One thing that Japan may have going for it is a negative erosion factor. With a ten-year interest rate of 1.315 percent, if nominal GDP rises at 5 percent per year (say, 2 percent real growth plus 3 percent inflation), the erosion factor would be negative 3.685 percent, which would be sufficient to offset a primary deficit of 3 percent of GDP. The question, though, is whether investors will tolerate negative real returns from holding Japanese government debt.

Suppose that investors wake up next week somewhat nervous about Japanese government debt. Suppose that the interest rate goes up to, say, 2.5 percent. It seems to me that this might be enough to make Japan’s long-term fiscal outlook untenable, in which case there is nothing to stop interest rates from climbing to, say, 10 percent, a point that rates have almost reached in Greece.

If the interest rate on Japanese debt were to hit 10 percent, then Japan would require 20 percent of GDP just to meet interest payments. Presumably, they would have no choice but to default.

The point here is that with such a high debt level and a high “operating loss,” the only thing that Japan might have going for it is a low (possibly negative) erosion factor, which in turn depends entirely on the willingness of people to lend to the government at low interest rates. A loss of willingness to lend would turn into a rapid fiscal death spiral. I suppose that the arguments for “this time is different” are largely cultural. Japanese savers are willing and able to supply massive sums at low interest rates, the Japanese political system could make drastic budget cuts quickly, or some such.

Where can I buy put options on Japanese bonds?