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The warning signs that the battle against inflation is far from won

The bond markets, for understandable reasons, attract less media scrutiny than equity markets.

A big fall in the stock market feels somehow more tangible, more close to home, to the man or woman on the Clapham omnibus - even though their retirement savings are just as likely, these days, to be invested in bonds as they are in equities.

However, as last year's lurches in the gilt (UK government bond) markets after Kwasi Kwarteng's mini-budget showed, what happens in bond markets affects us all.

And, just now, some very interesting things are happening in government bond markets.

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The yield (which rises as the price falls) on US Treasury bonds has, on Tuesday, hit its highest level since November 2007, when the global financial crisis was getting under way.

In Europe, too, bond yields are spiking.

In Germany, the yield on 10-year bunds - just about the benchmark for the eurozone - hit a 12-year high on Monday, taking it back to levels last seen in July 2011 when the eurozone sovereign debt crisis was in full swing.

In the UK, meanwhile, gilt yields - while off their recent highs - remain close to the levels they hit during the aftermath of last September's mini-budget.

So what's going on?

Well, there are some factors specific to individual markets.

For example, US Treasuries are partly selling off due to concerns over the US debt ceiling and the possibility, with the Democrats and Republicans at odds over government spending levels, of a government shutdown that would see hundreds of thousands of federal employees furloughed and government contractors going unpaid.

But the main factor at play is the dawning realisation among investors that central bank interest rates may remain at elevated levels for some time.

The US Federal Reserve and the Bank of England both hit the 'pause' button on further interest rate rises last week, following an increase imposed by the European Central Bank a week earlier.

Yet the commentaries from the US and UK central banks - particularly the Fed - hinted strongly at rates remaining at these multi-year highs for some time to come.

That has also been the case in the eurozone. One reason why bund yields are at a 16-year high is because some of the ECB's policymakers have been talking up the prospects of the bank's main policy rate remaining at the current 4% for the foreseeable future.

As for the Bank of England, which may still have at least one more rate hike in its locker, no-one in markets is seriously expecting an interest rate cut until around this time next year at the earliest.

Informing all of these interest rate expectations is the fact that the oil price has been trading at elevated levels.

A barrel of Brent crude last week hit $95.96 - a level not seen since November last year - while during this quarter, the three months to the end of September, the price has risen by roughly 25%.

That makes this quarter the strongest for Brent Crude since the rally seen during the first three months of last year following Russia's invasion of Ukraine.

This rise in oil prices has reminded investors that, even though the so-called 'energy intensity' of western economies is lower than it was in the 1970s and 1980s, the battle against inflation is far from won.

Inflation staying higher for longer means interest rates stay higher for longer and, just now, central bankers feel under no pressure to cut interest rates.

Accordingly, investors are adjusting to this new world.

Nowhere can this be seen more clearly than in the tech sector.

The share price of a company reflects what investors will be prepared to pay for that company's future cash flows and, as tech companies are deemed to have better long-term growth prospects, they tend to be rated more highly by the stock market.

When bond yields rise, though, the values of those expected future cash flows fall.

Investors find it harder to justify holding a highly valued tech stock in such circumstances when they could be holding a less risky asset, such as a US Treasury bond, paying them more at once. The same phenomenon was seen early last year when the Nasdaq briefly entered 'correction' territory.

Accordingly, since their most recent peaks in mid-July, shares of Microsoft are down by 13%, Apple by 11% and the Nasdaq Composite by 8%.

There are at least a couple of ways at looking at this sell-off in government bonds.

One is that this is a reversion to the mean. Jim Reid, head of global fundamental credit strategy at Deutsche Bank, reminded his clients this morning that, although 10-year US Treasury yields are at around 4.5% for the first time since 2007, they are, in fact, also back at what has been their average level for at least the last 230 years.

Those of a less optimistic persuasion, though, will be looking at the demographics.

In western economies, the baby boomers are now retiring in droves. It is now six years since Mike Wells, the former chief executive of the insurance giant Prudential, told Sky News that, over the next two decades, Americans would be retiring at the rate of 10,000 per day.

That is going to result in supply shortages in both Europe and the US, not least in terms of the labour force. That will be good news for those in work and with skills that are in demand.

Those supply shortages, though, are also likely to lead to inflation bursting out in all kinds of sectors. And that's bad for bonds.