The future is always clouded in markets. But even the past isn't as clear as it seems.

Sure, we know how prices have moved. Figuring out why they moved is crucial to having any hope of accurate predictions. And it's much harder to be sure than it seems-even in Treasury bonds, the foundation of pricing for almost everything.

This year's move in long-dated bond yields is a case in point. Treasury yields are up sharply, with the benchmark 10-year rising from 4.17% to just above 5% before pulling back a bit.

Did they rise so much because the economy is strong, jobs are plentiful and money is pouring into the artificial-intelligence sector? Interest rates need to be higher to keep the resulting inflationary pressures under control, and traders extrapolate out higher rates for longer into higher bond yields.

Or did yields rise because America's credibility is on the line? The Fed hasn't hit its inflation target in five years, the president is pushing for lower rates, government debt is high and rising inexorably, trade wars and erratic policymaking have deterred some foreign buyers of Treasurys and geopolitical shocks mean investors want compensation for volatile inflation.

The difference really matters. If yields rose for the good reason of a strong economy, that should help stocks. If they rose because U.S. credibility is crumbling, that should be a headwind to stocks.

Investors seem to be locked in a wrestling match over these extremes, contributing to big swings in bonds last week. Bond geeks have lots of measures that ought to allow us to tease apart the two stories.

The simplest is to look at what has happened to bonds maturing soon compared with those maturing in many years. Yields on the short-dated bonds have gone up a lot more, which tends to support the idea that the surge in yields is about the Fed raising interest rates in response to inflationary pressures. Since interest rates apply overnight, higher rates have more effect on bonds maturing soon than those maturing further away.

We can get fancier. A 10-year bond can be thought of as two five-year bonds, one maturing in five years plus another that starts when the old one matures. We can measure this in markets by comparing yields on five-year and 10-year bonds to get an implied yield for what's known on Wall Street as the "five-year, five-year" (a five-year bond starting in five years).

Yields for the first five years are up a lot this year, more than a full percentage point. Those for the five years starting in five years are up only half a percentage point. So one way to think of what has happened is that investors expect a bunch of rate rises from the Fed in the near term, but some cuts in the longer run.

We can also decompose bond yields into the expected inflation rate plus the real yield above inflation, measured by TIPS, or Treasury inflation-protected securities. Looked at this way, there has been only a small rise (from 2.25% to 2.33%) in the bond market's best guess at 10-year average inflation, known as the break-even. Most of the rise in yields is a rise in the real rate. The obvious interpretation is that investors believe Fed Chairman Kevin Warsh when he says he will bring inflation back down to 2%, but they think a stronger economy will require higher rates to achieve that.

Where it gets trickier is when we look at the best guess of credibility, the term premium. This is the extra yield a Treasury offers above where interest rates are expected to be between now and maturity.

It bakes in a bunch of things, including Fed bond buying, but can be thought of as the extra amount the government has to pay to lock in long-run loans compared with what it could in principle do with a series of short-run debts. When credibility falls, the term premium, and so yields, should rise.

The problem is that the term premium is a theoretical construct, not something we can easily observe. Handily, Fed researchers have produced two ways of modeling it, known from their authors as Adrian, Crump and Moench $(ACM)$ and Kim and Wright (KW). Not so handily, they tell completely different stories about what's happened this year.

The KW model shows the term premium rising sharply, up 0.4 percentage point to the highest since just after the 2008-09 financial crisis. This is about half the rise in the 10-year yield, and if that much is compensation for the risk of erratic policy, volatile inflation, less-willing foreign buyers and other bad stuff, that should be deeply concerning to the government, voters and investors.

The ACM model is much more reassuring. It suggests the term premium has actually fallen this year. In other words, investors think all the (waves hands) bad stuff is slightly less bad than before.

Warsh said at his press conference that the rise in yields was mainly because of a strong economy, competing bonds issued to finance AI, and geopolitics (i.e., the latest war in the Gulf pushing up oil and other commodity prices). I think this mix of the good and bad stories is probably right, although I'd add to the list foreign buyers steering clear of the U.S.

One final bit of geekery that can help us understand whether bond yields are up for good reasons or bad is what happens to stocks when yields rise. For the first two decades of the millennium, stocks and bond yields typically rose and fell together. The simplest explanation is that what mattered to both was the strength of the economy, and a stronger economy bolstered stocks more than they were hurt by the accompanying higher yields. Inflation was pretty stable and not worth worrying about.

Since 2020, as before 2000, investors have been much more concerned about inflation, and stocks have tended to fall when bond yields rise, and vice versa. Higher inflation means higher bond yields, but doesn't (reliably) bring the accompanying higher profits that a stronger economy does, so it doesn't offset the headwind to stock prices brought by higher yields.

Indeed, comparing the daily changes in the S&P 500 and the 10-year Treasury shows the correlation is now the most negative over a 200-day period since 1997. In day-to-day trading, stocks really don't like higher yields, even though over the year they have managed to rise anyway.

Given all these contradictory findings, it's tempting just to give up on rational explanations. In fact, they show just how hard it is to be sure what's going on-and should make us question confident predictions of what's going to happen next.