The rise in long-term bond yields is being blamed on a growing list of factors, but there is a much simpler explanation sitting in plain sight: oil prices are the main driver of the rise in long-term yields, and the Iran war is the reason oil is rising.Brent crude has pushed back above $100 a barrel as the US-Iran conflict escalated, while the 10-year Treasury yield has climbed above 4.8%, its highest level since 2023. Oil goes up, yields followThe key transmission mechanism is inflation. An oil price shock does not stay confined to the energy market. Higher crude prices feed into gasoline, diesel, transportation and production costs. If the shock persists, investors begin to worry that inflation will remain higher for longer, especially without a central bank's response. That matters enormously for long-duration bonds. If the inflation outlook deteriorates, investors demand a higher yield to compensate for the loss of purchasing power and the greater uncertainty around future interest rates.That is why the relationship between oil and long-term yields matters more right now than many of the other headlines competing for attention or suiting the price action. Below you can clearly see the tight correlation between the US 10y Treasury yield (red) and WTI crude oil (blue). The Iran war is the common denominatorIn the current context, oil and bonds are the same story. The escalation of the Iran conflict has increased the risk of further and longer disruption through the Strait of Hormuz. As a reminder, the waterway normally carries roughly a fifth of global oil and gas supplies.Brent closed above $100 on Wednesday for the first time since July, while physical oil prices have also surged as buyers compete for alternative barrels. S&P Global reported that Dated Brent jumped to $114.26 on September 9, highlighting how tight the physical market has become.This is where the bond market comes in. If the war pushes oil higher, the market has to reassess the inflation outlook. If inflation expectations rise, expectations for monetary policy can shift. Even if the Federal Reserve ultimately looks through a temporary energy shock, the market still has to price the possibility that the shock becomes persistent. That puts upward pressure on long-term yields.What about the Treasury buyback?The Treasury's buyback programme is important, but it is not the primary explanation for the broader move in yields. The Treasury announced plans to repurchase up to $6 billion of longer-dated debt. The idea is to improve liquidity and support the long end of the curve. Yet the 10-year yield continued to rise, reaching levels not seen since 2023. Much of that was because the announcement disappointed expectations, as there were talks of $10 billion or even 12$ billion buybacks, but the main reason is inflation concerns. The buyback can influence the mechanics of the bond market but it cannot make $100 oil disappear. Long-term yields have been rising across the globe and the only fixes for that are either central bank tightening (which could eventually trigger a recession) or an end to the Iran war. For now, oil is the signal. Everything else is just noise. This article was written by Giuseppe Dellamotta at investinglive.com.