The yield or interest rate on Treasuries will rise and fall due to various factors. One driver is the policy actions of the federal reserve who raise interest rates to dampen down inflation or currency devaluation. A major factor that cause long interest rates to shoot up, is when their is rising inflation and/or rising inflation expectations of the bond market.
In many but not all ways, the markets are stronger than the Government. Remember, the bond traders were the ones who forced Bill Clinton to scale back his ambitious plan for public investments in education and health care. This was after Clinton insisted that his budget wasn’t going to be “held hostage to some *@?#»! bond traders.
Early in 2001, the Federal Reserve began lowering interest rates to avoid a recession. By mid 2004, it reversed direction and began raising rates to avoid inflation. Even though the Fed was raising short-term rates, yields on long-term Treasury Note stayed constant due to sustained buying from Japan, China and oil-producing countries. Despite low yields, these Central Banks kept buying bonds in order to stabilize their own economies.
The above chart shows the yield on the 30 year Treasury Bond. The periods of highest yield correspond (lagged) to the periods of high inflation. Even after inflation was brought under control, high interest rates persisted due to investors fears that wicked inflation ogre was not quite dead.
When inflation rises 5%, the bond market, knowing that the extra 5% inflation will erode their returns, starts demanding that bonds pay them 5% more. Of course they can't demand that a bond due anything. What happens is that when the bid for bonds, they only pay a discounted price for the bonds that the discount gives a 5% extra yield.
TIPS are a different asset class, and do not behave like regular bonds. With the TIPs When inflation rises 5%, the TIP pay an inflation kicker of 5%, causing a total yield of 9% on TIPs.
Say you have a 10 yr treasury paying 4% and a TIP paying 1.5% + 2.5% inflation adjustment premium. Both pay 4%. Inflation is assumed to be 2.5% over the life of the bonds. Then predicted inflation goes up by 5% over the next ten years to a new inflation rate of 7.5%. The nominal bond market now demands bonds that paid 5% more (they would want bonds paying 9% to make them whole) they would trash the 4% bond. It would certainly drop in price, what you said is true.
In theory, the TIP would start paying 1.5% real yield plus an inflation kicker of 7.5%. Total yield is now 9%. .
Because TIPs adjust, bond holders would not have a reason to trash the TIP. In fact the inflation trade would flock to the bonds. Since the introduction of TIPS in 1997, a major bout of inflation has never occurred in the US. Even though the inflation-adjustment is contractually guaranteed under the terms of the TIP bond, the behavoir of US TIPS has never been field tested.