When someone asks a salty old bond market person why rates are doing what they'd doing, they might get a seemingly dismissive reply: "supply and demand!" No duh, salty old bond person. Of course supply and demand is going to determine the price of almost anything, but we were looking for the factors underlying the supply and demand. And the salty old bond guy might reply:
"No, dummy. I mean SUPPLY and demand! Look: https://home.treasury.gov/news/press-releases/sm1001 "
In other words, the conversation would concern the actual announcement of additional supply. Granted, a certain amount of supply is always to-be-expected when it comes to the bond market. Moreover, we already knew that Treasury supply would have to increase substantially in order to finance the coronavirus relief efforts (not to mention the revenue shortfall). But we didn't know exactly how that supply would look.
As it happens, Treasury is explicitly stating a preference to push more of the supply "out the curve" to longer duration securities. The additional of brand new 20yr bonds was all we needed to confirm such a thing, but they've upped amounts across the board (more long duration supply = bad for the rates we care about).
That's $43 billion additional dollars on the supply side of the equation in May. And keep in mind, these are "anticipated" changes. It's not uncommon to see them drift higher in the future. The net effect has been immediate and obvious.
While the longer-term chart doesn't look too troubling at the moment, we need to be cautious here. In a sideways environment where we're unavoidably waiting on market movers that can't possibly arrive any time soon, traders love to jump on opportunities to create some volatility. Money managers now have to reposition for higher-than-expected supply in longer-dated Treasuries. That process can't play out in a few minutes. Many of them will sell now in the hopes of buying more cheaply in the future.
Ultimately though, the coronavirus situation will be the key underlying narrative for the bond market. As long as it offers massive suppression of the global economy, it will be hard for rates to spike as quickly as they did in March. The other positive caveat is that this will naturally affect Treasuries more than MBS (but it will still affect MBS).