Interest rate curves for dummies

Some resurfaced a great Q&A thread but I don't understand a lot of the jargon around interest rates. This is my attempt to translate it for dummies like myself, so those of you in the know, please give this a look and try to explain further if you're feeling charitable this weekend. Unfortunately the OP Topside doesn't seem to be active on this forum any longer. For context all of these figures were as of Oct 2021 if the rate levels look off.

GBP 1y1y is trading at ~70bps vs a terminal rate of 100bps, the market is pricing in the BoE to fully front-load hikes.

Translation: The 1y rate 1y forward is 70bp. The 1y rate is expected to peak at 100bps this cycle ("terminal"), and 70bp of that is expected to be hiked within the next year?

Powell literally gave us the playbook last week. Rather than squashing the hawkish dot plot, he pretty much implied a Nov taper announcement (contemporaneously alongside treasury coupon issuance cuts), a completed taper by mid-summer, and likely a hike by Dec 2022. The market has already priced this in. So, at this stage, I think the belly of the curve (say 5s) are pretty fairly priced. If anything, 5s seem like an asymmetrical buy to me especially if you're paying/short 2y1y or 3s against it.

Translation: Paying 2y1y means you bet on the 3y rate going up relative to the 2y rate. Buying the 5y means you bet on the 5y rate going down. So on a relative basis, 2y rate down, 3y rate up, 5y rate down = you make money. How does what Powell did translate into you making this bet?

I think the best way to express this is via the fwd curves. If you look some of the fwd curves, they're already inverted which makes no sense. These curves typically only invert during peak market stress (which isn't the case since we're still easing) and during a peak hiking cycle (we haven't even tapered yet). Fwd curve steepeners, by virtue of fwd swap mechanics, will put you long the belly.

Translation: Forward curve inverting means, for example, the 1y rate 1y forward is higher than the 4y rate 1y forward, in other words the 2y rate is much higher than both the 1y rate and the 5y rate? Why does this only happen during peak market stress and a peak hiking cycle?

Especially if you have a 1y1y or 2y1y hedge against this position, I think you're in a good position. Because either you're right and COVID is still a risk in which case hikes will come off the table and steepen the curve, or the hikes will materialize and the terminal rate needs to be higher. With 1 hike in 2022, 3 hikes in 2023, and 3 hikes in 2024, 5y5y OIS at 1.70% is still too low. Either way, these curves need to be steeper. So I do disagree with your view on long-term yields. I think they're too rich and I think its been a function of a lot of P buying from pensions who are now better funded given how equities have performed. When we actually begin tapering, I think there will be more term premium injected into the fwd curves. To be clear, the fwd curves can steepen while the spot curves flatten which, all else equal, will probably continue especially as we near rate liftoff.

Translation: 5y rate 5y forward at 1.70% means the 10y rate is higher than the 5y rate (~halfway between the 5y rate and 1.70%). And the 10y rate needs to be even higher relative to the 5y rate, why? Forward curves steepen = 2y goes down relative to 1y and 5y, while spot curves flatten = 1y and 2y go up relative to 5y, which taken together means the 1y goes up a lot (relative to the 5y), the 2y goes up (relative to the 5y) but doesn't go up as much as the 1y? Why does nearing rate liftoff make this happen?

If the substantial pickup in inflation ends up being supply-driven, we run the risk of stagflation (low growth, high unemployment, high inflation) if we hike too quickly or too late. The Fed will do its best to avoid this outcome and will hurting the consumer. They will be patient on hikes by partitioning their tightening (taper first, then see how things fall before hiking - the market doesn't believe this though) and will only aggressively hike if inflation truly gets out of control (the breakeven curve is still inverted so the market isn't saying this yet).

Translation: If there is supply-driven inflation, hiking too quickly kills growth (hence the "stag") and hiking too late doesn't rein in inflation. Isn't this true regardless? Why is it conditional on the inflation being supply-driven? Does this logic change if it is demand driven? The breakeven curve being inverted means long term inflation expectations are lower than short term inflation expectations, so the market believes in the long term the Fed will get inflation out of control?

1y1y stays where it is and sets at ~70bps. Hikes priced in currently are fair.
1y1y rallies given transitory inflation. Hikes either come off the table entirely or they get pushed out the curve. Let's just assume it takes one hike off the table (moving 1y1y back down to say 50bps).
1y1y sells off to 100bps. Either longer-dated rates (like 3y1y, 2y3y, 5y5y, etc) also reprice to the terminal rate or they invert vs 1y1y which would be the market viewing the move as a policy mistake. The inversion can ONLY be significant if the market thinks the BoE will have to cut down the road given their over-tightening OR if they completely stomp out inflation (1 more hike seems unlikely to tip the balance on this though). 
1y1y sells off to over 100bps, let's say 2 more hikes to 150bps, as the terminal rate gets bumped higher by the BoE. Longer-dated rates and fwds either have to reprice even higher than 1y1y given the amount of hikes being priced in (which is what is happening to the EONIA curve already in EUR) or term premium is destroyed and the curve inverts if the market views these hikes as a policy mistake where the BoE is willing to temporarily contract the economy in an effort to completely eradicate inflation.

Translation: Long dated rate movements relative to the short end will reflect what the market thinks about the eventual outcome of hiking (lower long dated rates = hiking mistake which eventually reverses; higher long dated rates = hiking healthy and cements rates at higher level). Why are the 1y rate 3y forward, the 3y rate 2y forward, the 5y rate 5y forward etc. chosen as "long dated rates" to compare against the 1y rate 1y forward? Seems a bit arbitrary?

TLDR: I'm too stupid / lazy to understand implied interest rate curve takeaways from first principles. Please somebody tell me if it's safe to double down on my 30-40x EV/sales SaaS stocks which are down 50% from 3 months ago, thx.

 
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Translation: If there is supply-driven inflation, hiking too quickly kills growth (hence the "stag") and hiking too late doesn't rein in inflation. Isn't this true regardless? Why is it conditional on the inflation being supply-driven? Does this logic change if it is demand driven? 
 

^ On this, one theory is that the supply driven inflation is due to 2nd order thinking psychology. Firms believe there to be supply logjams and therefore order more inventory earlier, causing a feedback loop that further exacerbates supply logjams. The result is artificially tight supply and higher prices. The hikes would increase cost of borrowing and temper higher order prudent thinking to try to game supply logjams, whereas true demand would not be in excess and be inelastic.

 

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