> A 5-year bond now has a lower yield than a 3-year bond? How is that even possible? Wouldn't anyone who wants a 5-year bond just buy a 3-year bond and then put the cash under their mattress after 3 years?

Today's rates show the 3-year yielding 284bps and the 5-year yielding 283bps (the same as the 2-year) [1]. Let's consider three hypothetical buyers' outcomes. To keep things simple, we'll assume interest isn't re-invested.

One buys the 5-year. $10,000 of their principal would turn out $1,415 in interest [2]. Another buys the 3-year, keeping the principal as cash on redemption. $10,000 of their principal turns into $852 in interest [3]. Immediately, you see why the 5-year is a better buy for a 5-year investment horizon than the 3-year.

Consider a third buyer. They buy the 3-year with the aim of re-investing. To get the $563 difference between the 5-year and 3-year total interest pay-outs, they would need to buy a 2-year bond yielding 282bps when the 3-year matures [4]. If rates are lower 3 years' hence, the 5-year investor will have done better. If rates are higher, the 3-year buyer with intent on reinvesting will have done better.

This reinvestment risk, which incorporates the market's views on future interest rates, is what the yield curve essentially reflects.

[1] https://www.treasury.gov/resource-center/data-chart-center/i...

[2] 2.83% x $10,000 x 5 years

[3] 2.84% x $10,000 x 3 years

[4] [($1,415 - $852) / 2] / $10,000

Thats not how it works. If 5-year bond has yield x, for principal P you receive Px for 5 years. With 3-year bond with yield y, you get Py for 3 years. If y > x => after 3 years rates will be lower than y. So you will get lower than P*y for the last 2 years (of 5 years).

Ahh, got it.

So the overall yield is not lower, just the annualised yield.

That doesn't sound like nearly as much cause for alarm.

The alarm is that bond yields are more or less `yield = (k / economic confidence)` - if people are confident then they don't buy bonds, so the price of bonds falls, so the yield (which is annualized return) rises. (Thus recessions lead to falling interest rates as people seek safe harbors for money, making credit cheaper.)

What this means is that the bond market thinks available bond yields for cash-on-hand will be lower in three years than five, so they're willing to take a hit now to lock in the longer-term payout. That reflects serious economic pessimism.

It's not a cause for alarm per se, but the inverted yield curve means that the bond market is feeling pessimistic. Rate inversions often happen before recessions, but they're not a fool-proof indicator.

Which is why i think that describing the yield curve in terms of rates of bonds running from now until some date in the future (which is what we do when we talk about raw treasury rates, or zero-coupon bond rates, another common form) is really unhelpful, because it disguises this structure.

We should instead talk about it in terms of expected instantaneous, or at least short-term, forward rates. For example, what is the expected rate for a three-month T-bill starting 1, 2, 3, 4, or 5 years from now?

Right, but the 3 year bond would only pay 3 years of interest. If interest rates are significantly lower 3 years from now, then reinvesting in a new (lower interest) bond at that point would give you a lower return over 5 years than the marginally lower 5 year bond would give you now.

So, why does this happen? Well, it happens when the markets expect interest rates to drop between now and five years from now.

Why might that expectation exist? Well, it might if bond buyers were anticipating a recession.

At least that is how I understand it. Feel free to correct me.

I see it as investors betting that before 5 years from now we'll see another recession and the Fed will be forced to lower interest rates, hence why 5 year yields are trading below 3 year yields.

"A 5-year bond now has a lower yield than a 3-year bond? How is that even possible? Wouldn't anyone who wants a 5-year bond just buy a 3-year bond and then put the cash under their mattress after 3 years?"

Your confusion is precisely why it's a bad thing. Ideally, longer-term bonds have a higher yield, as that would mean we collectively are investing in high growth over a long period of time. That is, the economy grows.

When the inversion happens, then the short-term bonds have a higher yield, which means something is wrong with the economy in the long term. We don't know what's wrong with it, it's just a signal.

An inverse yield curve predicts lower interest rates in the future as longer-term bonds are being demanded, sending the yields down.

Suppose for instance you believe that the Federal Reserve's fiscal policy calls for it to raise short-term interest rates, and you expect that to cause a rise in long-term rates shortly as well. That belief would reduce your appetite for longer-term bonds, for the time being.

At large enough scale there is no mattress. Keeping a billion in cash has storage and transport overhead, while keeping it in bonds is a simple matter of accounting.

Maybe you will have a billion in physical cash if you are running a narco empire

The 5-year yield is lower to mitigate the uncertain risk (to the issuer) of paying above-market during years 4 and 5.

they buy the 5-year because they don't have trust in the US economy and want to lock into an interest rate before they decrease further

Yet they have enough trust in the US economy to assume that inflation won't ruin their earnings over the [longer] 5-year period.