While reading multiple articles about yield curve inversion, a common theme is that investors seeing an economic slowdown in the future which generally means lower interest rates so they want to lock in today's rate.
I'm confused as to why they wouldn’t just buy shorter dated maturities because the coupons from the longer term bonds will still have to be reinvested at current market rates so how can the investor “lock in” today's rate?
the coupons from the longer term bonds will still have to be reinvested at current market rates
The interest earned from reinvestment of the original bond's interest is a second-order effect. It is dwarfed by the first-order effect of reinvestment of the principal after maturity of a short-term bond; that means the entire investment will likely be earning a lower return in the future. The long-term bond locks in the higher return on the bulk of the investment.
Note, "interest on interest" can eventually grow greatly through compounding, but the terms and rates of bonds are typically not sufficient to reach the many-fold growth regime.
If I buy a 1 year bond for $10,000 paying (optimistically) 5%. Then after one year the interest rates drop to 1% and stay that way for 9 more years, I earn 5% for 1 year and 1% for 9 more years. And over the 10 years I make $1400.
If I buy a 10 year bond that pays %4 a year I make $4000 over the 10 years.
Long term bonds are a hedge against the interest rates dropping substantially for a sustained period as you are guaranteed the interest rate you have now for the full length of the bond (this is all assuming not callable bonds, callable bonds are a different beast).
Note the dividends paid by the bond will not always be possible to invest at the higher rates, only the original investment. However bonds are fundamentally an income rather than an accumulative security so I presume that the investor wants them as cash for expenses etc.
There are cumulative bonds which reinvest the interest in more bonds and pay it all at the maturity date, this would allow locking of compound interest too.
The yield curve inverts because an excess amount of participants are dumping their short term coupons to purchase a longer term rate to secure the yield at the lengthier duration (with the expectation that when the short term coupon turns over, the yield available on market will be substantially less than its current price).
Bob Baerker's answer demonstrates the risks that are involved with any sort of security with a yield. If you lock in a price there is one risk to factor in that your yield stays lower than market rate (if yields went up), another risk factor is that upon coupon expiration the market rate for that category of bonds will be much lower than the current market (yields went down).
A longer term coupon can be held through the rough time period, but the funds from the shorter coupon will have to either sit out of play (not always feasible if you're managing a fund) or you buy coupons at a poor yield which could have been avoided if you'd gone heavier with longer term rates back when yields were better. After the short coupon expires, the risk is that even longer duration coupons have a poor yield (compared to today's rate aka recession so everyone is buying safe haven assets) and you "lose" heavily when the rates pick back up (recession recovery) and you're still locked in with low yielding coupons.
tldr; a not insignificant number of market participants are expecting a recession and much lower rates in the near future. The inverted yield curve is an expression of that activity.
Here's a simple example using CDs.
A 6 month CD pays 2.00% and a 3 year CD pays 3.00%.
If I do the 3 year CD, I obviously get a higher yield and it is 'locked in' for 3 years.
Suppose in the next few months, rates drop to 1.50% and 2.50% respectively. If I had done the 6 month CD at 2.00%, at the end of 6 months, I can only get 1.50%.
How this plays out currently with CDs and bonds will depend on the rates available.
