I have, in a past life, been down to Liberty Street to "consult" with the Markets Division on asset pricing. For those maybe not au fait with the jargon, any interest rate can be broken down into parts. So a 30 bond yield can be broken into a 10y yield and a 10y20y yield (ie a 20 year rate of interest starting in 10 years time, that follows the yield received in the first 10 years). Together, these will compound to the 30y yield over the whole life of the bond. If I know what the first 10 year yield is, the next 20 years are a derivative of this. Which effectively allows me to create a series of forward interest rates for any period of time in the future.
So I could pay 9 year rates and receive 10 year rates, locking in the 9y1y rate (ie 1 year rate starting in 9 years time). This will typically (historically have been) higher than the actual 1 year rate then, which is the "term premium" referenced in the question. It's simple time-value-of-money, rather than arbitrage. Every reason I would require a risk premium for buying 10y paper over 1y paper says this should be in the 9y1y almost as much as in the 10y versus the 1y! And if it wasn't, that would create an arb.
So I'm wondering how your guys are measuring their "long run nominal fed funds" here ;-) This baseline, from which TP is measured, is the great unknowable but essential variable here...
Scratching forehead here,
ps so imagine a couponless 5 year rate at 2%. TR = 1.02^5 = 1.1041. Meanwhile, a couponless 10 year rate is 2.5%. TR = 1.025^10 = 1.2801. So the TR on the 5y5y = 1.2801/1.1041 = 1.5941. 1.5941^0.2 = 1.0300, so that's a 5y5y rate priced at 3.00%. The same applies with respect to your 10y20y versus 30y and 10y.