# Why is there a price difference between 30 year principal and interest STRIPS?

Sorry if this is obvious, I am not a professional. I like to trade 30 year treasury zero's.

I have noticed that the price for a 30 year principal payment is never the same as a 30 year interest payment. The difference is small (~.3%), and I haven't tracked it long enough to confirm if one is always greater than the other.

Can anyone tell me what is going on here? Is there a tax arbitrage at play here? Is it that the principal is considered slightly more guaranteed than the interest payment? (Or vice versa?)

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so I looked today and I found that consistently (4 samples between maturity dates of 1/2040 and 2/2041) the principal payment was worth a full 1% more than the interest payment. I am inclined to believe this has something to do with repayment risk as the margin seems to have widened from yesterday. –  Pablitorun Nov 10 '11 at 18:59
Hi Pablitorun, welcome to quant.SE. I doubt very much this is a function of repayment risk, as both payments seem equally at risk of default, and default risk in any case is so miniscule in the case of Treasuries. Not sure why you're seeing this, though. –  Tal Fishman Nov 11 '11 at 14:24
Thank you for the cleanup! Well I did find one example where the interest payment was trading for more than the principal payment so this all could be noise. (Although I thought noise like this was arb'ed out....) I should add that I am just looking at schwab online's trading platform, it could just be a function of their trading desk I suppose. It would be interesting if someone with more professional tools saw something similar. –  Pablitorun Nov 11 '11 at 18:35

## 2 Answers

This really is an arbitrage. It is caused by differences in supply and demand between the interest cashflow and the principal cashflow and by differences in the financing rates on the two STRIPS.

As you noted, the price difference is small, and it would take 30 years to guarantee convergence. In addition, the outstanding amount of the 30-year coupon strip (the interest payment) is quite small, since the only source of this cashflow is the 30yr bond itself and therefore the amount available is only half of the annual interest amount of the bond - if you're talking about the current 30yr, only \$250mm can be stripped compared to a \$16 billion principal amount. Therefore, it is currently not particularly attractive as arbs go.

Finally, if you were going to try to capture this arbitrage by shorting the principal strip and buying the coupon strip, you would need to borrow the principal strip and finance the coupon strip. A price difference of 1% is approximately equal to a yield differential on these two instruments of 3 basis points. As a result, if the interest you earned on your short proceeds was just 3bp less than the interest you paid to finance the purchase over the life of the trade, you would not make any money on the trade.

Generally speaking, the principal strips or "P"s usually trade rich to the coupon strips, but this is not a hard and fast rule. At times this arbitrage can become quite large, as much as a 3-5% price difference between two bonds.

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Great answer I really appreciate this. I have two followups if you don't mind. 1.) If interest rates go up would you expect the arb to shrink as the available pool of securities would move closer to equal size? 2.) As a (very small) individual investor buying either would be equivalent as long as I held the position long enough for any swings in the arb to neutralize? (So I would always buy the cheaper bond on the off chance that it was held to maturity.) –  Pablitorun Nov 18 '11 at 16:18

This may not apply in the US, but in some countries the interest income is taxed and the principal isn't, so in some markets the difference amounts to the implicit tax.

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well it is a global market, I guess, so there is probably some effect there. That was one of my first thoughts. IE principal payments would thus be more desired, but I don't think the difference is large enough for that to be the main factor. –  Pablitorun Nov 23 '11 at 17:22