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I was looking at government bonds/treasuries and I wondered if my line of thinking is correct:

1) In general, how is the coupon set? I found out that usually they are auctioned for (a bit) less than par value, which makes me think a coupon based on the market is set by the treasury and then it fetches a price according to market demands. Is this correct?

2) On bloomberg.com, you can view the 10y Treasury coupon. Now I was wondering: Is the coupon simply the coupon of the latest auction? If so, it it the same for long- and short-term debt (bills, notes, bonds)?

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1) Yes, the coupon is usually set so that the bond would be issued at par because that's what mainstream investors usually prefer (current yield close to interest rates). There are also issues of zero coupon which eliminate reinvestment risk and are preferred by other types of investors (insurers for instance). In the US, you can strip the coupons from the principal and thus get 0 coupons equivalents as well.

Short term bills are issued at a discount with 0 coupon because there's no reason bothering with coupons for a couple of months, it's just easier to price 0 coupons.

2) That's the coupon of what is called "on-the-run treasury", which is the latest 10Y issued (excluding retaps of older issues). 5Y coupon and 30Y coupon will be different because the yield curve is not flat (investors required additional yield for 30Y).

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