To illustrate how the government bond auction process works, let's look at this specific example of a 10 year US treasury issuance with a notional amount of $10 billion. In this auction, investors submitted competitive bids at different yields with each yield level reflecting a different level of demand. Here's how the stop yield and allocation play out. To find the stop yield, the treasury looks at the demand across the different yield levels, starting from the lowest yield and moving upwards until the total demand meets or slightly exceeds the issuance amount of $10 billion.

At yields below 4.524%, specifically at 4.522%, and 4.523%, the cumulative demand reached $8.3 billion below the total notional issuance size of 10 billion. Adding the demand at 4.524%, which is $2.5 billion, moves the cumulative demand to $10.8 billion enough to cover the issuance targets. Therefore, 4.524% becomes the stop yield because it's the highest yield at which the cumulative demand reaches or exceeds the $10 billion issuance. This yield level allows the treasury to meet its issuance goal while balancing the demand across the range of bids.

For bids below the stop yield of 4.524% demand reached $8.3 billion. Although these bids were placed at lower yields, all competitive bidders whose bids are accepted, including those bidding below the stop yield, will receive the same yield as the stop yield, which is 4.524%. This means that they get to buy the newly issued bonds at a slightly lower price than they were willing to pay. This is referred to as a Dutch auction. In a Dutch auction, lower yield bids simply have priority in allocation, but the final yield, and therefore purchase price, is consistent across all accepted bids. The stop yield in this auction was set at 4.524%. However, since this yield level would take the total demand to $10.8 billion, that's 8.3 plus 2.5 billion, which exceeds the issuance size of $10 billion. Not all of the demand at the stop yield will be filled. Investors bidding at the stop yield received a pro rata location, meaning they received a portion of their requested amount. In this example, they would receive $1.7 billion out of $2.5 billion.[ that was demanded, since that was the remaining unfulfilled demand at 4.523%. Investors who bid at yields higher than the stop yield in this example, 4.5 to 5% or above do not receive any allocation. These bids were excluded because they demanded a higher yield than the maximum accepted by the auction, and thus their bids were rejected. Once the stop yield is determined, the coupon for the bond is set. Coupons are typically set in increments of one eighth or 0.125% for US government bonds. The coupon is then rounded down to the nearest eighth to ensure that the bond is issued at or below par. In this case, although the stop yield is 4.524%, the coupon would be rounded down to 4.5%. This practice ensures that the bond is never issued above par, meaning investors pay at most the face value achieving the effective yield of 4.524% through buying the bond at a discount to the face value.