A government bond issuance done by auction is a great way to see the links between price, yield, and required rate of return.
The one point in time when every bond must be priced is at its issuance date, and government bonds are often issued by public auctions.
Bond auctions don't focus on price though.
Instead, investors submit orders specifying the yield or return that they desire.
Focusing on the yield or overall return means lots of characteristics like coupon rates and price don't need to be known.
Yield includes them both in one handy number.
This is useful as many of those characteristics like price and coupon may not be known until the actual issuance.
Let's see an example. Suppose the US government has announced plans to issue $10 billion of a five year bond via auction.
During the auction process, a number of bids are received for a yield of 4.522%.
Investors express demand for 3.4 billion worth of bonds, but for a slightly higher yield of 4.523%, the demand went up and another 4.9 billion is demanded investors like a bond that will give them a higher return.
If we assume that investors who were willing to buy it 4.522% would also be happy to buy a 4.523%, they definitely would be happy to receive that slightly higher yield.
Then we can aggregate the demand of the two at 4.523%.
The total demand amounts to 8.3 billion, which is the 3.4 billion, plus the 4.9 billion at a yields of 4.524%.
The aggregate demand exceeds the planned issuance of $10 billion.
Great for the governments, so we can say that this figure is the yield at which the bond is issued.
This yield 4.524% is essentially the return investors require during this issuance process.
In other words, this is the rate of return that investors expect in exchange for the risk they are taking by buying this particular government bond at this particular time.
