Yield curves

This track draws three points: the 2-year, the 10-year, and the 30-year. A full Treasury curve has many more maturities. Three points are enough to see a slope, a hump, or a twist.

A normal classroom curve has the 2-year at 3.50%, the 10-year at 4.00%, and the 30-year at 4.50%. Longer maturity, higher yield. That is one shape, not a law.

A spot rate is the yield from today out to one maturity, with no coupons along the way. A discount factor turns a future dollar into today’s value using that spot rate. One dollar received in one year, discounted at 4%, is worth 1 / 1.04, about $0.9615 today.

A forward rate is the rate agreed today for a loan that starts later. It is baked out of two spot rates. If the market will lend to year 1 at one rate and to year 2 at another, the rate from year 1 to year 2 is the forward. You do not need a new trade to see it. It is already in the curve.

A par rate is the coupon that makes a coupon bond price at par, 100. Bootstrapping walks from short par rates to longer ones and peels out the discount factors, one maturity at a time. The swap rate in the interest-rate swap lesson is a par rate on the swap curve: the fixed rate that makes a new swap worth about zero.

Normal means longer yields are higher. Inverted means shorter yields are higher. Flat means the yields are about the same. Humped means a middle maturity is the high point and both ends sit lower.

The shape is a description of today’s points. It is not a forecast that the curve will stay that way. Pick a shape and read the three numbers out loud.