# Shift, Twist & Curvature to explain all yield curve changes

Yield curve change is referring to as time passes, how the different yield changes for different maturity. Rather than calculate the difference for each single maturity, industry has always been seeking a way to simplify the and find a simple explanation. And the three key components behind any yield curve change is the famous shift, twist and curvature.

Just like you can use x, and y to explain all the positions on a 2D space, you can use shift twist and curvature to explain all the yield curve changes. These three components are also constructed as uncorrelated factors.

There is this great youtube video that further explained how the three components are being calculated using Principal Component Analysis.

Once we understand that three components of changes, the next step is usually to prepare the actions in anticipation of changes in each component. For example, if you have three different options of structuring your portfolio as laddered, barbell or bullet.

Then you can use them to list all the possible combinations of three factors, and calculate the potential outcomes.

You can weight the different scenarios differently based on your own forecast of the yield curve and use the probability weighted average as the expectation to pick the best action item.

Exhibit 76, and Exhibit 77 are screenshots from the CFA Curriculum and copyright reserved to them.