The risk that arises from inability of a hedger/ portfolio manager to hedge against a change in the shape of the yield curve, even after having effectively hedged long and short positions, of different maturities, in a portfolio against a parallel shift in yields. Parallel shifts come into play when a market development create a shock that equally affects the yields of securities with different maturities. On the other hand, changes in the shape of the yield curve occur when a market shock doesn’t equally impact the yields of securities with different maturities on the yield curve. For example, such an effect might be higher on short-term securities than long-term ones.

Broadly speaking, curve risk results from the market change affecting the slope/ curvature of the curve.

Curve risk is also known as yield curve risk or horizontal risk.