change in bonds price formula

Factor** 5 **20 Level –0.4352% –0.5128% Steepness –0.0515% –0.3015% Curvature 0.3963%

Calculate the expected change in yield on the five-year bond resulting from a one standard deviation decrease in the level factor and a one standard deviation decrease in the curvature factor. if i use the formula change in price = sensitivity * yield curve’s level - sensitivity* change in yield curve’s steepness - sensitivity* change in yield curves’ curvature i get 0.4352%- (-1*0.3963%)= 0.8315%. the answer says “Because the factors in Exhibit 1 have been standardized to have unit standard deviations, a one standard deviation decrease in both the level factor and the curvature factor will lead to the yield on the five-year bond increasing by 0.0389%” but curvature should be -0.3963% but the formula doesnt apply.

so its level is -0.4532%

steepness = 0.0515%

curvature is 0.3963%

This is quite easy. You need to add up all the impacts to level, steepness and curv. You made a mistake and did a subtraction,

The level is impacted by a decrease of 1 deviation while the curvature is affected by a decrease of 1 deviation.

level = -0.4352

steepness = 0.0515%

curvature = 0.3963

Decrease of the level means -1, so the impact is (-0.4352) * -1 = 0.4352

Decrease of curvature means -1, so impact is 0.3963 * 1 = -0.3963

There is no impact on steepness, means 0, so impact is 0.0515 * 0 = 0

Add them up 0.4352 + (- 0.3963) = 0.0389