# Yield Curve Twist Question

A given mortgage security is trading at par. The expected average price change from a projected change in a given market yield is 1 for the mortgage security and 0.4 and 2.0 for hedging instrument one and two respectively. The expected average price change from a projected twist in the yield curve is 0.4 for the mortgage security and 0.3 and 0.5 for hedging instrument one and two respectively. What positions in hedging instruments one and two should a manager take to hedge the price of the mortgage security from the projected market changes? For every dollar of face value of the mortgage security: A) sell \$0.75 of hedging instrument one and \$0.35 of hedging instrument two. B) buy \$2.5 of hedging instrument one and \$0.5 of hedging instrument two. C) sell \$2.5 of hedging instrument one and \$0.5 of hedging instrument two.

Answer B. Long \$2.5 of hedging instrument one and Short \$0.5 of hedging instrument two.

Answer is A. To answer this, we set up the following two equations and two unknowns. (NH1)(0.4) + (NH2)(2.0) = -1.0 (NH1)(0.3) + (NH2)(0.5) = -0.4, where NH1 and NH2 are the positions to take in hedging instruments one and two respectively. Multiplying the second equation by 4 and subtracting it from the first gives (NH1)(-0.8)=0.6, and thus NH1=-0.75. Substituting this into either expression and solving NH2 gives NH2=-0.35. (-0.75)(0.4)+(-0.35)(2)=-1 (-0.75)(0.3)+(-0.35)(0.5)=-0.4

? I need to go back to school. I have no idea what this is about.

easy way to write the equations 4x + 20y = -10 —I 3x + 5y = -4 —II Multiply eqation I by 4 THen subtract I - II x = -0.75 y = -0.35

my equations were: -1=0.4x+2y -0.4=0.3x+0.5y -> A

same thing maratikus… I just multiplied all my equation by 10 to get rid of the decimal.

For anyone who doesn’t understand it’s just basic simultaneous equations. I.e. 2 formulas are used to solve 2 unknowns. The solution can be found using either Substitution method or Elimination method (you can google this if you are unclear).

Blamey Wrote: > The solution can be found using either > Substitution method or Elimination method (you can > google this if you are unclear). Cramer’s rule can also be used. For some reason, my mom likes using it: http://en.wikipedia.org/wiki/Cramer’s_rule