# 2 bond hedge

What is the strategy? short a 2 year treasury and a 10 year treasury?

It depends on a lot of things… Here how I think it’s supposed to go: Step 1: Calculate the price of the MBS, 2-year, and 10-year securities assuming a level shift up in interest rates (Level scenario) Step 1b: Do the same but for a equal level downward shift Step 2: Do the same as Step1 and Step1b for an assumed steepening and flattening of the Yield curve respectively (Twist Scenario) Step3: Now you have two prices for each security for the “Level” shifts and two prices for each security for the “Twists” in the term structure… you now want to calculate the average price change for each one. So if in Step1 you see that when the rates went up your MBS declined by \$2.00 and when the rates when down your MBS increased by \$2.00, you would take the average of the two to get \$2.00 average price change for the MBS (level). Do this for all the securities in both the Level and Twist scenarios. Step4: Once you have all the average price changes you can set up a system of equations to solve for the optimal quantities of the 2-year and 10-year securities to invest in (Algebra 1)… They are: H2(AveChange in 2yr-Level) + H10(AveChange in 10yr-Level) = -AveChange in MBS-Level H2(AveChange in 2yr-Twist) + H10(AveChange in 10yr-Twist) = -AveChange in MBS-Twist Where: H2 = Number of 2year secuties needed per \$1 of MBS H10 = Number of 10year secuties needed per \$1 of MBS Solve for both H2 and H10… depending on whether or not they are negative or positive will tell you if you should long or short them. By investing in these you will hedge your MBS against both level shifts and twists in the term structure. (or at least get pretty close) _____________________ As usual somone correct me if i’m wrong

It depends on our exposure… But yes, usually you would have to short both in order to hedge securities that exhibit negative convexity… I doubt CFAI will ask to derive the exact hedge ratios to set up a hedge but you might as well read it in the curriculum as it appears they’ve asked it last year and people didnt do well… (check last year’s threads…) Basically, you would have to determine the absolute avg. delta in price for the: - MBS - 2Y Bond - 10Y Bond Under 2 scenarios - Parallel Shift (Up/Down) - Yield Curve Shift (Steepen/Flatten) And then using a system of 2 equations, you will be able to obtain the specific hedge ratio to use to hedge your MBS… That way, your MBS portfolio will be hedged (not 100% effective though) to both shifts & twists in the yield curve…

I meant TWIST: Under 2 scenarios - Parallel Shift (Up/Down) - Yield Curve TWIST (Steepen/Flatten)

Yikes. We don’t need to be able to perform this calculation do we?

Dont think so… If I recall correctly, the LOS says: Compare & Contrast

VinceMTL Wrote: ------------------------------------------------------- > Dont think so… If I recall correctly, the LOS > says: Compare & Contrast Personally i wouldn’t risk it. Its easy points if you just remember the steps… No real formulas or hard math. Just a few steps. Not to mention knowing how its found can really bolster your understanding.

I doubt they will test it but don’t worry… I made sure to master it…

they asked it last year, but the lost has been modified this year. you only need to understand it , not calculate it.