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# P1.T4.321. Fixed income single-variable regression hedge

#### Pam Gordon

##### New Member
Subscriber
AIMs: Explain the drawbacks to using a DV01-neutral hedge for a bond position. Describe a regression hedge and explain how it improves on a standard DV01-neutral hedge. Calculate the regression hedge adjustment factor, beta. Calculate the face value of an offsetting position needed to carry out a regression hedge.

Questions:

321.1. A trader shorts $100.0 million of nominal US Treasury 3 5/8s bonds and, in a relative trade, wants to hedge with a long in US Treasury Inflation Protected Securities (TIPS); the relative trade will express a view on inflation as reflected in the spread between the rate of the nominal bond and a TIPS. The yields and DV01s of each bond are shown below, in addition to the output from a regression of nominal yield changes against real (TIPS) yield changes: Which is nearest to the face amount of the long position in the 1 7/8s TIPS needed to carry out a regression hedge? a.$6.8 million face amount of TIPS
b. $68.83 million face amount of TIPS c.$75.30 million face amount of TIPS
d. $105.68 million face amount of TIPS 321.2. A trader shorts$100.0 million of nominal US Treasury 3 5/8s bonds and, employing a single-variable regression hedge, buys a face amount of 1 7/8s US TIPS. The bonds are show below in addition to the results of a regression of the nominal against real yield:

Which is nearest to an estimate of the daily volatility of the P&L of the hedged portfolio?

a. $2,380 b.$43,760
c. $67,323 d.$212,000

321.3. A trader shorts $100.0 million of nominal US Treasury 3 5/8s bonds and hedges with a purchase of a face amount of 1 7/8s US TIPS based on the regression results of a single-variable hedge, which are shown here: Each of the following are true about this regression hedge EXCEPT for which is false? a. The regression model estimates a correlation between changes in the nominal and real yields of about 82.5% b. We can be 95% confident that the true value of beta is unity (1.0) c. The daily volatility of the P&L of the hedged portfolio is about$88,000
d. The difference between a DV01-hedge and a regression hedge is about $17.14 million face amount of the TIPS Answers: #### [email protected] ##### New Member Good afternoon, everybody, here are the answers (in case of blunders please correct, thank you beforehand): 321.1 c 321.2 d 321.3 b #### David Harper CFA FRM ##### David Harper CFA FRM Staff member Subscriber Hi monte-carlo, let's just say i don't disagree.... thanks, #### johnson33445 ##### New Member hmm...great information well done and keep it up #### achieverbc ##### New Member Hi monte-carlo, let's just say i don't disagree.... thanks, hi...can u tell me the formulae used in the second question??? i.e. the formulae for calculating the volatility of the p&l of the hedged portfolio... #### cash king ##### New Member I use formula for calculating the volatility of the p&l of the hedged portfolio as follows: S.D.(hedged portfolio)=S.D.(error term of interest change regression)*DV01 of target position*Dollar amount of target position #### achieverbc ##### New Member Good afternoon, everybody, here are the answers (in case of blunders please correct, thank you beforehand): 321.1 c 321.2 d 321.3 b hi monte-carlo...can u plz explain how u solved the last two options of third question....I'm using the formulae ((beta*dvo1 of nominal/dvo1 of tips)-1) but not getting the answer...how to use the face amounts of bonds in this formulae?? TIA.... #### CarlosB ##### New Member Hi David, Hi monte-carlo, let's just say i don't disagree.... thanks, The answer to to question 321.2. is: Per Tuckman 6.13, Standard deviation of P&L =$100.0 million * 0.040/100 * 5.30 standard error
= \$212,000

Why do we divide the the DV01 for 100?

Thanks,
Carlos

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @CarlosB Because DV01 is expressed per 100 in face value; e.g., Tuckman: "Also, since DV01 values quoted in the text and shown in the figures are for 100 face amount, they have to be divided by 100 before being multiplied by face amounts." -- Tuckman, Bruce; Serrat, Angel (2011-10-11). Fixed Income Securities: Tools for Today's Markets (Wiley Finance) (Kindle Locations 3415-3416). Wiley. Kindle Edition.

I hope that explains, thanks!

#### Rohit

##### Member
how is this calculated? regression model estimates a correlation between changes in the nominal and real yields of about 82.5%

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
@Rohit in a univariate regression (ie, one independent) variable, the correlation, ρ = SQRT(R^2).

thanks!