Dollar duration hedge vs DV01 hedge

[wrongsaidfred]

Hi David,

This may be a dumb question, but when we perform a duration based hedge are we doing the same thing as a DV01 hedge? After a little algebra it seems like these two methods will provide the exact same results, just from slightly different approaches. Is this correct?

Thanks in advance for any help you could provide.
Mike

 

[David Harper CFA FRM]

Hi Mike,

That's basically correct and it's also why "duration" in our list of terms for GARP (e.g, along with "interest rates" w.r.t. compound frequency) in an overall request for terminology precision.
Your use of "dollar duration" in your title is quite correct as the comparator. So, at a high level:

• modified duration (~= effective duration, where effective approximates via re-pricing) is the sensitivity measure, but it's not directly useful for the duration hedge
• modified (or effective) duration * Price = dollar duration (aka, value duration) = slope of the tangent-to-price/yield curve: this is the quantity we hedge/neutralize (analogous to position delta for options)
• As Dollar duration (= mod duration * Price) = DV01 * 10,000; this difference is nothing but quantity/formatting. DV01 is per 1 basis point, DD is per 1.0 = 100% or 10,000 basis points (unrealistic, but totally valid as it's a straight line either way!). DD is just a huge number b/c it's the un-worldy price change implied by the slope line given a 1.0 unit in change in the X-axis (which is an unworldy 100%), but the dollar duration is still valid for the hedging/neutralizing by summing dollar durations.

so i like the analogy between DV01 (or dollar duration) and Position Greek (e.g, Position delta as opposed to percentage delta) because duration/percentage delta are the sensitivities per instrument, but you can't add/hedge/neutralize. For that, we need DV01/dollar duration/position Greeks

Hey, thanks for giving me a Q&A break over the last 1-2 days, i did notice! David

 

[wrongsaidfred]

No thanks are necessary on your part. I know I can be a pest so I have been trying my best to only ask when I find it absolutely necessary.

Speaking of which, I found a strange answer in one of the Hull problems that I do not have in front of me. I may email you about it when I get home.

Thanks again,
Mike

 

[Aenny]

Hi @David Harper CFA FRM CIPM ,

reviewing the single-variable-regression-based hedge (DV01 hedge) the following example is given, but unfortunately I do not get the concept.

Example: the trader is short a 100 MIO US Bond 3 5/8s and long some amount of TIPS 1 7/8s .
Now the question is what face amount of tips the trader should by so that the trade is hedge against interest rates .

The following formula is given:


F^R * DV01_ TIPS /100 = 100 mm * DV01_Bond / 100.

I have two questions:
1.) why is the dollar value duration divided by 100, I would divied by 10.000 (because of the definition of change by 1 basis point)
2.) do you know for what the R is standing for? (Is it regression, or am I missing a bigger concept here?

Thx

 

[David Harper CFA FRM]

Hi @Aenny , hope you are doing well?

1. Common question. It's because the DV01 are not in their raw units, they are given per $100 face amount. (this makes them more readable. We have DV01 of 0.03505 per 100 rather than 0.0003505)." Tuckman explains in Chapter 4: "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.
   
2. I *think* it simply refers to "real" as opposed "nominal" because he elsewhere uses F^N for nominal; i.e., TIPS earn a real (as opposed to nominal) rate of return. I hope that helps!