Interpreting Key Rate Duration in Mortgage-Backed Securities

# Key Rate Duration for MBSs greater than Key Rate Tenor


# Key Rate Duration for MBSs greater than Key Rate Tenor












Key Rate Durations (KRD) are essentially some fixed income instrument's price sensitivity to a non-parallel shift in interest rates (i.e., a shift at the "Key" Rate). For example, a 10-year bond's sensitivity to a 1% change in only the 5-year interest rate would be that bond's 5yr KRD.

Let me refer to any fixed-income instruments that are not straight bonds as exotics (e.g., MBSs, CMOs, ABSs, etc). Is it possible to get KRDs greater than the respective key rate tenor for exotic fixed-income instruments without leverage? I tend to see this behavior most often in MBSs. For example, I'm looking at the KRDs for some MBS (comprised of ARMs if I'm not mistaken) with CUSIP: 36225DA20. The KRDs from Bloomberg as of now are:

```
Key Rate    KRD
6mo         0.92
1yr         -0.72
2yr         -0.81
3yr         0.49
5yr         0.56
7yr         0.63
10yr        0.43
20yr        -0.08
30yr        0
```

A couple things stick out. The 6mo KRD is 0.92, which I thought would be too high. However, there are also several negative KRDs, (which I don't find as unusual).

Could anyone please shed some light on these figures and how they tie out?

Thanks!

## Answer by RndmSymbl (score 2)

https://quant.stackexchange.com/a/15472

You have already said that the negative KRD is not unusual, given that your are looking at an MBS, I recall a very lengthy discussion on a related matter elsewhere which I assume does not need to be repeated here.

I know very little about MBS in general and cannot look at details on the particular issue. However, given that you are looking at KRD you are probably interested in the optionality. I can only assume that the particular structure is probably getting much of the cash flows early and that is why you would see higher KRD in the early maturity bucket. While looking around I found a helpful article going into a little more detail on KRD than other (publicly available) sources. If available to you you may look at the original article introducing key rate duration (Ho 1992). Thomas Ho has since been establishing his own company, including some illustration of KRD.

EDIT: More general reasons why duration (for the entire length of an issue) might by higher have been discussed here.

## Answer by mark (score 0)

https://quant.stackexchange.com/a/21631

the negative and positives in the same series are a result of negative convexity. stated differently, the asymmetry in the series is a result of negative convexity. These relationships, however, are not permanent and may flip.