Financial Mathematics Text

Monday, October 15, 2012

Yield-Duration Curve

Most people are familiar with the "yield curve" which compares yield with maturity. I personally think a more useful curve looks at yield and duration.

Duration is a metric which gives a rough indicator of how much a change in interest rates will affect the price of a bond. Roughly speaking, if a bond has a duration of 10 years, a 1% change in interest rates (say from 4 to 5%) will result in a roughly 10% change in the price of the bond. So duration gives one information about interest rate risk.

While I don't currently have any theoretical reason why, it appears that the "Yield-duration curve" tends to be roughly linear over time. Here's a look at Vanguard bond ETFs:

As expected there's a difference in the intercepts reflecting the additional credit risk of the investment grade corporate bonds versus the "risk-free" US treasury bonds.

The other interesting thing (which probably relates to the credit risk) is the difference in slope. I was curious to see if this persisted over time.

Unfortunately I do not have historical duration data. Lack of data has never prevented research from going forth. If one doesn't have data, make it up!

FRED provides historical interest rate data for different maturities of assets. By making some assumptions, I was able to construct duration data for the series. While not ideal it still provides some interesting results. Here are some historical slopes for corporate and government bond yield-duration curves:

I'm not sure if there's anything useful to all of this as of yet. It definitely seems to me that one should get more yield for duration. Initially I thought to look at yield to duration as this article suggests but that supposes that the relationship is not only linear but intercepts at 0%, a conclusion not consistent with the evidence.

Another idea would be to consider those assets that are "above" the curve. In the case of the Vanguard ETFs, VCIT and VGLT are both above their respective curves indicating they may be getting more yield for their duration than the other funds.

In any event, I think this line of thought may provide interesting insights but some further research would be required.

Disclosure: Long VCSH and VCIT.

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