**Reading Source:** ERM-111-12 Study Note

**Topics Covered in this Reading:**

- Introduction
- Key Rate Durations
- Key Rate Duration Profiles
- Key Rate Durations in a Portfolio Context
- Conclusions
- Appendix: Adjusted Key Rate Durations

**Reading Source:** ERM-111-12 Study Note

**Topics Covered in this Reading:**

- Introduction
- Key Rate Durations
- Key Rate Duration Profiles
- Key Rate Durations in a Portfolio Context
- Conclusions
- Appendix: Adjusted Key Rate Durations

Hi

The explanation for the higher duration of the callable corporate bond for 8% vs. 9% coupon rate is that with a lower coupon rate, the probability of it being called is lower, which means higher duration. However for the GNMA pass-through PO, the lower the interest rate the higher the prepayment rate, which should lower the duration.

In both cases there is early repayment option, but why does the lower rate on their debt (coupon vs. interest) affect these two issuers differently in terms of prepayment?

You might need to help me work through this one with you.

First example: you are comparing two different callable bonds (one with 8% coupon rate and one with 9% coupon rate) but the interest rate is assumed to the same for both. The comparison made here is, the higher the coupon rate, the more likely it is to be called earlyâ€¦ thus shortening the duration. However, if interest rates were to increase, I think both bonds would be less likely to be called, so as interest rates increase, the duration will increase for both bonds.

The second example, we only have one item: a Principle Only GNMA. Here, if interest rates increaseâ€¦ the prepayment rate decrease, and so the duration will increase.

So I think both items react similarly to increasing interest rates in that their duration will increase.

Did that answer your question? Or do you disagree with something Iâ€™ve said?

I donâ€™t disagree, but I think what Iâ€™m trying to get at might be outside the scope of the syllabus; Iâ€™m trying to understand the early repayment probability relationship with the cost of debt from the issuer perspective.

For more background: the intuition behind my question is that if I have several debts, then I would want to pay off the one with the highest rate first if I have the option and the means, reducing my total interest paid. This intuition seems to line up with the explanation for a 9% vs. 8% coupon callable bond at first glance. But with the GNMA pass through, the underlying is still a debt, and Iâ€™m assuming the rate floats. Regardless of whether it is a bond or a mortgage, would the same intuition hold? Your answer states that both the 9% and 8% would be less likely to be called if the interest rate increases, but that might be for a different reason than for a consumers home mortgage (Iâ€™m thinking that for a firm, the bond would be less likely to be called because they would still need the capital, and reissuing new bonds after the interest rate goes up means that a higher rate is now required. On the other hand, the consumer is more concerned with minimizing interest paid).

Iâ€™m thinking it might just come down to different borrower profiles/goals that affect the prioritization of debt repayment.

I look at it this way:

The issuer of the bond chooses whether the bond is recalled. The higher the coupon rate, the more expensive it is to â€śborrow moneyâ€ť. If interest rates are low, there are cheaper ways to borrow money so they are more likely to call the bond and reissue the bond.

For the mortgageâ€¦ it is the owner of the mortgage who chooses to prepay or not. When rates are low, they are more likely to repay the current mortgage and take advantage of a lower mortgage rate. So when interest rates are low, the prepayment rate increases.

In either exampleâ€¦ when interest rates are lower, the odds of early repayment increase and so duration is reduced. Agree or disagree?

I agree with your response, I think I was getting stuck on assuming a scenario where once the mortgage is prepaid, it is just paid-off â€“ end of story. In reality people prepay to then get a better rate for the remainder of their mortgage term, as very few people would have the resources to just pay off their mortgage to minimize their interest paid.

Soâ€¦ with that, I think weâ€™ve gone far enough off-topic! Thanks for bearing with me.

Curious as too why the KRD is negative upon expiration of a call option? I canâ€™t quite rationalize this in my head.

Hi smoore29

Letâ€™s assume the expiration date is at time 10. I suppose one way to think about it could be, the call option gives you the right to buy the bond at time 10.

Therefore, there is a a chance we will be spending money to buy a bond at time 10.

If this occurs, this can be looked at as a cash outflow at time 10. If the 10 year interest rate were to increase, the PV of our outflow would be lower, which increases the value of the transaction. Therefore the negative duration helps explain the increase in value due to the formula: change in P = -D x P x change in yield.

On the other hand, the later payments have positive durations because increases in the interest rates there will reduce the present value of the potential coupons and face value that could be coming our way.