Callable bond duration

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Longdog
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Callable bond duration

Post by Longdog » Sat Apr 26, 2014 3:14 pm

What is the duration of a callable bond? If a bond matures in 10 years, but is callable in 5 years, you'll get your principle back in 5 years if it's called at the earliest call date, or some time later, up until the maximum of 10 years. I'm trying to understand, intuitively, what that should mean in terms of when you should expect your principle back.
Steve

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packer16
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Re: Callable bond duration

Post by packer16 » Sat Apr 26, 2014 3:47 pm

It depends upon the interest rate and credit quality of the issue at the call date. If they can refinance the debt at a lower interest rate then the bond you own will be called.

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RadAudit
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Re: Callable bond duration

Post by RadAudit » Sat Apr 26, 2014 3:48 pm

I've got a similar problem. I inherited a small number of bonds. Either, they'll all mature between 10 and 25 years from now or all will be callable with in one month to five years from now or some combination of the two. The combination is at the whim of the issuer.

I'm no bond expert, as you might guess. I believe the important impact is on the cost of the bond at issue based on the potential call date vs. the maturity date. 5% for five years should be worth more or less than 5% for 30 years based on the yield curve at the time.
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packer16
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Re: Callable bond duration

Post by packer16 » Sat Apr 26, 2014 3:56 pm

If your bond looks it is going to be called (based upon coupon being higher than re-fi rate), they will trade at yield to worst. You need to look at the bond specifics but bonds typically have multiple call dates with higher prices for earlier dates (this provides some protection to the bond holder providing a minimum yield (the yield to worst).

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Longdog
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Re: Callable bond duration

Post by Longdog » Sat Apr 26, 2014 4:05 pm

packer16 wrote:If your bond looks it is going to be called (based upon coupon being higher than re-fi rate), they will trade at yield to worst. You need to look at the bond specifics but bonds typically have multiple call dates with higher prices for earlier dates (this provides some protection to the bond holder providing a minimum yield (the yield to worst).

Packer
When would this evaluation be done? 6 months before the call date? 3 months? 1 month?

And if the difference between the coupon and re-fi rate is positive, but small (e.g 0.25%) would that really be enough to make it worth the costs associated with issuing a new bond?

I think what I'm hearing is "it depends on a lot of factors" so there is not a simple answer.
Steve

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grabiner
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Re: Callable bond duration

Post by grabiner » Sat Apr 26, 2014 4:09 pm

Duration is defined mathematically as the ratio of price change to interest-rate change (for mathematicians, it is the negative of the derivative of price with respect to interest rate). For a callable bond, a model must be used to estimate the probability of a call, and how that probability varies with interest rates.

If a bond is likely to be called, its duration will be close to its time-to-call (adjusted for intermediate coupon payments). If it is likely not to be called, its duration will be close to its time-to-maturity (again adjusted for coupon payments, and these will be more important since there are more of them). Thus the duration of a callable bond increases as interest rates change. A callable bond with a reported 9-year duration would lose 0.9% of its value if rates rise 0.1%, but it might lose 11% if rates rose 1% because the decreased call probability caused the duration to increase. This is known as negative convexity.

Conventional bonds have slightly positive convexity. If interest rates rise, payments further in the future lose more of their value, so the bond has more of its current value in the shorter-term coupons and the duration decreases slightly.
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packer16
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Re: Callable bond duration

Post by packer16 » Sat Apr 26, 2014 4:13 pm

I would say a few months before the call date to arrange the new re-fi with either a commercial bank or a new bond offering. The final go ahead is dependent upon interest rates at the call date itself so if there are large changes in rates then the whole deal can be called off. A useful metric is yield to worse as this is lowest return you will get (assuming the firm does not go BK) and your yield to maturity is highest yield. I doesn't give you a precise answer but at least you can get a range to compare to other alternatives.

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Longdog
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Re: Callable bond duration

Post by Longdog » Sat Apr 26, 2014 5:07 pm

Thanks grabiner and packer. I very much appreciate both the theoretical as well as practical perspectives. It would seem that if you buy an investment grade bond with a short call date at a high premium, it's likely to be called. The higher the premium, the more likely that is to occur.
Steve

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Re: Callable bond duration

Post by magician » Sun Apr 27, 2014 1:30 am

packer16 wrote:If your bond looks it is going to be called (based upon coupon being higher than re-fi rate), they will trade at yield to worst. You need to look at the bond specifics but bonds typically have multiple call dates with higher prices for earlier dates (this provides some protection to the bond holder providing a minimum yield (the yield to worst).
It will trade at yield to call (YTC), which may or may not be the yield to worst. For the yield to worst you need to consider the YTCs for each call provision (as you say, there are typically several), as well as the YTM.
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Re: Callable bond duration

Post by magician » Sun Apr 27, 2014 1:48 am

grabiner wrote:Duration is defined mathematically as the ratio of price change to interest-rate change (for mathematicians, it is the negative of the derivative of price with respect to interest rate).
Actually, duration (specifically, effective duration) is defined mathematically as the ratio of the percentage price change to the interest-rate (i.e., yield-to-maturity) change, not the ratio of the price change to the YTM change. For mathematicians, it is the negative of the derivative of the natural logarithm of price (ln(price)) with respect to YTM, not the negative of the derivative of the price with respect to YTM.
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Re: Callable bond duration

Post by magician » Sun Apr 27, 2014 1:50 am

packer16 wrote:A useful metric is yield to worse as this is lowest return you will get (assuming the firm does not go BK) and your yield to maturity is highest yield.
Again, it isn't necessarily true that YTM will be higher than all of the YTCs. It usually is, but it needn't necessarily be.
Simplify the complicated side; don't complify the simplicated side.

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Re: Callable bond duration

Post by Valuethinker » Sun Apr 27, 2014 10:12 am

SteveM wrote:What is the duration of a callable bond? If a bond matures in 10 years, but is callable in 5 years, you'll get your principle back in 5 years if it's called at the earliest call date, or some time later, up until the maximum of 10 years. I'm trying to understand, intuitively, what that should mean in terms of when you should expect your principle back.
As per all comments here your safest bet is to assume Yield to Call, and to assume it will be called at the first possible moment (and therefore that is its maturity) *unless* it is trading at a significant discount. In which case your maturity is probably the bond's maturity, and yield is yield to maturity.

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Re: Callable bond duration

Post by gerrym51 » Sun Apr 27, 2014 10:27 am

I would only buy a callable bond if you bought it at a big discount. usually the way to do this is buy on secondary market-but you need to buy only those you are pretty sure won't default.

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