# Investment Grade Bond vs Junk Bond, whose duration is larger?

Just wondering how to calculate duration when take credit risk into consideration.

I think if duration is calculated as weighted average of cashflow time, and weights are calculated using present values of cashflows, then Invest Grade Bond would have larger duration than Junk Bond.

Is that the truth???

• No, 'duration' assumes all future payments will be made; YTM reflects the risk.
– amsh
Feb 12, 2016 at 18:07
• @amsh, you should write this up in an answer.
– BKay
Feb 13, 2016 at 18:57
• @amsh, wondering how compare the duration between IG bond and Junk Bond Feb 13, 2016 at 19:22
• You don't. Seems like an XY problem, what are you actually trying to do?
– amsh
Feb 15, 2016 at 11:24
• Ytm is very important factor. It helps you in comparing risk. Apr 16, 2016 at 1:31

There are different measures and interpretations of duration. One, as has been pointed out already, has a formula weighting coupons and final contractual cashflow. Other definitions of duration take a broader perspective and relate it to the interest rate sensitivity of the security and not to a particular formula. These go by names such as effective or risk adjusted duration. Embedded options, for example, can be modeled into an interest rate tree, and the average of a one basis point increase and decrease in those rates and their impact on the price show the impact, or duration, of interest rates. Effective duration models can also incorporate credit risk but there is not an industry standard for that. It is important to not let a formula using the contractual final cash flow bias the results. For example, interest rate hedging may be done based on duration. A long term bond teetering on bankruptcy would have little or no effective duration, but using the contractual maturity might result in very inappropriate swap trades hedging risk that does not exist.

• The above points are reflected in the quoting conventions. IG is quoted in terms of spread to treasury while bonds closer to default are quoted in price. Jun 10, 2019 at 16:16

Duration is technically independent of credit risk. ANY bond's duration is just a matter of coupon, price, discount rate.

However, many issued high yield bond ARE typically shorter, because of a. high coupon (all else equal makes duration shorter) b. they can't issue too long: they themselves don't want to finance expensively, and investors don't want to be stuck with crappy name for 10 years.

Also given material default probability in high yield, there is a concept of "duration to worst" which is even shorter that's not in existence in investment grade market.

If you have a 0 coupon junk bond with the same time to maturity as a investment grade bond that pays coupons, the junk bond will have higher duration and visa versa. Calling it a junk or an ig bond doesn't change the duration, the formula is still the same so you can't say a ig bond always has a larger or smaller duration.

I agree with the assertion in the OP. If two bonds are identical then the interest rate sensitivity of the one with higher credit risk is lower. That's because the expected cash flows are smaller due to credit risk.

Duration is a decreasing function of yield. It's simple to consider that lower yielding bonds (in IG or sovereign credit) will increase line item duration when compared against HY.

Ditto to Larasing. Any bond's duration is just a matter of coupon, price, discount rate. Credit risk does not factor into this equation.

Credit risk factors into the discount rate and price.

Consider an investment-grade bond and a junk bond that have the same maturity and coupon.

Junk bond yield = benchmark + credit spread > Investment-grade yield

Holding the coupon and time to maturity constant for both bonds, the junk bond with the higher yield and lower price to compensate for credit risk will have a lower duration.

This doesn't hold if the junk bond is trading at a discount and the investment-grade bond is at par or a premium, which is more than possible. A bond at a discount has a duration ≥ duration of a premium bond. As time to maturity of both discount and premium bonds approach infinity, both durations converge as they approach the duration of a consol bond.