# deep discount bond

why does a deep discount bond have higher duration than a bond selling at par? doesn’t a deep discount bond have a higher coupon rate and thus a lower duration than a bond selling at par?

Generally a deep discount bond has no coupon rate…like a zero coupon bond.

As per Investopedia… Deep-Discount Bond are 1. A bond that sells at a significant discount from par value. 2. A bond that is selling at a discount from par value and has a coupon rate significantly less than the prevailing rates of fixed-income securities with a similar risk profile. and so, Low Coupon Rates indicates higher duration!! - Dinesh S

Make sure you understand the concept. These bonds would have to be deeply discounted to make the yield matched up with current market rates. So if you had a 3% coupon bond and new bonds were being issued at market rates 20%, the 3% bond would have to be deeply discounted in order to intice someone to buy it. Otherwise you would just buy to 20% (assuming all else equal).

being priced at discount/premium has absolutely nothing to do with duration. And it is not true that a deep discount bond would necessarily have a higher duration than a par bond. For example, take a 30yr 6% zero coupon bond vs. a 1yr 4% zero coupon bond in an environment with 6% risk free rate.

In your case, the yield to maturity has to be higher than risk-free rate of 6%. Let’s take YTM as 6% to derive the bond price: First bond: N=30 I/Y=6 PTM=0 FV=1,060 —> PV=-184.56 Second bond: N=1 I/Y=6 PTM=0 FV=1,040 —>PV=-981.13 Comparing the 2 bonds, the first bond has to be sold at deep discount (otherwise nobody would buy it) and have a longer duration (30 years). I do not agree with the statement “Being price at discount/premium has ABSOLUTELY nothing to do with duration”. At least the duration determines the price to be sold at higher or lower level (i.e. premium or discount).

FourCastles Wrote: ------------------------------------------------------- > being priced at discount/premium has absolutely > nothing to do with duration. And it is not true > that a deep discount bond would necessarily have a > higher duration than a par bond. For example, take > a 30yr 6% zero coupon bond vs. a 1yr 4% zero > coupon bond in an environment with 6% risk free > rate. Or a bond in default that is selling for 17 has no duration at all.

There are other factors that might impact a price of a bond (non-Treasury)…i.e. Liquidity, credit risk etc. A good example is what happend in August, an 30 yrMBS which used to trade at 100…suddenly got marked down to 90 as the credit spreads widened. (No impact on coupon, maturity & discount rates ofcourse). This decrease in price led to a higher YTM and thus lower duration.

>There are other factors that might impact a price of a bond (non-Treasury)…i.e. Liquidity, credit risk etc. >A good example is what happend in August, an 30 yrMBS which used to trade at >100…suddenly got marked down to 90 as the credit spreads widened. (No impact on >coupon, maturity & discount rates ofcourse). This decrease in price led to a higher YTM >and thus lower duration. That’s just an example of the market rate changing. But given 2 bonds with an identical YTM and identical market rates, the bond with the lower coupon (and therefore bigger discount if market rate > coupon) will have a longer duration.

>> sondin says: “At least the duration determines the price to be sold at higher or lower >>level (i.e. premium or discount).” This sentence defies the laws of English language. Not only are you wrong, you are also absolutely incomprehensible! >> chrismaths says: “But given 2 bonds with an identical YTM and identical market rates, the >>bond with the lower coupon (and therefore bigger discount if market rate > coupon) will >>have a longer duration.” Wrong. Time to hit the books again, my friend. To recap: duration is determined by the timing and amount of the cash flows. Remeber, Macaulay duration is the weighted average of the cashflow times. Price, on the other hand, can be absolutely anything you want it to be - no dependency on the duration whatsoever. See Joey’s example of the bond in default.