why do bonds with less yield have more interest rate risk?

why do bonds with less yield have more interest rate risk?


the way i think about it is like this and someone please correct me if i’m wrong.

if you have a bond that has a low coupon rate, there is a higher chance that the market yield will be higher than your coupon rate. so if that’s the case, then all of a sudden, your bond is trading at a discount. which in sense, means you just lost a boat load of money (assuming you started off at par)

but on the bright side is, lower coupon means you have lower reinvestment risk because less of your cashflows are going to be reinvested at that prevailing market rate.

does that make sense?

Recieving more cash now vs later is the reason.

If by ‘yield’ you mean the general level of interest rates then in low interest enivironment bond prices are more sensitive to interest rates moves than in high interest rate environment. This is which positive convexity is all about.

If by ‘yield’ you mean the coupon rate then it has to do with reinvesment risk: low coupons do not offset capital losses (if interest rates rise) as much as high coupon bonds. This is why zero-coupon bonds will have the highest convexity (all other paramaters being equal).

Duration son.

please correct me if am wrong,

if you consider the upward sloping normal yield curve you will notice that the lower the yield, the steeper the slope. yield is influenced by interest rates, therefore small changes in interest rates will have higher impact on yields in the short term than in the long term where the curve sort of levels of. its more of convexity issue i guess. therefore the lower the yield, the more responsive it is to interest rate fluctuations…

So simple to understand and remember:

Assume there are two bonds, one is of 3% coupon rate and second is of 7%. Market interest rate increaes by 200 bps (2%.). So how much these bonds should be affected ? just do some simple calculations, 3% bond should be affected by 67%. (2/3) and 7% should be affected by 29% (2/7).

Now you can understand that lower coupon bonds affect more than higher coupen bonds because of higher percentage change in them due to market interest rate changes.

Wow. This is getting complicated! It’s pretty simple actually… Higher yield bonds pay more in coupons sooner. So, changes in rates have less compounding effect on the present value.

Consider 1-year and 2-year payments where rates for both terms are 5%. The value of the 1-year payment is 1.05^-1. The value of the 2-year payment is 1.05^-2. So, if rates change, the “^-2” sign causes the value of the 2-year payment to change more than the value of the 1-year payment.

On a side note, if “yield” means the discount factor applied to the bonds, the same incremental change in rates actually has a lower effect on high “yield” bonds. This is because the present value of the higher discounted bond is lower. So, a % discount applied to the present value of the higher discounted bond will result in a lower $ change in the present value.

I do not want to confuse you but remember that all of the above concerns only bonds without emebedded options and by ‘interest risk’ are meant only price changes of the bond due to a parallel shift of the yield curve.

The most sensitive are long term low coupon bonds. If you can remember that and why because you money is locked in for a long term at a low rate you’ll see why sudden changes affect them the most, if interest rates increase substantially in a positive direction, no one wants your long term low coupon bond.

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And they’re more sensitive at low YTMs than at high YTMs (which I think was the point of the original question).

I wrote an article on duration that covers this idea: http://financialexamhelp123.com/macaulay-duration-modified-duration-and-effective-duration/

Consider two bonds:

  1. priced at $100 (lower YTM)

  2. priced at $90 (higher YTM)

Suppose now that nterest rates move my 10%. 10% of 1) is larger than 10% of 2), so it moves more in absolute terms.

  1. Moves by $10

  2. Moves by $9