bond question question

Elliotbay

silly question but i dont understand why a higher coupon means lower interest rate risk. vice versa.

can someone elaborate?

mdfb79

Interest rate risk addresses price sensitivity to changes in rates. For the bond holder it is the fall in price due to higher interest rates due to their inverse relationship. For a given maturity, a bond with a higher coupon will be less sensitive to an increase in price than a similar bond with a lower coupon . Since the spread between the lower coupon and interest rates is higher the discount factor is greater than in the case of the higher coupon so price is affected to a greater degree. Hope this helps.

Kapie

Actually, I think higher coupon does mean higher rate risk...more money has to be reinvested at the current yield to achieve the rate right?

WarrenB1

palantir, you're confusing that with reinvestment risk.

whew1110, think of it in terms of equities. everyone is suggesting investing in dividend-paying bonds recently to decrease their exposure to volatility. if they lose money due to a decease in stock price, the loss is partially offset by dividends. this is not the case if no dividends are paid. you can translate this to bonds.

Iginla2011

Consider a 9% 20-year bond selling to yield 6%. The price of this bond would be 134.6722. If the yield required by investors increases by 50 basis points to 6.5%, the price of this bond would fall by 5.13% to 127.7605

For a 6% 20-year bond selling to yield 6%, a rise in the yield required by investors to 6.5% will cause the bond’s price to decline from 100 to 94.4479, a 5.55% price decline.

(Level I Volume 5 Equity and Fixed Income, 6th Edition. Pearson Learning Solutions p. 354).

The 9% bond is fallen 5.13% whereas the 6% bond has fallen 5.55%. The bond with higher coupon rate has fallen less and this is precisely the interest rate risk - price sensitivity to change in interest rates.

DarienHacker

+1 for mohammad. The 9% coupon bond has a lower mod duration than the 6% coupon bond.

Excel has a modified duration function that allows you to play with various inputs to help you understand. Try this:

Today: 9/01/11
Settlement: 9/03/11
Maturity 9/1/2021
Coupon 9%/6%
Yield: 6%/6%
Frequency: 2/2
Price: =price(settlement,maturity,rate,yield,100,frequency)
Modified Duration: =mduration(settlement,maturity,coupon,yield,frequency)

As long as you don't hard code you can play around and see the price changes for the 9% and 6% coupon bond as you move yield up and down.

Edit: If you forget you can always work it via modified duration in your calc



Edited 2 time(s). Last edit at Monday, September 12, 2011 at 07:43PM by turbolt.

svgleeson

Higher coupon means lower duration so you get your money back sooner from what I understand. And lower duration means less sensitivity to a change in interest rates.

comp_sci_kid

Higher coupon = lower duration = get more money back sooner = higher reinvestment risk = less sensitivity to a change in interest rates


Lower coupon = higher duration = get less money back sooner = lower reinvestment risk = higher sensitivity to a change in interest rates.