# interest rate

why is the interest rate risk higher for lower yield bonds, but same coupon bonds. can someone please give the reasoning behind and prove it with an example

For any question like this, I would recommend you draw a price-yield curve and take a look at what it looks like at lower yields (it is much steeper) http://www.schaeffersinvestmentresearch.com/images/schaeffersu/advanced/advancedbonds/convexity3.gif Clearly the farther left you go the more extreme the movements are in price with the change in yield.

strangedays Wrote: ------------------------------------------------------- > Pepps, > just think about this: > > par: coupon rate=current yield=YTM > discount: couupon ratecurrent yield>YTM >premiun: coupon rate>current yield>YTM How does thinking about that explain that bond with lower yield has higher interest rate risk? Bond A: 8% YTM 6 Bond B: 8% YTM 5 All it says is that price of bond A should be lower than price of bond B, but both the bonds will be available at premium. However interest rate risk is greater with Bond B. Can you explain that?

pepp Wrote: ------------------------------------------------------- > strangedays Wrote: > -------------------------------------------------- > ----- > > Pepps, > > just think about this: > > > > par: coupon rate=current yield=YTM > > discount: couupon ratecurrent yield>YTM > >premiun: coupon rate>current yield>YTM > > How does thinking about that explain that bond > with lower yield has higher interest rate risk? > > Bond A: 8% YTM 6 > Bond B: 8% YTM 5 > > All it says is that price of bond A should be > lower than price of bond B, but both the bonds > will be available at premium. > > However interest rate risk is greater with Bond B. > Can you explain that? Sorry, pepps I think I misunderstood the question. In this case however, I think it is more a matter of sensitivity of the bond to Yield…so convexity kick in!

pepp Wrote: ------------------------------------------------------- > strangedays Wrote: > -------------------------------------------------- > ----- > > Pepps, > > just think about this: > > > > par: coupon rate=current yield=YTM > > discount: couupon ratecurrent yield>YTM > >premiun: coupon rate>current yield>YTM > > How does thinking about that explain that bond > with lower yield has higher interest rate risk? > > Bond A: 8% YTM 6 > Bond B: 8% YTM 5 > > All it says is that price of bond A should be > lower than price of bond B, but both the bonds > will be available at premium. > > However interest rate risk is greater with Bond B. > Can you explain that? my intuition is percentage let’s say a \$10 drop in value due to increase interest rate (i made this up) higher YTM: (50-40)/50 = 10/50 = 20% lower YTM: (40-30)/40 = 10/40 = 25%

> > > my intuition is percentage > let’s say a \$10 drop in value due to increase > interest rate (i made this up) > higher YTM: (50-40)/50 = 10/50 = 20% > lower YTM: (40-30)/40 = 10/40 = 25% I am still lost.

hmm… increasing in interest rate causes \$1 decrease in value of bond bond A is worth \$100 bond B is worth \$10 which bond is exposed to higher interest rate risk?

makes sense. thanks.

If you use an example this will help (this example is just made up for illustrative purposes): Bond A: 8% 5-year semi-annual \$1000 par value, priced at 6% YTM. Bond B: 8% 5-year semi-annual \$1000 par value, priced at 5% YTM. Use TVM to calculate current price: A: FV: \$1000; N: 10; I/Y: 3 (6/2); PMT: 40; CPT PV = \$1,426.51 B: FV: \$1000; N: 10; I/Y: 2.5 (5/2); PMT: 40; CPT PV = \$1,481.36 NOW, lets say the rates increase by 50 basis points, recalculate PV A: FV: \$1000; N: 10; I/Y: 3.25 (6.5/2); PMT: 40; CPT PV = \$1,400.06 B: FV: \$1000; N: 10; I/Y: 2.75 (5.5/2); PMT: 40; CPT PV = \$1,453.60 Now, calculate the % change in price: A: (\$1400.06/\$1426.51) - 1 = -1.85% change in price B: (\$1481.36/\$1453.60) - 1 = -1.87% change in price Back to your main question, Bond A has a lower yield (5%) than Bond B (6%), yet it showed more change in price (-1.87% vs. -1.85%). Hope that helps!

Thx, soxboys. made sense, when I was studying this, it made sense, suddenly two days later i forgot the idea behind it.

> > Sorry, pepps I think I misunderstood the question. > In this case however, I think it is more a matter > of sensitivity of the bond to Yield…so convexity > kick in! and duration. higher maturity and lower Y bonds = more risk = more sensitivity to deltas in rates.