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bond pricing, beginner question
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bond pricing, beginner question

  #1 (permalink)
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bond pricing, beginner question

Hi, just have two very basic questions in hope to get some answers for!

1. With the anticipation of a rate hike, lets assume US rate hike does come in the next a few months, the bond price should drop? if some bond price drop to a discount, wouldn't it be obvious to buy those bond?
2. I checked the price of some bonds online and found one bond has a 4% coupon rate and yield of 3.8x% (can't remember exactly). But this bond is trading @ a discount of 99.9x something. I found it a bit strange shouldn't a bond with a higher coupon rate (compared to the yield) trading at a premium. Or I shouldn't look at the yield found straight online but rather extrapolate the yield curve from e.g. par curve to find out the spot rate..?

Much appreciated if someone can help me out! PLEASE!

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  #2 (permalink)
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  #3 (permalink)
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Yes, if rates rise bond price should go lower And No discount doesn't mean that you buy, three reasons

a new bonds are issued at par, so if interest rates rise, the old bond must trade at discount to remain competitive in yield terms.
b. If your bond is trading at say 99, then how can you know if it wont trade at 98 or 90. So you can't buy just because its trading at discount. This is from a trading standpoint
c. during the financial crisis ABX bonds traded at 20cents to the dollar, discount of 80cents. Why? because market feared default.

2. The yield is the main thing with bonds, not sure if your yield on that bond is correct. if its trading at discount it should have a higher yield.

1yr par bond price 100 pays 4%, so you get $4 at eoy, so total of 104
1yr par bond price 100, trading at 99.9x should get u, principal difference (100-99.9x) + (interest) 4$ > 104 (remember coupon is paid on par value)

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shark505 View Post
Yes, if rates rise bond price should go lower And No discount doesn't mean that you buy, three reasons

a new bonds are issued at par, so if interest rates rise, the old bond must trade at discount to remain competitive in yield terms.
b. If your bond is trading at say 99, then how can you know if it wont trade at 98 or 90. So you can't buy just because its trading at discount. This is from a trading standpoint
c. during the financial crisis ABX bonds traded at 20cents to the dollar, discount of 80cents. Why? because market feared default.

2. The yield is the main thing with bonds, not sure if your yield on that bond is correct. if its trading at discount it should have a higher yield.

1yr par bond price 100 pays 4%, so you get $4 at eoy, so total of 104
1yr par bond price 100, trading at 99.9x should get u, principal difference (100-99.9x) + (interest) 4$ > 104 (remember coupon is paid on par value)

Hi! Thank you for your reply!
Further questions on my first question, if my investment horizon is 6 months and during this period a rate hike happens, therefore the scenario in your answer a) happens, if I buy a bond that is maturing in 6 months at a discount compared to today, by the time when the bond matures, wouldn't I be guaranteed the yield as return from my investment in this bond. also because the bond trading at a discount by the time it matures it goes back to par so i can get a more guaranteed capital gain comparing to buying it today?
Does my logic make sense? please critisize!

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  #5 (permalink)
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"Bond Math" as it's called is not simple math.

As already confirmed when yields go up, prices go down.
The longer the maturity of the bond, the greater the price move will be.
The lower the coupon of the bond, the greater the price move will be. (and yes there are zero coupon bonds!)

Bonds price so that bonds of the same tenure and credit worthiness have the same 'yield to maturity' whatever their coupon rate.
'Yield to maturity' is the combined yield of the capital profit/loss from buying a bond at a discount/premium and then redeemed at par, combined with the interest/coupon payments received while holding it.

For example imagine 3 bonds that all expire in a years time.
Bond A has a 8% coupon and is trading 101.9. In a years time you will get your 8 coupon but lose 1.9 when you redeem the bond at par. Total profit 8-1.9 = 6.1 / 101.9 = 6%
Bond B has a 6% coupon and is trading 100. In a years time you will get your 6 coupon. Total profit 6 / 100 = 6%
Bond C has a 4% coupon and is trading 98.1. In a years time you will get your 4 coupon but make 1.9 when you redeem the bond at par. Total profit 4+1.9 = 5.9 / 98.1 = 6%


fishtoeat View Post
Further questions on my first question, if my investment horizon is 6 months and during this period a rate hike happens, therefore the scenario in your answer a) happens, if I buy a bond that is maturing in 6 months at a discount compared to today, by the time when the bond matures, wouldn't I be guaranteed the yield as return from my investment in this bond. also because the bond trading at a discount by the time it matures it goes back to par so i can get a more guaranteed capital gain comparing to buying it today?
Does my logic make sense? please critisize!

If you buy a bond that expires in 6 months your sensitivity to interest rate changes is almost zero. As you say you are pretty much just guaranteed the 'yield to maturity' which little upside or downside.

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  #6 (permalink)
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SMCJB View Post
"Bond Math" as it's called is not simple math.

As already confirmed when yields go up, prices go down.
The longer the maturity of the bond, the greater the price move will be.
The lower the coupon of the bond, the greater the price move will be. (and yes there are zero coupon bonds!)

Bonds price so that bonds of the same tenure and credit worthiness have the same 'yield to maturity' whatever their coupon rate.
'Yield to maturity' is the combined yield of the capital profit/loss from buying a bond at a discount/premium and then redeemed at par, combined with the interest/coupon payments received while holding it.

For example imagine 3 bonds that all expire in a years time.
Bond A has a 8% coupon and is trading 101.9. In a years time you will get your 8 coupon but lose 1.9 when you redeem the bond at par. Total profit 8-1.9 = 6.1 / 101.9 = 6%
Bond B has a 6% coupon and is trading 100. In a years time you will get your 6 coupon. Total profit 6 / 100 = 6%
Bond C has a 4% coupon and is trading 98.1. In a years time you will get your 4 coupon but make 1.9 when you redeem the bond at par. Total profit 4+1.9 = 5.9 / 98.1 = 6%


If you buy a bond that expires in 6 months your sensitivity to interest rate changes is almost zero. As you say you are pretty much just guaranteed the 'yield to maturity' which little upside or downside.

Thanks to your comprehensive reply! I think I start to get a better pictures now but still hope you can help answer some further questions
1. Fluctuation in bond price is only sensitive to the change in the interest rate right..?because the cash flow is already pre-determined unlike stocks where we have no clues of the certainty of both cash flow and discount rate.

1. So how does one person determines a bond is undervalued or overvalued currently? Just based on his/her forecast of the interest rate movement?

2. Also, For example, many invest in stocks in hope to obtain more capital gain rather than dividend gain (needless to say many stocks don't even pay dividend). Are bond investors more looking at "yield to maturity" to see whether the YTM is sufficient enough for his/her required rate of return?

3. YTM assumes the investor can reinvest the coupon at the YTM rate right? in real life how does this implementation work? as a bond holder, I will receive the coupon and how do I reinvest those?

2. And with the anticipation of a rate hike coming up in the US, can you shed some lights on what are the possible trades that bond investors will make??

Thank you!!!!

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  #7 (permalink)
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fishtoeat View Post
Thanks to your comprehensive reply! I think I start to get a better pictures now but still hope you can help answer some further questions
1. Fluctuation in bond price is only sensitive to the change in the interest rate right..?because the cash flow is already pre-determined unlike stocks where we have no clues of the certainty of both cash flow and discount rate.

Or creditworthiness.


fishtoeat View Post
1. So how does one person determines a bond is undervalued or overvalued currently? Just based on his/her forecast of the interest rate movement?

I'm not a bond trader but I believe that you will find a) the market is illiquid enough to a retail trader that your choices are limited and b) thats the game of the big bank fixed income desks.


fishtoeat View Post
2. Also, For example, many invest in stocks in hope to obtain more capital gain rather than dividend gain (needless to say many stocks don't even pay dividend). Are bond investors more looking at "yield to maturity" to see whether the YTM is sufficient enough for his/her required rate of return?

Sorry don't understand or don't know


fishtoeat View Post
3. YTM assumes the investor can reinvest the coupon at the YTM rate right? in real life how does this implementation work? as a bond holder, I will receive the coupon and how do I reinvest those?

Agree. One of the flaws of 'basic bond math'. Also assumes that interest rates are level for the duration of the bond which obviously isn't the case.

fishtoeat View Post
2. And with the anticipation of a rate hike coming up in the US, can you shed some lights on what are the possible trades that bond investors will make??

I'm a futures trader with a math background who has learnt some bond math in prior years, unfortunately I'm not a bond trader.

I will say this though. CBOT have futures contracts on the 2 year, 3 year, 5 year, 10 year and 30 year treasury bond so if you want to speculate that rates are going to go up, ie that prices are going to go down, you could just sell some Treasury Futures. Of course you need to be confident that the market hasn't already priced the increase in.

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  #8 (permalink)
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Not sure if this is what you're after but you could take position in eurodollars, probably the spreads so that you're protected against parallel shifts in the curve.

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fishtoeat View Post
1. With the anticipation of a rate hike, lets assume US rate hike does come in the next a few months, the bond price should drop? if some bond price drop to a discount, wouldn't it be obvious to buy those bond?


smajdah View Post
Not sure if this is what you're after but you could take position in eurodollars, probably the spreads so that you're protected against parallel shifts in the curve.

Not sure if this is what @smajdah meant but found this interesting piece "CURVATURE TRADING APPLICATIONS, Application #1: DIRECTIONAL TRADING" which seems to address exactly what you are asking.
Looking at the graph of butterflies derived from the same curve provides additional information. Chart 2 shows the 6 month butterflies around each of the same contracts from the same two days. March 19 was the infamous FOMC press conference where Yellen attempted to define “considerable time” used in the FOMC statement by saying it “probably means something on the order of around six months.

One common interpretation of curvature in this current market environment is as an indicator of FOMC liftoff and landing probabilities around various contracts. The points of negative curvature (where the curve is convex) at the front of the curve is a function of when the markets expect the FOMC to start hiking. It should be no surprise that the negative curvature got lower around EDH5, as many people expected the FOMC liftoff to occur in the second quarter of 2015. The negative curvature after EDU5 was reduced, as hikes were moved forward. Similarly, the points of positive curvature (where the curve is concave) is a function of when the markets expect the FOMC to stop hiking.”
The piece is 8 months old now but you could probably use the same technique.

http://www.cmegroup.com/education/curvature-trading.html

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Bond Z Spread vs duration


Hi.
Can anyone explain how is bond Z spread related to duration. I mean does higher duration necessarily mean higher Z Spread?
Thanks

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