Fixed Income Questions

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I’ll provide answers after 5 responses.
1) A bond has a par value of $1,000, a 6% semiannual coupon, and three years to maturity. What’s the percentage change in price of the bond if required yield decreases from 6% to 3% given yield to maturity of 3%, 6%, and 12%?
A) 8.55%
B) 1.09%
C) 4.02%
2) Consider a 6% Treasury note with 1.5 years to maturity. Spot rates (expressed as semiannual yields to maturity) are: 6 months = 5%, 1 year = 6%, 1.5 years = 7%. If the note is selling for $992, what’s the arbitrage profit per bond?
A) $13.45
B) $5.45
C) $8.00
3) A $1,000, 5%, 20-year annual-pay bond has a yield of 6.5%. If the yield remains unchanged, how much will the bond value increase over the next three years?
A) $13.58
B) $13.62
C) $13.78
4) An analyst observes a 20-year, 8% option-free bond with semiannual coupons. The required semiannual-pay yield to maturity on this bond was 8%, but suddenly it drops to 7.25%. Prior to this sudden change in required yield, what was the price of the bond?
A) 92.64
B) 100.00
C) 107.85
5) Treasury spot rates (expressed as semiannual-pay yields to maturity) are as follows: 6 months = 4%, 1 year = 5%, 1.5 years = 6%. A 1.5 year, 4% Treasury note is trading at $965. The arbitrage trade and arbitrage profit are:
A) buy the bond, sell the pieces, earn $7.09 per bond
B) sell the bond, buy the pieces, earn $7.91 per bond
C) sell the bond, buy the pieces, earn $7.09 per bond
 
No more info needed for number #1. You want to calculate the price with the YTM at 3%. And then compare it to the price at 6%. If the coupon is 6% and the YTM is 6%, then we know the price is par.
 
1. The first question isn’t clear, so there could be a few solutions
2. B
3. B
4. C - I suppose, that market react very quickly, so the price should rais.
5. A
 
Erykus Wrote:
——————————————————-
> 1. The first question isn’t clear, so there could
> be a few solutions
> 2. B
> 3. B
> 4. C - I suppose, that market react very quickly,
> so the price should rais.
> 5. A
Concerning #4 - The question asks “prior to the change in yield what is the price?”. I think that’s what is mixing you up here. I agree though, and it’s good that you recognize that if the yield goes down the price will rise.
This seems like a question to teach you not to skim through the question too fast.
 
marjuhrene Wrote:
——————————————————-
> Erykus Wrote:
> ————————————————–
> —–
> > 1. The first question isn’t clear, so there
> could
> > be a few solutions
> > 2. B
> > 3. B
> > 4. C - I suppose, that market react very
> quickly,
> > so the price should rais.
> > 5. A
>
> Concerning #4 - The question asks “prior to the
> change in yield what is the price?”. I think
> that’s what is mixing you up here. I agree though,
> and it’s good that you recognize that if the yield
> goes down the price will rise.
>
> This seems like a question to teach you not to
> skim through the question too fast.
FYI, the question is asking for the price prior to the drop in rates. Since Coupon rate=YTM then that would imply the bond was at par value prior to the drop in rates.
My answers for the questions are:
1. A (Confusing question)
2. B
3. B
4. B
5. A
 
Will try and get the answers to these shortly. Can’t remember where I saved them.
 
1.) A (kind of confusing)
2.) Not sure
3.) B
4.) B
5.) A
Thank you for the questions!
 
Could someone go through the math solving a couple of these, I have a lot of trouble with problems like this.
 
#2 and #5: use spot rates to discount cash flow, (cpn payments and principal at mty), to compare present value to mkt trading price. buy the less expensive one, sell pieces, vice-versa.
rest can be solved with fiancial calc, but have similar methodolgy, discounting cash flow to find prsent value, yield to mty.
for # 4 you know bond was trading at par because YTM was equal to cpn
 
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