Constructing a Zero Coupon bond

[Spurious]

This might be a really dumb question, but I ask it anyways:

I got 3 bonds, for example:
Bond 1: Face value 1000, Coupon 6%, 0.6Y maturity, paid annually
Bond 1: Face value 1000, Coupon 5%, 1.5Y maturity, paid semi-annually
Bond 1: Face value 1000, Coupon 8%, 3Y maturity, paid annually

Now I hope that I didnt choose a poor example.

How would that work?

Thanks in advance!

 

[Tsotne]

To be honest I didn't really get what the question is...

How would that work?

??? Are you interested in pricing those bonds or what??? Maybe you want to evaluate some characteristics of the portfolio holding these instruments... Be more specific..

 

[Spurious]

Oh damn, forgot to include my actual question. I am sorry!

With those values I want to construct a 3Y Zero Coupon Bond, would that be possible?

 

[Tsotne]

Willing to include derivatives instruments? Still not sure what you mean. From these 3 bonds it is impossible to do what you ask for. (If I got the point correctly)

 

[iHateVariance]

if i understood ur question right you would like to replicate cash flows of the 3y zero with coupon bonds. Ideally you want that tennors of the cash flows match. suppose you have:
b1 1y zero
b2 2y 6% coupon annual
b3 3y 8% coupon annual

then holding long 93% of b3 and short 7% of b1 and short 7% of b2 will replicate zero. you can write down the cashflows of all your hedging instruments and your target claim then solve the linear problem. if tenor structure of your hedging instruments dsnt mtch ur target claim you can do duration/convexity neutral and dynamically trade ur hedges.

 

[Spurious]

Willing to include derivatives instruments? Still not sure what you mean. From these 3 bonds it is impossible to do what you ask for. (If I got the point correctly)

I basically want to replicate the 3Y bond as a zero coupon bond.
I should have included prices in the OP, but I dont think it matters too much.

In other words:
How much would a 3Y Zero coupon bond cost?

if i understood ur question right you would like to replicate cash flows of the 3y zero with coupon bonds. Ideally you want that tennors of the cash flows match. suppose you have:
b1 1y zero
b2 2y 6% coupon annual
b3 3y 8% coupon annual

then holding long 93% of b3 and short 7% of b1 and short 7% of b2 will replicate zero. you can write down the cashflows of all your hedging instruments and your target claim then solve the linear problem. if tenor structure of your hedging instruments dsnt mtch ur target claim you can do duration/convexity neutral and dynamically trade ur hedges.

This is kind of what I want, with the difference that your bonds are multiples of each other, but I want to do it with bonds with different maturities (that arent multiples of each other).

My teacher replied to my mail and said I would need a more sophisticated method (or in practice a computer program).

Would constructing a yield curve with those 3 bonds and then interpolating get me anywhere?

 

[iHateVariance]

relative pricing and replication pricing is not the same thing. sure you can put a level on the 3y zero from the constructed forward curve, then u still need to figure out how to hedge ur position.

 

[Spurious]

Ok makes sense, I guess foremost I would be more interested in the pricing part, since that seems to be difficult enough for me atm.