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Construct synthetically a zero-coupon bond from coupon bonds

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The prices of the following coupon bonds are as follows:

Maturity Coupon Price
1 4.75% 103.675
2 7.5% 111.753
3 9.375% 121.445
4 6.25% 114.130
5 5.50% 112.158

How can I construct synthetically a 3-year zero-coupon bond? Which coupon bonds would I have to invest in? What are the proportions in which I will have to hold those coupon bonds in order to replicate the discount bond?

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Solution Summary

The solution provides step by step instructions on the creation of zero coupon bonds using coupon bonds. Matrix algebra is used to arrive at the number of bonds to buy or sell.

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How can I construct synthetically a 3-year zero-coupon bond? Which coupon bonds would I have to invest in? What are the proportions in which I will have to hold those coupon bonds in order to replicate the discount bond?

A 3 year zero coupon bond will have the following cash ...

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