Bonds and zero rates

Question

I don't get how to do this one, is a bond similar to compounding interest?

Answer 1

Perhaps I am missing something, but it would see to me that you could buy ${8 \over 14}$ of the #1 bond and sell ${6 \over 14}$ of the #2 bond for a net cost of ${8 \over 14} 95 - {6 \over 14}97 \approx 12.71$. Then the semi-annual payments would be zero (since ${1 \over 2} ({8 \over 14} 0.06 - {6 \over 14}0.08) = 0$), and the value after 5 years would be ${8 \over 14} 100 - {6 \over 14}100 \approx 14.29$.

Then solving $(1+r)^5 = {14.29 \over 12.71}$ gives $r \approx 2.4$%.

(This assumes that you can short the bond, of course.)

The following table illustrates the idea, I have used integral units of stock to simplify. \begin{array}{c|ccccccccccc} \text{cash flow}& 0 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline \\ \text{buy 8 #1} & -760 & & & & & & & & & & 800 \\ & & 24 & 24 & 24 & 24 & 24 & 24 & 24 & 24 & 24 & 24 \\ \text{sell 6 #2} & 582 & & & & & & & & & & -600 \\ & & -24 & -24 & -24 & -24 & -24 & -24 & -24 & -24 & -24 & -24 \\ \hline \\ \text{net} & -178 & & & & & & & & & & 200 \\ \end{array}

Hence $r = \sqrt[5]{{200 \over 178}}-1 \approx 2.35\%$.