Explanation:

This can be achieved by making the trade DVO1-neutral. Johnson has to buy the $F^R$ face amount of the TIPS such that:

$F^R \times 0.092/100 = \`$ 230` \text{ million} \times (0.056/100)$

$\Rightarrow F^R = \`$ 230` \text{ million} \times (0.056/0.092)$

$= \`$ 140` \text{ million}$

Things to Remember

Duration and convexity are important concepts in fixed income trading and risk management.
DVO1 (Dollar Value of 01) is a measure of the change in the market value of a bond or portfolio for a 1 basis point change in yield.
Being DVO1-neutral means that the change in the market value of the bond or portfolio due to a 1 basis point change in yield is offset by the change in the market value of the hedge instrument.
Calculating the face amount to be purchased for a trade to be hedged involves setting up an equation based on the DVO1s of the bonds involved.

Bond Yield% DVO1
Tips `$2`\frac{5}{7} $s of `$ 17`^{\text{th}}$ January 2020 1.096 0.092
`$4`\frac{6}{7} $s of `$ 17`^{\text{th}}$ February 2020 3.461 0.056

Compute the TIPS face amount that should be purchased for the trade to be hedged against the interest rate levels.

Bond	Yield%	DVO1
Tips `$2`\frac{5}{7} $s of `$ 17`^{\text{th}}$ January 2020	1.096	0.092
`$4`\frac{6}{7} $s of `$ 17`^{\text{th}}$ February 2020	3.461	0.056

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