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Explanation:
To hedge the short nominal bond position with TIPS, we need to calculate the hedge ratio using the formula:
Hedge Ratio = (DV01 of T-bond × Yield Beta) / DV01 of TIPS
Given:
$100 millionCalculation: Hedge Ratio = (0.065 × 1.03) / 0.088 = 0.06695 / 0.088 = 0.7608
Amount of TIPS to purchase:
$100 million × 0.7608 = $76.08 million
This hedge ratio ensures that the price sensitivity of the TIPS position offsets the price sensitivity of the short T-bond position, accounting for the relationship between nominal and real yields captured by the yield beta.
Q-70. Assumes that bond trader, Jayme Ryan, wishes to make a relative value trade by selling a U.S. Treasury bond (T-bond) and purchasing a U.S. Treasury Inflation Protected Security (TIPS). Ryan decides to short $100 million of the nominal bond and determines that the DV01 of the TIPS is 0.088 and the DV01 of the T-bond is 0.065. Ryan then runs a least squares regression based on changes in the nominal yield and real yield and finds a yield beta of 1.03 basis points. What is the amount of TIPS that Ryan should purchase in order to hedge the short nominal bond?
A
$73.86 million
B
$76.08 million
C
$135.38 million
D
$139.45 million
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