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Answer: Yes, by $2.46 million (purchase additional TIPS).
## Explanation This is a hedge ratio adjustment problem involving nominal bonds and TIPS (Treasury Inflation-Protected Securities). **Given:** - Short position in nominal bond: $100 million - Long position in TIPS: $89.8 million - Regression coefficient (beta): 1.0274 (nominal yield changes by 1.0274 bps per 1 bp change in real yield) **Calculation:** The hedge ratio should be adjusted based on the regression coefficient. The current hedge assumes a 1:1 relationship, but the regression shows that nominal yields are more sensitive than real yields. Current hedge ratio: $89.8 million / $100 million = 0.898 Adjusted hedge ratio: 0.898 × 1.0274 = 0.9226 Additional TIPS needed: $100 million × 0.9226 - $89.8 million = $92.26 million - $89.8 million = $2.46 million **Interpretation:** Since the regression coefficient is greater than 1, nominal yields are more volatile than real yields. To properly hedge the short position in nominal bonds, the trader needs to purchase additional TIPS worth $2.46 million to maintain the appropriate hedge ratio. Therefore, the correct answer is **B** - Yes, by $2.46 million (purchase additional TIPS).
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Assume that a trader is making a relative value trade, selling a U.S. Treasury bond and correspondingly purchasing a U.S. Treasury TIPS. Based on the current spread between the two securities, the trader shorts $100 million of the nominal bond and purchases $89.8 million of TIPS. The trader then starts to question the amount of the hedge due to changes in yields on TIPS in relation to nominal bonds. He runs a regression and determines from the output that the nominal yield changes by 1.0274 basis points per basis point change in the real yield. Would the trader adjust the hedge, and if so, by how much?
A
No
B
Yes, by $2.46 million (purchase additional TIPS).
C
Yes, by $2.5 million (sell a portion of the TIPS).
D
Yes, by $2.11 million (purchase additional TIPS)