Final answer:
The capital gain of a TIPS in dollars, given the change in CPI from 195.8 to 205.1 and an issue CPI reference of 187.1, is $54.78. The capital gain in percentage is 2.93%.
Step-by-step explanation:
To calculate the capital gain of a Treasury Inflation-Protected Security (TIPS) in dollars, we need to consider the change in the Consumer Price Index (CPI) over the period. Since TIPS principal adjusts with inflation as measured by the CPI, the capital gain will be proportional to the change in CPI from the beginning to the end of the year.
The original CPI reference for the TIPS issue is given as 187.1. At the beginning of the year, the CPI was 195.8, and by the end it was 205.1. To find the capital gain in dollars, we need to calculate the change in CPI:
Capital Gain = (Ending CPI / Beginning CPI) × (CPI reference × face value)
= (205.1 / 195.8) × (187.1 × face value) - face value
Becuase the face value is not provided, we assume a common face value of $1000 for TIPS, so the calculation would be:
Capital Gain = (205.1 / 195.8) × (187.1 × 1000) - 1000
= ($1054.78) - $1000
= $54.78
To then determine the capital gain as a percentage:
Capital Gain Percentage = (Capital Gain / (CPI reference × face value)) × 100
= (54.78 / (187.1 × 1000)) × 100
= 2.93%
Note: The CPI reference is an important factor when calculating the adjustment to the principal of a TIPS due to inflation.