Answer :
The forward rate in an Forward Rate Agreement is 3.4%.
To estimate the forward rate in a Forward Rate Agreement (FRA), we can use the concept of the futures price and the expected change in the short-term interest rate.
Eurodollar futures quote for the period between 5.1 and 5.35 years in the future: 97.3
Standard deviation of the change in the short-term interest rate in one year: 1.4% (expressed as a decimal)
The futures price represents 100 minus the annualized interest rate for the period. Therefore, the implied annualized interest rate for the Eurodollar futures is 100 - 97.3 = 2.7%.
To estimate the forward rate in an FRA, we need to consider the expected change in the short-term interest rate over the period in question. In this case, the period is 5.1 to 5.35 years.
To estimate the forward rate, we can use the formula:
Forward Rate = Futures Rate + Expected Change in Interest Rate
The expected change in the short-term interest rate can be estimated using the standard deviation provided. Assuming a normal distribution, we can use the formula:
Expected Change in Interest Rate = Standard Deviation * Square Root of Time
In this case, the time is 0.25 years (5.35 - 5.1).
Expected Change in Interest Rate = 1.4% * sqrt(0.25) = 0.7%
Now we can calculate the forward rate:
Forward Rate = 2.7% + 0.7% = 3.4%
Therefore, the estimated forward rate in the FRA would be 3.4%.
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