A T-Bill with a face value of $100 that will mature in one year is sold at $96 today. If you deposit $100 in a saving account, you will get $110 in three years. Calculate the term spread (%) between 3-year and 1-year rates (Is there a yield curve inversion?).
To calculate the term spread between the 3-year and 1-year rates, we need to compare the yields on the two investments. The yield on the T-Bill can be calculated using the formula:
Yield on T-Bill = (Face Value - Purchase Price) / Purchase Price
Yield on T-Bill = ($100 - $96) / $96
Yield on T-Bill = $4 / $96
Yield on T-Bill = 0.0417 or 4.17%
The yield on the saving account can be calculated using the formula:
Yield on Saving account = (Future Value - Present Value) / Present Value
Yield on Saving account = ($110 - $100) / $100
Yield on Saving account = $10 / $100
Yield on Saving account = 0.1 or 10%
The term spread is the difference between the two yields:
Term Spread = Yield on Saving account - Yield on T-Bill
Term Spread = 10% - 4.17%
Term Spread = 5.83%
Therefore, the term spread is 5.83%.
Since the yield on the 3-year saving account is higher than the yield on the 1-year T-Bill, there is no yield curve inversion. A yield curve inversion would occur if the yield on the longer-term investment is lower than the yield on the shorter-term investment.
To calculate the term spread between the 3-year and 1-year rates, we need to find the yield for each period first. The yield can be calculated using the formula:
Yield = (Face Value - Purchase Price) / Purchase Price
For the 1-year T-Bill:
Yield = ($100 - $96) / $96 = $4 / $96 = 0.0417 or 4.17%
For the 3-year savings account:
Yield = ($110 - $100) / $100 = $10 / $100 = 0.1 or 10%
The term spread is then calculated by subtracting the 1-year yield from the 3-year yield:
Term Spread = 10% - 4.17% = 5.83%
Therefore, the term spread between the 3-year and 1-year rates is 5.83%.
To determine if there is a yield curve inversion, we need to compare the short-term rates (1-year) with the long-term rates (3-year). In this case, the 3-year yield is higher than the 1-year yield. Therefore, there is no yield curve inversion.