Question

Suppose that i f​=5%(n=1), and that future short term interest rates for the next 4 years are not expected to change. The liquidity premium l n,ε for n=2,3, and 4 is 0.25%,0.35% and 0.5% respectively. Calculate i n,t for n=2,3, and 4. SHOW ALL WORK. Plot the yield curve.

Answer 1

To calculate the term interest rates, add the liquidity premium for each year to the year one short-term interest rate of 5%. For a 2-, 3-, and 4-year term, the interest rates would be 5.25%, 5.35%, and 5.5%, respectively. Plotting these on a yield curve would show an upward-sloping line.

Step-by-step explanation:

The question involves calculating the term interest rates given the expectations of the future short-term interest rates and liquidity premiums for various terms. The interest rates for years two to four can be calculated by adding the liquidity premium to the given short-term interest rate for year one, which is 5%. Following this method:

• Year 2 interest rate (f2,t): 5% + 0.25% = 5.25%
• Year 3 interest rate (f3,t): 5% + 0.35% = 5.35%
• Year 4 interest rate (f4,t): 5% + 0.5% = 5.5%

To plot the yield curve, these interest rates would be plotted on the Y-axis against the time to maturity (n=2, n=3, n=4) on the X-axis. We would expect to see an upward-sloping curve indicating higher interest rates for longer maturities given the positive liquidity premiums.