Question

1.Consider the following spot rate curve:

• 6-month spot rate: 7%.
• 12-month spot rate: 11%.
• 18-month spot rate: 14%.

What is the forward rate for a 6-month zero coupon bond issued one year from today? Equivalently, the question asks for f₁², where 1 time period consists of 6 months. Remember, like spot rates, forward rates are expressed as bond-equivalent yields.

Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

2. Consider the following spot rate curve:

• 6-month spot rate: 8%.
• 12-month spot rate: 10%.
• 18-month spot rate: 14%.

What is the forward rate for a one-year zero coupon bond issued 6 months from today? Equivalently, the question asks for f₂¹, where 1 time period consists of 6 months.

Assume semi-annual compounding. Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

Assume semi-annual compounding. Round your answer to 4 decimal places. For example if your answer is 3.205%, then please write down 0.0321.

Answer 1

1. (1 + 12 month spot rate per 6 months)^2 * (1 + 6 month rate after 1 year) = (1 + 18 month spot rate per semi annual period)^3

(1 + 5.50%)^2 * (1 + 6 month rate after 1 year) = (1 + 0.07)^3

(1 + 6 month rate after 1 year) = 1.10064

6 month rate after 1 year = 10.065% per semi annual

6 month rate after 1 year = 0.2013 (answer)

Annual basis:

(1 + 12 month spot rate ) * (1 + 6 month rate after 1 year) = (1 + 18 month spot rate )^1.5

(1 + 0.11) * (1 + 6 month rate after 1 year) = (1 + 14%)^1.5

(1 + 6 month rate after 1 year) = 1.21719 / 1.11

(1 + (6 month rate after 1 year/2)) = 1.0966

6 month rate after 1 year = 0.1931

2. (1 + 12 month spot rate per 6 months)^2 * (1 + 6 month rate after 1 year) = (1 + 18 month spot rate per semi annual period)^3

(1 + 5%)^2 * (1 + 6 month rate after 1 year) = (1 + 7%)^3

(1 + 6 month rate after 1 year) = 1.1112

6 month rate after 1 year = 11.12% per semi annual

6 month rate after 1 year = 0.2223 (answer)