The one-year, two-year and three-year spot rates are 5.5%, 5.1% and 4.9%, respectively.

a) What is the price of a bond with three years to maturity if the coupon rate is 4%?

What is the price of a zero-coupon bond with three years to maturity?

What is the effective interest rate for the zero-coupon bond and why are zero-coupon bonds always at a discount?

Explain briefly, without making any calculations, whether the effective interest rate for the coupon bond is higher or lower than the effective interest rate for the zero-coupon bond. Given that the expectation hypothesis holds, what does the market expect the annual spot interest rate to be in one and two years?

b) What is the duration of the zero-coupon bond mentioned above and what is the duration of a zero-coupon bond that matures in two years?

Which zero-coupon bond is most exposed to interest rate risk? Give a brief justification.

Prove that your conclusion is correct by calculating the real price change for each of the bonds, given that the effective interest rate today falls by 0.5 percentage points.

The one-year, two-year and three-year spot rates are 5.5%, 5.1% and 4.9%, respectively.

a) What is the price of a bond with three years to maturity if the coupon rate is 4%?

What is the price of a zero-coupon bond with three years to maturity?

What is the effective interest rate for the zero-coupon bond and why are zero-coupon bonds always at a discount?

Explain briefly, without making any calculations, whether the effective interest rate for the coupon bond is higher or lower than the effective interest rate for the zero-coupon bond. Given that the expectation hypothesis holds, what does the market expect the annual spot interest rate to be in one and two years?

b) What is the duration of the zero-coupon bond mentioned above and what is the duration of a zero-coupon bond that matures in two years?

Which zero-coupon bond is most exposed to interest rate risk? Give a brief justification.

Prove that your conclusion is correct by calculating the real price change for each of the bonds, given that the effective interest rate today falls by 0.5 percentage points.