1) Current (annualized) US Treasury spot rates are as follows: Assuming that Z-spread is equal to 135 basis points, calculate the bonds arbitrage-free price. Show calculation

6 months-0.9%

1 year -1.0%

18 months - 1.1%

2 year -1.3%

1. If the bond is bought today at the arbitrage-free price and sold on 21 Aug 2019 at $99.30, what will be realised rate of return on bond, if no reinvestment of coupons is assumed. Show calculations

2. From the US treasury spot rates above and assuming a Z-spread of 135 basis points, calculate appropriate discount rates (implied spot rates) for this bonds cash flows. Show calculations

3. Using bond-specific spot rates you calculated in ABOVE Question 3, derive six-monthly forward rates, including six- months forward rate 6 month from now - _0.5f_0.5, six-month forward rate 12 months from now - ₁f_0.5, and six-months forward rate 18 months from now - _1.5f_0.5 for the bond. Show calculations.

4. Estimate the bonds arbitrage free price using forward rates calculated in question ABOVE Question 4 and comment on comparability of spot rate and forward rate pricing Show calculations.

5. There is another Amazon.com 2.5 year semi-annual 2% coupon paying bond in the market priced at $97.8. Using bond-specific spot rates as calculated in ABOVE Question 3 (for 0.5 year, 1 year, 1.5 year and 2 years), bootstrap 2.5-year spot rate for the bond. Show calculations