Bond quesstions dirty full price Fixed income

9. A large international bank issues at par a 1½ -year $150 million bond in the Eurobond market. The bond is denominated in U.S. dollars. The coupon rate is the six-month London Interbank Offer Rate (LIBOR) plus 15 basis points (bps). The bond pays interest semi-annually and the interest payment made at the end of a period depends on the six- month LIBOR at the beginning of the period. At the time the bond is issued, six-month LIBOR is 0.75%. Note that both six-month LIBOR and the coupon spread of 15 bps are expressed as annual rates compounded semi-annually. Suppose that six-month LIBOR takes the following values over the life of the bond:

T ime f rom issuance Six-month L I B O R 6 months 0.68%

1 year 0.53% 1½ years 0.86%

(a) [8] Fill in the following table. Calculate price immediately after the coupon has been paid on a coupon date. Show your work.

T ime f rom issuance C oupon payment made to bondholde r

Pr ice of the bond

0 months 6 months

1 year 1½ years

(b) [2] nd two months after it is issued if six- month LIBOR at that time is 0.61%? (c) [2] credit worthiness has strengthened because of positions that it has taken in derivatives. As a result, the spread over six- falls from 15 bps (per annum compounded semi-annually) to 12 bps (per annum compounded semi-annually). What is the value of the bond six months from the time of issuance (immediately after the coupon has been paid) in this circumstance? 10. Consider a 20-year, 6.25% coupon semiannual-pay bond. Suppose that a financial institution buys $50 million par value of the bond and uses it as collateral to create a floater and an inverse floater. The financial institution uses a 40-60 split, that is, 40% of the collateral par value is allocated to the floater and 60% to the inverse floater. Suppose that the coupon rates are reset every six months based on the following formulas: Floater coupon rate: Reference rate + 0.5% Inverse floater coupon rate: x% - L × Reference rate