Question

On January 20 the 5-year GoC bond with a coupon of 1.55% was quoted at a clean price of 1,001.526 per $1,000 of par value. The GoC 1.55% bond has a January 1, 2024 maturity date.

A bond dealer purchased $1,000 par value of the bond for settlement on January 22, 2020. She would also like to finance the bond trade for 1 day (so repo the bond out for 1 day). The repo settlement date is January 23, 2020. The repo rate for a term of 1 day is 1.75%. There is no 'hair cut' on this transaction.

Using this information, what is the total money borrowed by this dealer on January 22, 2020? Be specific as it relates to all the components of the trade (accrued interest, repo term interest, total settlement value for both sides of the repo). Show all work and assume an actual/365 day count convention. Three decimal places.

Answer 1

Answer

1.55% 5 year GOC Bond Clean price as on Jan-20: $1,001.526 per $1,000. The bond matures on Jan-1, 2024. Therefore, the last interest would have been due on Jan-1, 2020.

Purchase price of the bond as of Jan-22: Clean price + Accrued interest; clean price is the price that does not include accrued interest.

Accrued interest for 21 days (between Jan-02 to Jan-22): 1000*(1.55/100)*(21/365) = $0.892

Therefore, Purchase price = $1,001.526 + $0.892 = $1,002.418.

Repo rate: 1.75%

Period of financing: 1 day

Repo interest is: $1,002.418*(1.75/100)*(1/365) = $0.048

Therefore, the total money borrowed is the market price of the bond or $1,002.418

The amount repaid is: Market price + Repo interest or $1,002.418 + $0.048 = $1,002.466.

To sum up, the:

Total money borrowed: $1,002.418

Accrued interest: $0.892

Repo interest: $0.048

Amount repaid: $1,002.466