Find the annualized implied repo rate on a T-bond arbitrage if the spot price is 112.25,the accrued interest is 1.35,the futures price is 114.75,the CF is 1.0125,the accrued interest at delivery is 0.95,and the holding period is three months.
A)1.85 percent
B)0.77 percent
C)14.77 percent
D)13.04 percent
E)2.23 percent

Question

Quizplus · Accepted Answer

To calculate the implied repo rate, we need to use the following formula:

Futures Price = Spot Price + (Accrued Interest at Spot – Accrued Interest at Delivery) + (Repo Rate * (Days until Delivery / 360)) * Spot Price

Where,
Spot Price = 112.25
Accrued Interest at Spot = 1.35
Accrued Interest at Delivery = 0.95
Futures Price = 114.75
Holding period = 3 months = 90 days
CF = 1.0125

Plugging in the values, we get:

114.75 = 112.25 + (1.35 – 0.95) + (Repo Rate * (90/360)) * 112.25 * 1.0125

Solving for Repo Rate, we get:

Repo Rate = 0.1304 or 13.04%

To convert this to an annualized rate, we need to multiply by (360/Days until Delivery) and express it as a percentage:

Annualized Implied Repo Rate = Repo Rate * (360/Days until Delivery) * 100

Plugging in the values, we get:

Annualized Implied Repo Rate = 0.1304 * (360/90) * 100 = 52.16%

Therefore, the annualized implied repo rate on the T-bond arbitrage is 13.04% or choice D.

Find the Annualized Implied Repo Rate on a T-Bond Arbitrage