If interest is not paid before the delivery date of treasury bonds futures, the common calculation formula of implied repo rate is as follows:
Implicit repo rate = (invoice price-purchase price)/purchase price *(360/n)
Where n is the number of days before the delivery date.
If the interest is paid before the delivery date, the implied repo rate at this time is the financing rate that makes the forward price of treasury bonds equal to the invoice price of treasury bonds futures contracts. The relevant calculation assumes that the interest payment during the period will imply the repurchase rate for reinvestment. Assuming that there is only one interest payment before the delivery date, the implied repo rate can be calculated by the following formula:
Implicit repo rate = [(invoice price+annual interest rate /2- purchase price)/(purchase price-annual interest rate /2) ]*(360/n)
Where n is the number of days from the coupon payment date to the delivery date, and a year is calculated as 360 days.
Implicit repo rate is a lockable rate of return. At any time, investors can buy cash bonds and sell treasury bonds futures at the same time, and hold cash bonds until maturity, in which they should buy cash bonds and sell futures according to the ratio of (1: conversion coefficient) to lock in future cash flow.
Implicit repo rate is a theoretical rate of return. In the calculation, it should be assumed that for a certain number of treasury bonds long positions, the corresponding number of treasury bonds futures contracts are shorted, and the corresponding conversion factor is CF, and the interest income at any time is reinvested at the implied repo rate. Even so, investors can only get a rough rate of return because of the change of margin payment of futures contracts. When the price falls, you can get profits from short positions, which can be reinvested to increase investment income. When the price rises, the change margin will be paid, and these losses must pay the corresponding financing costs, which will lead to a decrease in the income from holding cash positions. Of course, as far as the national debt can be financed through the repurchase market, there may be offset mortgage cash flows in the repurchase agreement. In this case, the difference between the actual rate of return and the theoretical rate of return may be small.
Implicit repo rate is a theoretically lockable rate of return, but there may be some risks in actual investment. First, on the maturity date, there will be some deviation between the price of short selling treasury bonds and the final settlement price, which makes the yield obtained at this time deviate from the value calculated by the above implicit repo rate formula. But generally speaking, the final settlement price of delivery is calculated according to the weighted average of the transaction price of the whole day on the last trading day, so the settlement price of delivery will not be much different from the closing or opening price of the last trading day; Second, if we operate according to the requirements of term arbitrage, that is, after buying government bonds and shorting government bond futures contracts, the price of government bond futures will rise instead of falling. At this time, there will be insufficient margin and forced liquidation. Once this happens, investors will not be able to obtain the implied repo rate through due delivery.