For the national debt strategy, arbitrage opportunities can be judged according to the implied repo rate, which has certain advantages over other methods. Investors should specifically grasp the application of implied repo rate in arbitrage strategy.
Correct understanding of implied repo rate
When it comes to implied repo rate, it is important to calculate implied repo rate and set assumptions.
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 =
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 the national debt equal to the invoice price of the national debt futures contract. 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 =
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.
Application of Implicit Repurchase Interest Rate in National Debt Strategy
As mentioned above, the so-called arbitrage is usually to buy bonds and sell the corresponding bond futures contracts, but there are different ways to grasp the arbitrage opportunities. This paper mainly judges whether there is arbitrage opportunity by the index of implied repo rate.
Usually, the bond with the highest implied repo rate is the cheapest deliverable bond. Short positions in treasury bond futures contracts can lock in the biggest gains by holding the cheapest deliverable bonds. If the implied repo rate is higher than the fund interest rate of the same period and the same term, there is an opportunity for spot arbitrage. If you borrow cash, buy the cheapest deliverable bonds at the current market interest rate, sell the corresponding treasury bond futures contracts at the conversion factor ratio, and then hold them until maturity, so that the rate of return is the implied repo rate, and finally you can get the arbitrage net rate of return by removing the interest rate of borrowed funds, namely:
Arbitrage net income =
Implicit repo rate-interest rate of funds
This paper assumes that the conversion option problem is not considered, that is, the change of the cheapest deliverable bonds on the maturity date is not considered, and the futures short sellers choose to deliver bonds that are more beneficial to them, thus obtaining a yield higher than the implied repo rate.
The theoretical price formula of treasury bond futures without considering conversion options is:
It can be seen that the existence of arbitrage opportunities can be judged by comparing the implied repo rate of the cheapest deliverable bonds with the interest rate of funds in the market at the same time. When the implied repo rate of the cheapest deliverable bonds is higher than the market capital interest rate of the same term and the same term, the actual price of treasury bonds futures is higher than the theoretical price. At this time, there is basically no room for the price of treasury bonds futures to rise, so you can short treasury bonds futures for arbitrage. When the implied repo rate of the cheapest deliverable bond is less than the market capital interest rate of the same term and the same term, the actual price of treasury bond futures is less than its theoretical price. At this time, there is still room for the price of treasury bonds futures to rise, which is not suitable for short-selling treasury bonds futures arbitrage.
To sum up, the implied repo rate of the cheapest deliverable bond is a rate of return that can be determined in advance. By comparing the implied repo rate of the cheapest deliverable bond with the market capital rate of the same term and the same term, we can judge whether there is arbitrage space, but we need to pay attention to three points in actual operation: First, the implied repo rate is the rate of return that can only be realized when the bond is held and delivered. Before the due delivery, if the basis of the national debt has been expanded to ensure the arbitrage income, it should be liquidated; Before the due delivery, if the price of treasury bonds futures rises by a large margin, there will be insufficient margin to force liquidation, and arbitrage will fail at this time. Second, in arbitrage, it is necessary to establish 1 unit of treasury bonds spot bulls and convert them into treasury bonds futures short units in order to obtain corresponding yields. In the actual implementation process, if the above position ratio cannot be established due to the limitation of the number of treasury bond futures contracts, there will be some deviation between the actual treasury bond futures price at maturity and the current futures price, resulting in some deviation between the actual yield and the implied repo rate. Thirdly, in view of the importance of liquidity in the spot market of treasury bonds, the cheapest deliverable bonds should be calculated according to the actual inquiry results in the spot market of treasury bonds.