If no interest is paid from holding to delivery, the yield formula is as follows:
Ft is the futures price at time t;
CF is the conversion coefficient;
AIt is the accrued interest at time t, and similarly AIT is the accrued interest at time t;
T is the due date.
For this formula, investors can understand it as follows: 365/(T-t) is annualized, and the rate of return is annualized; Pt+AIt is the investment cost, that is, net price+accrued interest; Ft×CF+AIT-(Pt+AIt) is the investment income during the period, that is, the futures settlement income; Ft×CF+AIT is bond purchase.
When other factors are the same, the internal rate of return of the far-month contract will be lower; Other factors being equal, the higher the futures price, the higher the yield.
skill
Implicit repo rate with interest from holding to delivery
If it is assumed that IRR can be used as the reinvestment rate for interest payment during the bond holding period, then:
IRR has the following formula to solve:
CPNi is the first interest payment during the period from holding bonds to delivery;
Ti is the time when I paid interest for the first time, which is recorded as Ti.
If it is assumed that the interest-bearing reinvestment during the bond holding period can't get any return, or no longer invests, that is, the reinvestment income is 0, then:
situation
The full price of a bond is 100 yuan, the accrued interest in the current period is 1 yuan, the accrued interest on the delivery date is 1.25 yuan, the futures price is 99 yuan, and the conversion coefficient is 1.0 1. The total number of days from the trading day to the delivery date is 44 days. What is the implied repo rate?
Implicit repo rate is also a concept of yield to maturity. Yield to maturity assumes that the rate of return on investment is the same as that of yield to maturity, so it is reasonable to assume that the rate of return on reinvestment is implicit repurchase rate in theory. However, in the real world, when the implied repo rate is relatively high, the reinvestment rate is often lower than the implied repo rate, while when the implied repo rate is relatively low, especially below 0, the reinvestment rate is often higher than the implied repo rate. Therefore, from the perspective of reinvestment rate, the implied repurchase rate may be different from the return obtained in the real market. In addition, due to the impact of delivery costs and market shocks, the actual income is lower than the implied repo rate.
If the reinvestment income is assumed to be 0, it is a cautious assumption, because the reinvestment income can generally obtain the income of reverse repurchase. A more cautious return is not expected to exaggerate the return on investment, but it may make investors miss some opportunities.
In the specific use, investors are advised to comprehensively consider the reinvestment return of funds.
How to judge CTD with implied repurchase rate?
The higher the implied repo rate, the higher the return on holding and delivering bonds. If the yield is high, it is relatively low, so it is the cheapest deliverable bond. The higher the implied repo rate, the cheaper the bond.
For example, we found that TF 1303 contract has the following deliverable bonds, and 100002 with the highest implied repo rate is the cheapest deliverable bond of TF 1303 contract (see the table below).
List of deliverable bonds