Hedging principle
In the hedging operation of treasury bond futures, investors will establish a future positions in reverse according to the spot position, with the aim of making the risk of futures and spot portfolio positions as neutral as possible. The main reasons for this operation are: first, there will be a strong correlation between futures and the spot price of the target; Second, as the expiration date of futures contracts approaches, the spot market and futures market prices tend to be consistent.
It should be noted that investors also lose the opportunity to make profits by changing the price in a favorable direction in hedging, because the profits gained in one market will be offset by the losses in another market. Therefore, hedging not only locks the risk, but also locks the profit and loss of future transactions.
Operating principles of hedging
Hedging should generally follow the principles of the same or similar target varieties, opposite trading directions, equivalent quantity and the same or similar month.
The principle of the same or similar varieties. When doing hedging transactions, the selected futures varieties should be the same as the spot varieties to be hedged. If there are no same futures varieties, the closest futures varieties should be selected for hedging. Only when the futures target and the spot price to be hedged are the same or similar, it is possible to form a close relationship between the futures price and the spot price to be hedged, and the reverse operation of the two markets can effectively avoid risks.
Reverse trading principle. Hedgers should take opposite trading behaviors in the spot and futures markets when doing hedging transactions, that is, they are in opposite trading positions in the two markets. Because futures and the corresponding spot prices move in the same direction, only by following the principle of opposite trading directions can traders lose money in one market and make profits in another market, thus achieving the goal of risk neutrality.
Principle of equivalence. The quantity equivalence here does not mean that the futures quantity is consistent with the spot quantity, but points out that the number of futures contracts needed for hedging purposes has a certain relationship with the spot quantity, and the number of futures contracts must be reasonably determined according to the spot quantity.
Same month or similar month principle. The principle of the same month or similar month means that the delivery month of the selected futures contract should be the same as or similar to the time when the trader actually buys or sells the spot in the spot market in the future. Because with the arrival of the delivery date of futures contracts, futures prices and spot prices tend to be consistent, and the profit and loss of hedging are less affected by the price difference between the ending futures and spot prices, but are completely determined by the opening futures and spot prices.
Calculation method of hedging ratio
In the process of hedging treasury bonds futures, the most important thing is to determine the hedging ratio. Hedging ratio refers to the ratio of the price change of bond spot portfolio to the price change of futures contract. Because of the different sensitivities of various bonds to interest rate changes, the relationship between the spot value of fixed-income bonds and the value of required treasury bond futures contracts is not 1: 1. Under complete hedging, the loss of spot price fluctuation caused by interest rate fluctuation should be exactly offset by future positions's profit, that is, bond portfolio price change = futures contract price change × hedging ratio.
From this, we can get: hedging ratio = bond portfolio price change/futures contract price change.
1. basis point value method
Duration of use
The above two calculation methods of hedging ratio are based on certain empirical rules.
Rule of thumb 1:
Rule of thumb 2:
The term of a futures contract is equal to the term of the cheapest deliverable national debt.
The above rule of thumb is fatally flawed. When the yield is lower than the conversion yield, the slope of the theoretical futures price curve is higher than that of the conversion price curve of the low-term national debt (CTD). Then, if the DV 0 1 given to futures contracts (dv01of CTD bonds) is lower than its actual basis value, the hedging ratio generated by the rule of thumb is too high. When the yield is higher than the conversion yield, the slope of the theoretical futures price curve is smaller than that of the conversion price curve of long-term national debt (CTD). Then, if the DV 0 1 given to futures contracts (dv01of CTD bonds) is higher than its actual basis, the hedging ratio generated by the rule of thumb is too low. When the yield is converted into the yield, the rule of thumb will lead to the discontinuous jump of futures DV0 1, and the change of one basis point may lead to great changes in the hedging ratio. However, the above shortcomings can be improved by some methods, such as DV0 1 option adjustment or beta yield.
Hedging profit and loss analysis
In the hedging of treasury bonds futures, it is inevitable to involve treasury bonds and treasury bonds futures contracts. Therefore, when analyzing the profit and loss of hedging, it is necessary to analyze the profit and loss of treasury bonds and treasury bond futures contracts respectively.
Profit and loss of national debt = net price change of national debt+interest income during the period (reinvested income including interest)-financing cost of national debt.
Profit and loss of treasury bonds futures = price change of treasury bonds futures (net price)
One assumption of the above formula is that there is no coupon payment in the hedging period.
When there is coupon payment in hedging, coupon income and capital gain cannot be directly expressed by the change of the full price of national debt in hedging. When treasury bonds are paid without coupon during the hedging period, the interest income is equal to the accrued interest increment of treasury bonds during the holding period of treasury bonds futures, that is, the coupon is multiplied by the actual holding days. When the national debt is paid with coupon during the hedging, assuming that debt interest pays it once a year, the interest income is equal to the reinvestment income of the coupon actually received plus accrued interest.
Factors affecting hedging effect
The use of treasury bonds futures to hedge treasury bonds reduces the risk of spot price changes of treasury bonds to basis risk, which greatly reduces the risk position, but the risk exposure has not yet dropped to zero, and it still faces basis risk. Therefore, the existence of basis risk affects the hedging effect.
Changes of yield difference of bonds with different maturities
If the hedger holds non-CTD bonds, then unexpected changes in the yield difference may generate profits and losses. Especially, if the yield of hedged treasury bonds decreases relative to that of CTD bonds, or the degree of decline is higher than that of CTD bonds, then the yield of treasury bonds is higher than expected, or the loss in futures trading is low, that is, the relationship between CTD bonds and hedged treasury bonds can be predicted by β estimated by historical data.
Changes in the value of delivery options
Short sellers of treasury bonds futures have the right to choose CTD bonds from a series of deliverable bonds, that is, delivery options. The core of option value change is volatility. If the actual volatility is greater than the expected volatility, the option value will rise, which will increase the income of short hedging positions. If the actual volatility is less than the expected volatility, the option value will decline, resulting in a decline in the return of short hedging positions.
Changes in repo rate
The repurchase rate of the corresponding period will lead to the change of futures price, which has nothing to do with the change of spot yield. For hedgers, if there are no measures to expose the repurchase risk, the change of repurchase interest rate in the corresponding period will become an additional source of profit and loss of hedging positions. However, China's money market lacks suitable hedging tools, which may affect the hedging effect. The rise of repo rate usually brings losses to futures bears, while its decline will benefit futures bears.
Basis risk
Basis plays a key role in hedging. Hedgers change absolute spot price risk management into relative basis risk management. In practice, perfect hedging is often difficult to achieve. This is because the basis risk may come from the following aspects: first, the assets that need to be hedged against the price risk may not be exactly the same as the underlying assets of the futures contract, so it is necessary to use cross hedging instead of direct hedging, but there are many uncertainties in the yield difference between the two markets; Second, hedgers may not be sure when to buy and sell assets; Third, the hedger may need to close the futures before the maturity month.
Therefore, in order to avoid basis risk as much as possible, hedgers should consider two factors when choosing futures contracts: one is to choose the underlying assets of futures contracts; The second is to choose the delivery month. Specifically, if the hedged assets coincide with the assets of the futures target, then the first choice is easy. In other cases, it is necessary to determine which futures contracts can be used and the price of the hedged assets is most closely related. The choice of delivery month is related to several factors. If the hedging time is consistent with the futures delivery month, the futures contract in that delivery month will be directly selected. In practice, hedgers usually choose a futures contract for delivery in the next month to avoid the instability of futures prices in the delivery month and the risk that futures bulls have to accept asset delivery when they hold contracts in the delivery month. If the hedging time does not coincide with the futures delivery month, try to choose the delivery month contract closest to the hedging time.