OLS method is based on historical data and analyzed with existing time series data, so that the results of regression analysis can better explain the relationship between spot and futures prices.
In the hedging operation, we take LLDPE as an example to analyze the optimal proportion of hedging, so that enterprises can avoid risks through hedging.
We select the data of 1 month to estimate the first-phase hedging ratio of the hedging operation plan, and get the following results:
We selected 3 months' data to estimate the hedging ratio in the second stage, and got:
We select the data of five months to estimate the hedging ratio of the third period, and get the following results:
Therefore, we can draw the following conclusions: the hedging ratio of three-stage hedging is:
In the specific operation process, according to the above conversion formula of hedging ratio and contract quantity, the purchased contracts are:
LLDPE0907 contract 10000*0.0333=333 tons about 66 contracts.
LLDPE0909 contract 8000*0. 1236=989 tons 198 contract.
LLDPE09 1 1 Contract 6000*0. 1223=734 tons 147 contract.
For the five-month data, we give a comparison chart between the predicted spot rate of return and the actual spot rate of return obtained through OLS hedging. From the figure, we can see that although the spot yield fluctuates greatly, some price fluctuations can be eliminated and the risk of price fluctuations can be reduced through OLS optimal hedging.
According to the principle of minimum variance (MV) model, suppose we have a portfolio containing LLDPE spot and futures contracts, and the positions of spot and futures in the portfolio are sum respectively, and the return rate of the portfolio can be expressed as:
In the above formula, it is the hedging ratio, that is, the variance of the hedging position on the return of the portfolio is obtained. The analytical formula of the first-order conditional optimal hedging ratio is: this is also the definition expression of dynamic hedging position. Among them,, and represent the standard deviation of spot and futures returns and their correlation coefficients respectively.