Commercials application of computer system for short term forecast the prices of primary aluminium. Operation on forwards and optimization the hedging

Introduction

In our publications [1-4] were developed the models of commodities and base metals prices forecasting up to three months ahead using the current exchange parameters and the official statistic data of economy development in the Western countries.

Basing on analyses of relations between the market participants we created an analytical system containing four interconnected equations determining the prices, volume of trade and stocks of the metal by sellers and buyers at the market.

This system gives the opportunity to forecast these parameters for the future using its values at the current and at the past time in form of dynamic equations as function of WW statistics of economic and LME data of daily trade. The structure of the analytical system is based on Kalman`s filter of forecast.

As a result of the research it was established that price forecast could be reliable for the time in the future not more than 1-2 quarters forward as correlation links between the future prices and current fixed parameters are reducing rather fast at the time.

The analytical equations were used to forecast the average prices for the quarter, month, 8 days, 3 days and for the next day ahead as interconnected multi frequency system where at first average quarterly price is forecasted, then average monthly price as additives to forecasted quarterly value and so on till the price forecast for the next day ahead. Such approach gives the opportunity to improve substantially the accuracy of forecasting the directions of the prices which is most important for forecasting in general.

Developed analytical system is distinguished by quite high significance of the average prices forecast and their direction as it is based on a rather limited number of empirical coefficients (4-6) with their identification using large volume of daily LME and statistical data for 1985-2004.

It is concluded that the directions of the prices for the next trading day, 3 day MA, 8 day MA, 20 day MA (monthly) and 65 day MA (quarterly) are predicted correctly in 70-75% of cases.

Such results could not have received by standard econometric approach including the regression equations for price forecast which needs substantial number of empirical coefficients causing low significance of the model in monthly and quarterly prices forecasting .

However forecasts based only on the determination of average prices and their directions are not enough for any commercial application.

A new scientific approach is aiming to solve this task. .

An analytical estimation of the probability was applied in estimating, whether the price forecasted for the current trading day will be maximum or minimum for the period of three days- quarter forward. While calculating it is necessary to use only available data of accuracy of the models for forecasting average prices and average variations of daily prices. However such probability is not enough either to make commercial decisions on the date and volume of transactions.

For it the thresholds probabilities must be determined by identification of the system for the period in the past when maximum commercial profit was achieved. The relation between calculated probability and threshold value determine that estimation of maximum or minimum prices for the next day are actually significant for making commercial decisions on dates and their volumes.

Eventually a reliable system of short term price forecast for commercial application was accomplished. Such task in the sphere of commodities or base metals had not been solved earlier.

This research has allowed providing forecasting of maximum prices in relation to additional pricing at aluminium sale of manufacturers to traders. Since 1999 It has been applied [16] as well to optimize procurement and sale of physical metal to traders at LME [17].

The developed models make it possible to create computer programs for deals with 1M forwards and hedging the sales of base metals at LME securing maximum profit.

The report in brief presents the common approach to this problem and its concrete application for speculation on 1 M forwards and hedging the sales of primary aluminium at LME.

The detailed report or a computer program may be sent upon request.

Basic model provisions for speculations on 1M forwards at LME

The mathematical computer model describes the strategy of exchange transactions at purchase and sale of aluminium forwards.

The purpose of these transactions is gaining the maximum profit at limited investments and optimal risk of insufficient investment for margin variation covering.

A player deposits a pledge to the account of broker at LME and obtains a possibility to open positions – to buy forwards for metal purchase or sale (delivery) using for speculations usually 40-70% share of the pledge. This part is corresponding to limit of pledge which can be used for opening position or speculation at LME. Thus it is possible to receive the forwards for metal with total cost tending to be substantially higher than the pledge by broker used for opening these positions. It is accepted that ten percent of total cost of the metal at forwards must not exceed the pledge for opening the positions by the broker. It reduces the loss risk of the broker.

Positions can be closed before the forward prompt date (by purchasing forwards of the opposite type for the remaining period) or due to the prompt date coming.

Thus the obligations are repeatedly resold at a stock exchange of metals.

In order to gain maximum profit from transactions it is necessary to open forwards for the purchase at the minimum prices and to close them at the maximum prices. The situation for forward of sale is just the reverse – positions should be opened at maximum prices and they should be closed at the minimum ones.

At every moment the deposited funds are divided into three parts: 10% cost of opened positions (by the prices of forwards), current variation margin value and the pledge balance – free money.

Variation margin is determined by the amount of potential loss, which can occur if all positions are closed at the current LME price. If money variation increases and free money is over, then the pledge deficit occurs. This is a crucial situation, and the deficit should be immediately redeemed either by reducing the cost of the opened positions (by their closing), or by extra investments (by increasing of the funds invested). If the first option is insufficient and the second one is unacceptable, the speculation is over with the loss of all funds invested. Naturally, there must be some limited number of opened positions (limit of forwards reserve). In this case the risk of pledge deficit is reduced, but the profit from the transaction per time unit will be also reduced

Besides, the player can constantly increase the pledge at the expense of adding the capitalized profit. This technique allows either to reduce the risk of pledge deficit eventually, or to increase limit of forwards reserve, or to combine the both approaches favorably in order to maximize the allocated profit. Obviously there is an optimal risk of the pledge deficit, and its level depends on the one hand on the prices behavior and on the other hand on the accuracy of their forecasting by the player.

Hence it is reasonable to carry out optimal distribution control of the profit (allocated and left or capitalized in the pledge) and limit of pledge reserve for opening positions.

As a result, besides the control of moments and volumes of positions opening and closing, the player’s strategy should envisage two more control levels – profit distribution and limit of reserve for opening positions.

Thus, the optimal system of speculation at forwards presents a three-level hierarchic control system.

Enlarged structural scheme of the control system of the forward transactions consists of 4 functional units and it is showed in chart 1.

The received forecasts give maximum possible information on future prices, whereas this information is to be processed for making decisions on transactions of forwards opening and closing.

In order to make optimal decisions, it is necessary to know the future prices behavior, specifically the nearest maximum and minimum prices and their correlation with the price forecasted for current day.

Obviously, it is impossible to forecast for certain the dates and extremis amplitudes of prices, but they are not compulsory for optimizations on forward transaction. It is sufficient to have the information on whether the future maximums will be under the price forecasted for current day or the future minimums will be over this price.

Actually, the first situation (all future prices will be under the current day price) is favorable at opening forwards for sale and closing forwards for purchase. Similarly, the second situation (all future prices will be over the current day price) is favorable at opening forwards for purchase and closing forwards for sale.

As the price forecasting has a probability character, the adequate indicator arising from the above situations is the probability that the future maximums will be under the current day price and the probability that the future minimums will be over the current day price. For the purpose of brevity the first of them will be further referred to as the prices maximums probability and the second – as the prices minimums probability. These probabilities are calculated by the special model on the basis of the above range of average prices forecasts. This model has been made analytically on the basis of mathematical apparatus of random processes probabilities. When the maximums probability or the minimums probability is high enough (over the accepted threshold value), decision is made on opening or closing the forwards of respective types.

Unit “forward transactions control”

Solutions on forward transactions are given as recommendations for the broker to open or to close positions indicating their quantity. The recommendations are calculated by the system before the start of trade at LME using the data of trades for previous days.

For this purpose probabilities of maximums and minimums are compared with established threshold values. If the prices maximum probability is over the threshold probability, a recommendation is issued to open sale forwards and to close purchase forwards. Similarly the recommendation for prices minimum probability is formed. The number of opened and closed positions is proportional to the excess of probability over its threshold value. Besides, it is proportional to the share of the forwards current reserve out of the limit of this reserve. In principle, the threshold values are empirical and can be assessed only in the course of the system adjustment by the maximum of the profit gained at some past period.

Unit “economical model”

The main purpose of financial balance is calculation of the current balance profit, full accumulated profit, realized profit, allocated profit and control over the pledge expenditure.

Fixed profit is formed at positions closing and it is actually realized at the moment of forwards effective period expiration (prompt dates). Naturally, positions can be closed with negative profit, i.e. with losses. Profit sum from all closed positions by the current moment forms full fixed profit.

Balance-sheet profit characterizes the total financial would be result by the speculation completion at the current moment. It is equal to the total realized profit plus potential profit, which will be gained out of closing of all opened positions at the current exchange price.

At the closing of the positions the profit or losses are formed , with their values fixed really only at the dates of payments for forwards (prompt dates). The total sum of such profits (or losses) from the start of speculation forms full realized profit. At the increase of realized profit it is distributed by two parts. Some part of the profit can be excluded from the speculation and is transferred to the account of player. The other part is capitalized and is allocated to the pledge to broker for expansion of the speculation.

The value of full fixed profit is an objective characteristic of speculation results.

Unit “profit management”

Limit in reserve of open positions is common for the both forward types. It is calculated on the basis of the given pledge share meant for positions opening.

System optional adjustment and results the test of speculations on 1M forwards

Adjustment of the system parameters was carried out virtually for the maximum of the fixed profit for past rather long period of 5.6 years from May 1998 to the end of 2003. For this aim a simplified model programmed for PC was used.

Eventually we established the optimal limit of pledge used for opening position, optimal share of capitalization of realized profit and thresholds probabilities.

These optimal parameters were used for testing the system in the past.

At fig. 4 one can see the result of the test for period from January 2004 to August 2005 at initial pledge $ 1mln and capitalization 40% realized profit.

The following results by MA were produced in this test during the period of 20 months: full fixed profit 130 % per year from initial pledge, allocated profit 100 % per year from initial pledge. The system mostly is winning, but sometimes the prices change unexpectedly contrary to the forecasts and it causes the losses. Statistically the average values of full profits and its SD are equal for quarterly period. It means that it is necessary to use or test the system during the period more than one quarter in order to have positive results.

Such results represent very high efficiency of developed system for short term operations on primary aluminium forwards at LME. Nevertheless all risks can not be excluded and it is natural as it is for any game based on positive statistic. It is most important that the system gives very high average results, which can be received while using it for quite a long time (recommended for more than one quarter).

The received results of approbation of system of speculation on forwards show comprehensible accuracy of the developed forecasting models within one quarter forward at an analytical estimation of the future maxima and minimum of the prices, and also a high system efficiency with reference to speculation at a metal exchange.

There were no similar systems developed earlier.

This system is principally different from strategic speculations on commodities which are used usually by hedge funds.

The developed system is based on scientific short term price forecast, which is correct only within the quarter forward. The system does not apply any forecasts of economic development or decisions based on intuition. All recommendations are calculated by computer programs processing only actual statistic data. It gives the opportunity to open the positions of 1M forwards at LME rather often with closing positions of sale and purchase on the average in about 60 cases per year with losses only in 6 cases (10%). It provides very high fixed profit – 130% from initial pledge to broker in recalculation for a year.

Hedge funds are using different strategy. When they define the market of commodities as underestimated ( basing on current statistic of economic development and its forecasts), they are opening new positions and close it to fix profit after increasing of the prices till their estimated maximum. So it can be considered strategic playing or art based on experience and intuition.

Application the System of short term price forecast for hedging the sales of primary aluminium at LME

It is clear that hedging gives the opportunity to fix the prices of sale for producer or purchase for consumer at acceptable level securing acceptable profit.

But it is not clear when to open the positions for hedging so as to provide maximum possible profits. Usually it is solved by some intuition.

For long term hedging our system of long term price forecast can be applied. However it can give only approximate results as accuracy of estimation of the prices for the future is not enough for fixing the forward position at maximum level and depends on accuracy of initial data for the future at variation WW IP characterizing consumption and commissioning new capacities of smelters. Nevertheless long term forecast gives the probable trends of the prices with estimation of average levels of their maximum and minimum.

After it the dates of hedging with maximum possible profit can be solved in short term by application of developed system.

At speculations on 1M forwards was solved the problem of opening 1M forward position for sale or purchase and its closing before the prompt dates for securing maximum profit at speculations.

Similar system is used for hedging the sales of primary aluminium by manufacturers at LME with maximum possible profit. The developed system of short term price forecast is solving this task.

The system of price forecast helps to estimate the probability that current daily price of forwards will be the maximum during some time period ahead. However it is necessary to define the threshold probabilities to make some commercial decisions for timing and amount of the metal for hedging. This problem is solved in the way absolutely similar to opening the positions at speculation on forwards. The optimal terms of hedging can be fixed by identification the model at the past securing maximum profit from hedging in relation to average cash prices for all period.

Below are the results of optimal terms of hedging the sale of primary aluminium for producer at LME.

The developed system gives the opportunity to open the forwards of sale which with the price highly probable to be higher then any daily price within the quarter forward.

At hedging all opened forward positions of sale must be closed at prompt dates. Thus in hedging it is necessary that the prices for opening positions at forwards should be higher than the average cash prices at regular sales of metal without hedging.

It is natural that the accuracy of daily price forecast is reducing rather quickly at the time in forward. Therefore it is necessary to define optimal terms of forwards for hedging securing maximum profits.

It is obvious that at hedging by opening forward position of sale the optimal terms of forwards must be estimated by empirical tests as it depends on accuracy of the system. Such an aim can be achieved by tests during a rather long period for different forwards.

In each case it is important to establish optimal threshold probabilities for opening positions by forwards of sale corresponding to maximum profit, average difference between weighted average price of hedging and average cash prices for this period, the average annual volume of hedging and relation between the investment for hedging and annual volume of hedging the metal. Such data give the opportunity to select optimal terms of hedging securing maximum profits and minimal specific investments.

Fig. 5-9 introduces the results of test for hedging the sales of primary aluminium at LME at opening different forwards positions: 1 day, 3 day, 8 day, 22 day and 63 day.

In all cases the positions were closed by cash prices at prompt dates. For hedging the pledge to account of broker $ 550k for opening positions was used.

The tests for selecting optimal terms of hedging were made for the period in the past from July 2000 to July 2005.

For every case the optimal threshold probability for opening positions of forward was established corresponding to maximum average profit.

As example in fig. 5 the average results of annual MA at hedging using 8 day forwards are given. A simplified model was applied for it. From fig. 5 it is clear that optimal threshold probability for 8 day forwards is 0,08 and it gives the opportunity to receive maximum profit from hedging at LME and increase the prices of sale by 45 $/t.

The detailed results of backtests are given in the table and fig.8. The total profit by hedging is calculated as profit at LME minus the expenses related to hedging. Profits at LME include the expenses for commissions of broker (1/16% from all transactions).

The expenses at hedging are defined by losses of interest (5% annually) for deposit to broker and increase of working capital for additional stocks of metal ( by cash official prices).

As it is clear from received results most effective is hedging by opening positions to sale 3 days forwards as it gives the opportunity to increase by maximum the average profit by optimal hedging. This result is achieved at optimal thresholds probability 0,02. . The total profit from hedging is 27% to working capital. In this case the increase of weighted average sales at hedging to average cash prices of aluminium at LME (in absence hedging) is 18 $/t. For optimal hedging by 3 day forwards it is necessary to deposit to the account of broker as investment 5 $/t aluminium per year. Besides at this case we have minimum retio of working capital to volume of metal hedging per year (about 73 $/t/a).

The optimal results of hedging on 8 day forwards are total efficiency 24%, increase of sales by 44 $/t, specific total investments 254$/t/a.

At fig. 7, 8 are given the results of the backtest on 3 day forwards for period since July 00 till July 05.

Quite the same system can be used for hedging the sales of different commodities by opening 3-8 day forwards of sale with increase the average sales by 1-3% to average cash prices.

For optimization the purchases commodities by consumers a similar system of hedging can be used.

Rather similar to hedging we used the system for additional pricing at sales of the metal by manufacturer to trader or consumer. In this case the manufacturer has the first payment for metal by LME cash official price for the date of relies of metal and has the opportunity (during 3 month) to appoint in forward the date of additional pricing for some part of sold metal. Shall the price of additional pricing be higher than at the first payment, the manufacturer will have premium, otherwise- discount.

After using the system of price forecast and special computer program for three years it was possible to have average premium at additional pricing 40-50 $/t to average cash price for the period of pricing independently on the fact whether the prices are growing or falling.

Conclusion

1. The system has been developed for primary aluminium optimal transactions of one-month forwards at London Metal Exchange. The system is based on quantitative and qualitative forecasting of average prices up to 3 months ahead using LME daily parameters of trade (prices, stocks, futures turnover, open interest) , as well as statistic data on industrial production indices in Western countries; IP and Dow Jones indexes at USA. The price forecasting is the basis of the probability approach for determining optimal timing and volumes of transactions on one-month forwards securing maximum profits.

The system for futures transactions on one-month aluminium forwards has been optimized for maximum profits at the period of over 5 years (from 1998 till 2003).

The optimal results are provided when the pledge share 50-55% is used for opening positions, and the norm of realized profit capitalization is 40%.

The system has been tested virtually by issuance of daily recommendations to a broker for opening and closing the positions of 1M forward at LME from January 2004 to August 2005, the pledge initial volume being $1 M at capitalization realized profit 40%. As a result of the test the value of fixed profit 130% annually to the initial pledge was provided.

The produced result shows high efficiency of developed short term price forecast system .

The same system can be used for operations on forwards of any metal traded at LME.

2. The system was developed for hedging the sales of primary aluminium by manufacturers at LME. It was tested in the period of 2000-2005 and gave the opportunity to increase the sales of aluminium at LME by 19-44 $/t (1-3 % from average cash prices of primary aluminium) at opening 3-8 days forwards for sale the metal at specific total investments 73-254$/t/a. The average annual net profit from hedging at LME minus all expenses is about 25% to working capital (deposit to broker plus working capital for additional stocks of metal at forwards), at specific investments as pledge to broker 5-60 $/t metal per year.

Quite the same system can be used for hedging the sales or purchase of different commodities with increase the average sales by 1-3 % to average cash prices.

The similar system was used for additional pricing at sales of the metal by manufacturer to trader or consumer. By its terms the manufacturer has the first payment for metal by LME cash official price for the date of relies of metal and has the opportunity (during 3 months ) to appoint in forward the date of additional pricing for any part of sold metal.

Application of the system of price forecast and the special computer program made it possible to have average premium at additional pricing about 40-50 $/t.

The developed computer programs can be delivered to consumers by contract obligations.

References

[1] B.Arlyuk, M.Fiterman. A model for short and medium-term aluminium price forecasting and its commercial application for additional pricing. Aluminium, 2001, v.77, № 9, p.699-705.

[2] B..Arlyuk, M.Fiterman. Optimizations of trader strategy on the basis of primary aluminium price forecasts. Aluminium, 2002, v.78, № 1/2, p.8-14.

[3] B.Arlyuk Short term price forecasting for primary aluminium. The Conference of Metallurgists. Hamilton, August 2004.