The aim of this article is to extrapolate the concepts related to portfolio management for the optimization of price adjustment clauses in service and material supply contracts.

Given that the Argentine Republic is recurrently affected by inflation, private service contracts and material supply contracts in the oil and gas industry normally include price adjustment clauses, which allow the parties to keep prices at a reasonable level for the term of the contract.

The below chart shows the Wholesale Domestic Price Index from December 2015 to June 2020 published by the INDEC (Argentina’s Bureau of Statistics, for its acronym in Spanish). This index measures the price change over time for domestic market products:

Source: INDEC (Argentina’s Bureau of Statistics)

As may be observed, the price of domestic market products has increased by 368% from December 2015 to June 2020. This data clearly shows the inflation affecting the Argentine Republic and the impact it has on market prices.

The purpose of the so-called adjustment clauses is to reasonably update the prices of contracts periodically. From the supplier’s perspective, the clauses will determine the price change over time and its resulting impact on the business’ benefits. From the purchaser’s perspective, it is essential to determine and negotiate appropriate adjustment clauses, since the prices fixed by such clauses will directly affect the company’s costs and profits.

**Price adjustment clauses**

Price adjustment clauses are tools usually used in contracts which, based on a polynomial formula, allow to adjust prices depending on the defined variables’ behavior.

The polynomial formula monitors the variables behavior during the life of the contract and the impact on prices as variables increase or decrease. The contract must clearly set forth the reference date to measure such variation.

Price adjustment clauses are related to the composition of costs for a given good or service, and for each portion of such cost it is necessary to establish a measurable variable. See below an example of a price adjustment polynomial formula for a third-party inspection contract in the oil and gas industry in Argentina:

Click here for an example of a polynomial formula for a price adjustment clause under a third-party inspection contract for the oil and gas industry in Argentina:

However, the polynomial formula is not the only component of an adjustment clause. There are other important concepts:

**Base:** date to be considered to define the variables’ base values for the calculation of the Am coefficients.

**Calculation’s periodicity:** the coefficient described above must be calculated regularly. In the oil and gas industry in Argentina, calculations are usually made monthly, quarterly or biannually. Service and material suppliers should seek monthly or quarterly adjustments, and purchasers will negotiate biannual or annual adjustments.

**Trigger events:** some adjustment clauses provide for trigger events. This means that, regardless of the agreed-upon periodicity, the Am coefficient must be calculated because of an unexpected variation of one or more variables which could not be foreseen when defining the formula and the adjustment clause. For example, a price adjustment formula will be revised every 6 months, unless the Am coefficient variation exceeds a fixed percentage (e.g. 5%). In that case, the formula will be calculated in the month in which the Am coefficient is higher or lower than 5% with respect to the last measurement, regardless of the agreed-upon periodicity.

**How may these portfolio management concepts be applied to a price adjustment clause negotiation for a service contract?**

If we know the index’s average value and volatility (Diesel oil, WDPI, ER (USD/ARS), Wages) before negotiating the weightings in a polynomial formula for coefficient calculation, any of the parties — purchaser or supplier — may create a tool which indicates the ideal weightings that should be selected.

In a negotiation, the purchaser will look for the weightings in the indexes as per an *ex-ante* analysis and the polynomial formula that results in lower average and volatility values. The other party, *i.e.* the service supplier, will try to weigh the indexes in a way that the average value resulting from the polynomial formula for the coefficient calculation is as high as possible and, like the purchaser, the supplier will seek as low volatility values as possible.

Following the same example as before, the following monthly variations of the indexes mentioned above were obtained for the last 12 months:

The following average and volatility values were obtained for each index:

**Average values:**

**Volatility:**

With this information, both the purchaser and the supplier may come up with countless combinations in the weightings of the polynomial formula for the coefficient calculation, which may result in different average and volatility values, not for each index in particular, but for the formula as a whole.

Taking the information given as example, 5000 points were displayed in the below graph for 5,000 different combinations in the polynomial formula weightings for the coefficient calculation, which consider the Diesel fuel, WDPI, ER (USD/ARS) and Wages indexes.

**5,000 different polynomial formulas:**

The graph shows the average and volatility values for each of the 5000 examples of different weightings, thanks to which an efficient set of combinations is obtained. Such set is composed by the examples that are closer to the red curve. These are efficient combinations, since they represent lower volatility values for a given average range.

Any weighting placed to the east of such red curve will be inefficient for the following reasons:

Among two weighting combinations with the same average, both the purchaser and the supplier will choose those which ensure lower risk and volatility.

We therefore designed a tool that allows the purchaser to look for index weightings in a way that the average and volatility values are as low as possible (lower red arrow), and a tool that enables the service supplier to find a suitable weighting combination in the indexes and obtain the highest average value possible, while keeping volatility as low as practicable.

It must be finally considered that the weightings may not be selected only based on the average and volatility values resulting from the polynomial formula; there must be a close relation between them and the goods or services contracted. A good approximation of the weightings in a third-party inspection contract would be 70% wages index, 20% WDPI index, 5% diesel fuel and 5% exchange rate (USD/ARS).

**How to calculate average and volatility values **

The average value for a weightings combination in a polynomial formula is obtained after multiplying each weighting by the individual index average. Click here for the formula.

For example:

Suppose that we have the following polynomial formula and we want to find its average value by using the information obtained from the individual indexes from May 2019 to May 2020.

Now the weighting of each index (5%, 20%, 5%, 70%) should be simply multiplied by the average value for each index:

**Average values:**

Therefore, the average of the weightings combination in the polynomial formula described above will be equal to:

2.0% * 5% + 2.7% * 20% + 3.6% * 5% + 3.0%*70% **= 2.92%**

Calculating the volatility of the weightings combination in a polynomial formula is a little more complex. A covariance matrix for the indexes will be necessary. The covariance matrix may be easily calculated with the Solver add-in for Microsoft Excel. The only requirement is having the monthly variations of the indexes. The below chart shows the indexes’ covariance matrix based on variations from May 2019 to May 2020.

**Covariance matrix:**

It is also necessary to obtain the volatility of the individual indexes:

**Volatility:**

The calculation of the variance of the weightings combination in a polynomial formula should be as follows:

Thus, the volatility will be equal to the square root of the result obtained from the variation formula.

Here is an example of a volatility calculation of the same polynomial formula:

By using the variance formula described above, the variance will therefore be equal to:

(5%^2 * 3.7%^2) + (20%^2 * 3.2%^2) + (5%^2 * 7.3%^2) + (70%^2 * 2.2%^2)

+ 2*5%*20%*0.03% + 2*5%*5%*0.042

+ 2*5%*70%*-0.004% + 2*20%*5%*0.063%

+ 2*20%*70%*0.005% + 2*5%*70%*0.535%

= 0.0308%; the volatility will then be equal to the square root of the variance **= 1.76%**

So, all these mathematical and statistical tools can help SCM areas to optimize, define better conditions for the contracts, and also reduce the risk and uncertainty for long-term contracts.