Robert BoslegoThe Boslego Corp.

Winchester, Mass.

In my article on hedging management here 2 years ago (OGJ, Feb. 1, 1988), 1 discussed the major weaknesses I had identified in many hedging programs.

One weakness was the lack of a reliable, ongoing assessment of the level of price risk, and I mentioned the use of frequency distributions as a tool for developing future price probabilities (Fig. 1).

This article will focus on some of the elements of price probability analysis and why it is critical to sound hedge decision making.

Without price risk analysis, you cannot know whether, or to what extent, you should be hedged; indeed, if there is no risk, there is no reason to be hedged. There are three major dimensions to price risk: the magnitude of a potential loss (real or opportunity), the probability of a loss, and the timing of the loss.

The probability of a loss is certainly a key dimension of risk in that a small chance of a given loss is obviously a smaller risk than is a large chance of the same loss, everything else being equal. It is also essential to keep in mind that these dimensions to risk change continuously.

Therefore, risk analysis must also be an ongoing process if the hedge is to correctly reflect the risk exposure at any specific time.

### MEASURING PRICE RISK

Price risk can be measured objectively using the market's assessment, or subjectively using the company's. Because many oil producers' and refiners' crude acquisition costs or sales prices correlate with futures market prices, their price risk will generally match that indicated by futures prices.

The market's price distribution can be quantified by using the information provided by crude oil options prices. Specifically, the values that the market attaches to out-of-the-money "puts" and "calls" are a reflection of the probabilities the market is assigning to those prices.

The expiration price of any futures contract (or spread) can be thought of as a continuous distribution of prices vs. probabilities (Fig. 2). In such a distribution, the latest price at which the futures contract traded is the market's probability-weighted mean; that is, according to the market as a whole, there is a 50-50 chance of the price rising or falling (in this case from $19.93).

The price risk is how much the final price of crude is likely to diverge from the market's current assessment. For the purposes of risk analysis, it is this measure of the likely dispersion of prices that is significant,

A useful measurement of divergence is the standard deviation. One standard deviation encompasses about 68% of the area around the mean in a "normal" distribution.

Though an oil producer may be most concerned with the downside half of the price distribution as his risk, and the refiner may be most concerned with the upside half of the distribution as his risk, it is illogical for either to ignore the other side of the probability distribution in risk analysis.

The magnitude and probability of "favorable surprises" are just as important to take into account as are the potential for "unfavorable surprises." This complete distribution of prices can more usefully be described in a cumulative frequency distribution (Fig. 3). It shows the cumulative probability of the price being less than or equal to (or alternatively, greater than or equal to) each dollar value indicated.

Such assessments of the market-assigned" probabilities can be useful. For oil producers and refiners who are new to the oil futures market, they may be a better indicator than assessments they make without the benefit of experience. For any market participant, they are objective and provide a legitimate set of probabilities.

If one were to accept the market's assessment of price risk, then the hedging decision would depend mainly on the company's risk profile and the implied profitability to the company at the available futures prices.

For example, if the June 1990 crude futures price were $21.00, and the company felt that price level provided a good return vs. the upside potential and downside price risks, then it might hedge some percentage of its sales for that month at that price, depending on its hedge criteria and strategy.

If a company believed there was as much chance of higher prices as lower prices and it were risk-neutral, it would logically be 50% hedged.

For example, from the viewpoint of a crude seller, the more risk-averse and/or bearish on prices vs. the market, the greater the short hedge should be above 50% (i.e., with 100% hedged being the extreme point).

On the other hand, the more bullish and greater the appetite one had for risk, the less the short hedge should be below 50% (i.e., with 0% hedged being the other extreme). This is consistent with the observation that "partial" hedging is far more common than complete hedging.1

As an alternative or additional method, many successful companies develop their own price expectations, or subjective risk assessments. Almost all companies, however, do it intuitively rather than formally developing explicit price probabilities.

We have found that explicitly developing one's own probability distributions and updating them as they change can improve hedging decisions. It breaks down the hedging decision into steps that can permit a closer examination for objectivity, consistency, and clarity of logic.

It also provides essential output for monitoring and controlling the hedging process, as well as for evaluating and improving it.

### EXAMPLE RISK ANALYSIS

In doing your own price forecasting and risk analysis, there are several important factors to consider. A framework for discussing them is provided by an analysis for a U.S. refiner of the August 1989 gasoline/crude futures spread as a potential hedge vehicle.

Although probability distributions for a number of futures contracts and spreads were constantly being updated, we will focus on the situation as of Mar. 28, 1989. As of that date, the latest closing value (Mar. 27, 1989) of the August 1989 gasoline/crude spread was $5.85/bbl.

The recent trend in the spread had been rising, and this was the highest closing value in the life-of-contract to date. The lowest closing value had been $3.24 and the mean value of all daily closes was $4.23. Gasoline inventories as of the week ended Mar. 24, 1989 Oust released) showed a large drawdown in stocks of 4.6 million bbl to 236.6 million bbl, up 6.7 million bbl vs. the prior year.

However, in the 4 preceding weeks, gasoline demand had exceeded supplies (i.e., production plus imports) by 380,000 b/d, faster than the drawdown rate experienced during the same weeks in 1988. In fact, it was the fastest drawdown in gasoline stocks for those weeks since 1986 due to low gasoline production (i.e., the 4-week trend in production was down 5.3% vs. the same weeks in 1988).

The first factor to consider is the entire historical experience for the spreads being evaluated. This establishes general norms for comparison purposes. The use of historical frequency distributions as a tool for developing subjective probabilities is common in statistics but represents a departure from traditional technical futures price studies or the fundamental analysis that is widely done for projecting oil prices.

In a sense, it adds a "fundamental" dimension to futures price analysis and a "futures price" dimension to fundamental analysis.

In our example, for all gasoline/crude spreads up through the April 1989 future contracts, the following "analytical facts" were known about their trading history from June 1983-to- date (Fig. 4):

- The mean value of daily closes for all contracts was $3.28.
- The standard deviation was $0.53.
- The highest closing value (i.e., at expiration) was $6.72.
- The lowest closing value was $1.09.

Based on the entire history of the spread, the current spread was higher than 99+% of them.

A second important factor is seasonality; many futures prices and spreads are highly seasonal. Since gasoline/crude spreads are highest during the summer, it is important to remember that this is a summer gasoline/crude spread.

By selecting those months that are nearest to August (i.e., July, August, and September) we found that the mean value of this frequency distribution was $4.00, with a standard deviation of $0.68 (Fig. 4). The frequency distribution of August spreads alone shows that the mean is $4.10 and the standard deviation is $0.78 (Fig. 4).

The current price of $5.85 was higher than 99% of the experience for July-August-September spreads combined, and higher than about 97.5% of August-only gasoline/crude spreads.

A third important factor is the likely U.S. supply and demand situation during the relevant time period; the distribution of historical futures prices and spreads usually varies significantly as a function of these conditions.

For the August 1989 gasoline/crude spread, this meant projecting U.S. supply and demand trends for all weeks up to and including those of the week ending July 14, 1989. This is the last week for which statistics from the API would be available when the August 1989 gasoline/crude spread expired on July 20, 1989.

We also forecasted somewhat beyond the actual closing date because futures prices may behave differently if supply/demand trends can be expected to change much thereafter.

The forecasting approach we use is to project supplies and demand under the assumption that futures prices remain constant from the date on which the forecast is made. Our methodology is discussed at greater length elsewhere.2

The purpose of this approach is to discover which prices appear to be over or under-valued relative to historical values. Thus, according to our outlook, the then-existing high gasoline/crude spreads had two implications:

- That refinery utilization rates would be high in the summer and
- That the gasoline yield would also be high.

In particular, as of Mar. 28, we forecast gasoline production at 7.320 million b/d for the 4 weeks ending July 14, 1989.

### HANDLING UNCERTAINTIES

A major complication clouding projections in the spring of 1989, though, was an impending change in Rvp requirements that could have a limiting effect on U.S. gasoline production during the summer.

To deal with this uncertainty, we added a new constraint (temporarily) to our model-that gasoline production could not rise above levels previously reached for the period. Because our projections were indicating levels not previously reached, our gasoline production forecast for the period ending July 14 was constrained at 7.172 million b/d.

Another factor being discussed at the time was the effect the Rvp regulations might have on the cost of producing gasoline. However, we discounted this as ultimately irrelevant for spreads in their final month of trading-before expiration-because the commodity market ultimately does not care about the cost of production once a commodity has been produced.

As published in our forecast dated Mar. 28, 1989, our gasoline supply/demand outlook indicated ending gasoline stocks of 221.8 million bbl for the week ending July 14. Although this would be below the "average" ending gasoline stock level corresponding with the August gasoline/crude spread expiration of 226 million bbl, it would be substantially higher than the ending level of gas stocks of 209.0 million bbl in the same week in 1988.

We also knew that the August 1988 gasoline/crude spread had expired at $5.70, slightly below the current futures price for the August 1989 spread.

To develop the probability distribution further, we compiled frequency distributions under the specific conditions that we expected to combine all three of the important factors discussed earlier.

Two cases were examined. The first included all gasoline/crude spreads for July, August, and September contracts that traded when gasoline inventories were in the 215-225 million bbl range and the number of trading days remaining (i.e., before expiration of the spread contracts) was 75 or less. This was to correspond approximately with the amount of time remaining on the August 1989 spread.

We also limited the time period from July 1985 through September 1988, believing that data before that time were less important.

The mean of this conditional frequency distribution was $4.61 and the standard deviation was $0.49 (Fig. 5).

As the second case, we used the same conditions but limited the time remaining to just 22 trading days to see what the tendency was during the final month of trading. The mean of this distribution was $4.81 and the standard distribution was $0.34 (Fig. 5).

Taking into account these important factors-the entire history, seasonality, and supply/demand conditions in the relevant time period-on Mar. 28, we set a mean price expectation of $4.75 for the closing value of the spread, with a standard deviation of $0.40 (Fig. 5).

Essentially, we believed that there was about a two-thirds probability that the spread would close between $4.35 and $5.15; 1-in-6 chance it would close below $4.35; and a 1-in-6 chance it would close above $5.15.

The mean and standard deviation are specified and it is assumed that the distribution is "normal," rather than list the probabilities of each potential ending price level. This approach is flexible enough to adequately describe our outlook; for example, Fig. 6 shows how an outlook would change based on the use of three different standard deviations.

This approach also has the additional benefit of simplifying the calculations that can be done in order to realize the full benefits of this effort.3

Of course, this example involved an assessment on a specific date: Mar. 28, 1988. As previously discussed, price assessments and risk analysis must be updated continuously to take into account changes in the supply/demand forecast and changes in the time remaining.

This August gasoline/crude assessment, for example, was revised downward five times from Mar. 28-ultimately to $3.00-as conditions evolved and price expectations changed.

Based on the probability distribution as of Mar. 28, the expected monetary value of the hedge at $5.85 was $1.10. In other words, at this price level this hedge should result in a net financial benefit of $1.10 to the refiner.

In addition, the hedge significantly reduced the price risk that the refiner faced, because if the gasoline margin fell $0.50/bbl or $1.50/bbl from the then-current level, the refiner would benefit. Alternatively, if the spread increased, the refiner would lose in proportion in the futures market but gain in the wet market, assuming a constant wet/futures "basis."

This is a case in which the hedge was expected to provide the benefits both of a higher return and a lower risk.

The hedging strategy of the refiner would depend on other factors beyond the price risk analysis. For example, the refiner's risk profile and basis risk are particularly important. A major value of this sort of explicit price risk analysis, however, is that it can be evaluated separately from hedge trading results. Specifically, it allows companies to evaluate their hedge programs based not just on one particular outcome, but on whether all of the facts that could have been known at the time the assessment was made were properly considered.

Only in this way can it be determined whether the hedging decision was proper for the price risk at the time.

For those who would look it up anyway, gasoline stocks ended at 222.9 million bbl and total mogas production averaged 7.373 million b/d in the 4 weeks ending July 14. The August gasoline/crude spread averaged $3.82 over the final 4 weeks of trading, $3.24 in its final week of trading and expired at $2.82.

On Mar. 28, 1989, the market had in fact overvalued the August gasoline/crude spread vs. its ultimate value.

### REFERENCES

- Sharpe, William F., Investments, Prentice-Hall, 1985, p. 535.
- Boslego, Robert, Futures Magazine, February 1990.
- Boslego, Robert, "How options improve crude oil hedging strategies," Futures Magazine, February 1989.

*Copyright 1990 Oil & Gas Journal. All Rights Reserved.*