24 Table 7: Comparison of Returns and Cumulative Losses Using Different Averaging Periods for January 2003−March 2013 for Heating Oil

|**Parameter**|**No**<br>**averaging**|**1-0**|**3-0**|**6-0**|**9-0**|**1-1**|**3-3**|**6-3**|**9-3**|
|---|---|---|---|---|---|---|---|---|---|
|Minimum return|-0.11|-0.27|-0.24|-0.16|-0.13|-0.23|-0.21|-0.16|-0.09|
|Maximum return|0.11|0.22|0.15|0.09|0.07|0.14|0.12|0.10|0.08|
|Coefficient of<br>variation|48|7.1|5.1|3.7|2.9|5.9|4.9|3.6|2.8|
|Cumulative loss, US$ million for 10,000 bpd|n.a.|27|58|102|147|5|13|57|103|

_Sources_ : EIA 2013b and author’s calculations. _Note_ : Except for the column labeled “no averaging,” for which daily spot prices are used, all other prices are monthly average prices of spot and futures prices for no. 2 heating oil in the New York Harbor. The first number, “n,” in “n-m” stands for the number of past months for averaging prices, and the second the number, “m,” of months in the futures contracts. For example, “6-3” is the average of the past six months and the average of the next three months, taking the futures contract prices for one, two, and three months ahead. Returns = differences in logarithms of successive prices; coefficient of variation = ratio of standard deviation to average; n.a. = not applicable.

The results show that, as expected, increasing the averaging period reduces price volatility: the coefficient of variation, which is one measure of volatility, is largest when daily prices are taken with no averaging, and smallest when the prices from 12 months—the previous nine months and the next three months—are averaged. Cumulative losses increase with decreasing volatility. Inclusion of future prices, however, reduces cumulative losses markedly without sacrificing the benefit of volatility reduction. The number of months when world and domestic prices move in the opposite direction—which could be politically awkward—is also reduced substantially when futures contract prices are included. For example, adding the futures prices for the next three months to the past nine months in the averaging basket reduces the percentage of the time when world and domestic prices move in the opposite direction from 50 to 30 percent. Although not shown, adjusting prices daily rather than monthly increases volatility and decreases the cumulative loss for the same averaging period.

When there is no strong trend in the underlying international prices, smoothing schemes can operate without incurring an excessive fiscal burden for the government in the long run. Even in that case, however, the pattern of oil price changes can result in the scheme running a deficit for a lengthy period. The choice of moving average is important. The longer the moving average, the lower will be the volatility of the regulated price but the more vulnerable the scheme will be to periods of sustained price increases. There tends to be a trade-off between cumulative losses and the extent of smoothing. The incorporation of several futures prices into the moving average may help reduce volatility without incurring an additional fiscal burden. However, futures contract prices are available largely for crude oil, and much less for oil products.

Based on the belief that the economic cost of volatility could be reduced with price stabilization and other price control mechanisms, many governments tried to dampen price volatility after the first oil shock of 1973. As the U.S. experience demonstrates, however, government interventions to smooth price volatility on the world market proved costly, and were soon abandoned in a number of countries. The economic cost of oil price volatility is little researched and difficult to quantify. Recent experience suggests that no smoothing scheme in the past decade has managed to achieve substantial smoothing without a corresponding fiscal burden or taking out large loans (Kojima 2013, Table A1.1). As such, there are large opportunity costs associated with government interventions targeting significant price smoothing, and the costs and