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<title>Gas Price Volitility: Friend or Foe?</title>
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<p align="left"><font face="Arial"><strong><small>About The Author:</small></strong></font></p>
<p align="left"><font face="Arial"><!--webbot bot="HTMLMarkup" startspan --><A name=olsoinfo><!--webbot bot="HTMLMarkup" endspan --></font><font size="2">Joseph
P. Mathew is the President of Hybrid Energy Advisors, Inc. Hybrid Energy
Advisors, Inc., based in Houston, TX, </font><span lang="EN">
<font size="2">provides independent business advisory services to the
natural gas industry and related markets. Their advisory services include
business development, risk management, asset and corporate valuation and
optimization analysis, corporate, project and public finance, general
industry research and analysis, and corporate credit risk analysis.</font></span></p>
<p align="left"><font size="2">For more detail, please visit their website
at
<a href="http://www.hybrid-advisors.com/" style="color: blue; text-decoration: underline; text-underline: single">
www.hybrid-advisors.com</a> or contact Hybrid Energy Advisors, Inc.
directly by e-mail at
<a href="mailto:[email protected]" style="color: blue; text-decoration: underline; text-underline: single">
[email protected]</a> or call 713-666-9007.</font></p>
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<font SIZE="6"><p><b><br>
Gas Price Volitility:<br>
Friend or Foe?<br>
</b></font><b><i>Joseph P. Mathew<br>
President<br>
Hybrid Energy Advisors, Inc</i><span style="font-size: 12.0pt">.</span></b><strong><br>
</strong><font face="Arial" size="2">(<em>originally published by PMA OnLine
Magazine: 2003/01</em>)</font></p>
<p><font FACE="Palatino" SIZE="2"> </p>
</font>
<p class="MsoNormal">One of the most prevalent subject matters in recent
gas market articles and headlines is volatility. Although the term is
widespread, the pure definition of volatility and its relevance to the
natural gas market is sometimes misunderstood. Volatility itself is not
the prime culprit which negatively affects the market, but it is the level
of volatility and its relation to the general trend, or �average price�,
of gas that a watchful eye must be kept.</p>
<p class="MsoNormal" style="text-align:justify">If prices were low and
stable, perhaps the concept of volatility would not be as rampant an issue
in gauging the operations of a gas market participant, whether a net buyer
or a net seller. However, with the advent of deregulation, financial
contracts and new market entrants (such as traders, marketers and brokers)
from the early 1990�s to present, a much more dynamic market place has been
created. Combined with underlying market fundamentals that are causing
upward gas price pressure, volatility is something to be investigated. </p>
<p class="MsoNormal" style="text-align:justify"><b><u>What is Volatility?<br>
</u></b>Volatility, in analytical terms, is also known as a numerical
variance, or more precisely, standard deviation from a �mean� or average
price trend. It says nothing about the direction of price movement. It can
be defined in terms of nominal integers to convey orders of magnitude from a
finite mean. However, volatility is typically expressed as a percentage.
Therefore, it is not calculated using nominal price data alone, but also the
changes in those prices from one estimation period to the next expressed in
percentage terms (periodic �<i>rates of return</i>�). In the gas market,
daily price settlements are best to use when calculating volatility, as each
day can count as one estimation period and each price will count as one
observation. Analytically, the greater frequency of observations utilized
in periodic calculations, the more accurate the measurement of volatility. </p>
<p class="MsoNormal" style="text-align:justify"><b><u>Preliminary
Definitions<br>
</u></b>In its most simple form, we can define rates of return as: </p>
<p class="MsoNormal" style="text-align:justify"><b>i.) R = (P<sub>T</sub>-P<sub>t</sub>)/P<sub>t</sub></b> </p>
<p class="MsoNormal" style="text-align:justify"><i>Where</i></p>
<p class="MsoNormal" style="text-align:justify"><i>R: the periodic rate of
return<br>
P<sub>T</sub>: the current price of an asset, time period T<br>
P<sub>t</sub>: the preceding price of an asset, from time period t</i></p>
<p class="MsoNormal" style="text-align:justify">Gas prices exhibit what is
called lognormal behavior due to the simple fact that prices have no real
upside constraint, but the downside is constrained by zero, as market prices
can never go negative. Therefore, over a large sample space of prices, a
resulting random distribution (bell-shaped curve) will be skewed to the
positive around a sample mean (or �average�) price. This is the essence of
gas price lognormalcy. Although commodity prices, like stock prices, follow
a lognormal distribution over a given period of time, the <i>percentage
return</i> of such price movements <i>can</i> either be positive or
negative, approximating a more normal distribution. A log of the relative
prices (P<sub>T</sub>/P<sub>t </sub>is called the �price relative�)<b> </b>
must be calculated to effect continuous compounding of returns in the
market. This is an important fact when calculating the price of options
(the right, but not obligation, to buy or sell an asset at a specific price
in some predetermined time period) on physical and financial gas contracts.</p>
<p class="MsoNormal" style="text-align:justify">Similar to the simple rate
of return equation above, the lognormal expression of continuously
compounded returns on gas prices can be expressed as:</p>
<p class="MsoNormal" style="text-align:justify"><b>ii.) X = ln(P<sub>T</sub>/P<sub>t</sub>)<br>
<br>
</b><i>Where </i></p>
<p class="MsoNormal" style="text-align:justify"><i>X: the normal periodic
rate of return<br>
P<sub>T</sub>: the current gas settlement price, time period T<br>
P<sub>t</sub>: the preceding gas settlement price, from time period t</i></p>
<p class="MsoNormal" style="text-align:justify">To calculate the mean rate
of return for the period being evaluated, the following formula can be
used: </p>
<p class="MsoNormal" style="text-align:justify"><b>iii.) X� = ∑(X<sub>i</sub>)/n</b></p>
<p class="MsoNormal" style="text-align:justify"><i>Where <br>
<br>
X�: the mean, or average, value of all return observations X<br>
X<sub>i</sub>: one observation of periodic rate of return<br>
n: the total number of observations<br>
∑: greek symbol for �the sum of�</i></p>
<p class="MsoNormal" style="text-align:justify"><b><u>Historic Volatility<br>
</u></b>Given the continuously compounded return and the mean return
formulae for gas prices, volatility can now be addressed and defined. The
following formulae define variance and its relation to standard deviation
(which is synonymous with volatility) for an observed set of empirical price
data:</p>
<p class="MsoNormal" style="text-align:justify">Variance:</p>
<p class="MsoNormal" style="text-align:justify"><b>iv.) V = [∑(X<sub>i</sub>-X<sub>�</sub>)<sup>2</sup>]/(n)</b></p>
<p class="MsoNormal" style="text-align:justify"><i>Where <br>
<br>
V: the variance of prices observed<br>
X<sub>i</sub>: one observation of periodic rate of return<br>
X<sub>�</sub>: the mean, or average, value of all return observations X<br>
n: the total number of observations<br>
∑: greek symbol for �the sum of�</i></p>
<p class="MsoNormal" style="text-align:justify">Standard Deviation
(Volatility):</p>
<p class="MsoNormal" style="text-align:justify"><b>v.) S = SQRT{[∑(X<sub>i</sub>-X<sub>�</sub>)<sup>2</sup>]/(n)}<br>
<br>
</b><i>Where <br>
<br>
S: the standard deviation of prices observed (square root of the variance)<br>
X<sub>i</sub>: one observation of periodic rate of return<br>
X<sub>�</sub>: the mean, or average, value of all observations X<br>
n: the total number of observations<br>
∑: greek symbol for �the sum of�</i></p>
<p class="MsoNormal" style="text-align:justify">If the data being analyzed
is a large enough sample size as compared to the total data which describes
the primary variable, then no adjustment needs to be made to the above
volatility formula. However, the smaller the data sample size from the
entire amount available, an adjustment factor needs to be included (so as to
�standardize� the variance). Statistically speaking, this adjustment is
referred to as adding <i>one degree of freedom</i> to the sample. This can
be achieved by subtracting one from the total number of observations in the
sample. Thus, the sample formulae look like this:</p>
<p class="MsoNormal" style="text-align:justify">Variance (Standardized):</p>
<p class="MsoNormal" style="text-align:justify"><b>vi.) V = [∑(X<sub>i</sub>-X<sub>�</sub>)<sup>2</sup>]/(n-1)</b></p>
<p class="MsoNormal" style="text-align:justify">Standard Deviation
(Standardized):</p>
<p class="MsoNormal" style="text-align:justify"><b>vii.) S = SQRT{[∑(X<sub>i</sub>-X<sub>�</sub>)<sup>2</sup>]/(n-1)}</b></p>
<p class="MsoNormal" style="text-align:justify">So far, the equations have
dealt with generic periodic volatility, but in the financial markets and in
calculating options, volatilities follow an annualized convention. To
adjust volatility from a specific period (i.e., a daily, weekly, monthly,
quarterly or semi-annually) to an annualized basis, the following formula
must be used:</p>
<p class="MsoNormal" style="text-align:justify"><b>viii.) S<sub>A</sub> = S<sub>P</sub>*SQRT[#
periods in a year]*</b></p>
<p class="MsoNormal" style="text-align:justify"><i>Where <br>
<br>
S<sub>A</sub>: annualized volatility<br>
S<sub>P</sub>: periodic volatility (daily, weekly, monthly convention)<br>
<span style="font-size:8.0pt">*Simple algebra will allow reverse conversion,
from annual volatility to periodic volatility</span></i></p>
<p class="MsoNormal" style="text-align:justify">These standardized formulae
are most typically used in industry practice due to the fact that analysts
who calculate volatility utilize chosen periods, or samples, of data from an
entire historic data stream. The reason for this is that proper studies of
historic volatility must be evaluated concomitantly with the underlying
fundamentals observed in the market during that specific period of time.
Evaluating an average volatility over a prolonged period of time may prove
inaccurate when forecasting volatility under new economic circumstances.
Different periods of time have different underlying economic and fundamental
events that create unique periodic price movements. Examples of such
underlying fundamentals include changing regulations, storage, demand,
supply, transmission and weather. Other major economic factors such as
legislation, monetary and fiscal policy must be concurrently reviewed.</p>
<p class="MsoNormal" style="text-align:justify">A plethora of analytical
techniques, such as single, multivariate and non-linear regression, can be
used to gauge the relationship between these underlying fundamentals and
their effect on then-prevalent prices as well as on future prices (and
resulting volatility). Forecast volatilities can either be estimated
through logical extrapolation of historical analysis (<i>�forward
volatilities�</i>) or can be calculated by deduction utilizing traded
options (<i>�implied volatilities�</i>).</p>
<p class="MsoNormal" style="text-align:justify"><b><u>Implied and Forward
Volatility<br>
</u></b>Traded gas option prices are published daily and calculated using
five primary parameters*:</p>
<ul style="margin-top: 0in; margin-bottom: 0in" type="disc">
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Current Price of the underlying gas contract</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Exercise Price</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Interest Rate relative to maturity time remaining on the option</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">Time
to Maturity</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Volatility of the underlying asset</font></li>
</ul>
<p class="MsoNormal" style="text-align:justify"><i>
<span style="font-size:8.0pt">*storage costs and convenience yield
associated with physical natural gas are ignored here for simplicity</span></i></p>
<p class="MsoNormal" style="text-align:justify">These five parameters are
utilized in the Black-Scholes commodity option pricing formula. The first
four are observable, but the fifth, volatility, must be estimated. To
calculate the implied volatility of a gas contract, one can create a simple
equation using a published option price on that gas contract and the Black-Scholes
formula.</p>
<p class="MsoNormal" style="text-align:justify">On the left-hand side of the
equation is the published option price. On the right-hand side of the
equation is the Black-Scholes formula. By plugging in the four known
parameters, the volatility parameter (the sole unknown parameter remaining)
can be solved for algebraically. Since the algebra involved in such a
complex equation can be both intimidating and exhausting, the best approach
would be to solve for this parameter iteratively on a computer spreadsheet
such that there exists equality between both sides of the equation.</p>
<p class="MsoNormal" style="text-align:justify">Using a series of similar
options with successive maturities, a forward volatility curve can be
constructed. However, this term structure of volatility will only be as
protracted as option prices are liquidly traded. Therefore, most analysts
use a combination of implied and historic analysis to ascertain optimal
forward opinions on volatility.</p>
<p class="MsoNormal" style="text-align:justify"><b><u>Applying the
Volatility Formula to Gas Prices<br>
</u></b>In a market where sudden, massive price spikes or falls are
observed, periodic volatility may be high, as seen many times on sudden
changes in expectation, the release of fundamental data, observations of
unexpected weather patterns, short trading position covering and calendar
year �shoulder� months (winter-to-spring and summer-to-winter). This can
lead to critical demand-side price management using methods such as dollar
cost averaging or financial product risk management. Dollar cost averaging
is a simple method of hedging characterized by the buying or selling of
contracts spread over a predetermined period of time rather than entering a
contract for the full volume at one point in time. This method is intended
to �smooth� market-timing price risk. On the other hand, financial products
such as futures, forwards, swaps, options, or a �hybrid� of any can be
used. These types of products are also intended to protect net income,
mitigate cost oscillation and strengthen cash flows. From a supply-side
perspective, excessive volatility can wreak havoc in decisions regarding
construction of new gas exploration projects. Similar hedging mechanisms
can be utilized by suppliers to protect revenues, project returns and create
cash flow stability.</p>
<p class="MsoNormal" style="text-align:justify">Despite the incidence of
volatility in the energy market, many buyers and sellers do not hedge price
risk. In the 5-year period of 1995-1999 with respect to Henry Hub physical
gas prices, one can see that volatility averaged around 60% using formula <b>
vii</b>. This calculation utilized a mean gas price of approximately $2.10/mmbtu,
calculated using formula <b>iii</b>. If one were to compare this to another
5-year period of Henry Hub gas prices, for example 1992-1996, volatility is
around the same value. What this means is that over almost a decade, gas
price volatility was approximately 60% on an overall basis, whether looking
at the first 5 years, the latter 5 years, or the entire term.</p>
<p class="MsoNormal" style="text-align:justify">This observation does not
hold true when �slicing the pie� further. For example, recent market
prices, from the years 2000-2002, portray periods of excessively high gas
price volatility. At times, monthly price volatility was exorbitantly high
(as much as 100% or more) when annualized using formula <b>viii.</b> This
compares to two other periods of time, the winter of 1996/1997 and winter of
1998/1999. What were the similarities? The analyzed answers are inadequate
gas production and ill-equipped gas storage capacity management relative to
sudden demand surges due to unpredicted weather patterns and plant outages.
These factors were significant independent variables which increased demand
and gas price volatility. These protracted periods of high volatility could
be a foreboding message of the times to come given long-term gas supply and
delivery ambiguity.</p>
<p class="MsoNormal" style="text-align:justify">To evaluate the financial
impact of volatility on market participants, one must consider it in both a
high price environment and a low price environment.</p>
<p class="MsoNormal" style="text-align:justify"><b><u>Observations in a Low
Price Market<br>
</u></b>For the vast majority of the 1990�s, Henry Hub gas prices average
approximately $2.10/mmbtu. During this time, annualized volatility averaged
approximately 60%. Numerically, it can be suggested that with 68%
confidence, gas prices were expected to be within $0.84/mmbtu and $3.36/mmbtu
and with 95% confidence, gas prices were expected to be between $0.00/mmbtu
(gas prices can never be negative, thus lognormal) and $4.62/mmbtu. The
two-way finite difference from the mean (the absolute volatility) is $1.26/mmbtu,
in terms of order of magnitude.</p>
<p class="MsoNormal" style="text-align:justify"> </p>
<p class="MsoNormal" style="text-align:justify"><b><u>Observations in a High
Price Market<br>
</u></b>During the 2000�s, gas prices have averaged approximately $4.50/mmbtu.
Eliminating the largest spikes in prices, volatility exhibited its 10-year
historic characteristic and averaged 60%. It can be suggested that with 68%
confidence, gas prices were expected to be within $1.80/mmbtu and $7.20/mmbtu
and with 95% confidence, gas prices were expected to be between $0.00/mmbtu
and $9.90/mmbtu. The two-way finite difference from the mean (the absolute
volatility) is $2.70/mmbtu, in terms of order of magnitude.</p>
<p class="MsoNormal" style="text-align:justify">From looking at both
low-price and high-price scenarios, it is clear that general levels in price
play a significant factor in the actual dollar amount at risk when
considering an equal volatility percentage measurement. Thus, it is not the
volatility figure itself that is provocative. Rather it is the gross dollar
effect of a similar volatility measurement in either price environment that
may result in vastly different economic outcomes on a market participant�s
financial position and decision-making process.</p>
<p class="MsoNormal" style="text-align:justify">This observation shows that
natural gas supply must be abundant and fluid enough to reduce the general
level of prices in order to minimize the effect of absolute volatility on
the cost structure of a buyer and the revenue structure of the seller.
Therefore, abundant gas supply, optimal storage management and
transportation/pipeline efficiencies can not only play a key role in
minimizing general price levels, but also in reducing absolute volatility.</p>
<p class="MsoNormal" style="text-align:justify"><b><u>Observations in the
Current Gas Market<br>
</u></b>Given the proportionately small amount of storage to provide price
buffers, increasing fundamental demand, unpredictable weather patterns,
demand-driven transportation capacity constraints and the higher
unpredictability and marginal cost of procuring reliable natural gas supply,
the United States is feeling greater upward gas price pressure.</p>
<p class="MsoNormal" style="text-align:justify">This year, the Energy
Information Administration (EIA) anticipated medium-term gas prices to range
from $3.25/mmbtu to $3.50/mmbtu and long-term gas prices to be close to
$4.00/mmbtu. In analytically forecasting natural gas prices (and other
price curves, for that matter), one can assume that the gas price itself is
a �dependent� variable (dependent on the underlying fundamentals that drive
the price) and the underlying fundamentals are the �independent� variables
(that influence the dependent variable).</p>
<p class="MsoNormal" style="text-align:justify">In the spring of 2002,
Hybrid Energy Advisors, Inc. (HEAI), using such analytic techniques,
predicted Henry Hub financial gas prices, the dependent variable, to hold
between $3.35 and $4.10 through the winter months of 2002/2003 (within a 90%
confidence interval). They also estimate ten-year price forecasts of
$2.25-$2.80/mmbtu during the summer months and $3.70-$4.25/mmbtu during the
winter months (also within a 90% confidence interval). These estimates
utilize stochastic price forecasting methods with the aforementioned natural
gas fundamentals serving as the independent variables. HEAI believes that
ten-year city gate prices of gas on the West Coast and Midwest United States
will trade approximately equivalent (�flat�) to Henry Hub prices. Similarly,
they expect upper East Coast prices to trade at an approximate 45-65 basis
point (cents/mmbtu) premium to Henry Hub prices.</p>
<p class="MsoNormal" style="text-align:justify">New sources of gas and its
optimal dissemination into the market can be used to mute this upward price
pressure. Close analysis must be performed as to where this physical gas
comes from, what it will cost, what market prices will support expected
project returns and when it will be available to the market. Some sources
of new gas, each with its own unique cost structure, are projected to be
from:</p>
<ul style="margin-top: 0in; margin-bottom: 0in" type="disc">
<li class="MsoNormal" style="text-align: justify"><font face="Arial">The
United States Gulf Coast (offshore, deeper wells)</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">The
Western Canadian Sedimentary Basin</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Eastern Canada</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">The
MacKenzie Delta in Northwest Canada (Yukon Territory)</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Alaska</font></li>
<li class="MsoNormal" style="text-align: justify"><font face="Arial">
Liquified Natural Gas (LNG)</font></li>
</ul>
<p class="MsoNormal" style="text-align:justify"><b><u>Conclusion<br>
</u></b>When calculating volatility, one must do an �apples-to-apples�
comparison. That is, the analytical techniques used to calculate volatility
and create opinions about current and future volatility must be considered
in conjunction with the underlying fundamentals that were prevalent during
the estimation periods. Also, any new information regarding changes in
fundamentals must be incorporated in volatility assessments.</p>
<p class="MsoNormal" style="text-align:justify">As the market currently
heads into a higher price environment, awareness of volatility should
increase due to its greater absolute effect on financial position, given a
similar volatility measurement in a lower price environment as seen in the
1990�s.</p>
<p class="MsoNormal" style="text-align:justify">Volatility is healthy for
the market as long as it is not exorbitant. The potential for volatility is
a primary reason traders look to enter any market. There is compelling
empirical evidence by Fama, French and Roll that a market with trading
creates greater volatility than a market without trading even while
considering the discovery of new information regarding underlying
fundamentals. However, traders, marketers and brokers in the gas markets
play a critical role in creating competition, market price transparency,
liquidity and overall strength. Thus, contrary to popular current belief,
it would be a loss to the gas markets (and thus power markets) in the long
run if the merchant energy trading business disappeared.</p>
<p class="MsoNormal" style="text-align:justify">A more prudent focus would
be that on increased gas supply, demand-side management, alternative fuel
potential, optimal storage management and efficient transportation
networks. This would lead to a lower gas price environment and reduced
overall volatility, which bodes well for the residential, commercial,
industrial and power generation markets. A joint focus on improving
fundamentals with proper hedging techniques allows buyers and sellers to
prosper in a market with inherent volatility and healthy trading.</p>
<hr color="#FFFF00">
<blockquote>
<p align="left"><font face="Arial"><!--webbot bot="HTMLMarkup" startspan --><A name=olsoinfo><!--webbot bot="HTMLMarkup" endspan --></font>Joseph
P. Mathew is the President of Hybrid Energy Advisors, Inc. Hybrid Energy
Advisors, Inc., based in Houston, TX, <span lang="EN">provides independent
business advisory services to the natural gas industry and related
markets. Their advisory services include business development, risk
management, asset and corporate valuation and optimization analysis,
corporate, project and public finance, general industry research and
analysis, and corporate credit risk analysis.</span></p>
<p align="left">For more detail, please visit their website at
<a href="http://www.hybrid-advisors.com/" style="color: blue; text-decoration: underline; text-underline: single">
www.hybrid-advisors.com</a> or contact Hybrid Energy Advisors, Inc.
directly by e-mail at
<a href="mailto:[email protected]" style="color: blue; text-decoration: underline; text-underline: single">
[email protected]</a> or call 713-666-9007.</p>
</blockquote>
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