Most MBA student
interns would love to work on a project like this. The results of this analysis should be a 25 to 30-page slide
presentation, which could be placed in a three-ring binder and consulted
frequently. The outline for this
presentation should follow the six main stages of an acquisition: financial
analysis, valuation, purchase price negotiation, deal structuring, financing,
and closing. Sections of this
presentation could be extracted and shown to senior managers, and the presentation
could provide the basis for negotiated tolling agreements on the plant.
(2) Quantify the
relationship between electricity prices and weather, represented by proxy as
degree-days. Alternatively, quantify
the relationship between electricity load and degree-days. Temperatures should be the single most
important determinant of electricity demand and also a significant determinant
of natural gas demand. Yet simply
regressing electricity prices or gas prices on degree-days will likely show
little or no significant explanatory power with that variable. However, by finessing the regression
equation, one of my former colleagues at Tennessee Valley Authority (TVA)
successfully derived a highly significant relationship between degree-days and
electricity prices. He was a mechanical
engineer with an extensive knowledge of statistics. He had also served as one of the founders of the Chattanooga
chapter of the heating, ventilation, and air conditioning (HVAC) professional
society. He used several tricks to get
the relationship to emerge: (1) he took the square of the degree-days variable,
rather than a linear or cubic model;
(2) for some months he measured degree-days as deviations from 50 or 55
degrees, instead of the standard 65 degrees; (3) for some months he showed a
lagged impact of degree-days on prices.
His HVAC knowledge gave him the intuition to find the degree-day impact
with each month’s price data.
This
project requires someone like Superman, who can use X-ray vision (read
statistical factor analysis) to isolate the impacts of temperature changes from
various other factors that affect electricity or gas prices. This project would combine
engineering-economics with econometrics modeling. A graduate student with a background in HVAC would be ideal. First, the temperature data needs to be
transformed to appropriate degree-day data.
Then the statistical relationship could be estimated using a flexible
functional form such as a Box-Tidwell regression or a spline.
For readers unfamiliar with Box-Tidwell
regressions, it is an econometric technique in which the data is allowed to fit
itself to a linear or nonlinear functional form. The Box-Tidwell technique extends the Box-Cox transformation of
the dependent variable to each of the separate explanatory variables
(degree-days, prices of fuels, transmission constraints if measurable,
etc.). The Box-Cox transformation of X
looks like [Xl
-1]/l
and has the interesting property that when l = 1, the functional form
is linear. As l approaches 0, the functional
form is lognormal. But when l =
3.7539, for example, the functional form is a nonlinear polynomial where X is
raised to the power 3.7539.
A professor at NCSU felt that the
Box-Tidwell regression would not be flexible enough to capture the nonlinearities
in electricity prices and degree-days.
He suggested spline curve fitting techniques would be more
appropriate. Splines are essentially
lines with multiple kinks in them to fit through as many data points as
desired.
The problem
with Box-Cox transformations and splines is that they have no economic
content. There is no economic theory
that suggests degree-days should impact electricity prices through an exponent
with value, say, 3.7539. Similarly, no
economic theory suggests the spline should have a kink here and another kink
there just to accommodate the data.
However, I would defend the use of these flexible functional form
techniques in two situations. First,
the flexible functional forms can be used to test standard linear or lognormal
econometric models for misspecification.
Second, the flexible functional forms can be useful to detect nonlinear
relationships where no economic theory has predicted the precise nature of that
relationship. To that end, raising an
explanatory variable to power 3.7539 is no better or worse than raising it to
any other exponential power. In the
absence of an economic theory to predict the nonlinear relationship, we should
follow the Latin maxim Res Ipsa Loquitur (the thing speaks for itself)
and allow the data to tells us what functional form is best.
My TVA colleague derived a
significant relationship between degree-days and electricity prices without
having to resort to Box-Tidwell transformations or cubic splines. So that illustrates one of the beauties of
financial research: two researchers
might approach the problem with different techniques, and in the end, they
could both be right! But knowing that
your competitors have figured out a way to price trades off a consistent
relationship between degree-days and electricity prices should energize firms
to investigate that relationship as well.
(3) Monte Carlo
simulations with 20 years of temperature data.
The modern era of unregulated wholesale power trading began around
1996 or 1997. Since that time, we have
had five years of quasi-competitive market clearing prices for 1997 –
2001. It would be interesting to
determine what equilibrium power prices would have prevailed under some prior
year’s weather patterns, e.g., if 1981 weather patterns had occurred in the
1999 power markets. This research
project entails collecting temperature and other weather data for a twenty-year
period, such as 1980 – 2000. Then the
weather-years from that twenty-year sample should be randomly drawn and applied
to the market dynamics of 1999 or 2000 or 2001. Of the recent deregulated wholesale trading history 1997 - 2001,
probably 2001 best represents a typical year in with new combined cycle
generating capacity, although 2002 will be even better. This Monte Carlo simulation project will
enable analysts to learn where the long-run equilibrium prices for any given
month are likely to settle.
If we take the arithmetic average price for June power in
1997 – 2001, then we will have a first approximation to the long-run equilibrium. However, imagine how much more robust the
analysis would be if instead we had 10,000 Monte Carlo simulations for
equilibrium prices based on recent market conditions for twenty years (or
thirty years for that matter) of temperature-weather patterns. This project cannot be completed unless a
firm is willing to embark on agenda item (2) and attempt to quantify the
relationship between degree-days and prices, or at least between degree-days
and load (demand). Without that
relationship, an analyst cannot determine the impact of alternative
temperature-weather patterns on the power markets.
(4) Develop a
contingent claims power option evaluation (POE) tool. Contingent claims analysis refers to a
framework developed by economists Arrow and Debreu in the 1950s, in which
market participants trade futures contracts that payoff contingent upon what
state of the world is revealed. The
state variable is exogenously determined and represents the sum total of all
the uncertainty in the model. To
translate this abstract framework into something practical for the power
trading industry, we could conceive of five separate demand and five separate
supply scenarios: very high, high,
normal, low, very low demand and supply.
These exogenously determined scenarios combine to form a 5x5 matrix
comprising 25 “states of the world” and a unique price in each element of the
matrix.
Demand
Scenarios
|
|
Very
High
|
High
|
Normal
|
Low
|
Very
Low
|
|
Very
High
|
P1
|
P6
|
P11
|
P16
|
P21
|
|
High
|
P2
|
P7
|
P12
|
P17
|
P22
|
|
Normal
|
P3
|
P8
|
P13
|
P18
|
P23
|
|
Low
|
P4
|
P9
|
P14
|
P19
|
P24
|
|
Very
Low
|
P5
|
P10
|
P15
|
P20
|
P25
|
Supply
Scenarios
Each of the five demand scenarios
will have a unique probability assigned to it; the same is true for the five
supply scenarios. For ease of
illustration, let’s assign probability 0.1 to Very High and Very Low scenarios,
probability 0.2 to High and Low scenarios, and probability 0.4 to Normal
scenarios. Then price P13 in the Normal Supply – Normal Demand state
occurs with probability 0.16, and price P18 in the Normal Supply –
Low Demand state occurs with probability 0.08.
The expected price for power is given by the sum of each of the 25
prices times its probability of occurring.
Essentially, we have reduced the
complex probability distribution over future prices to a tabular form. Note that we did not exogenously specify a
probability distribution over prices, which is a technique frequently used in
what economists refer to as partial equilibrium analysis. Instead, prices are endogenous variables in
this POE model and depend on the general equilibrium foundation of demand and
supply. Knowing the prices in future
states of the world and the probability assigned to those states is all the
information required to determine the fair value of an option. That is why option pricing theory is often
referred to as a subset of contingent claims analysis.
To see how this works in practice,
let’s suppose that we are trying to evaluate a daily-strike call option with
strike price $30/MWh. Suppose that
strike price corresponds approximately to the value of P8, which is
expected to occur in a High Demand – Normal Supply scenario. The call goes in the money when prices
exceed the strike price, i.e., when they rise above the value of P8. Increased demand or decreased supply, or a
combination of the two could cause higher equilibrium prices. These external events (very high demand and
low or very low supply) have resulting state prices of P3, P4,
P5, P9, and P10. In fact, in some cases P2 > P8, and we
would include the High Supply – Very High Demand state as well in calculating
the value of a $30/MWh strike option.
The compound probabilities (the
probability of the demand scenario times the probability of the supply
scenario) assigned to state-prices P3, P4, P5,
P9, and P10 times each of those prices, respectively,
will indicate the value of a $30/MWh strike option in this example. Let’s illustrate this point for one
element. Suppose the price (P5)
in the Very High Demand – Very Low Supply scenario is $60/MWh. That element has probability 0.1 x 0.1 =
0.01 assigned to it. That means that
particular element of the matrix will contribute $0.60 to the calculation of
the risk-neutral expected value of the option.
To that $0.60 we would add the probabilistic values associated with
state prices P3, P4, P9, P10, and possibly even P2.
Separate POE price matrices will
need to be developed for each month or monthly pair, as the case may be. Thus the matrix for July-August will have
different prices than the one for September or June. Also, separate matrices would be required by region. It should be obvious that developing and
calibrating a POE tool will be major intellectual investment by any power
trading firm. However, TVA was able to
develop a POE model for TVA-based options in less than a year and using only
1.5 full-time equivalent staff. It is
tempting to say that if a stodgy old government agency can produce such an
innovative option pricing tool, then any private firm should be able to match
that accomplishment. But TVA had a
uniquely qualified HVAC specialist, who knew statistics and how to fit
distributions around possible prices for each state in the 5x5 matrix.
For any firm ambitious enough to
develop the POE framework, the project will yield multiple spinoffs and
benefits. In the process of developing
these demand and supply scenarios, market analysts will learn from the
operations people how to classify normal, low, very low, high, and very high
load for a given month. Similarly, they
will have to learn what it means physically to have very high supply
versus high supply. Also, the
pitfalls and traps of the Black-Scholes framework will become evident, e.g.,
the assumption that prices follow a geometric Brownian motion process will seem
absurd in a general equilibrium framework where prices move in response to
shocks to external factors affecting demand and supply.
TVA has used this POE option
pricing tool to beat competitors consistently in valuing options for power to
be delivered at TVA. TVA has profited
at the expense of sophisticated shops like Enron, Southern Company, and
PG&E Energy Trading from buying or selling options. A word to the wise, TVA’s quantitative
analysts do not use the Black or Black-Scholes formulas to determine the fair
value of options, although they do use those formulas as a benchmark to figure
out what their counterparties believe about option prices.
Finally, in case it is not obvious,
agenda items (2) and (3) are helpful precursors to developing a POE model. Without some detailed knowledge of the relationship
between power prices and degree-days, it will be difficult, but not impossible,
to assign various prices into groups for High Demand, Normal Demand, Low
Demand, and other scenarios. Also, without the Monte Carlo simulations using
past weather-year histories, the analysts may not have enough data points to
form a statistical distribution and populate the Very Low and Very High entries
in the state-price matrix.
(5) Develop a
more appropriate energy trading floor risk metric. The power and natural gas trading industry’s
standard risk metric, Value-at-Risk (VaR), is a house of cards with layers of
intertwined assumptions. If we pull out
one of the cards, the whole house comes tumbling down. Most frequently, problems with VaR crop up
with computing correlations across traded positions in the portfolio: how do you compute a correlation with SOCO
off-peak prices when you have no data?
How does VaR distinguish between different positions that all have very
low price correlation to the main liquid hubs (the multicolinearity
problem)? And of course, VaR assumes
prices are normally or lognormally distributed, depending on whether the
analytic variance-covariance approach or a Monte Carlo simulation approach is used. More than enough articles have already been
written about the numerous failings of VaR, and how some firms diligently
reporting daily VaR nevertheless experienced massive trading floor losses.
Given this checkered history of
VaR, the power and gas trading industry needs to develop better risk metrics
that are tailored to power and natural gas price dynamics. In addition, the new risk metrics need to
reflect the true risk exposure from trading floor activities, not the price
movements expected on a normal day. VaR
is a misnomer, because it only reflects the losses that would be sustained
during the defined holding period under normal market conditions. But firms frequently need to liquidate
positions during extreme market conditions. It comes as little comfort to
shareholders and the Board of Directors to inform them that losses from trading
floor activities occurred because of a six-sigma or nine-sigma movement in
prices outside the ambit of VaR.
The Board wants to know what is the
Maximum Expected Loss (MEL) that the trading floor will sustain, not the
perceived loss with wishful thinking (that market conditions will be normal
when someone needs to unwind his position).
If the trading floor has bet the farm, then the risk manager needs to
report that the entire farm is at risk.
With VaR as the risk metric, the risk report would blandly and
erroneously state something like a small fraction of the value of the farm is
at risk from trading floor activities.
Betting a small fraction of the
value of the farm is not the same thing as betting the entire farm, and VaR
masks the real potential losses in a worst-case scenario. The MEL metric, which has yet to be defined,
should reflect mathematically the total capital at risk on the trading floor in
a worst-case scenario. No firm ever
went out of business from being aware of what was at risk in a worst-case
scenario. If MEL did nothing more than
capture the worst case scenario risk, then it would be a vast improvement over
VaR.
But MEL can be a better risk metric than VaR in a number of other ways.
Readers of
this newsletter may recall from the January issue an article presented detailed
information on the historical spot power price distributions for hubs such as
Cinergy or PJM. Spot market prices at
these hubs tended to fit best the Inverse Gauss, Logistic, and Pearson 5
distributions, among others. These
distributions were skewed and had more kurtosis (fatter tails) than the normal
or lognormal distributions. The first
order of business in developing a new trading floor risk metric is incorporating
these kinds of exotic, non-standard distributions for power prices. Assuming the normal and lognormal
distributions apply to energy commodity markets, even for a nonstorable
commodity such as power, certainly makes the risk easier to calculate. But we have moved beyond the days of quick
and dirty risk metrics that are easy to compute. For the future, we must strive for accurate and fully
accountable risk metrics.
A new risk
metric that can incorporate distributions like the Inverse Gauss or Logistic
has the appealing property that it will tend to get better over time. As more evidence is collected to support the
choice of a particular (non-normal) distribution, the new risk metric will be
able to adapt to it. With VaR, the user
is stuck with the unrealistic lognormal or normal distribution
assumptions. That assumption in VaR
will be a no more realistic in energy markets in 2005 than it was in 2000 or
1995. This fallacy of maintaining
unrealistic assumptions with no hope for improvement is discouraging news to
talented risk managers who take pride in their work.
If we can prove statistically that
a given month’s prices follow, say, the Beta distribution, then we ought to
have a risk metric that can utilize the Beta distribution in valuing the risk
of adverse price movements. Similarly,
as markets evolve, if the price distribution switches from Logistic to the
Extreme Value distribution, then the new risk metric will be able to reflect
that change. The VaR methodology tries to force every
asset into the same normal and lognormal framework. The VaR methodology has numerous pitfalls we want to avoid, and a
few advantages we want to incorporate, in the design of a new risk metric. On the positive side, VaR shows that risk in
one part of a portfolio will generally affect the risks associated with another
part of the portfolio.
On the negative side, VaR fails to
account for liquidity risk. Liquidity
risk is particularly important in light of the NYMEX’s decision to delist its
power futures contracts due to a lack of liquidity and trading. VaR has no mechanism to represent the lack
of liquidity; VaR simply takes the prices of all products as inputs and treats
liquid and illiquid prices alike. To
account for liquidity problems, VaR proponents recommend multiplying VaR by a
factor of 2 or 3, but this is the same ad hoc method proposed to account for
the fat tails in energy price distributions.
Maybe the scalar multiplied to VaR accounts for both liquidity risk and
kurtosis. But we can expect a new risk
metric to address liquidity risk for transactions outside the major hubs,
rather than utilize an ad hoc method such as multiplying the VaR result by 2 or
3 before reporting it.
(6) A
macroeconomic project: the relationship
between economic growth and electricity demand. Historically from 1994 - 1999, a 1% growth in United States
gross domestic product (GDP) caused approximately a 0.8% growth in national
electricity demand. More recently, electricity price forecasting
firm Cambridge Energy Research Associates (CERA) proposed in October 2001 that
a 1% growth in GDP now equates to a 0.66% growth in electricity demand. But whether the relationship between
economic growth and electricity demand has dropped from 80% to 66%, the numbers
quoted are national averages. Most
firms are interested in the electricity demand for a much smaller region or
service territory.
For example, Entergy’s territory
stretches from New Orleans to Little Rock and includes portions of Texas and
Mississippi. No government agency
collects economic growth data for a territory that stretches across state
borders. Economic growth data is
generally available at the state level, but then trying to extrapolate data for
just part of the state will be problematic.
Thus, economic growth in Entergy’s service territory must be
approximated using a weighted average of economic growth in Louisiana,
Arkansas, and Texas. The weightings
would depend on the total megawatt hours (MWh) supplied by Entergy to each
portion of a state.
Depending on the difficulty in
obtaining economic growth data for their territories, some readers be unable to
pursue this research agenda item. If
meaningful economic growth data is available for a service region, it would be
important to see how that relationship between economic growth and electricity
demand compares to a national average of 66% - 80%.
Second, the reader should confirm
that Internet usage and the related digital economy are having a negligible
effect on local electricity demand. Although at the national level the
expanding Internet is having only a slight effect on power consumption, and
economic growth remains the primary driver of electricity demand, the
Internet’s infrastructure could create small pockets of intense power demand. The Internet’s infrastructure includes
certain facilities called carrier hotels (for interconnections among
long distance carriers’ networks) and server farms (for web page
hosting) that are known to have a much higher intensity of power demand than
ordinary office buildings.
The following is one of my favorite
quotes describing this new phenomenon:
"The entire University of Washington, from stadium lights at the
football game to the Medical School, averages 31 megawatts per day. We have
data center projects in front of us [for a single building or a small group of
buildings] that are asking for 30, 40 and 50 megawatts." Bob Royer, director of communications and
public affairs at Seattle City Light, quoted in John Cook, “Server farms'
voracious appetite for electricity sparks several concerns,” Seattle
Post-Intelligencer (September 5, 2000).
Thus the
reader will want to determine whether the infrastructure of the Internet is
creating pockets of intense demand in select cities within a given trading
region. Alternatively, demand for
electricity required by the Internet may blend in with overall electricity
demand.
A) Internet
facility electricity demand: hype or
reality. A nice master's degree
thesis topic could focus in detail on experiences with electricity demand for
carrier hotels or server farms already in operation in the reader’s service
territory or trading region.
Small-scale versions of these facilities exist all across the country,
and larger-scale, multiple facilities exist in the Santa Clara -
Silicon Valley area; Seattle - Richmond, Washington area; the northern Virginia
suburbs of Washington, D.C. (nicknamed Digital Alley); and large cities such as
New York, Chicago, and Los Angeles.
A master’s
degree student at the University of California, Berkeley, completed research on
electricity demand for one such facility near Santa Clara. She concluded actual electricity demand at
that facility would be closer to 3 MW, rather than the projected 30 MW. It turns out that many of the electricity
demand forecasts for these facilities were based on a footprint of an entire
building rather than just the space where actual computer servers or network
connection equipment would operate.
Hallways, office space, stairs, and unleased and unoccupied rental space
should all be excluded from the calculation of areas requiring intense
electricity supply. According to this
student’s research the heralded intense electricity demand of Internet
facilities was mostly hype and not reality.
The
Internet infrastructure industry has suffered enormously from the economic
recession and the sharp downturn in capital expenditures for
telecommunications. The pockets of
intense demand associated with these facilities may pop up as soon as the
economy begins growing more rapidly. On
the other hand, the initial forecasts for electricity requirements for these
facilities may come from unrealistic assumptions about occupancy rates and
growth in the demand for high-speed Internet services. Electricity trading firms will want to know
whether the regions that they trade can expect a surge in demand once the
economy starts to grow, or whether they should expect the usual slow, steady
growth in electricity demand that characterized the recent past.
(7) The
relationship between risk adjusted return on capital (RAROC) and VaR limits. If a firm increases the VaR allocation for
its trading floor, how should its RAROC change? For example, if a firm increases the capital at risk from trading
floor operations from $15 million to $40 million, should the firm expect to
receive a higher, lower, or the same risk-adjusted return on that $40
million? Those who are in the business
of allocating capital reason that with more working capital, the traders ought
to be able to pursue more creative trades and achieve higher returns. However, from the traders’ perspective, it
is easier to achieve a given targeted return with 150 MW and 200 MW positions
than if those positions were scaled up to 500 or 600 MW positions. In fact, not all trades are scalable. The profits would vanish and the traders
would find they move illiquid power markets, if they tried to put on 500 MW
positions in a given month.
Thus we have a clash between the
treasury group and the traders over what is a reasonable return to expect from
trading floor operations. One of the
more comical tasks a risk manager may confront is trying to get the formula for
RAROC to kick out what return the company should expect from its trading floor. RAROC equals the trading floor’s actual dollar
return divided by VaR. Thus, if a
trading floor achieves $4.5 million in profits and its annualized VaR
allocation was $15 million, then the firm achieved a 30% RAROC. If we treat the annualized VaR allocation as
a proxy for the capital at risk, and increase this amount to $40 million, then
a $4.5 million profit translates to a RAROC of 4.5/40, or about 11%.
Nothing in the formula for RAROC
will tell senior managers what percentage return they should expect to receive
from increasing to $40 million the capital at risk allocated to the trading
floor. Unfortunately, this message
often falls on deaf ears. Some senior
managers keep insisting that if the risk analysts just play with the RAROC
formulas long enough, the risk analysts can show that with $40 million at risk,
the firm has a right to expect a return of at least 30%. In fact, the 30% return expectation was
pulled out of thin air.
The correct method to determine the
return expectation for the trading floor is to compare the firm’s alternative
investment choices. If a firm could use
$40 million to enhance or retrofit a generating plant and achieve at least a
15% return on that investment, then the firm should only allocate that capital
instead to the trading floor if it believes the trading floor will yield a
return greater than or equal to 15%.
These well-known principles of choosing among alternative investments
are so obvious that they scarcely need mention here. Yet for some reason, energy trading firms seem to stumble when it
comes to identifying the next best investment alternative.
Few firms can identify where they
would allocate capital if not to the trading floor. If firms do not have a clue about the return they can achieve
from their next-best (non-trading floor) investment, then it is not surprising
that they have to pick out of thin air the RAROC and targeted return for
trading floor operations. Everyone
would like the trading floor to be as profitable as possible. However, that does not address the issue of
what return the trading floor must achieve in order for the firm to have an
efficient allocation of capital. A
graduate student with a strong background in microeconomics and investment
theory would be excellent for this project.
The
graduate student can explain that the “more risk, more reward” relationship
depends on traders being able to invest in riskier strategies in order to meet
the higher return expectations - not just scale up the size of their existing traded
products. If the traders are restricted
to trading the exact same products under an increased capital at risk
allocation, then the traders’ expected return cannot increase with simply more
of the same. To achieve higher expected
returns, the traders need more freedom to trade a wider mix of products within
the energy sector and even to trade outside the energy sector.
For example, database software
vendor Logical Intelligent Machines (www.lim.com) has energy trading firm
clients who at times trade the S&P 500 stock index futures or soybean
futures to augment income opportunities in the energy commodities markets. It may seem strange for an energy trader to
gain expertise on non-energy products, but most traders have the knack for
trading anything with price volatility. Trading outside of the traditional
energy commodity markets raises the interesting research question of how energy
trading firms could hedge their energy commodity risk in non-energy
markets.
Hedging outside the energy markets
would be an interesting research project for either an MBA student or a finance
graduate student. However, unless the
firm’s management is willing to think outside the box and examine profit
opportunities apart from the gas, power, coal, and oil markets, then the time
and energy spent on analyzing non-energy hedges would be wasted.
Once the appropriate RAROC for the
trading floor is established by comparison to the return on the next-best
alternative investment, the RAROC should be translated into a practical month-by-month
benchmark for the traders. Monthly
benchmark performance measures are commonly used with stockbrokers and
financial advisers. Each month, a
stockbroker can tell whether his gross commissions are above or below the
company’s targeted return for him. By
showing a power or natural gas trader’s performance each month in relation to
the RAROC targeted level, a trader will know whether he needs to become more
aggressive in trading or whether his existing trade volumes are keeping him on
target.
(8) Develop marks-to-market the value of non-hub
transactions. Without exception,
every energy trading firm transacts at non-hub locations, where no observable
prices are available. In the power industry, prices have been published for
futures contracts with delivery into hubs such as Palo Verde, the
California-Oregon border, TVA, Cinergy, Entergy, and the PJM pool. However, NYMEX’s recent decision to delist
its power futures contracts may limit the number of observable prices even at
the former power futures hubs.
If finding a price at a
quasi-liquid hub is now difficult, then firms face an even tougher task in
deriving a mark for the market value of power sold into or out of non-hub
locations. Deriving a consistent
methodology for non-hub marks would be a great way to introduce a graduate
student with quantitative skills to the physical side of power and gas
trading. Some students might be tempted
to show the cost of power in a non-hub location is simply the cost of power at
a regional hub plus one or two wheels to reach the non-hub location. But non-hub prices are likely lower than
that. For example, while the cost of
wheeling power from TVA to Carolina Power and Light (CP&L) may be $4.50/MWh
and the cost of wheeling power from Cinergy to CP&L is $6.00/MWh, the actual
cost of power at CP&L is only a dollar or two higher than the hub
prices. On occasion, the price of power
delivered to CP&L may even be lower than the hubs.
In the
spring and summer of 2001, power in the Virginia-Carolinas (VACAR) region
traded at approximately a $2/MWh premium over the price of power at the TVA
futures hub. By January 2002, that
relationship had fallen apart, as the price of TVA power no longer traded at a
premium to Cinergy but was often trading at a discount to Cinergy. VACAR prices in January 2002 were close to
TVA prices, not at the $2/MWh premium observed in the prior year.
Electricity
can travel to a non-hub destination from a hub through multiple paths. In some cases due to transmission line
constraints, power prices may be more closely correlated to a hub farther away
from the destination point than to the closest hub. For example, electricity
can reach VACAR from PJM, Cinergy, or from the South through SOCO. The transmission lines connecting TVA to
CP&L have such limited capacity or availability that power rarely flows
directly east from TVA, the closest hub.
For that reason, some firms use the PJM price plus $2/MWh as a proxy for
the price of power in VACAR.
Deriving a
consistent methodology for non-hub power prices will require constant updating
of correlations in a dynamic market.
Thus, the goal of this project is not to derive a set of non-hub marks
for power transactions; the goal is to develop a consistent methodology that
can be applied daily to find calculate reasonable proxies for non-hub power
prices. The cost of wheeling power from a hub may impose an upper bound on how
far non-hub prices can deviate from the closest hub. However, risk analysts need to use reasonable marks for non-hub
prices, not the upper bound based on wheeling arbitrage. If a consistent methodology can be developed
for non-hub marking to market, then the risk analysts will be able to develop a
forward price curve for excess generation sales of plants located in non-hub
areas.
(9) The
value of merchant power generation plants (combustion turbine and
combined-cycle) as spark spread options between the gas and power forward
prices. Nearly all firms in the
power generation industry already use the binomial approximation to the spread
option value to calculate the value of their gas-fired generation assets. These plant valuations require analysts to
know the natural gas basis (the cost of getting natural gas delivered to the
plant) as well as transmission routes to sell the power from the plant to end
customers. When the spark spread is
positive, the plants are turned on to generate power. When the spread is negative, the plants are left idle. A familiarity or interest in plant heat
rates (efficiency) and option pricing theory would be helpful for this project.
The three
key inputs to the spark spread option formula are the volatility of gas, the
volatility of power, and the correlation of gas and power prices. The weakest link in any option pricing
formula involving two or more underlying assets will be the correlation
input. The Middle Offices of energy
trading firms need to defend their derivation of the inputs to the spread
option formula, particularly when this formula is used to determine the value
of expensive $300 - $700 million dollar assets. Changes in the basic assumptions of the model can have a huge
impact on decisions to invest in these assets.
These assumptions and key inputs should be documented and reviewed by
external auditors. However, it may come
as a surprise to learn that probably less than 10% of the firms in the
industry, if pressed on this issue, could justify the correlation coefficients
that they are plugging into these spread option formulas. Thus, most firms need a graduate research
assistant or their professional staff to develop quantitative data support for
their inputs to the spark spread option formula.
Even though
the spread option formula is a familiar tool for the energy risk analyst, the
power generation industry still has a few things to learn about the
formula. For example, a somewhat arcane
fact in Black-Scholes option pricing theory is that the N(d2) term,
which is the value of the cumulative normal distribution evaluated at d2,
can be interpreted as the probability that the plain vanilla call or put option
will go in the money. For the case of
merchant plants valued as spread options, the spread option formula’s N(d2)
term could be interpreted as the probability that the unit will be dispatched. This would be an excellent research topic
for a quantitative finance graduate student with a detailed knowledge of option
pricing theory.
Another
important research project relates to developing the correct option pricing
formula for gas-fired generating plants that are less than 100% reliable. Suppose a plant is 97% reliable, and 3% of
the time the plant will not start or is otherwise unavailable when needed. This fact pattern is similar, although not
identical, to a down and out option, which expires and becomes
unavailable when the price of the underlying security crosses some barrier
price. In the case of power generation
plants, the option becomes unavailable due to operational constraints with the
plant, not with price movements of the underlying commodity. Nevertheless, the same principle of down and
out options applies to power generation plants: with a particular probability, the option will not be available
for exercise.
In essence,
the value of a power plant operating with 97% reliability is 0.97 (Option A) +
0.03 (Option B), where Option A represents the value of a down and out option,
and Option B is left to the interested reader to determine. The value of a 97% reliable plant is not
merely 0.97 times the regular spread option value of the power plant, because
multiplying the spread option formula by 0.97 effectively prices a spread
option of 97% of the output of the plant, which is not the same as 100% output
with 97% probability of success.
(10) Calibrate the Energy Dispatch Model. Most electric utilities have an in-house
dispatch model utilizing the cost of generating power with alternative
fuels. This dispatch model is
calibrated to prices for the utility’s territory. The model tries to predict the next day and balance of the week
power prices so that the operations department can plan whether particular
units will be dispatched.
Unfortunately, these dispatch models often have an average absolute
error rate for price forecasts on the order of 10% or more, which is too high
to yield trading signals. Enter an
engineering graduate student with a modicum of knowledge about generating
plants and the mechanics of transmitting power across a grid. The engineering student should be given a
project to calibrate or tweak the in-house dispatch model to reduce its
absolute error rate. The benefits from
this project will be enabling the power plant portfolio managers to dispatch
units more efficiently and giving the short-term traders a more precise
forecast of local prices.
(11) Oil price analysis.
Utilities in Florida and other states own power generating plants
that can burn either gas or oil. The
Florida utilities purchase large quantities of residual oil as fuel to support
electricity generation for their native loads.
Miami-based Florida Power & Light and Tampa-based Florida Power rank
among the nation’s top three purchasers of residual oil. For any firm hoping to trade power in the
Florida market, or in other regional market where residual oil is an
economically competitive generating fuel, an analysis of residual oil prices
will help determine the profitability of their power trades. Someone should collect historical pricing
for (residual) oil and complete a statistical analysis of those prices:
characterize the distribution, determine average prices by month, look for
potential trading signals. The
statistical analysis may in turn lead to optimal oil trading strategies. A graduate student with a background in
econometrics and forecasting would be well-suited for this project.
(12) A paper (or mock) trading program. Several power trading firms have
successfully implemented a mock trading group consisting of Middle Office
staff, research staff, schedulers, and others who want to explore power
trading. The mock trading program
allows analysts to step into the shoes of traders and confront real-time
trading decisions. This paper trading
initiative -
where profits and losses are on paper only - serves several purposes:
(1) educate staff on the range of products available in the market and their
price dynamics; (2) hone trading skills of non-traders, develop in-house
quant-trader talent; (3) develop “lessons learned” on trading strategies that
can be shared with the Front Office traders.
Actual traders often dismiss mock
trading groups as completely unrealistic exercises. They would argue that junior traders do not really learn about
markets until they have experienced losses and developed the discipline to cut
their losses. These traders are
right. Mock trading does not involve
the same intensity as actual trading, and mock traders are spared sleepless
nights worrying about whether they will still have jobs if their trading
positions turn unprofitable. But
suppose the goal of the mock trading exercise is more than just simulating the
jobs of real traders. Suppose one goal
of the exercise is to teach analysts how to take the next step and turn their
technical reports into profitable trading ideas.
Sometimes those who build models
feel frustrated when the traders will not follow the recommended strategies
from their models. Unless someone tests
the models’ recommendations, no one will know whether these models yielded
profitable trading signals. A paper
trading group can implement these model-based strategies and maintain a track
record of each model’s performance.
The optimal mock trading group size
is about six people. If more than six
take part in the group, it will become difficult to achieve consensus on
particular trading strategies. Having
set up these mock trading groups at several firms, I have seen the same pattern
of enthusiasm recur. For the first two
meetings of the mock trading group, everyone feels enthusiastic and honored to
take part in the experiment. But by the
time the third meeting comes around, the group members are being pulled by
short-term deadlines in their regular work, and they start missing meetings. Eventually, the mock trading group stops
meeting, because it becomes so difficult to find a time when all six members
have time to research assigned trades and meet as a group.
Having a part-time graduate student
research assistant to follow through with the group’s proposed transactions and
investigate their profitability would have helped immensely with the “homework”
required for paper trading. Unlike
actual traders, the mock traders are still performing their full-time jobs in
addition to participating in the mock trading program. Consequently, the mock traders do not have
time to investigate the majority of ideas that surface as potential trades in
the strategy sessions. If the research
assistant could gather data and other information on proposed investment
strategies, it would enable the mock trading group to meet its goals and
continue to explore new trading strategies.
The benefits to the company from this exercise include having a
successful track record on paper or power or natural gas trading ideas,
teaching others about the lessons learned from mock trading, and honing the
knowledge and trading skills of Middle Office and analytical staff. These benefits could easily justify the
meager wages paid to a part-time graduate student to assist the group.
(13) Survey the field for best practices in
forward curve modeling and generation for commodities that have little
(gas) or no (electricity) storage capacity.
Survey the field for best practices with respect to Value-at-Risk and
newer metrics, if any, for trading floor risk. Every firm has a duty to its shareholders to investigate best
practices in the industry. Yet the
professional staff at gas and power trading firms generally do not have the
time to go to the library and read articles on the state of the art in forward
curve modeling and risk metrics.
Graduate students frequently can make the time to pursue this research,
and it will often be directly related to their studies.
(14) Develop tools to monitor the accuracy of the
forward prices and forward volatilities.
One of the tools might be a red flag that is raised whenever forward
prices or forward volatilities change by more than 10% over the previous day’s
value. Another tool would be to
visually compare graphs of today’s forward prices and volatilities with
yesterday’s and see if any outliers emerge as candidates for bad data
points. Also, firms need to determine
how many forward prices need to be randomly verified and validated each day in
order for the Middle Office to have 95% confidence that the forward prices in
aggregate are accurate and timely.
There is a formula in statistics that will tell firms how large the
daily sample of validated prices should be.
One area that will need immediate
attention is a methodology for populating forward volatilities necessary for
the spark spread valuations. Some firms
choose to use the sigma-square root of time (SST) rule to populate missing
volatility points. This rule takes the
volatilities of options today and
carries that same term structure forward by holding the SST constant. Thus as we go further out in time, the
forward volatilities become smaller, because the square root of time becomes
larger, and the combined product of volatility times the square root of time is
held constant.
The SST rule follows directly from
the Black-Scholes assumption the prices follow a geometric Brownian motion
(GBM) process. The SST rule has a
number of shortcomings most notable of which is the fact that volatilities tend
to explode in the few days immediately prior to expiration. With SSTs held constant, the square root of
time becomes very small just prior to expiration, which leads to a concomitant
jump in the volatility estimate. Of
course, the jump in volatility is not a true economic phenomenon, it is merely
an aberration of the GBM assumption and its SST rule.
Any
graduate student with a knowledge of option pricing theory and statistics could
make significant contributions by developing a process to determine that
volatilities used for marking to market are reasonable. Where necessary, the volatilities should be
adjusted to make them reflect reality.
The graduate student could also formulate volatilities for minor hubs
and non-hubs, which will be based on volatilities at hubs or other places where
power options are traded. Volatility
estimates can become stale quickly, so a process must be established to update
the volatilities on a regular basis.
Finally, the graduate student could also examine whether it is
meaningful to estimate off-peak power volatilities for base load products.
Some Middle
Office managers insist that if their portfolios contain any off-peak power
sales from generating plants, then the Middle Office must have some number - any
number -
for off-peak volatilities to perform marking to market with the spark spread
formula. These managers would argue
that plugging in even a poor estimate for off-peak volatility is better than
leaving the entry blank, but I disagree with that philosophy. Volatility estimation techniques have to be
transparent and defendable. If no data
exist on off-peak prices and therefore on off-peak volatilities, then risk
analysts should report the data limitations and not use sophistry as a
substitute for sound analysis of volatilities.
(15) Refine a regional price forecasting computer model
to develop the company’s proprietary view of power prices next month, next
quarter, in six months, and in 1-year time horizons. Virtually all electric utilities and power
marketing firms employ a regional price forecasting model, such as PROSYM or
PROMOD. These models contain very
detailed information on all the generating assets as well as the load for that
region. Invariably these models yield
price forecasts that traders do not respect, because the forecasts seem wrong
50% of the time.
Regional price forecasting models
are systems of simultaneous equations subject to constraints. These
equations are solved with linear programming algorithms and other computational
techniques well-known to operations research graduate students. An operations research graduate student
working side-by-side with the firm’s existing custodians of the regional price
forecasting model could yield valuable synergies. Together, this project team should review the merits of
alternative regional price forecasting models.
Once the best regional price forecasting model is selected, the model
should be back tested and calibrated to prices that prevailed in 2001.
Once the model is calibrated, the
project team should prepare regional price forecasts for next month, next
quarter, six months and one year out.
Then the accuracy of the model can be compared to the accuracy of the
forward markets in predicting where prices ultimately settled in
equilibrium.
(16) Provide quantitative support on derivatives
and basis trading for the natural gas traders. The items on this research agenda were tailored to the power
markets. In most firms that trade both
power and natural gas, power trading is usually given more of the firm’s resources
and support than natural gas trading.
This last research agenda item recognizes that natural gas trading has
unique products and market features that justify devoting at least one
part-time graduate student to analyze data and provide quantitative support for
natural gas trading strategies.
© Copyright 2007 by Michael A. S. Guth. All Rights Reserved.
No portion of this site, including the contents of this web page may be copied,
retransmitted, reposted, duplicated, or otherwise used without the express
written permission of Dr. Michael Guth.
Reprinted from The Risk Desk (Feb., March, April 2002) with
permission of the publisher, Scudder Publishing Group, LLC. www.scudderpublishing.com.
