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vbnmqwertyuiopasdfghjklzxcvbnmqwertyuiopasdfghjklzxcvbnm
BACKTESTING
AUTOMATED ALGORITHMIC RULE BASED TRADING SYSTEM PERFORMANCE EVALUATION-=
GAS
ETN ROI LOOK AHEAD LAGGED MULTIPLE REGRESSION BUDGET FORECAST ANOVA &am=
p;
VARIANCE ANALYSIS HOLDOUT SAMPLE Avi and Sara Rushinek, University of Miami,
arush@mia mi.edu arushine@aol.com (305)0666-7890 8/27/2010 i |
7-20-8_DOC_G=
AS Performance Evaluation- GAS
ETN ROI LOOK AHEAD MULTIPLE REGRESSION HOLDOUT SAMPLE BUDGET FORECAST VARIA=
NCE
ANALYSIS
8-27-10_DOC_=
GAS Performance Evaluation- GAS
ETN ROI LOOK AHEAD MULTIPLE REGRESSION HOLDOUT SAMPLE BUDGET FORECAST VARIA=
NCE
ANALYSIS
BACKTESTING AUTOMATED ALGORITHMIC RULE= BASED TRADING SYSTEM PERFORMANCE EVALUATION- GAS ETN ROI LOOK AHEAD LAGGED MULTIPLE REGRESSION BUDGET FORECAST ANOVA & VARIANCE ANALYSIS HOLDOUT SAMPLE
= ;
Avi and Sara Rushinek, University of M= iami, arush@miami.edu arushine@aol.com (305)0666-7890=
BACKTESTING AUTOMATED ALGORITHMIC RULE= BASED TRADING SYSTEM PERFORMANCE EVALUATION- GAS ETN ROI LOOK AHEAD LAGGED MULTIPLE REGRESSION BUDGET FORECAST ANOVA & VARIANCE ANALYSIS HOLDOUT SAMPLE
= ;
Abstract
Programmers of automated trading syste= ms frequently omit a formal forecast, variance analysis, and adjusting entries that result from such variance analysis.&n= bsp; Furthermore, textbook authors of elementary accounting textbooks frequently reverse the signs of an accounting variance analysis, thinking t= hat omitting or reversing the arithmetic sign of a variance makes it more intuitively appealing, and easier to teach and learn.&= nbsp; Thus a favorable price variance will have a positive sign, since intuitively "favorable" and "positive" or "+"= is more appealing to the lay reader. In reality, a favorable price variance means that the firm forecasted cost exceeded the actual cost, and compared to forecast the firm saved mone= y, therefore, an adjusting credit entry has to reduce the current budgeted cos= t to the lower actual cost. This reduction, has to have a negative, "-" minus sign assigned to it,= so it reduces the overstated cost by a credit entry, bringing it down to the correct actual cost, to be presented in the financial statements. Unlike people, or human traders, m= achine automated trading systems do not have any intuition, and have to act on the correct sign of the variance. Namely, they have to perform a deduction operation on the overstated balance of the cost, due to a favorable price variance. Furthermore, most accounting textb= ook authors are using manufacturing examples of variance analysis that may not fully apply to the service industries, especially the securities trading industries, including futures, commodities, equities, fixed-income, currenc= ies, and indexes. This study illus= trates how a rule based automated international portfolio trading system may use s= uch a forecast variance analysis and its respective adjusting entry to better understand forecasting error bias of the trading system and correct it As S= oon As Possible (ASAP). This pape= r uses an example of GAS ETN converting linear & polynomial daily open functio= ns, fresh separation & significant statistical R-squared and p-values entry, exit, & stop loss swinging trade rules. The authors will test such syst= ems on commercial trading platforms such as Trade Station®, Ninja Trader®, Stock= Finder®, eSign= al®, using= mixed international securities, and brokers, such as Gain®, Trade Station®, as we= ll as in Microsoft Excel®,<= /span> in a variety of markets.*
--------------------------------------= ---------------------------------------------------------------------------= ----
* The authors have omitted some detail= s to save space and shorten the discussion, such additional details will be prov= ided by the authors upon written requests.
C:\Users\a\Documents
8-27-10_DOC_GAS Performance Evaluation= - GAS ETN ROI LOOK AHEAD MULTIPLE REGRESSION HOLDOUT SAMPLE BUDGET FORECAST VARIA= NCE
8-27-10_MHTM_GAS Performance Evaluatio= n- GAS ETN ROI LOOK AHEAD MULTIPLE REGRESSION HOLDOUT SAMPLE BUDGET FORECAST VARIA= NCE
GAS ETN CONVERTING LINEAR & POLYNO= MIAL DAILY OPEN FUNCTIONS, FRESH SEPARATION & SIGNIFICANT STATISTICAL R SQUA= RE AND P-VALUES ENTRY, EXIT, & STOP LOSS SWINGING TRADE RULES
Overview
This study develops a program trading strategy. The trading program= uses the GAS ETN fund using multiple linear regression analyses of daily open functions, as the main indicator for the entry into a 1 week holding period= of a trade. The models have a hi= gh R Square. The models need to ha= ve a significant statistical R Square and P-values for entry, exit, & stop l= oss swinging trade rules. Since t= he semiannual model is superior to the monthly linear model, it suffices to te= st the monthly linear model and assume that the statistical significance of the monthly linear model also applies to the semiannual model.
This study dev=
elops
Gas ETN Trading Rules using Linear & Polynomial Daily Open Regression
models. It forecasts using
Automated HTML (Hyper Text Markup Language) and Java Script Software
Development methods. This way=
the
software can run on any HTML Java script compatible device. Initially we developed the softwar=
e in
Microsoft Excel and then we have converted it to HTML and Java script. Exchange Traded Notes (ETNs) Gas
funds are traded securities listed by Yahoo.com. The “iPath® S&P
GSCI™ Gas Total Return Index ETN is a sub index of the S&P
GSCI™ Commodity Index. The S&P GSCI™ Gas Total Return Index
reflects the returns that are potentially available through an unleveraged
investment in the West Texas Intermediate (WTI) Gas futures contract plus t=
he
Treasury bill rate of interest that could be earned on funds committed to t=
he
trading of the underlying contracts.” as http://www.ipathetn.com/G=
AS-overview.jsp
describes it.
We can trade the fund just like stocks, except that they are not sim= ple stocks, and they represent the Crude Gas industry index. As tradable instruments, traders c= an trade them, and for this purpose the traders may want to forecast their next day values. The purpose of th= is study is to develop a method that facilitates such forecasts and trades, as well as evaluates the risk. T= his study builds several linear and polynomial models regressing Open and Close= Gas ETN values on date, and forecasting the values. These forecasts help measure the e= rrors and develop a methodology for automated, continuous quality improvement in = the trading rules. The system con= ducts testing hypotheses using ANOVA regression and residual analysis and plots, compares and contrasts various methods and concludes with some recommendati= ons.
INTRODUCTION AND LITRATURE REVIEW
Forensic Science Research Multi Discip= linary Integration of Finance, Economics, Accounting, Statistics, Forecasting and Stock Market Technical Analysis
Too frequently traders fail to integra= te a multi disciplinary approach and trading strategy. This may results in gigantic loss = and lawsuits, similar to the sub-prime wave and the investment banking home mortgage crisis of 2008. This= study tries to integrate forensic science research multi-disciplinary integration= of finance, economics, accounting, statistics, forecasting and stock market technical analysis.
We
will review some work that demonstrates such integration as it applies to t=
he
current study. A trader is tr=
ying
to design an impute control system, much like Rushinek, A. and Rushinek, S.
design an "Input Control of Accounting Information Systems,"
(September 1982), enter predictor variables, and output the forecasted rank=
ing.
Following the trader as Rushinek, A. explains has to use "Capital
Budgeting Techniques, the Payback Period, The Net Present Value, The Intern=
al
Rate of Return and Their Computer Applications," (1983) to decide whet=
her
the trade is worth it.
At
this time the trader has to develop a variance analysis, as Rushinek, A.
Next
the organizations should report the financial results, as Rushinek, A. sugg=
ests
in "Costing Aspects of Segmented Reporting and Its Contribution
Approach," (1983) produce a forecasted contribution income statement to
ensure that the revenues exceed the costs.=
In the event that the costs are too high, as Rushinek, A. and Rushin=
ek,
S. suggest apply "Cost Control Systems," (1983) make sure that the
expenses do not exceed the cash available and the expected benefits. All of these forecasted reports ha=
ve to
be segmented by trades, each trade considered a separate segment.
The
investment model is next, as Rushinek, A., Rushinek, S., Chang, L. and Most=
, K.
imply we can use "The Construction of an International Investors'
Perception Model for Corporate Published Forecasted Financial Reports for t=
he
United States, Great Britain, and New Zealand," (December 1983) even i=
f an
individual organization is not a corporation, in this case we should emulat=
e a
corporate environment, since we are dealing with the stock market, we need =
to
consider the market psychology and traders perceptions.
At
this point we are ready to allocate resources as Rushinek, A. and Rushinek,=
S.
explain in "Economic Decisions and Resource Allocation in Managerial
Accounting,"(March 1984) dedicate sufficient resources to setup a
Management Accounting Information Systems to evaluate the process for cash
management, as Rushinek, A. and Rushinek, S. explain in "Management
Accounting Information Systems," (1985), controlling the system through
standard costs, and following their alumni salaries and careers.
As
Rushinek, A. and Rushinek, S. explain use "Control Through Standard Co=
sts
and Variance Analysis," (February 1986), set up standards for new trad=
es,
and then apply variance analysis.
In
the case of a additional fund allocation to a trade, we are all familiar wi=
th
the saying “trade the trend,” as Rushinek, A. and Rushinek, S.
explains in "Additional Fund Allocation Constraints for Common Stock I=
nvestments: An Empirical Analysis of Regional
Portfolios in the Common Market and the United States," (Spring 1986)
depending on the market, whether it is in the US or outside the US, for
example.
Likewise,
we have to plan the solvency of such efforts as Rushinek, A. and Rushinek, =
S.
describe in "Using Financial Ratios to Predict Insolvency," (1987)
make sure that you do not overspend and drive the trader into insolvency.
Much
like an ERP (Enterprise Resource Planning) system, as Rushinek, A. and
Rushinek, S. describe in "Manufacturing Resource Planning Systems (MPR)
Case Study: Feature Selection System (FSS) for Microcomputer Users and
Manufacturers", (1989) we have to apply it to a business logic and cash
management to the marketplace outlook.&nbs=
p;
As we deal with Oil and Gas we deal with international trade and a
bundle of additional issues. =
As
Rushinek, A. and Rushinek, S. suggest "Multinational Transfer-Pricing
Factors: Tax, Custom Duties, Antitrust/Dumping Legislation, Inflation,
Interest, Competition, Profit/Dividend, and Financial Reporting", (198=
9)
should be used in a variety of relevant countries. For this reason we have included
multi-national issue programs in our sample. Accordingly, we should allocate the
resources, as Rushinek, A. and Rushinek, S. describe in "Economic
Decisions and Resource Allocation in Managerial Accounting", (August,
1989) match the resources to the expected revenues.
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>We are using rating and=
ranking
of trading programs much like Rushinek, A. and Rushinek, S. describe in
"Rating and Ranking Best Practices of the British Petroleum Oil Company
and the Oil & Gas Industry: Sales to Cash Forecasting Univariate Regres=
sion
Trend Analysis and Computer Modeling, (December, 1997). We are dealing with=
the
same construct but it can be with different industries, oil and gas and
industries other than Oil and Gas. <=
/span>
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>We should avoid litigat=
ions and
legal problems as we try to improve the diversity as soon as possible. Thus, the trader may be better off
trading funds, rather than the original securities to get instant
diversification and litigation cost reduction, at the same time. As Rushinek, A. and Rushinek, S. e=
xplain
in "Litigation in Pennzoil and the Petroleum Refining Industry: A
Financial Ratio Automated Peer Review Analysis of Variance Internet Software
Development” (September, 1998) compare the company to its peers to en=
sure
compliance with regulations and standards.
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>Sometime, we may use fo=
rensic
accounting as Rushinek, A. and Rushinek, S. describe in "The Role of t=
he
Forensic Accountant in Calculating the Damages Using the 'But-if Analysis i=
n a
Case of Internet Day Trader & Online Broker Misconduct Litigation",
(2001) avoid administrative misconduct as you try to improve the performanc=
e of
the trades. In the unfortunate
event that investors sue a trader, a trading company, a hedge fund or an in=
vestment
banker, such as Bear Stearns (2008) the experts may have to use the
“But-if” analysis. Use
a 'but-if' or an 'if then' analysis to evaluate a variety of alternative,
investigating potential risk of damages and recoveries in alternative tradi=
ng
strategies. What is the best =
time
period for holding the stocks, for calculating the models, etc. For example, our stock forecast mo=
del
can help improve the performance of the trader, the ROI, as well as provide
evidence that the trader has exercised due diligence in the case of unavoid=
able
and unforeseeable losses.
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>
<=
span
lang=3DEN style=3D'mso-fareast-font-family:Calibri'>
In
the event that trades have gone wrong
it is important for the traders to keep proper accounting and audit
trails as Rushinek and Rushinek demonstrate in “Rushinek, S. and Rushinek, A. "Educatio=
n,
Scheduling and Administration Related to Computer User Satisfaction: An
Interactive On-line Expert System Using Diagnostic Audit Trails Through
Telecommunication Networks." In the “International Journal Of
Applied Engineering Education”(1987). Even if the hedge fund deals with
investors they must also deal with their satisfaction much like computer us=
ers,
especially if they are also software developers as the authors of this study
are. This study demonstrates =
how to
document a trade and provide sufficient accounting reports and analysis to =
show
due diligence and care in conducting a risky trade.
Traders and
hedge fund should think of themselves as if they were training somebody, as
Rushinek and Rushinek explain in “Training Software Case Study: A Pro=
duct
Evaluation and Selection System", and "Matching Program Code
Generators to Software Developers' Needs", to review their decision ma=
king
process and improve their performance continuously. The traders and hedge=
rs
do not want to be involved with Rushinek and =
Rushinek
in “Using Experts for Detecting and Litigating Computer=
Crime” (1993) as it applies to their auto=
mated
trading programs.=
=
Much
like Rushinek. and Rushinek explain in "Project Management Software
Feature Profitability: Windows, Networks, Mainframes, Filtered Task Diagram=
s,
Schedules, and Calendars,” ( Summer 1997). An automated trading program is ba=
sically
a project management scheduling program.&n=
bsp;
The traders are scheduling entry, exit, and alternative courses of
trading actions in the stock market.
Thus they have to apply similar controls and due diligence. Like the case of Rushinek. and Rushinek of &=
#8220;Internet Fraud Auditing: A Simulated Health Care In=
dustry
Case Study”( 2000), trading has become an internet dependent
occupation base on gathering information as well as executing trades, and
avoiding frauds of all kinds. Trading the stock and fund markets is h=
ighly
dependent on an information server.
Therefore, as Rushinek and Rushinek suggest “What Makes Users Unhappy: Share-Point Team Servi=
ces
Web Server Security” (2005) are important to carry out a
successful trading plan, evaluate it and improve it.
Literature
Review of Multiple Linear and Non-linear Regression Analysis for Forecasting
Future Events
This
study deals with price and cost forecasting methodology. As Rushinek and Rushinek suggest &=
#8220;Managerial auditors' mixed cost forecasting assumpt=
ion
departure error estimates for litigation and …” in “Managerial
Auditing Journal, 1997” the forecaster may make certain assumptions t=
hat
sometimes are not perfectly met.
Such departure from the assumptions can be corrected (emeraldinsight=
.com
... Page 7. [ 291 =
] Avi
Rushinek and Sara Rushinek) by the Managerial auditors’=
mixed
cost forecasting, by assumption departure error estimates for litigation
This
article deals with “Managerial auditors’ mixed cost forecasting
assumption departure error estimates for litigation and professional liabil=
ity
risk reduction” in the “the electronic security
industry.” Our current =
study
is not limited to any industry, although, the internet industry is very clo=
se
to the electronic security industry, and the trading industry. As the article states “Manag=
erial
auditors (MAs) are frequently relying on mistaken mixed costs (MC) forecast=
ing
assumptions. Two such assumptions are that MC are linear within the relevant
range and variable costs vary proportionately with activity levels. Departu=
re
from these assumptions can lead to understating expenses, overstating profi=
ts,
and even to fraud, litigation, and mounting professional liability risk.
Develops a forecasting model of mixed cost error estimates, or error differ=
ence
(ED).
In
the current study we are dealing with error measurement and minimization.
Like another study we are
“forecasting sales and expenses” like the study about “Forecasting sales, expenses and stock market values=
by
quarterly financial statement ratio analysis” by A Rushinek, SF
Rushinek - Managerial Auditing Journal, 1995 - emeraldinsight.com.
As
this article describes “sales forecasting models…forecast stand=
ards
of sales and costs, and applies them to a budgeted financial statement vari=
ance
analysis for the EE (electronic and electrical) industry. Develops the conc=
ept
of industry base standards, integrating them into the more traditional
statistical and accounting concepts of quality control standards. Provides =
an
implementation example, and reviews possible improvements to the current
methodology and approach. Uses a similar methodology to forecast the stock
market value with some exceptions. Models sales and costs of an individual
company and an industry based largely on aggregate industry databases. For =
this
purpose, we use a multivariate linear trend regression analysis for the sal=
es
forecasting model. We define and test related hypotheses and evaluate their
significance and confidence levels. For an illustration uses the EE industry
and the APM company. Also it demonstrates a microcomputer-based Financial
Systems Ratio Analyses (FSRA) software that speeds, facilitates, and helps =
to
accomplish the stated objectives. The FSRA software uses industry financial
statement databases, computes financial ratios and builds forecasting
models,” much like the
current study.
Likewise,
the current study deals with “sales forecasting models…forecast
standards of sales and costs, and applies them to a … variance analys=
is
for the” internet and domain name auction “… industry. The
study develops the concept of industry base standards, integrating them into
the more traditional statistical and accounting concepts of quality control
standards. It provides an implementation example, and reviews possible
improvements to the current methodology and approach. We use a similar
methodology to forecast the .. value” of funds “with some
exceptions. The study models sales and costs of an individual company and an
industry based largely on aggregate industry databases. For this purpose, t=
he
study uses a multivariate linear trend regression analysis for the sales
forecasting model. We define and test related hypotheses and evaluates their
significance and confidence levels. For an illustration we use the” G=
as
funds “… industry and the” … Oil and gas…R=
21;
company.
Looking
at the Oil and Gas industry from the viewpoint of an “EDP auditors' role in evaluating computerized accou=
nting
information systems efficiency by queuing, …=
” as Rushinek &
Rushinek explain ( Proceedings of the fourteenth
SIGCSE technical symposium on …, 1983 - portal.acm.org)=
“...<=
/b>
scant at this point to forecast which routines” optimizes t=
he
objective of stocks or funds seller or buyer. An “EDP (Electronic Data Processing)
auditors' role in evaluating computerized accounting information systems
efficiency by queuing, simulation and statistical models” will include
risk assessment. Just like a =
trader
that schedule trades based on a plan, so do auditor of accounting systems.<=
span
style=3D'mso-spacerun:yes'> This risk assessment is the focus =
of the
present study with an X Coefficient representing the risk of suboptimal
selection of the type of auction for domain name sales. The risk of sub-optimizing the auc=
tion
type equal to the X Coefficient for 1 domain name selling price (http://doi.acm.org/10.1145/952978.801048).
“This study is a summary of the various relevant aspects related to
evaluating system efficiency in computerized accounting information systems.
During recent years a vast body of knowledge central to the problem of comp=
uter
performance evaluation has accumulated. Unfortunately, however, the work on=
the
subject demonstrates enormous disparity.
On the one ha=
nd, one
finds numerous reports and documents that present masses of empirical data
obtained from measurement or simulation. On the other hand, theoretical pap=
ers
are, more often than not, couched in advanced mathematics, not easily
accessible to engineers and/or Electronic Data Processing (EDP) Auditors. A=
mong
a number of mathematical disciplines related to system modeling, “que=
uing
model,”“simulation method,” and “statistical
analysis” are the most important quantitative techniques. This paper
provides a cohesive introduction to the modeling and analysis techniques for
evaluating system efficiency. These techniques will certainly be applicable=
to
modeling activities of complex systems in general, and not merely computer
systems.” Likewise, the
current study develops a statistical model for cost forecasting of recovery=
for
the traders that need to apply a hold out sample methodology and a look ahe=
ad
forecasting model with risk assessment, built into an accounting and report=
ing
system.
In “The=
control
of computerized information relating to branch manpower management follow-up
systems for banks Source ACM =
SIGCPR
Computer Personnel archive,” (Volume 12 , Issue 1 (April 1989) Pages: 1 - 12 Year of
Publication: 1989 ISSN:0160-2497) A. Rushinek S. Rushinek (Publisher ACM
Exchange Traded Notes
As Wikipedia, the free encyclopedia (http://en.wikipedia.org/wiki/Exchange_Traded_Not=
es)
explains as follows:”Jump to: navigation,
Exchange Traded Notes (ETNs)= are senior, unsecured, unsubordinated debt securities issued by an underwriting bank. Similar t= o other debt securities, ETNs have a maturity date and are backed only by the credi= t of the issuer.
ETNs are designed to provide investors= access to the returns of various market benchmarks. The returns of ETNs are usually linked to the performance of a market benchmark or strategy, less investor fees. When an investor buys an ETN, the underwriting bank promises to pay t= he amount reflected in the index, minus fees upon maturity. Thus an ETN has an additional risk compared to an ETF - upon any reduction of credit ratin= gs or if the underwriting bank goes bankrupt, the value of the ETN will be advers= ely eroded.
Though linked to the performance of a = market benchmark, ETNs are not equities or index funds, but they do share several characteris= tics of the latter. Similar to equities, they are traded on an exchange and can = be shorted. Similar to index fun= d, they are linked to the return of a benchmark index. But as debt securities, ETNs don't actually own anything it is tracking.
The first ETN, marketed as the iPath Exchange-Traded Notes, was issued by Barclays Bank PLC on 12 June 2006. This was soon followed by Bear Stearns, Goldman Sachs & Swedish Export Credit Corp. In 2008, additional issuers entered the market with their own offerings; these inclu= de Deutsche Bank, UBS,= Lehman Brothers, Morgan Stanley and Credit Suisse. As of April 2008, there were 56 ETNs from nine issuers tracking different indexes. The popularity of ETNs is mainly due to the advantages t= hat it offers to investors.
The returns of ETNs are linked to the performance of a market benchmark or strategy, less investor fees. Currentl= y, there are four types of ETNs, Commodity ETNs, Emerging Market ETNs, Currency ETNs and Strateg= ies ETNs available in the market. (Please refer to Appendix A for a list of available products in each category.)
As discussed previously, ETNs are debt= notes. When held to maturity, the investor will receive a cash payment that is lin= ked to the performance of the corresponding index during the period beginning on the trade date and ending at maturity, less investor fees. Typically, ETNs = do not offer principal protection.
ETNs could also be liquidated before t= heir maturity by trading them on the exchange or by redeeming a large block of securities directly to the issuing bank. The redemption is typically on a weekly basis and a redemption charge may apply, subjected to the procedures described in the relevant prospectus.
The investor fee is calculated cumulat= ively based on the yearly fee and the performance of the underlying index and increases each day based on the level of the index or currency exchange rat= e on that day. Because the investor fee reduces the amount of return at maturity= or upon redemption, if the value of the underlying decreases or does not incre= ase significantly, the investor may receive less than the principal amount of investment at maturity or upon redemption.
Since ETNs are unsecured, unsubordinated debts, they are not rated, but are backed by the credit of underwriting banks. Like other debt securities, ETNs do not have voting rights. But unlike other debt securities, interest will not be paid during the term of the most ETNs.
Pros and Cons of ETNs
Advantages
Tax efficiency
ETN offers a tax-efficient way to inve= st. It is treated for tax purposes as prepaid contracts (A prepaid contract is a financial instrument, such as a forward contract. The owner of a prepaid contract pays an initial amount in order to receive a future contingent pay= ment based on the value of an index or other underlying benchmark at a specified time).
Very often index m= utual funds and ETFs are required to make yearly income and capital gains distributions to fund holders which are taxable. Meanwhile, for ETF, when a fund is forced to sell stock to change its composition. For example, when an index rebalances, the fund holders have to pay tax on whatever the capital = gain was, when the stock is sold.
In contrast, for ETN, there is no interest payment and dividend distribution. The timing of the realization of gains or losses on the ETN is based on when investors buy and sell their investments. Since the entire ga= in is treated as a capital gain, the investor can defer any gain until the security is either sold or it matures. Because long-term capital gains are treated more favorably (Holding more than 1 year, all the gai= ns will be taxed as long-term gains at 15%) than short-term capital gains and interest, the tax treatment of ETNs should be more favorable than that of E= TFs. There is no way to avoid capital gains, but delaying it is valuable because= the amount that would have been paid as tax can continue to accumulate wealth. Control over the timing of this capital gain is a big benefit to any invest= or looking to defer the payment of income taxes.
Recent tax rulings have additionally s= uggested that ETNs may be qualified tax shelters for the purpose of changing current interest income into deferred capital gains income.[1]
ETNs give investors a broad-based index without any tracking error to the index, doing away with the discrepancies = that exist between the returns of many ETFs and their underlying indexes. One re= ason of the tracking error observed in ETFs might be attributed to the diversification issues that stem from the inability of a fund to replicate = an index due to an upper limit on the maximum asset allocation to a single sto= ck. But for ETN, this constraint does not exist, because though ETN is also tracking the index, the return is not based on the underlying securities. T= he ETN issuer guarantees the holder a return that is an exact replica of the underlying ind= ex, minus expense fees. The bank also agrees to pay large shareholders the exact value of the note on a weekly basis through redemption, which helps the ETNs track very closely to the underlying index return.
ETN is a significant innovation to imp= rove liquidity of structured products. Not like other buy-an= d-hold structured products, ETNs can be bought and sold during normal trading hour= s on the securities exchange. For institutional size redemption, investors may o= ffer their ETNs for repurchase by the issuer on a weekly basis. Investors can ea= sily track the performance of their ETNs. In this sense, ETN is structured to resemble ETF. But an ETN is different from ETF, as they consist of a debt instrument with cash flows derived from the performance of an underlying as= set – a structured product.
<=
span
lang=3DEN>Access to new markets and strategies
ETNs have provided access to hard-to-r= each exposures, such as commodity futures and the Indian stock market. Certain a= sset classes and strategies are not easily accessible to individual investors. F= or example, the “momentum investing” strategy, which is used in SPECTRUM La= rge Cap U.S. Sector Momentum Index, is to take advantage of the varied performa= nces of the 10 sub-indexes of the S&P 500 Total Return IndexSM (SPTR) relative = to each other and to the SPTR. The weights of the 10 sub-indexes are computed = each day based on performance and correlation. This makes SPECTRUM Large Cap U.S. Sector Momentum Index difficult to track through ETF. On the contrary, ETN provides opportunities to gain exposure to these types of investment strate= gies in a cost-efficient way.
Disadvantages
<=
span
lang=3DEN>Credit Risk & Lack of Risk Metrics
ETNs, as debt instruments, are subject= to risk of default by the issuing bank as counter party. Even though the possibilit= y of default turning into a reality is relatively low, it ought to be measured a= nd accounted for. ETN investors will require a credit risk metric that facilit= ates answer to questions regarding the magnitude of the risk and its variation w= ith time. With new players foraying into the ETN space, how will the risk vary = by issuer? Who will take up the risk evaluation process? If and when the ETN sector grows, in order to participate, retail and institutional investors w= ill need a source for ETN key data which is easy to assimilate.
Illiquidity
Given its relative newness, there is a= flurry of ETNs hitting the market. They are, however, yet to engage the market pla= yers enthusiastically, several of whom are probably opting for the wait and watch approach. Under such circumstances, the liquidity of the notes in the secon= dary markets may be threatened should they fail to gain sufficient trading momen= tum. The effectiveness of ETNs at tracking indices is contingent on their abilit= y to garner enough support in the market.
Another flipside of ETNs relates to th= eir redemption feature. While ETNs can be sold daily on the secondary markets or held until maturity, institutional investors who wish to redeem blocks of 50,000 units or more directly with the issuer can only do so once a week. In contrast, other structured products, ETFs for instance, can be redeemed any= time during a trading day.
Tax benefits speculative
The ETN issuers are using tax efficien= cy as their trump card. As things stand, there is significant tax saving to be ga= ined from investing in ETNs. In reality, however, the Internal Revenue Service is yet to decide on the proposed tax treatment. So, the tax benefit status is still arguable.
ETNs have their worth decided by two f= actors:
• Performance of the index they = are set to track
• Credit ratings of the issuer
Suppose the issuing bank has been impa= cted negatively, if only marginally, by a crisis like the recent (2007-2008) subprime mortgage turmGas and the ratings agencies depreciate the overall credit rat= ing of the issuer to reflect the event.
In the aforementioned set-up, even tho= ugh the index it is tracking is showing growth, a decline in rating of an ETN issuing financial institution could negate the worth of an ETN.
Unprofitable trading strategies=
The GSCI has lost nearly 20% of its va= lue since January 2006, despite soaring commodity prices, all thanks to Contango. This is one instance where ETN tracked commodity indices like GSCI have ended up doing exactly the opposite of what they had set out to do.
Contango is a scenario where the cost = of the next-month futures contract is costlier than the current month contract. In this event, the issuing bank books a loss each time a current month contrac= t is sold and the next month contract is bought. Contango has hit hard the energy futures over the past few years and markedly brought down the returns from energy markets. Indices are taking varied steps to hedge against the condit= ion. Their results remain to be seen though.
The UBS Bloomberg Constant Maturity Co= mmodity Index (CMCI) addresses the issues of Contango and b= ackwardation by introducing the concept of constant maturity, which provides diversifica= tion across futures contract maturity dates. This is intended to smooth out the volatility often associated with commodity investments.
= ;
Prospect and Conclusions<= o:p>
As a new product, ETN has a very short history. However, it has been growing very rapidly. The ETN represents a ni= fty product structure that is gaining respect and funding in the market. By 18 July= 2006, just one = month after the launch of first two ETNs, GSP and DJP, GSP had attracted more than $40 million in assets, and DJP had pulled in more than $130 million for Barclays. Investments in iPath ETNs surpassed $2 billion by late April 2007= . In just over a year Barclays has gathered close to $3 billion in eight funds. Encouraged by the good performance of the ETNs launched by Barclays, other financial institutions have either launched their own products or are drawi= ng plans to partake of the ETN space. We believe more ETNs will be launched to raise more equity for financial institutions. For the customers, the advant= ages such as tax-efficiency and good liquidity of ETNs will attract more investo= rs to this innovative structured product. All of these imply that ETN is becom= ing more and more popular.
However, now the question is whether t= his trend is going to last long. Several industry gurus point to factors that m= ay well dampen the initial euphoria surrounding this product of financial engineering. The lack of historical record – upon which to base their decision to make ETNs a part of their portfolio or not – could be keep potential investors at bay. More importantly, the issuing banks advertise tax-efficiency as ETNs USP. If the IRS rules in the issuers’ favor, t= he implications of which have been discussed at length in Chapter 3, ETN sales could explode. But what if the IRS delivers an unfavorable word-or never ru= les? A line of thought that is doing rounds is that even if the IRS delivers an unfavorable word-or never rules at all-the ETNs could still be enormously successful. The reason is that ETNs provide efficient access to segments of= the market that would otherwise be difficult for retail investors to reach. But= how could we expect that the investors would still prefer ETNs to ETFs, or any = of the multitudes of other structured products out in the market, if there is = no tax-efficiency for ETNs. Drawing a comparison to ETFs, another structured product, which suffers from only market risk, ETNs face both counter party = risk and market risk. ETNs, bereft of their tax advantage, may lose their shine = in the eyes of an entire class of investors.
To conclude, ETNs have performed very = well so far as a new kind of structured product with lower fees, better liquidity a= nd tax-efficiency. However, both financial institutes and investors should kee= p an eye the status of the tax opinion from the IRS on ETNs while seeking ETNs as business or investment possibility.”
Regression Analysis Forecasting Impact= of Independent Variables on a Dependant Variable
Just like in = “What Mak= es Users Happy?” Rushinek And Rushinek use Forward stepwise multiple regression analysis to determine the relationship between the overall satisfactions of computer us= ers, this study uses regression to determine the overall impact on the Open stock market values (Communications of the ACM, July 1986). Another similar example is “forecasting sales, expenses and stock market values by quarterly financial statement ratio analysis: a microcomputer software development model.” Such study of “Forecas= ting sales, expenses and stock market values by quarterly financial statement, “ has been done by using ratio analysis and “a microcomputer software development model,” as the Author(s) Rushinek and Rushinek describe, in “Managerial Auditing Journal,” Year: 1995. =
The present = case study demonstrates a financial statement ratio analysis (FSRA). This analysis mat= ches company to industry data and builds sales forecasting models. FSRA imputes forecast standards of sales and costs, and applies them to a budgeted finan= cial statement variance analysis for the EE (electronic and electrical) industry. The present s= tudy is similar in dealing with an industry, except that the current industry is= the Gas and Gas industry (Gas). Likewise, this study demonstrates a financial statement ratio that is the daily growth rate of the Gas ETN.
That study “Develops the concept of industry base standards, integrating them into the more traditional statist= ical and accounting concepts of quality control standards. Provides an implementation example, and reviews possible improvements to the current methodology and approach and uses a similar methodology to forecast the sto= ck market value with some exceptions.”&= nbsp; Likewise, the current study develops the concept of industry base standards, of the daily Gas ETN growth rate, integrating them into the more traditional statistical regression analysis of forecasting the next day val= ue, and accounting concepts of quality control standards, to gauge standard deviants and distinguish them from abnormal deviants. As long as the real growth follows= the model within the bounds of the standard error, it is considered to be a nor= mal deviant. As soon as it exceed= s the standard, it is considered an abnormal deviant, and a sell order is issued.=
That study provides an implementation exa= mple, and reviews possible improvements to the current methodology and approach a= nd uses a similar methodology to forecast the stock market value with some exc= eptions. Likewise, the current study does t= he same except that it uses new software techniques that were not available before. Instead of forecasting an individual stock market value the current study forecast the entire fund. The previous study described a “Models sales and costs of an individual company and an industry based largely on aggregate industry databases.” The current= study is using the ETN index fund, which resembles the Gas industry. The previous study “uses a multivariate linear trend regression analysis for the sales forecasting model.” This study is u= sing a Univariate (1 independent variable, the Julian date) instead of a multivari= ate (more than 1 independent agruement variables). The previous study used only linear regression; the current study adds non-linear (Polynomial) regression, to t= he mix.
Like the previous study, this study also “Defines and tests related hypotheses and evaluates their significance and confidence levels.” For an illustration the previous study uses the EE industry and the APM Company, while the current study uses the Gas industry and the ETN fund. The current study also demonstrates microcomputer-based software similar to the “FSRA software that speed= s, facilitates, and helps to accomplish the stated objectives” of forecasting the next day value, and deciding whether to keep or sell the fund. The current study like = the “FSRA software uses industry financial statement databases” from Yahoo. It computes a financial ratio of ETN daily growth rate and builds forecasting models, to forecast i= ts next day value.
This study applies the theories and concepts related to Budg= eting, Financial statements, Models<= /span>, Ratios<= /span>, Sales forecasting, and Sta= tistics, as they apply to the Case study of the GAS ETN. (Article URL: htt= p://www.emeraldinsight.com/10.1108/02686909510079620)
THE GAS AND GAS INDUSTRIES LITRATURE R= EVIEW
As Rushinek and Rushinek show we need = to integrate the current multiple linear regressions, with other statistical methods such as univariate linear and polynomial regressions (http://www.ona= free.com/PortfolioManager/7-12-8_MHT_GAS%20ETN%20CONVERGING%20LINEAR%20POLY= NOMIAL%20DAILY%20OPEN%20FUNCTIONS.mht ). As the reader can see R= 20;Gas ETN Converting Linear & Polynomial Daily Open Functions, Fresh Separati= on & Significant Statistical R Square And P-Values Entry, Exit, & Stop Loss Swinging Trade Rules” (July, 2008) applies to the current study. Both studies develop automated program trading strategies. The trading program uses the GAS ETN fund converging linear & polynomial daily open functions, as the main indicator for the entry into a= 1 week holding period of a trade. The convergence has to have a fresh degree of high separation between the model= s R Square. The models have to ha= ve a significant statistical R Square and P-values for entry, exit, & stop l= oss swinging trade rules. Since t= he Polynomial model is superior to the linear model, it suffices to test the linear model and assume that the statistical significance of the linear mod= el also applies to the polynomial model.
Likewise, the traders should also cond= uct relevant sector analysis, such energy related fund like Oil is a good examp= le, since it is highly correlated to Gas. As Rushinek and Rushinek demonstrate in “OIL ETN Trading Rule Linear & Polynomial Daily Open & Close Regression Forecasts- Automa= ted Html Java Script Software Development” may have direct application to other Oil and Gas industry trades. As we can see both studies deal with regression analysis, testing hypothesis, and forecasting stock market prices, based on sector specific f= unds OIL ETN http://www.onafree.com/PortfolioManager/7-10-8a_mht_Oil%20ETN%20Tradi= ng%20Rule%20Linear%20Poly%20Daily%20Open%20Close%20Regression%20Forecasts.m= ht (July, 2008).
The Gas and Gas industries are a unique industry with some special characteristics. Rushinek, A. and Rushinek, S. Explain some of these characterist= ics in "Gas and Gas Mandated Accounting Changes and Debt Covenants: Debt to Equity Maturity, Dividend/Retained Earning Reduction & Refinancing Cost Ratios", 1991, which impact ETNs.&nbs= p; Since ETNs are based on debt covenants they affect a variety of issu= es related to the risk of losses.
As we discussed earlier the quality of= the ETNs investments “Dependence on credit ratings.” ETNs ha= ve their worth decided by the Credit ratings of the issuer. If the issuer is a collapsing comp= any like Bear Stearns, then investors may have to settle for a steep loss, converting their ETN into cash on a short notice. One way to be sensitive to such is= sues is to monitor the growth rate of the funds market values. As soon as the issuer suffers decl= ining credit rating the index may also reflect some of the risk in a slower growth rate. The objective of this s= tudy is to spot just risks and alert the investor to exit the investment before = it becomes worse.
= ;
Rushinek, A. and Rushinek, S. show that "Net Income-to-Sales Ratio Grouping For the Crude Petroleum and Natural Gas Industry Sector” is related to “A Company to Peer Comparati= ve Variance Analysis (1995).” In other words companies within an industry influence their peer’s performance; therefore, taking a fund of an entire industry increases diversification, and reduces risk of dealing with individual companies. For example if a company, as Rushi= nek, A. and Rushinek, S. explain experiences "Damage” using “Co= st Calculation Model for Exxon Corporation and the Gas and Gas Industry.”= ; A situation that describes “Fraud… (March 1996) will have a very devastating impact on a single company. Likewise, as Rushinek, A. and Rushinek, S. describe a "Tax Fraud…For the Petroleum Refining Industry… Shell Gas, (1997)” will also have a terrible decline stock market value effect on such a company. The rating and ranking of a company including their credit rating is likely to be affected by a discovery of fr= aud, and its publicity in the press.
As Rushinek, A. and Rushinek, S. descr= ibe the negative and the positive news affect the ”Rating and Ranking Best Practices of the British Petroleum Gas Company” and it extends to the entire “Gas & Gas Industry,” and eventually affects their “ Sales to Cash …Univa= riate Regression Trend Analysis..( 1997).”= Fraud publicity even if it is without merit may lead to an immediate decline in the value of the company, and thus lead to expensive litigations. As Rushinek, A. = and Rushinek, S. describe the “Litigation in PennzGas and the Petroleum Refining Industry” and their impact on “Financial Ratio Automat= ed Peer Review Analysis of Variance Internet Software... ( 1998).” Investors and traders pay attentio= n to the press as Rushinek, A. and Rushinek, S. shows how ”Correlating Investors’ Preferences to Stock Characteristics” may affect the stock markets values and eventually the ETN. Of the...” Crude Gas &am= p; Refining Industry ( 1999).”
Rushinek, A. and Rushinek, S. Show another example of the same p= attern in the ”Oil & Gas Market, Sector & Company Relative Strength Congruity Trading Theory...” in which they use “An Internet Automation Approach Applied to Chevron Corporation’s Stocks (2000).” This approach = is similar to the current study that is trying to produce a similar internet software model for ETNs. Such= models can be used, as Rushinek, A. and Rushinek, S. shows for “Forensic Aud= its of Stock Market Forecasts.” In this case they applied the model to “Texaco & the International Gas and Gas Industry.”= Using “Financial Models for Online Broker Litigation (2003),&#= 8221; they may help provide expert witness testimony and litigation support.
Rushinek, A. and Rushinek, S. use a si= milar approach in an “Automated Internet Trading Forecast Variance Analysis” for the “Gas and Gas Industry and BP Corporation̶= 1; in a Case Study (2003).” Likewise, Rushinek, A. and Rushinek S. demonstrated “Internet Web S= erver Comparative Forecasting Sales Models” using “Reversed Accountin= g of Texaco Corp and The Gas & Gas Industry” and applying “linea= r, Exponential, Power, Polynomial & Logarithmic Univariate Regressions (2005).” The current st= udy is using the same method, except that it applies them to ETNs instead of individual companies. The pro= blem that they encountered is violating some regression assumptions. As Rushinek, A. and Rushinek S. demonstrate in “An Automated Business Intelligent Stock Market Matchi= ng Engine for the Gas and Gas Industry,” the normality assumption may be violated. We can control the problem of the “Materiality of Violating the Normality Assumption of Linear Regression… in the GAS, GAS, & ENERGY industry (2007).” Rushinek, A. a= nd Rushinek S. show the “Optimal Forecasting Models for the Gas & Gas Industry” will take into consideration some problems and deal with th= em effectively. “A Study o= f the Daily Dow Jones U.S. Gas & Gas Index and ConocoPhillips” is simil= ar to the current study in that it deals with an index, which is similar to an ETN. Using the “Aid of = the Virtual Internet Office,” they are solving some problems of improving= the performance of the investors (2008).”
As Michael Werner and Kumen Jones demo= nstrate in the most elementary accounting textbook “Introduction to Manage= ment Accounting – A User Perspective”, (Second Edition, Prentice Hall, M-135, 2003), an XY scatter chart is the most basic way to forecast forward and add a trend line. As they describe a “Microsoft Excel Sca= tter Graph with a trend line,” Exhibit 5-16 and 5-17, they show how to forecast the cost forward into the future.= This study does the same, but in addition to the chart and the mathe= matical function it also deals with the statistical test of hypothesis.
Data Collection
Appendix A shows the last week of data collected from Yahoo.com. Usi= ng Microsoft Excel we have calculated the following models. As we converted the calculations f= rom the excel format, to HTML (Hyper Text Markup language) format with java scr= ipt, we can perform this analysis, without Microsoft Excel being present on eith= er the server or the client computer. &n= bsp; Likewise, it will also run on any device that supports HTML and Java. Such devices may be por= table cell telephones, personal digital assistants, etc.
The Linear Regression Analysis and the= Least Squares Method Model of Total Cost Calculations
As Michael Werner and Kumen Jones show “The Linear Regression Analysis and the Least Squares Method Model of Total Cost Calculations” follows this format, except that we are using multiple x variable x(i), where i=3D1-6:
Y=3D a + bx
Where:
Y =3D the dependant variable in our ca= se the daily value of the ETN daily Open+I Lag fund, where i ranges from 1-5 depen= ding on how many days forward it looks ahead
a =3D the intercept of the value of Y = when X is equal to zero, which is the Julian date value
b =3D the slope coefficient the change= in Y the ETN daily value as a result of an increase of 1day, change of X
X(i) =3D i=3D1-6, where X1 (I=3D1) is = the 1st independent variable, the Julian date of the ETN stock market values, Date,= and the rest of these variables, as follows:
X-Labels Varia= ble
x1&nbs= p; Date
x2&nbs= p; Open
x3&nbs= p; High
x4&nbs= p; Low
x5&nbs= p; Close
x6&nbs= p; Volume
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Table 0 |
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Regression |
Y Open + I days =3D +X1Date &=
nbsp; &nbs=
p; +x2Open+x3High =
; +x4Low+x5Close+x6Volume
+ Intercept |
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Monthly
Model |
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Regression
Statistics |
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Multiple R |
0.97369 <= o:p> |
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R Square |
94.81% |
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Adjusted R Square |
94.62% |
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Standard Error |
2.64346 <= o:p> |
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Observations |
177 |
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Table 0 shows the “Linear Models of Regressions of Open on Date of a Month Semi Ann= ual models. We want to find out w= hich time period is better. The R = Square measures the quality of the regression line the highest possible value is 1= 00%, a perfect predictor, and the lowest possible value is zero, which means no predictive abilities. The tab= les show several models, a linear Monthly (129 days) and Semi Annual (177 days)= .
---Chart 1 --- Insert here
Monthly Model
Semi Annual Model
Date Residual Plot
Chart 1 describes the Open on Date Mon=
thly
model (Monday, April 07,2008-Wednesday, May 07, 2008) Date Residual Plot;
The trend is clearly linear, with an R= Square of 88.7094%.&nb= sp; Likewise, it is obvious that the Semi Annual function does have a mu= ch better fit, with an R Square of 94.81%= . The difference between the R Square values of both functions is the degrees to which the independent variables explain the dependant variable.
Fresh Separation to Catch the Gain at = the Beginning and Nip It in the Bud
Likewise, fresh separation means that =
we want
to catch the separation at the beginning, nip it in the bud. As you can see, we want to trade
immediately after the Poly crosses the linear function. That is, we want to go long, or sh=
ort,
on the next Open. The differe=
nce in
the R Square between the linear and the Poly models should be maximized.
Hypothesis Testing Rejects the Null Hy= pothesis in Favor of The Alternate Stating that the Coefficients are Different from = Zero
The trading program has tested the R S=
quare of
the entire linear model and rejected the null hypothesis that it is zero.
Table 0a Gaz ETN 5 Day Long (Buy) Trade (Green) and the Regression Data Hold Out Sample (Blue) and Data (Yellow)
|
Date |
Open |
High |
Low |
Close |
Volume |
Adj Close |
GainDaily |
Cum%Gain |
Formula |
|
|
1 |
Wednesday,
May 14, 2008 |
72.9 |
73 |
72 |
72.1 |
18600 |
72.09 |
0.91 |
3.05% |
=3D(B42-$B$46)/$B$46 |
|
2 |
Tuesday, =
May
13, 2008 |
71.99 |
72.4 |
70.4 |
71.2 |
17600 |
71.18 |
0.53 |
1.77% |
=3D(B43-$B$46)/$B$46 |
|
3 |
Monday, M=
ay
12, 2008 |
71.46 |
72.1 |
70.2 |
70.4 |
32900 |
70.36 |
0.28 |
1.02% |
=3D(B44-$B$46)/$B$46 |
|
4 |
Friday, M=
ay
09, 2008 |
71.18 |
72.1 |
70.6 |
71.9 |
24500 |
71.92 |
0.44 |
0.62% |
=3D(B45-$B$46)/$B$46 |
|
5 |
Thursday,=
May
08, 2008 |
70.74 |
71 |
69.8 |
70.2 |
27400 |
70.24 |
1.31 |
0.00% |
=3D(B46-$B$46)/$B$46 |
|
1 |
Wednesday, May 07, 2008 |
69.43 |
71.2 |
69 |
70.5 |
38100 |
70.51 |
-0.7 |
Holdout Sa=
mple |
|
|
2 |
Tuesday, May 06, 2008 |
70.13 |
70.7 |
69.1 |
69.2 |
30200 |
69.15 |
1.76 |
Holdout Sa=
mple |
|
|
3 |
Monday, May 05, 2008 |
68.37 |
69.8 |
68.3 |
69.7 |
19400 |
69.65 |
2.62 |
Holdout Sa=
mple |
|
|
4 |
Friday, May 02, 2008 |
65.75 |
67.1 |
65.5 |
66.9 |
18200 |
66.9 |
-1.34 |
Holdout Sa=
mple |
|
|
5 |
Thursday, May 01, 2008 |
67.09 |
67.1 |
65.5 |
65.9 |
47500 |
65.91 |
-0.68 |
HoldoutSam=
ple |
|
|
6 |
Wednesday,
April 30, 2008 |
67.77 |
68.5 |
66.6 |
68 |
33300 |
67.99 |
-2.61 |
||
|
7 |
Tuesday,
April 29, 2008 |
70.38 |
70.4 |
67.2 |
67.4 |
25600 |
67.38 |
-0.37 |
||
|
8 |
Monday, A=
pril
28, 2008 |
70.75 |
71.2 |
69.8 |
70.3 |
34900 |
70.32 |
1.82 |
||
|
9 |
Friday, A=
pril
25, 2008 |
68.93 |
69.5 |
68.8 |
69.5 |
11200 |
69.49 |
1.22 |
||
|
10 |
Thursday,
April 24, 2008 |
67.71 |
69.3 |
67.2 |
68.2 |
28400 |
68.21 |
1.45 |
||
|
11 |
Wednesday,
April 23, 2008 |
66.26 |
68.7 |
65.9 |
68.7 |
13400 |
68.65 |
-1.09 |
||
|
12 |
Tuesday,
April 22, 2008 |
67.35 |
68 |
66.9 |
67.7 |
23600 |
67.68 |
0.74 |
||
|
13 |
Monday, A=
pril
21, 2008 |
66.61 |
67.8 |
66.4 |
67.6 |
17800 |
67.6 |
1.87 |
||
|
14 |
Friday, A=
pril
18, 2008 |
64.74 |
66.8 |
64.5 |
66.8 |
38800 |
66.78 |
-0.51 |
||
|
15 |
Thursday,
April 17, 2008 |
65.25 |
66 |
64.9 |
65.1 |
14000 |
65.05 |
1.29 |
||
|
16 |
Wednesday,
April 16, 2008 |
63.96 |
65.8 |
63.2 |
65.3 |
19700 |
65.28 |
0.06 |
||
|
17 |
Tuesday,
April 15, 2008 |
63.9 |
64.3 |
63.7 |
64.3 |
10500 |
64.26 |
1.35 |
||
|
18 |
Monday, A=
pril
14, 2008 |
62.55 |
63.1 |
62 |
63.1 |
5300 |
63.12 |
-0.09 |
||
|
19 |
Friday, A=
pril
11, 2008 |
62.64 |
62.6 |
61.8 |
62.2 |
25400 |
62.17 |
-1.35 |
||
|
20 |
Thursday,
April 10, 2008 |
63.99 |
64.3 |
62.8 |
63 |
22400 |
62.95 |
1.3 |
||
|
21 |
Wednesday,
April 09, 2008 |
62.69 |
63.6 |
62.7 |
63.4 |
36600 |
63.44 |
0.91 |
||
|
22 |
Tuesday,
April 08, 2008 |
61.78 |
62.1 |
60.7 |
61 |
4000 |
60.95 |
1.51 |
||
|
23 |
Monday, A=
pril
07, 2008 |
60.27 |
61.4 |
60 |
61.3 |
10000 |
61.32 |
0.83 |
The Program Keeps the Trade for 5 Cons= ecutive Days Starting By Buying On the Open
Table 0a shows the Gaz ETN 5 Day Long = (Buy) Trade (Green) and the Regression Data (Yellow).&= nbsp; It describes the Date, Open, and the rest of the data that this prog= ram ignores including: High, Low, Close, Volume, Adj Close, GainDaily, Cum%Gain, and the Formula. The numbers = on the left shows the exit 5 days after starting the trade. The program keeps the trade for 5 consecutive trading days starting on Thursday, May 08, 2008, buying on the = Open of $70.74, and selling 5 days later on the Open of Wednesday, May 14, 2008 = at an Open price of $72.91, with an ROI of 3.05%, calculated by the following formula =3D(B42-$B$46)/$B$46.
The preparation period is a month of d= ata prior to the trade with the last day being line 1 Wednesday, May 07, 2008, going backward in time 129 observations.
Data Analysis
This study describes to models, the Mo= nthly (129 observations) and Semi Annual (177 observations) Models, based on the number of observations or days in the regression analysis. One of the objectives is to test t= he null hypothesis that the more days the higher the R Square of the model and= the lower the error rate. Table 1= shows the gain of the R Square of about 95%-89%=3D6% due to the additional observations.
THE TRADE OFF BETWEEN THE NUMBER OF CA= SES OBSERVED AND THE MODEL RELIABLITY AS MEASURED BY R SQUARE
|
|
Table 1 |
|
|
Regression Statistics |
|
|
|
Multiple R |
94.1857%<= o:p> |
|
|
R Square |
88.7094%<= o:p> |
|
|
Adjusted R Square |
88.1542%<= o:p> |
|
|
Standard Error |
2.4707386=
2 |
|
|
Observations |
129 |
Semi Annu=
al
Model |
||
|
Regression
Statistics |
||
|
Multiple R |
0.97369 <= o:p> |
|
|
R Square |
94.81% |
|
|
Adjusted R Square |
94.62% |
|
|
Standard Error |
2.64346 <= o:p> |
|
|
Observations |
177 |
SUMMARY OUTPUT, in Table 1, shows the =
Regression
Statistics, with Multiple R 94.1857%, R Square 77.=
521%, and Adjusted R Square of 76.450%. It conclude=
s that
the date plus the rest of the independent variables explain over
Table 1a Gains in R Square due to addi= ng more observations, and the ratios of cases observed to the number of variables
|
Table 1a |
|||||
|
L |
M |
N |
O |
P |
|
|
Regression |
Cases |
R Square |
Variables |
Cases per |
|
|
Models |
Observed |
Calculated |
Y+X |
Variables |
|
|
Line 17 |
Semi Annual |
177 |
94.81% |
7 |
25.28571<= o:p> |
|
Line 18 |
Monthly |
129 |
88.71% |
7 |
18.42857<= o:p> |
|
Line 19 |
Gain |
27.12% |
6.43% |
27.12% |
|
|
Formula: |
=3D(M17-M18)/M17 |
||||
|
=3D(N17-N18)/N17 |
Table 1a shows the gains in R Square d= ue to adding more observations, and the ratios of cases observed to the number of variab= les. &= nbsp; &nbs= p; &= nbsp;
Due to an addition of 27.12% more observations, the model’s R Square gained 6.43%, using the Formula:=3D(M17-M18)/M17, and =3D(N17-N18)/N17. Eventually, there will be diminish= ing returns to adding more observations, especially as the environment changes = and the old observations no longer apply. It seems that we have not reached that point yet, and therefore, the model may still be improved by adding additional cases. However, some time such additional= data points are not available especially for new funds, or new companies.=
HYPOTHESIS TESTING
Monthly Model
|
ANOVA |
Table 2 |
||||
|
|
df |
SS |
MS |
F |
Significance F |
|
Regression |
6 |
5851.5057=
49 |
975.25096=
|
159.7581<= o:p> |
2.54E-55<= o:p> |
|
Residual |
122 |
744.75502=
02 |
6.1045493=
|
||
|
Total |
128 |
6596.2607=
69 |
|
|
|
|
Table 3 |
|||||
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
|
Intercept |
$
(1,461.12) |
255.19253=
35 |
-5.725569=
1 |
7.55E-08<= o:p> |
-1966.3 |
|
Date |
$ 0.03731 |
0.0065179=
19 |
5.723794<= o:p> |
7.61E-08<= o:p> |
0.024404<= o:p> |
|
Open |
$ 0.28559 |
0.4662858=
61 |
0.6124832=
|
0.541358<= o:p> |
-0.63747<= o:p> |
|
High |
$ 0.09071 |
0.4385638=
32 |
0.2068282=
|
0.836489<= o:p> |
-0.77747<= o:p> |
|
Low |
$ (0.20817) |
0.5442135=
62 |
-0.382522=
3 |
0.70274 |
-1.2855 |
|
Close |
$ 0.64106 |
0.4751479=
88 |
1.3491723=
|
0.17978 |
-0.29955<= o:p> |
|
Volume |
$
(0.00006) |
2.45549E-=
05 |
-2.438706=
7 |
0.01618 |
-0.00011<= o:p> |
|
Semi Annual Model |
|||||
|
ANOVA |
Table 2 |
||||
|
|
df |
SS |
MS |
F |
Significance F |
|
Regression |
6 |
21690.73 |
3615.121 |
517.3428 |
2.2E-106 |
|
Residual |
170 |
1187.937 |
6.987865 |
||
|
Total |
176 |
22878.66 |
|
|
|
|
Table 3 |
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
|
Intercept |
-1594.44 |
263.5012 |
-6.05097 |
8.92E-09 |
-2114.59 |
|
Date |
0.040713 |
0.006729 |
6.05048 |
8.94E-09 |
0.02743 |
|
Open |
0.207208 |
0.397058 |
0.521858 |
0.602449 |
-0.57659 |
|
High |
0.204224 |
0.378172 |
0.540029 |
0.589884 |
-0.54229 |
|
Low |
-0.22532 |
0.455905 |
-0.49422 |
0.621789 |
-1.12528 |
|
Close |
0.60177 |
0.402967 |
1.493348 |
0.1372 |
-0.19369 |
|
Volume |
-5.4E-05 |
1.61E-05 |
-3.36344 |
0.000951 |
-8.6E-05 |
The ANOVA (Analysis of Variance), in T= able 2, shows the statistical significance of both the Monthly and the Semi model, = and its intercept and slopes. It includes the column headers of: df, SS, MS, F, and Significance F. The Regression Date line with an F of 517.3428, and Significance F of 2.2E-106, is much less than the threshold of = 5% to reject the null hypothesis, for the entire model. Thus, we reject the null hypothesis stating the R Square equal to zero, in favor of the alternative hypothesis = that it is greater than zero.
--- Table 3 Insert Here
Table 3 shows the rejection of the null
hypothesis regarding the intercept and the X variable, Date. It shows the headers of Coefficien=
ts,
Standard Error, t Stat, and P-value, as well as Lower 95%, and Upper 95%.
Notice that the slope is $ 0.040713, daily gain that exceeds 4
cents per trading day. Since =
it is
positive, the program adds as the date is more recent and the Julian value =
is
higher.
Table 4
|
RESIDUAL OUTPUT |
PROBABILITY OUTPUT |
||||||
|
Observati=
on |
Predicted
Open |
Residuals=
|
Standard
Residuals |
Percentil=
e |
Open |
||
|
1 |
74.61933<= o:p> |
-4.76933<= o:p> |
-1.83577<= o:p> |
0.282486<= o:p> |
44.26 |
||
|
2 |
72.33293<= o:p> |
1.877071<= o:p> |
0.722504<= o:p> |
0.847458<= o:p> |
45.01 |
||
|
3 |
79.52856<= o:p> |
-6.15856<= o:p> |
-2.37049<= o:p> |
1.412429<= o:p> |
45.03 |
||
|
4 |
82.68489<= o:p> |
-5.78489<= o:p> |
-2.22666<= o:p> |
1.977401<= o:p> |
45.09 |
||
|
5 |
81.82999<= o:p> |
-7.03999<= o:p> |
-2.70977<= o:p> |
2.542373<= o:p> |
45.1 |
The RESIDUAL OUTPUT, Table 4, shows the PROBABILITY OUTPUT, it includes the Observation, Predicted Open Residuals, Standard Residuals, Percentile, and Open Gaz ETN values of the last day goi= ng backward in time. Accordingly, observation 1 shows the day value of 74.61933 and its stock market value of $74.69, for the last observation, and the last day, prior to trading.
The Residual Output displays th= e extent to which some of the regression assumptions are met. As we can see the residuals are not exactly randomly distributed around the mean of zero. The violation of this regression assumption leads to our recommendation to construct a Poly model just to confirm that the loss or R Square is not too high, due to the distribution = of the residuals. As Rushinek, A= . and Rushinek S. suggested “An Automated Business Intelligent Stock Market Matching Engine for the Gas and Gas Industry” may include the compari= son of the Poly and the linear models R-Square difference. The larger the difference th= e more material is the violation and the departure from the regression assumptions concerning the residual distribution around the mean of zero. Likewise, the normality assumption= violation may be assessed in a similar way. Look at the “Materiality of Violating the Normality Assumption= of Linear Regression Control Analysis”, as the GAS, & ENERGY QUARTER= LY describes (2007).
Chart 5 a Normal Probability Plot show= s that the distribution approaches half a bell curve as we increase the period to = over 6 months. Keep such violation= under control by monitoring this plot on a regular basis.
|
Table 3.1 |
Monthly Model |
||||||||
|
5 Days Look Ahead Forecasti=
ng
Model Back testing Variance Analysis Rounding Errors |
|||||||||
|
Function |
Coefficients |
||||||||
|
Column J |
K |
L |
M |
N=3DK*M |
O |
P=3DN-O |
Q |
||
|
Line 18 |
Intercept |
-1461.122=
|
X-Labels |
X-Values |
$ (1,461) |
||||
|
Line 19 |
Date |
$ 0.03731 |
x1 |
&nbs=
p;
39,568 |
$ 1,476.2 |
=3DK19*M19 |
|||
|
Line 20 |
Open |
$ 0.28559 |
x2 |
$ &nbs=
p;
67.77 |
$ 19.355 |
=3DK20*M20 |
|||
|
Line 21 |
High |
$ 0.09071 |
x3 |
$ 68.50
|
$
6.213 |
=3DK21*M21 |
|||
|
Line 22 |
Low |
$
(0.20817) |
x4 |
$ &nbs=
p;
66.59 |
$ (13.862) |
=3DK22*M22 |
|||
|
Line 23 |
Close |
$ 0.64106 |
x5 |
$ &nbs=
p;
67.99 |
$ 43.585 |
=3DK23*M23 |
|||
|
Volume |
-5.988E-0=
5 |
x6 |
&nbs=
p;
33,300 |
$ (1.994) |
O |
P=3DN-O |
Q |
||
|
Forecasted Open of Hold Out
Sample |
4/30/2008=
|
$
68.35 |
$ &nbs=
p;
68.31 |
$ &nbs=
p;
0.04 |
Rounding Errors |
||||
|
Actual Open of Hold Out Sam=
ple |
4/30/2008=
|
$
69.43 |
Y-Dependent |
5 Days Look Ahead Forecasting Model Back testing Variance Analysis
Rounding Errors
This table describes the 5 Days Look Ahead Forecasting Model Back te=
sting
Analysis Rounding Errors Hold Out sample data of the last 5 observations. <=
/span> These are the last 5 days data, taken out of the
regression, hence the Hold Out sample data name, to back test the regression
before deploying it on the real trade.
Table 3.1 shows the Forecasted compare=
d to
Actual Known Hold Out sample test Gas ETN values using the 1 week holding o=
ut
period of the trade last 5 working days observed, in an Excel template. They include the Columns J, K, L, =
M, and
N, and show how the traders back test before they apply the model of Y=3Da+=
bX(i)
to the forecast the trade. Li=
ne 18
shows the Coefficient of the Intercept.&nb=
sp;
The Intercept=3Da, with a value of -1461.122 days. Line 19 is the Slope variable
coefficient of Date=3Db with a $0.03731, which is abou=
t $.38
daily growth rate of a Gaz ETN share.
Line 19, Today=3DX, is the last Date value of this study, which is <=
/span>Wednesday, =
May
14, 2008, the Date’s Julian, converts the Date
format to its numerical counter part of 39,568=
. In the right most column, the table
shows the Excel formula behind the number, in this case =3DK19*M19<=
/span>, the product of the coefficient and the Julian value, which is t=
he
formula. After Line 23, shows=
the
sum of the intercept plus the coefficient effects on the forecasted value,
Forecasted=3DY, $ 68.35, applying the Excel formula
---Screen Shot 1 Formula Auditing Trace Precedents and Dependents of=
5
Days Look Ahead Model Back Testing Variance Analysis Rounding Errors of the
Monthly Model
FORMULA AUDITING TRACE PRECEDENTS AND DEPENDENTS BACK TESTING VARIAN=
CE
ANALYSIS ROUNDING ERRORS ANOVA INTERNAL CONTROL AND ERROR TRAPPING PROCEDUR=
ES
ARROW HEADS WORKFLOW AND THE FORMULA FLOWS
Screen Shot 1 shows the Formula Auditing Trace Precedents and Depend=
ents
of 5 Days Look Ahead Model Back Testing Variance Analysis Rounding Errors of
the Monthly Model . The reade=
r can
see how table 3.1 picks up the multiple linear regression coefficients from=
the
ANOVA table. It starts from t=
he
Intercept K18, and the Date K19, the Julian date with a value of 39,568, wh=
ich
is 4/30/2008. Multiplying the
coefficient times the value of the 1st independent variable resu=
lts
in the product of the coefficient times the X1 value of $1,476.20 contribut=
ion
to the Open +5 price forecast. As
the model repeats the same procedure in each line of the table, it lists the
Excel formula in column O, =3Dk19*m19, etc.
The sum of the column in cell n25 contains the 1 forecast of the Ope=
n +
5 Lag, $68.50, and the adjacent cell contains another independently calcula=
ted
forecast of $68.31, and the rounding error of $.04 in cell P25. This demonstrates how to audit the
triple checked calculations to make sure that no errors are sneaking into t=
he
back testing procedure. The t=
rader
should use redundant calculations plus formula audit trace precedents and
dependence to double and triple check all the calculations, and document th=
ese
internal control and error trapping procedures. The blue arrow heads originating w=
ith a
circle show the workflow and the formula flows. The circle shows the source of the
formula, while the arrow head shows the target of the formula.
Screen Shot 1 illustrates how the Inco= me Statements calculates the net income for the budgeted and the actual trades= , as well as the variances and the adjusting entries for these variances. For example, it shows that on 5/14= /2008 the trader sold 1 share at $72.90 compared to a forecast of $70.15, underst= ating the actual revenue by the variance of $2.75. Therefore, to adjust the Sales acc= ount, the accounting system has to enter a credit to Sales to raise the balance of the sales account from the original understated forecast, to the actual hig= her Open+5Lag value. This is for a holding period of 4 days, as line 34 shows the purchase date of 5/8/2008, 14-8=3D6 days less 2 weekend days leaving 4 work holding days.
Exit Strategy and Automated Stop Rules= and the Hold out Data Observations (Future)
In the Hold Out period, the period of trading that is excluded from the
regression (Past), if we experience 2 consecutive losing days, the program
triggers the Stop Loss and exits the trade. The Past refers to the period of
the regression, while the Future refers to the period of the trade, 5 days
subsequent to the production of the regression models. The Hold Out period, the Future,
displayed by iPath S&P GSCI Gas Tot Ret Idx ETN (GAz) including the Dat=
e,
Open, High, Low, Close, Volume, and Adj. Close starting on Thursday, M=
ay
08, 2008, for the next 5 days, ending on Wednesday, May 14, 2008. This date has not=
been
included in the production of the previous forecasting models that have been
completed 1 day ago. So this day is a sort of a “hold-out” data
sample, to which the trading program will apply the forecasting model, and =
the
trading strategy.
|
Table 3.8.1 |
** |
Monthly Model |
||||||
|
Income Statement for 1 Gaz
Trade (1 Buy and Sell) |
||||||||
|
Actual % |
Actual $ |
Budgeted |
Variance |
|||||
|
Actual |
For the Week Ended
on…………….. |
5/14/2008=
|
5/7/2008<= o:p> |
7 |
Days |
|||
|
Trade Income Statement for =
Gaz
Fund on |
A |
B |
=3DB-A |
Entry |
Account |
|||
|
5/14/2008=
|
4 Day Revenue |
100.00% |
$
72.90 |
$ &nbs=
p;
70.15 |
(2.75) |
Cr. |
Sales |
|
|
5/8/2008<= o:p> |
Cost |
-97.04% |
(70.74) |
(66.10) |
(4.64) |
Dr. |
COGS |
|
|
6 |
Profit Margin |
2.96% |
$ &nbs=
p;
2.16 |
$ &nbs=
p;
4.04 |
(1.88) |
Dr. |
Margin |
|
|
1.00% |
Commission |
($0.73) |
($0.70) |
(0.03) |
Dr. |
Com. Cost |
||
|
Per Unit |
Unit Contribution Margin |
$ &nbs=
p; 1.43
|
$ &nbs=
p;
3.34 |
(1.91) |
Dr. |
UCM |
||
|
10=
,000 |
Total Contribution Margin |
$ 14,310 |
$ &nbs=
p;
33,432 |
(19,122.32) |
Dr. |
TCM |
||
|
Trading Room Rent |
($300.00) |
($300.00) |
0.00 |
Fixed Cost |
||||
|
Net Income |
$ 14,010 |
$ &nbs=
p;
33,132 |
(19,122.32) |
Dr. |
Net Income |
Table 3.8.1 is using the Monthly Model= of the Income Statement for 1 Gaz Trade (1 Buy and Sell), it includes the Actual %= , Actual $, Budgeted, Variance, it starts with the Actual “For the Week Ended on……………..”5/14/2008 5/7/2008, 7 Days. It shows the “Trade Income Statement for Gaz Fund on” A B, and the difference =3DB-A. Following is the Accounting Entry,= and the Account, to which it is applied. For example, at 5/14/2008, the 4th Day Revenue is 100.00%, which is $72.90, the actual known last day of the Hold Out sample, compared= to its forecasted $70.15, with a (2.75) Cr., credit entry to the Sales account= .
System Entered The Budgeted, Forecaste= d Value Initially Until The Actual Value Becomes Available Dr. AR and Cr. Sales
The traders need to credit the Sales a= ccount due to understated forecasted hold out sample value. In other words, the system entered= the budgeted, forecasted value initially until the actual value becomes available. At this time, prio= r to the trade transaction, the accounting system uses forecasted standard value= s. In this case the understated the s= ales value by the Variance. Theref= ore, they have to debit accounts receivables, and credit sales. Dr. AR and Cr. Sales at $2.75 to a= djust the balance of the AR and Sales accounts, from the forecast to the actual s= ales value.
Likewise, at 5/8/2008 the actual UNKNO= WN Cost of the Future data, of -97.04%, (70.74), negative due to the cost being a d= ebit balance account, and (66.10), with an entry of (4.64) Dr. COGS, Cost of Goo= ds Sold, which is the cost of the security that the traders are selling. The 6 day forecasted Profit Margin= is 2.96%, or $2.16, excluding commission. The budgeted $4.04, overstat= ed the cost, a debit entry. To corre= ct or adjust such a debit entry to a debit account the traders have to debit it,<= span style=3D'mso-spacerun:yes'> Thus, they enter a (1.88) Dr. entr= y into the Margin account.
Notice, the known historical Future da=
ta Unit
Contribution Margin (UCM) of $1.43, is lower than the forecasted UCM of
$3.34. Therefore, we have to =
adjust
it as well, (1.91), Dr. UCM account, to bring it down to the correct amount=
. For a trade of 10,000 shares, the =
Total
Contribution Margin of $14,310, the known historical Future data, compared =
to
budget of $33,432, which the traders have to debit by (19,122.32) Dr. to the
TCM. To that the traders may =
have
to add the fixed cost component, similar to a Trading Room Monthly Rent of
($300.00), which is forecasted perfectly well due to a contractual agreemen=
t of
($300.00). Therefore, there i=
s no
variance to deal with 0.00 Fixed Cost.&nbs=
p;
In reality, the traders may have to break down the fixed overhead and
charge part of it, and not the entire amount to each transaction. However, for the sake of simplicit=
y, we
have eliminated that step, to control the complexity of this calculation.
Finally, the unknown future actual Net= Income of $14,010 is compared to the forecasted overstated income of $33,132, and = the forecasted, which is initially recorded in the books is downgraded by (19,122.32) a Dr. entry to the Net Income account. All of that was done for now, on t= he unknown Future data after successful back testing and confirming that this forecasting model works, on the Hold Out known historical sample data. Only after back testing the model = and verifying that it works, reasonably well on the, the traders are ready to deploy the model on a live trade. Most times the traders should repeat these back testing procedures numerous times continuously refining them until such time that they have ma= de sure that the model is not overly optimized for a single set of know histor= ical values, at the expense of future unknown value. For the sake of simplicity we skip= these trials in the present study and move on to the next step, which is deployin= g the model on unknown future data. Using the actual trade data of the unknown future, we have calculated the ROI.
After Back Testing the Model and Verif= ying that It Works Calculate The ROI Return On Investment Of A Single Transactio= n
|
Table 3.8.2 |
Monthly Model |
** |
|
ROI=3DReturn on Investment<= o:p> |
||
|
Profit |
2.96% |
|
|
Hold Days |
6 |
Days |
|
Per Day |
0.49% |
ROI |
|
Days |
360 |
Year |
|
Annual |
178% |
ROI |
Table 3.8.2 shows the Monthly Model, a= nd its ROI=3DReturn on Investment, of 2.96%, for 6= Days, a single transaction of 0.49%, per day and the ROI
For 360 days in a Year of an annual 17= 8%, ROI. This is an enormous ROI, considering the going interest rate is close to less than 5%, annually. Keep in mind that this application= of the model has been carried out on unknown future data after having complete= d a back test on a hold out sample of known historical hold out observations of= the last 5 days of records.
|
Table 3.7 |
Monthly Model |
|||||||
|
Variance Err |
Forecast |
Possible Holding Period From
1-4 Days |
||||||
|
%Error |
$Error |
Open |
Day1 |
Day2 |
Day3 |
Day4 |
Holding Period |
|
|
Forecast5 |
3.922% |
$ 2.75 |
$ &nbs=
p;
70.15 |
>------------- |
>------------- |
>------------- |
72.90 |
4 Day Revenue |
|
Forecast4 |
3.051% |
$ 2.13 |
$ &nbs=
p;
69.86 |
>------------- |
>------------- |
71.99 |
>------------- |
3 Day Revenue |
|
Forecast3 |
1.553% |
$ 1.09 |
$ &nbs=
p;
70.37 |
>------------- |
71.46 |
>------------- |
>------------- |
2 Day Revenue |
|
Forecast2 |
4.462% |
$ 3.04 |
$ &nbs=
p;
68.14 |
71.18 |
>------------- |
>------------- |
>------------- |
1 Day Revenue |
|
Forecast1 |
7.013% |
$ 4.64 |
$ &nbs=
p;
66.10 |
(70.74) |
(70.74) |
(70.74) |
(70.74) |
Cost |
|
|
3.961% |
$ 13.65 |
$ &nbs=
p;
344.62 |
$ &nbs=
p;
0.44 |
$ &nbs=
p;
0.72 |
$ &nbs=
p;
1.25 |
$ &nbs=
p;
2.16 |
Profit Margin |
Table 3.7 Monthly Model, describes the= Variance Error, Forecast, and Possible Ho= lding Period From 1-4 Days, of the Gaz shares that the traders purchased. It shows the %Error, $Error, Open = of an “if then” analysis of different holding periods of Day1, Day2, Day3, Day4, Holding Period of the shares.&= nbsp; This table describes various possible scenarios of holding periods.<= span style=3D'mso-spacerun:yes'> Forecast5, deals with a 4 day hold= ing period, the planned holding period generated an error of 3.922%, and $2.75 = out of $70.15, actual Open, which is also the actual unknown selling price, compared to a forecasted value of $72.90, of a 4 Day holding period Revenue. The rest of the line= s in the table, describes the same thing, but for a shorter holding periods of 3 days, 2 days, and 1 day. Some= time the traders will decide to exit the trade prior to the original plan of a 4= day holding period. For that 4 day holding period we go down to the line that describes the cost, skipping to Forecast1, which is the forecast of the purchase price, at the first Open, following the last day, the day of planning the trade, 5/8/2008, Thursday, = May 8, 2008. Across from Forecast1 the $(70.74) Cost, the Open of the 1st<= /sup> day of the purchase of the shares, is deducted from the 4th Open, which is the selling price producing the 2.16 Profit Margin.
|
Table 3.7.1 |
Buying at the Open at $70.74 and Selling 4 d=
ays
later at $72.90 |
||||||||||
|
Date |
Open |
High |
Low |
Close |
Volume |
Adj Close |
Open+5Lag |
Daily Gain |
|||
|
Wednesday,
May 14, 2008 |
72.9 |
73 |
72.03 |
72.09 |
18600 |
72.09 |
71.41 |
$0.01264 =
|
|||
|
Tuesday, =
May
13, 2008 |
71.99 |
72.41 |
70.36 |
71.18 |
17600 |
71.18 |
69.67 |
$0.00742 =
|
|||
|
Monday, M=
ay
12, 2008 |
71.46 |
72.14 |
70.16 |
70.36 |
32900 |
70.36 |
69.6 |
$0.00393 =
|
|||
|
Friday, M=
ay
09, 2008 |
71.18 |
72.12 |
70.64 |
71.92 |
24500 |
71.92 |
71.88 |
$0.00622 =
|
|||
|
Thursday,=
May
08, 2008 |
70.74 |
71.02 |
69.8 |
70.24 |
27400 |
70.24 |
72.73 |
$0.01887 =
|
|||
|
|
=3D$72.9-$70.74 |
|
|
|
|
|
=3DB45 |
=3D(B50-B55)/B55 |
Table 3.7.1 shows the unknown future d= ata in which the trade took place. It shows the Buying at the Open at $70.74 and Selling 4 days later at $72.90, = at the Open of the 4th day, using a 4 day holding period. It shows the Date, Open, High, Low, Close, Volume, Adj Close, Open+5Lag, and Daily Gain. The 1st line, Wednesday= , May 14, 2008, shows the selling price at the Open of $72.9. Likewise, the last line shows the purchase price at the open on Thursday, May 08, 2008. On this Open of $70.74, the trader= s purchased the Gaz shares at the Open value, which becomes the cost per share. Notice,= the Weekly Holding Gain = $2.3 Hold Out Sam= ple Before Actual Trade
Notice that this table shows the diffe= rence between the Open and the Open + 5 lag.&nbs= p; For the semiannual model (177 days), we have included this set of da= ta in which the 1st line of the Y, the dependant variable, Open +5 = Lag, which is the Open of the next Thursday, of $71.41, has been regressed on the independent variables X1-X6, Open through Volume,
In contrast, table 3.5 shows the last = 5 days before the trade. This is the= Hold Out Known Historical sample data, the last 5 days prior to the trade. The Monthly model regression of 12= 9 days excludes these holding out sample data from the regression analysis to use = it for back testing purposes. Notice the Weekly Holding Gain $ 2.2 during the hold out data and c= ompare it to the Actual Trade Days
|
|
|
|
|
|
|
|
|
||||
|
Table 3.5 |
|
|
|
|
|
|
|
|
|||
|
Back Testing the Trading
Strategy on Historical Data Applied Above to Actual Future Data |
|
||||||||||
|
Date |
Open |
High |
Low |
Close |
Volume |
Adj Close |
Holdout |
Historical |
|||
|
Wednesday,
May 07, 2008 |
69.43 |
71.15 |
69 |
70.51 |
38100 |
70.51 |
Revenue4 |
($0.00998) |
|||
|
Tuesday, =
May
06, 2008 |
70.13 |
70.74 |
69.08 |
69.15 |
30200 |
69.15 |
Revenue3 |
$0.02574 =
|
|||
|
Monday, M=
ay
05, 2008 |
68.37 |
69.84 |
68.3 |
69.65 |
19400 |
69.65 |
Revenue2 |
$0.03985 =
|
|||
|
Friday, M=
ay
02, 2008 |
65.75 |
67.08 |
65.54 |
66.9 |
18200 |
66.9 |
Revenue1 |
($0.01997) |
|||
|
Thursday,=
May
01, 2008 |
67.09 |
67.1 |
65.51 |
65.91 |
47500 |
65.91 |
Cost |
($0.01003) |
|||
|
=3D$69.43-$67.09 |
||||||||||
Table 3.5 shows the Hold Out Sample Da= ta for Back Testing Trading Strategy of Weekly Holding Period. Keep in mind that its main purpose= is to Exclude it from the Multiple Regression Coefficients Calculations data, so we can test it objectively.
---Screen Shot 2 Hold Out Historical Known Past Data Sample Back Test Data and Future Unknown Data Revealed after the forecast a= nd actual trade & Projected Holding Period Budgeted Margin Calculations Au= dit Formula Precedents and Dependents
Screen Shot 2 shows the Hold Out Histo= rical Known Past Data Sample used for Back Testing of the past known historical data. Likewise, it shows the = Future Unknown Data Revealed after the forecast and actual trade as well as the Projected Holding Period Budgeted Margin Calculations Audit Formula Precede= nts and Dependents.
FORECASTED UNKNOWN FUTURE TIME<= /p>
The Forecasted Unknown Future Time, co= lored green, is the time period for which the trader applies the forecast. In this case, it ranges from Thurs= day, May 8, 2008, the purchase day on the open, Open+1 Lag, with the Open value = of $70.74, the cost per share. A= s we move across the line 53 notice that the open plus 5 arrow head shows that t= his Open + 5 Lag value of $72.73 will be regressed on the remaining independent variables Open, High, etc for the full Semi Annual model of 177 days. Therefore, its formula of =3Db45 p= oints to a higher cell of a future time. As we move further to the right on line 53, the reader can see that the foreca= st was off by about 7.013%, with an error of $4.64, due to understated forecas= t of $66.10 of Thursday’s Open, on the preceding Wednesday.
As we move up to line 49, we reach Wed= nesday, May 14, the last holding day, on which the trader exits on the Open, at $72.90. Goring further to the right, following the blue trace dependence line, we cross the Open + 5 Lag,= the Error, following the arrow, the reader reaches the blue arrow head and circ= le at Q49, carrying forward the selling price, on the exit of the trade, of $79.20. Going down with the b= lue Trace Dependence arrow head, we reach the actual cost of ($70.74), negative= due to the fact that this is a cost rather than revenue figure, and finally the Profit Margin of $2.1 6 per share. The following line contains the formula that shows how the Profit Ma= rgin has been calculated, =3DSum(p49:p53).
Next, down in line 59, the screen show= s the hold out sample data, from the known last 5 days of historical data, prior = to the forecast, starting on Thursday, May 1, 2008, and ending on Wednesday, M= ay 7, 2008, colored blue. We hol= d out this sample data, so the trader can test the validity of the Monthly forecasting model on real known data, and assess the bias of the model, to decide whether it is good enough to apply to the unknown data and trade on = it, so called back testing. Keep = in mind that normally such back testing process should be repeated many more t= imes than once, but for the sake of simplicity we skip the extra back testing procedures, since they are methodologically identical to the first time.
Line 59 shows the exit of the weekly t=
rade on
the Open of $69.43, which the forecasting model overstated by 3.922% and $2=
.75
to be, $70.15. As the readers=
move
to the right of this line they can see how this model applied the regression
function to the values, starting with the Intercept, Date, and Open etc.
--- Screen Shot 3 Table 3.4 Actual 5 D= ay Look Ahead compared to Hold Out Data Sample and Back Test Data Profit Margin Calculation for Weekly Holding Period of the Monthly 129 Days Model<= /p>
Screen Shot 3 shows Table 3.4 Actual 5= Day Look Ahead compared to Hold Out Data Sample and Back Test Data Profit Margin Calculation for Weekly Holding Period of the Monthly 129 Days Model. Notice the Weekly Holding Gain on = the Hold Out Historical Sample data of $2.30 (Red on yellow) compared to the Ac= tual 5 Day Look Ahead future data of $2.20, slightly lower than the hold out sample. This screen shot demonstrates clearly how the model defines the Open + 5 Lag vector. For example, for the 1st actual data set (yellow), for Wednesday, April 30, 2008, that is included in the regression, the Open+5Lag dependence point to =3Db59, or the Open on Wednesday, May 7, 2008. Basic= ally, the model shifts back the Open 5 observations, so the data on every Wednesd= ay will forecast the Open on every following Wednesday, a week into the future. Likewise, each Tuesday’s data will forecast the Open of the next Tuesday, or the nex= t 7 working days.
--- Table 3.2 Historical Data Used In Multiple Linear Regression
|
Table 3.2 |
Historical Data Used In Multiple Linear
Regression Calculations |
|||||||
|
Regression of Open+5Lag on
Market Quotes of the Trading Historical Data Applied Above to Holdout &am=
p;
Actual Future Data |
|
|
|
|
|
|
||
|
X1-Independent |
X2 |
X3 |
X4 |
X5 |
X6 |
Y-Dependent |
||
|
Date |
Open |
High |
Low |
Close |
Volume |
Adj Close |
Open+5Lag |
|
|
Wednesday,
April 30, 2008 |
67.77 |
68.5 |
66.6 |
68 |
33300 |
67.99 |
69.43 |
=3DB59 |
|
Tuesday,
April 29, 2008 |
70.38 |
70.4 |
67.2 |
67.4 |
25600 |
67.38 |
70.13 |
=3DB60 |
|
Monday, A=
pril
28, 2008 |
70.75 |
71.2 |
69.8 |
70.3 |
34900 |
70.32 |
68.37 |
=3DB61 |
|
Friday, A=
pril
25, 2008 |
68.93 |
69.5 |
68.8 |
69.5 |
11200 |
69.49 |
65.75 |
=3DB62 |
|
Thursday,
April 24, 2008 |
67.71 |
69.3 |
67.2 |
68.2 |
28400 |
68.21 |
67.09 |
=3DB63 |
|
Wednesday,
April 23, 2008 |
66.26 |
68.7 |
65.9 |
68.7 |
13400 |
68.65 |
67.77 |
6 |
|
Tuesday,
April 22, 2008 |
67.35 |
68 |
66.9 |
67.7 |
23600 |
67.68 |
70.38 |
7 |
|
Monday, A=
pril
21, 2008 |
66.61 |
67.8 |
66.4 |
67.6 |
17800 |
67.6 |
70.75 |
8 |
|
Friday, A=
pril
18, 2008 |
64.74 |
66.8 |
64.5 |
66.8 |
38800 |
66.78 |
68.93 |
9 |
|
Thursday,
April 17, 2008 |
65.25 |
66 |
64.9 |
65.1 |
14000 |
65.05 |
67.71 |
10 |
|
Wednesday,
April 16, 2008 |
63.96 |
65.8 |
63.2 |
65.3 |
19700 |
65.28 |
66.26 |
11 |
|
Tuesday,
April 15, 2008 |
63.9 |
64.3 |
63.7 |
64.3 |
10500 |
64.26 |
67.35 |
12 |
|
Monday, A=
pril
14, 2008 |
62.55 |
63.1 |
62 |
63.1 |
5300 |
63.12 |
66.61 |
13 |
|
Friday, A=
pril
11, 2008 |
62.64 |
62.6 |
61.8 |
62.2 |
25400 |
62.17 |
64.74 |
14 |
|
Thursday,
April 10, 2008 |
63.99 |
64.3 |
62.8 |
63 |
22400 |
62.95 |
65.25 |
15 |
|
Wednesday,
April 09, 2008 |
62.69 |
63.6 |
62.7 |
63.4 |
36600 |
63.44 |
63.96 |
16 |
|
Tuesday,
April 08, 2008 |
61.78 |
62.1 |
60.7 |
61 |
4000 |
60.95 |
63.9 |
17 |
|
Monday, A=
pril
07, 2008 |
60.27 |
61.4 |
60 |
61.3 |
10000 |
61.32 |
62.55 |
18 |
|
Friday, A=
pril
04, 2008 |
59.44 |
59.4 |
58.4 |
58.4 |
6900 |
58.39 |
62.64 |
19 |
|
Wednesday,
October 31, 2007 |
53.32 |
55.4 |
53.3 |
55.3 |
6600 |
55.33 |
52.3 |
125 |
|
Tuesday,
October 30, 2007 |
53.74 |
54.1 |
53.2 |
53.2 |
3800 |
53.23 |
53.96 |
126 |
|
Monday,
October 29, 2007 |
52.52 |
53 |
52.5 |
53 |
3300 |
53.03 |
54.44 |
127 |
|
Friday,
October 26, 2007 |
51.7 |
51.7 |
51.4 |
51.6 |
4200 |
51.57 |
57.03 |
128 |
|
Thursday,
October 25, 2007 |
50.85 |
51.9 |
50.9 |
51.9 |
12900 |
51.85 |
55.83 |
129 |
Table 3.2 shows the historical data us= ed in multiple linear regression calculations.&n= bsp; This regression of the Monthly model is the
regression of Open+5Lag on market quot= es of the trading historical data applied above to holdout & actual future data. It regresses the next w= eek Open (Open+5Lag, Open Plus 5 working days lag +2 weekend days=3D7 total day= s in a week) on today’s data including, X1-Independent, X2, X3, X4, X5, X6=3DY-Dependent, the next week Open. The column headers show the independent variables followed by the dependent variable as follows: &= nbsp; Date, Open, High, Low, Close, Volume, skipping Adj Close (too dependent on Close)= and the Dependent variable, Open+5Lag. &n= bsp; The 1st observation data is: Wednesday, April 30, 2008, 67.77. Notice, the formula of= the dependent variable being “=3DB59.” Notice also that after 19 first re= cords of observation, the authors have cut out the remaining observations, up to observation 125 to save space. Finally, at the end, is the last observation for the Monthly model, observation number 129.
--- Table 3.3 Back Testing Regression Coefficient Applied Above to Holdout Sample Historical Data &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; &= nbsp; &nbs= p; =
|
Table 3.3 |
Forecasting Errors |
Equation: |
Forecast |
Intercept |
Date |
Open |
High |
Low |
Close |
Volume |
|
%Error |
$Error |
Open |
-1461.122=
|
0.037307<= o:p> |
0.285592<= o:p> |
0.09071 |
-0.2082 |
0.6410565=
|
-6E-05 |
|
|
Revenue4 |
1.64% |
$ 1.12 |
$
68.31 |
(1,461.12) |
1,476.13 =
|
$ 19.35 |
$ 6.21 |
(13.86) |
43.59 |
(1.99) |
|
Revenue3 |
-1.24% |
$ (0.88) |
$
71.01 |
(1,461.12) |
1,476.10 =
|
$ 20.10 |
$ 6.38 |
(14.00) |
45.08 |
(1.53) |
|
Revenue2 |
-1.58% |
$ (1.09) |
$
69.46 |
(1,461.12) |
1,475.99 =
|
$ 20.21 |
$ 6.46 |
(14.52) |
44.55 |
(2.09) |
|
Revenue1 |
-5.48% |
$ (3.81) |
$
69.56 |
(1,461.12) |
1,475.95 =
|
$ 19.69 |
$ 6.30 |
(14.31) |
43.73 |
(0.67) |
|
Cost |
-2.40% |
$ (1.65) |
$
68.74 |
(1,461.12) |
1,475.91 =
|
$ 19.34 |
$ 6.29 |
(13.98) |
44.01 |
(1.70) |
|
Division |
-9.09% |
$ (6.31) |
$ 69=
.42 |
=3DA72*$O$55 |
||||||
|
Formula: |
=3DL72/M72 |
=3DAVERAGE(M67:M71) |
=3D$P$66*B71 |
|||||||
|
=3DSUM(L67:L71) |
--- Table 3.3 shows the back testing o= f the regression coefficient applied above to holdout sample historical data. It includes the back testing regre= ssion coefficient applied above to holdout sample historical data. Table 3.3 shows the back testing o= f the regression coefficient applied above to holdout sample historical data. It includes the back testing regre= ssion coefficient applied above to holdout sample historical data. Table 3.3 shows the Forecasting Er= rors of the Equation: Forecast=3DIntercept+Date+Open+High+Low+Close+Volume, and = its related %Error, and $Error. T= he table applies it to multiple scenes, depending on the holding period by days. Revenue 4 shows the cas= e of 4 working days holding period, while revenue 1 shows the case of 1 day holding period. For the case of 1 day= , the traders buy on the open of Thursday, May 08, 2008, at $70.74, the Open purc= hase price, hold it for a day and sell on the next Open, on Friday, May 09, 2008= at $71.18, pocketing the difference of $0.82, for holding the share 1 day duri= ng Thursday, May 08, 2008. Even = if the traders originally planned to hold it for 4 days, until Wednesday, May 14, 2008, the traders may change their mind and exit after only 1 day, taking t= he money and running. Notice the last record Division shows the average error = as -9.09%, which is less than 12% maximum error rate the R Square projects.
|
Table 3.4 |
||||||||||
|
Forecasting Errors |
Projected Possible Holding
Period Income Calculation "If Than" From 1-4 Days |
|||||||||
|
%Error |
$Error |
Open |
Day1 |
Day2 |
Day3 |
Day4 |
Holding Period |
|||
|
Revenue4 |
1.64% |
$ 1.12 |
$
68.31 |
>------------- |
>------------- |
>------------- |
$
68.31 |
4 Day Revenue |
||
|
Revenue3 |
-1.24% |
$ (0.88) |
$
71.01 |
>------------- |
>------------- |
$ 71.01 |
>------------- |
3 Day Revenue |
||
|
Revenue2 |
-1.58% |
$ (1.09) |
$
69.46 |
>------------- |
$ 69.46 |
>------------- |
>------------- |
2 Day Revenue |
||
|
Revenue1 |
-5.48% |
$ (3.81) |
$
69.56 |
$ 69.56 |
>------------- |
>------------- |
>------------- |
1 Day Revenue |
||
|
Cost |
-2.40% |
$ (1.65) |
$
68.74 |
(68.74) |
(68.74) |
(68.74) |
(68.74) |
Cost |
||
|
Sum |
-9.05% |
$ (6.31) |
$ 69=
.42 |
$ &nbs=
p;
0.82 |
$
0.72 |
$ 2.27 |
$
(0.43) |
Profit Margin |
||
|
Difference |
0.04% |
Rounding Error |
$ 0.82 |
|||||||
|
=3DM74-M75 |
Table 3.4 shows the Forecasting Errors=
for
various levels of Projected Possible Holding Periods of Income Calculation. It looks at an "If Than"=
analysis
of a range of holding periods of the purchased Gaz Shares, From 1 to 4 Days,
for the historical hold out period.
We can see that this model is optimized for a longer than 1 day hold=
ing
period as we observe the error size, the error decreases with the holding
period. Notice that Revenue4,=
the
longest holding period of 4 days, errs only of 1.64%, compared to a much la=
rger
error of -5.48% for Revenue1, representing 1 holding day. Yet, the profit margin diminishes =
as the
holding period increases. The=
daily
cumulative profits of $0.82, $0.72, $ 2.27, turn into a forecasted loss aft=
er a
4 day holding period of $ (0.43) Profit Margin, which is actually a loss.
Table 3.6
|
Table 3.6 |
Variance Err |
|
Forecast |
Intercept |
Date |
Open |
High |
Low |
Close |
Volume |
|
|
%Error |
$Error |
Open |
-1461.122=
|
0.037307<= o:p> |
0.285592<= o:p> |
0.09071 |
-0.2082 |
0.6410565=
|
-6E-05 |
|
HoldOut1 |
3.922% |
2.75 |
70.15 |
(1,461.12) |
1,476.43 =
|
19.83 |
6.45 |
(14.36) |
45.20 |
(2.28) |
|
HoldOut2 |
3.051% |
2.13 |
69.86 |
(1,461.12) |
1,476.40 =
|
20.03 |
6.42 |
(14.38) |
44.33 |
(1.81) |
|
HoldOut3 |
1.553% |
1.09 |
70.37 |
(1,461.12) |
1,476.36 =
|
19.53 |
6.34 |
(14.22) |
44.65 |
(1.16) |
|
HoldOut4 |
4.462% |
3.04 |
68.14 |
(1,461.12) |
1,476.25 =
|
18.78 |
6.08 |
(13.64) |
42.89 |
(1.09) |
|
HoldOut5 |
7.013% |
4.64 |
66.10 |
(1,461.12) |
1,476.21 =
|
19.16 |
6.09 |
(13.64) |
42.25 |
(2.84) |
|
3.961% |
13.65 |
344.62 |
=3DA63*$O$58 |
=3DB63*$P$58 |
=3DD63*$R$58 |
|||||
|
=3DL64/M64 |
=3DSUM(M59:M63) |
=3DC63*$Q$58 |
=3DE63*$S$58 |
|||||||
|
=3DSUM(L59:L63) |
Table 3.6 shows the forecasting errors= for the Holdout sample data for 5 consecutive days. This model uses the same coefficie= nts for all 5 days. Table 3.6 cop= ied the regression function coefficients and transposed them horizontally start= ing with the Forecast Intercept, at the left side, and proceeding to the Date, Open, High, Low, &n= bsp; Close, and last X the Volume. = At the end of the table, we can see the Excel formula used to calculate and apply = the X coefficients to the X values to calculate the forecasted Open as follows: =3DA63*$O$58, =3DB63*$P$58, =3DD63*$R$58, =3DL64/M64, =3DSUM(M59:M63), =3DC= 63*$Q$58, =3DE63*$S$58, and =3DSUM(L59:L63).<= span style=3D'mso-spacerun:yes'> It further reinforces the applicat= ion of the same coefficients to different holdout sample days.
Appendix A shows the TOP INSTITU=
TIONAL
HOLDERS. It may be important =
to
know and examine the financial state.
If they are in trouble, and they will all try to cash their Gas ETNs=
at
the same time, it may lead to a liquidity problem.
COMBINING TECHNICAL, FUNDAMENTAL AND S= TATISTICAL ANALYSIS MAY IMPROVE THE OVERALL PERFORMANCE ROI
Appendix B shows the technical analysi= s of the Gaz ETN. Traders may want to consult such charts to see any unusual patterns that may lurk in the data a= nd defy this strategy. The trade= rs may want to confirm that the pattern is present consistently over time, like in this case of rising prices over several months. It also compares the ETN to several other market indices such as Standard & Poor’s, Dow Jones, and make sure that the standard th= at you are using outperforms the other indices.
Technical Analysis
Looking at the charts and their indica= tors such as RSI, Stochastic, 100-day MA (Moving Average), 10-DAY EMA (Exponenti= al MA),5-DAY EMA, and the
Parabolic SAR, riding below the stock = market prices for the week following Thur. May 8, 2008, together with the Candle Sticks p= oint to a surge in the stock market values of Gaz. In contrast, the indices of GSPC- S&P, DJI-Dow Jones, IXIC- Nasdaq are somehow flat for this period, indicating that the public of traders and investor view Oil and Gaz as defensive strategies, when the rest of the market stagnates.
Appendix C shows a sample data from Ya= hoo.com of the Gaz ETN, as Yahoo displays it. It needs to be checked to find out if there are any anomalies that are abnormal and may raise the ris= k of the trade.
SUMMARY, CONCLUSIONS AND IMPLICATIONS<= /span>
Summary
We have compared across multiple regre= ssions monthly and semiannual models. We have defined the strategy to a profitable trade, including using a hold out sample to back test the models the multiple linear regression and the R Squares. We have exceeded a m= inimum of 80% validity as measured by R Square, and concluded a very profitable sw= ing trade strategy, of a holding period of 1 to 4 days. We have tested statistically signi= ficant linear models and optimized the number of observations. Likewise, semiannual model is superior to a linear monthly model for the ETN Gas fund, but even = if the difference is small, it is significant. The higher the number of observati= ons, the larger the expected R Square and ROI, Return on Investment. A linear model is good enough, and= that may explain, why people tend to use it.&nb= sp; We have tested and rejected the null, stating that the coefficients = are all equal to zero, in favor of the alternative hypothesis, that they are not equal to zero.
Conclusion
The semiannual model is better than the monthly linear model, but the difference increases as we decrease the numbe= r of periods. We conclude th= at the model works for the Gas ETN, but we have to back test it on more observatio= ns and on other industries and commodities.&n= bsp; In our sample test of 1 trade, we got a good return, ROI, but it may= be a too small sample. This stra= tegy should be back tested on hundreds of test data and confirmed before trading= on it in the open market. All th= ings being the same, the traders will be better off using as many observed cases= as possible, as long as the R Square keeps rising.
Implications
Gas ETN seems like a good and profitab= le investment strategy, but we have to monitor it continuously. Our holding period is limited to 1 working week, or 5 working days. Additional strategies may be developed for a different holding perio= d, and different trading strategies. It can turn on a dime, as soon as a new war in the Middle East breaks out over night. Therefore, we= have to place stop loss conditions and enforce them consistently. In such a case, investors and trad= ers should be very careful and notice that tensions are building up. Price of Gas may rise again increa= sing the profitability of such Gas ETNs. On the other hand, if normality returns to the market place, the Gas markets may settle, and the abnormal profits will decline with it. If that is the case, do not wait u= ntil it is too late to cash in and take the profit, because in another day it ma= y be gone. This study presents an automated decision tools to exit on time, and to see warning on time. Using an automatically recalculati= ng regression analysis with daily forecasts and variance error analysis will h= elp spot trend changes early enough to maximize the return on investment (ROI) = on the Gas ETN.
The implications are particularly impo= rtant for programmers of automated trading systems, who frequently omit a formal forecast, variance analysis, and adjusting entries that result from such variance analysis. Some of the reasons may include, but are not limited to, the desire to understate the errors of the automated trading system, in favor of overstating its profita= bility. Another reason may be the lack of accounting knowledge, along with the additional complexity that such efforts may overload the system, slowing it down, and confusing the users. Future studies will investigate the reasons for the lack of formal variance analys= is both in practice and in theories, textbooks and other writing with the aim = of finding out what profitability and accuracy gain may be achieved due to such addition to robotic automated rule based algorithmic trading systems. That maybe particularly relevant t= o the example of the energy sector and GAS ETN since they have been so volatile, leading to so many forecasting and forensic anomalies
References
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Rushinek,
SF Rushinek - ACM SIGMIS Database, 1983 - portal.acm.org ... =
By Avi
Rushinek & Sara E Rushinek ... Second, many
statistical models i.e., multiple regression and analysis of
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1113493
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International Investors' Perception Model for Corporate Published Forecasted
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...
AVI RUSHINEK SARA F. Rushinek ... Similarly, the
mean utility score of cost of goods sold (COGS) is 64.7739 for buying decis=
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Avi
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Rushinek, A. and Rus= hinek, S. "Health Marketing and Sales Distribution Software Related to Comput= er User Satisfaction," HEALTH MARKETING QUARTERLY, Vol. 3, No. 1, 79-101, Fall 1985.
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=3Da746867740~db=3Dall
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software related to computer user satisfaction: an interactive online expert
system using diagnostic audit trails through telecommunication networks,&qu=
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in Science and Technology, Volume 17, Issue 3 May 1986 , pages 285 – =
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SINGAPORE ACCOUNTANT, Vol. 2, No. 2, 30-33, February 1986.
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"Additional Fund Allocation Constraints for Common Stock
Investments: An Empirical Ana=
lysis
of Regional Portfolios in the Common Market and the United States," THE
INTERNATIONAL JOURNAL OF ACCOUNTING, Vol. 21, No. 2, 69-89, Spring 1986.
Rushinek, A. and Rushinek, = S. "The Effects of Communication Monitors on User Satisfaction," INFORMATION PROCESSING AND MANAGEMENT, Vol. 22, No. 4, 345-351, January 198= 6.
WHAT MAKES USERS HAPPY?=
-AVI RUSHIN=
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multiple regression analysis was used to determine the
relationship between the overall satisfaction ... Cited by 71 - Related Articles - Web Search
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S. "What Makes Users Happy," Communications of the ACM, Ju=
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1986, Vol. 29, No. 7, 594-598.
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A. and Rushinek, S. "Usi=
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Vol. 15, 1987.
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User Satisfaction: An Interactive On-line Expert System Using Diagnostic Au=
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Applied Engineering Education, Vol. 3, No. 4, 399-412, 1987
Rushinek, S. and Rus= hinek, A. "An Application Model for Computer Assisted Design and Manufacturing Using a Product Evaluation and Selection System," Computers & Industrial Engineering, 1987, Vol. 12, No. 3, 173-180.
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Microcomputer Users & Manufacturers," SINGAPORE ACCOUNTANT, Vol.4,
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Microcomputer Users and Manufacturers", COMPUTERS & INDUSTRIAL
ENGINEERING, Vol. 16, No. 2, 321-328, 1989.
Rushinek, A. and Rushinek, S. "Multinational Transfer-Pri=
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Factors: Tax, Custom Duties, Antitrust/Dumping Legislation, Inflation,
Interest, Competition, Profit/Dividend, and Financial Reporting", INTE=
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A. and
Rushinek, S. "Training Software Case Study: A Product Evaluation and
Selection System", Journal Of Education For Business, 1989
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An
evaluation and selection methodology of microcomputer training software:
Implications for human … - all
2 versions »SF Rushinek, A Rushinek - Proceedings=
of
the ACM SIGCPR conference on Management of …, 1988 - portal.acm.org...
Sara F. Rushinek Avi Rushinek University of =
...
1 or 0), reasonableness, sequence, completeness (no omissions), and correct
algebraic sign (i.e. price always position ... Cited
by 1 - Related
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Rushinek, A. and Rus=
hinek,
S. ,"Training softwa=
re (TS)
case study: feature selection system (FSS) for computer personnel," ACM
SIGCPR Computer Personnel, Volume 12 ,&nbs=
p;
and Issue 1 (April 198=
9),
Pages: 21 - 33, 1989, ISSN:0160-2497, ACM&=
nbsp;
New York, NY, USA
The control of computerized information relating to=
branch
manpower management follow-up systems for …<=
span
style=3D'font-family:"Arial","sans-serif"'> - all 2 versions » A Rushinek,
S Rushinek - ACM SIGCPR Computer Personnel, 1989 - portal.acm.org...
Avi Rushinek Sara Rushinek School of ... For
example, historical cost accounting reports are accurate since they depict
actual events which are recorded ... Related Articles=
- Web Search
A. Rushinek S.
Rushinek, “The control of computerized information relating to branch
manpower management follow-up systems for banks,” Source ACM SIGCPR Computer Personnel arch=
ive
Volume 12 , Issue 1 (April 1989) Pages: 1 - 12 Year of=
Publication:
1989 ISSN:0160-2497 Publisher ACM
New York, NY, USA
Bibliometrics Downloads (6 Weeks): 5, Downloads (12 Months): 48,
=
Rushinek,
A. and Rushinek, S. "Matching Program Code Generators to Software
Developers' Needs", OMEGA: The International Journal Of Management Sci=
ence,
Vol. 18, No. 3, 1990
Rushinek, A. and Rushinek, S. "Ga= s and Gas Mandated Accounting Changes and Debt Covenants: Debt to Equity Maturity, Dividend/Retained Earning Reduction & Refinancing Cost Ratios", GAS & GAS TAX QUARTERLY, Vol. 40, No.2, 1991, 316-329.
Rushinek, A. and =
S. Rushinek “Using Experts for Detecting and Litigating Computer=
Crime” Managerial Auditing Journal, 1993 =
- emeraldinsight.com
ISSN: 0268-6902
Rushinek, A. and Rus=
hinek,
S. "Improving Profit=
ability
with Segmented Income Statements for Local Area Networks" Industrial
Management & Data Systems, 1994 Volume: 94 Issue: 2 Page: 7 - 15 DOI:
10.1108/02635579410055828 Publisher: MCB UP Ltd
Improving Profitability with Segme=
nted
Income Statements for
- all 2 versions »L=
Area
- Industrial Management & Data Systems, 1994 - emeraldinsight.com...=
7-15 © MCB University Press Limited, 0263-5577 Avi Rushinek<=
/b>
and Sara F. Rushinek Page 2. ... Table I. Multiple Regress=
ion
Summary Table Page 5. ... Related Articles - Web Search http://www.emeraldinsight.com/10.1108/0263557941=
0055828
Avi Rushinek, Sara F. Rushinek "Forecasting sales, expenses and stock market values by quarterly fina= ncial statement ratio analysis: a microcomputer software development model," Managerial Auditing Journal, Year: 1995, Volume: 10, Issue: 2, Page: 7 R= 11; 33, DOI: 10.1108/02686909510079620, Publisher: MCB UP Ltd URL: http://www= .emeraldinsight.com/10.1108/02686909510079620
Avi Rushinek,=
Sara F.
Rushinek, “Forecasting sales, expenses and stock market values by
quarterly financial statement ratio analysis: a microcomputer software deve=
lopment
model,” Managerial Auditing Journal, Year: 1995, Volume: 10, Issue: 2,
Page: 7 - 33, DOI: 10.1108/02686909510079620, Publisher: MCB UP Ltd http://www.emeraldinsight.c=
om/10.1108/02686909510079620
Rushinek,= A. and Rushinek, S. "Net Income-to-Sales Ratio Grouping For the Crude Petrole= um and Natural Gas Industry Sector: A Company to Peer Comparative Variance Analysis", GAS AND GAS TAX QUARTERLY, June, 1995, Volume 43, No.4, 713-728.
Rushinek, A. and Rushinek, S. "Da= mage Cost Calculation Model for Exxon Corporation and the Gas and Gas Industry: A Simulated Fraud Decomposition of Expert System Software Controls", GAS= AND GAS TAX QUARTERLY, Vol. 44, No. 3, March 1996, 337-350.
Managerial auditors' mixed cost forecasting assumpt= ion departure error estimates for litigation and … - all 4 versions »A Rushinek - Managerial Auditing Journal, 1997 - emeraldinsight.com <= span style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'>...<= span style=3D'font-size:10.0pt;font-family:"Arial","sans-serif"'> Page 7. [ 291 = ] Avi Rushinek and Sara Rushinek Managerial auditors’ mixed c= ost forecasting assumption departure error estimates for litigation ... = Related Articles= - Web Search - BL Direct=
Rushinek A.,
"Managerial auditors’ mixed cost forecasting assumption departur=
e error
estimates for litigation and professional liability risk reduction: the
electronic security industry" Journal: Managerial Auditing Journal, 19=
97,
Volume: 12, Issue: 6, Page: 285 - 297, DOI: 10.1108/02686909710180643,
Publisher: MCB UP Ltd http://www.emeraldinsight.c=
om/10.1108/02686909710180643
Rushinek,= A. and Rushinek, S. "Tax Fraud Forecasting For the Petroleum Refining Industr= y: Financial Ratios & Reversed Accounting Theory Applied to Shell Gas"= ;, GAS AND GAS TAX QUARTERLY, March, 1997.
=
Rushinek,
A. and Rushinek, S. "Project Management Software Feature Profitability:
Windows, Networks, Mainframes, Filtered Task Diagrams, Schedules, and
Calendars, Journal Of Computer Information Systems (JCIS), Vol. 37, No. 4,
Summer 1997, 48-55
Rushinek, A. and Rushinek, S. "Rating and Ranking Best
Practices of the British Petroleum Oil Company and the Oil & Gas Indust=
ry:
Sales to Cash Forecasting Univariate Regression Trend Analysis and Computer
Modeling, OIL AND ENERGY QUARTERLY, December, 1997.
Rushinek, A. and Rushinek, S. "Litigation in Pennzoil and=
the
Petroleum Refining Industry: A Financial Ratio Automated Peer Review Analys=
is
of Variance Internet Software Development" OIL, GAS & ENERGY QUART=
ERLY,
Vol.47, No.1, September, 1998, 17-32.
Rushinek, A. and Rushinek, S.”Correlating Investors’ Preferences to Stock Characteristics:= An Algorithm for Internet Software Decision Support System Development in the Crude Gas & Refining Industry”&n= bsp; GAS, GAS & ENERGY QUARTERLY, Vol. 48, No.1, September, 1999, 87-= 101.
Rushinek, A. and Rushinek, S. ”G= as & Gas Market, Sector & Company Relative Strength Congruity Trading Theory (MSCRSSCTT): An Internet Automation Approach Applied to Chevron Corporation’s Stocks” GAS, GAS & ENERGY QUARTERLY, Vol. 48, No.4, June, 2000, 671-682.=
Rushinek, A. and =
S. Rushinek “Internet Fraud Auditing: A Simulated Health Care In=
dustry
Case Study” - Journal of Forensic Accounting, 2000 -
rtedwards.com
Rushinek, A. and Rushinek, S. "The Role of the Forensic
Accountant in Calculating the Damages Using the 'But-if Analysis in a Case =
of
Internet Day Trader & Online Broker Misconduct Litigation", JOURNA=
L OF
FORENSIC ACCOUNTING, 2001.
Rushinek, A. and Rushinek, S. "Fo= rensic Audits of Stock Market Forecasts For Texaco & The International Gas and= Gas Industry & Financial Models for Online Broker Litigation", GAS, GA= S, & ENERGY QUARTERLY, Vol. 51, No. 4, June, 2003, 659-678.
Rushinek, A. and Rushinek, S. “A= utomated Internet Trading Forecast Variance Analysis: A Gas and Gas Industry and BP Corporation Case Study”, GAS, GAS, & ENERGY QUARTERLY, Volume 52 Number 1 September 2003, 35-54.
Rushinek, A. and Rushinek S. “In= ternet Web Server Comparative Forecasting Sales Models: Reversed Accounting of Tex= aco Corp and The Gas & Gas Industry linear, Exponential, Power, Polynomial & Logarithmic Univariate Regressions”, GAS, GAS, & ENERGY QUARTERLY, Volume 54, No. 2, November 2005, 87-95
Rushinek, A. and =
S. Rushinek “What Makes Users Unhappy: Share-Point Team Servi=
ces
Web Server Security” Ubiquity, Volume 6, Issue2, Jan. 25=
-
Feb. 1, 2005.
Rushinek, A. and Rushinek S. “An= Automated Business Intelligent Stock Market Matching Engine For the Gas and Gas Indus= try: Materiality of Violating the Normality Assumption of Linear Regression Cont= rol Analysis”, GAS, GAS, & ENERGY QUARTERLY, Volume 56, No. 2, Novemb= er 2007, 435-448.
Rushinek, A. and Rushinek S. “Op= timal Forecasting Models For The Gas & Gas Industry: A Study Of The Daily Dow Jones U.S= . Gas & Gas Index And ConocoPhillips With The Aid Of The Virtual Internet Off= ice”, GAS, GAS, & ENERGY QUARTERLY, Volume 57, No. 1, June, 2008.
Rushinek, A. and Rushinek S. “GA= S ETN Converting Linear & Polynomial Daily Open Functions, Fresh Separation &= amp; Significant Statistical R Square And P-Values Entry, Exit, & Stop Loss Swinging Trade Rules”, http://www.ona= free.com/PortfolioManager/7-12-8_MHT_GAS%20ETN%20CONVERGING%20LINEAR%20POLY= NOMIAL%20DAILY%20OPEN%20FUNCTIONS.mht (July, 2008).
Rushinek, A. and Rushinek S. “OI= L ETN Trading Rule Linear & Polynomial Daily Open & Close Regression Forecasts- Automated HTML Java Script Software Development” http://www.onafree.com/PortfolioManager/7-10-8a_mht_Oil%20ETN%20Tradi= ng%20Rule%20Linear%20Poly%20Daily%20Open%20Close%20Regression%20Forecasts.m= ht (July, 2008).
Michael Werner and Kumen Jones “Introduction to Management Accounting – A User PerspectiveR= 21;, Second Edition, Prentice Hall, M-135, 2003.
Appendix A
|
iPath DJ AIG Natural Gas TR Sub-Idx ETN (GAZ=
) |
|
||||
|
TOP INSTITUTIONAL HOLDERS |
|||||
|
Ho=
lder |
Sh=
ares |
% =
Out |
Va=
lue* |
Re=
ported |
|
|
CITIGROUP INC. |
12=
,350 |
1.=
54 |
$7=
81,384
|
31=
-Mar-08 |
|
|
MORGAN STANLEY |
11=
,732 |
1.=
47 |
$7=
42,283
|
31=
-Mar-08 |
|
|
RBC Dominion Securities, Inc. |
9,=
675 |
1.=
21 |
$6=
12,137
|
31=
-Mar-08 |
|
|
UBS AG |
9,=
520 |
1.=
19 |
$6=
02,330
|
31=
-Mar-08 |
|
|
GOLDMAN SACHS GROUP INC |
4,=
326 |
0.=
54 |
$2=
73,706
|
31=
-Mar-08 |
|
|
RBC PRIVATE COUNSEL (USA) CORPORATION |
1,=
000 |
0.=
13 |
$6=
3,270 |
31=
-Mar-08 |
|
|
Ameriprise Financial, Inc. |
25=
0 |
0.=
03 |
$1=
5,817 |
31=
-Mar-08 |
|
|
U.S. BANCORP (MINNESOTA) |
22=
5 |
0.=
03 |
$1=
4,235 |
31=
-Mar-08 |
|
|
MetLife Securities, Inc. |
50=
|
0.=
01 |
$3=
,163 |
31=
-Mar-08 |
|
|
BARCLAYS PLC |
5,=
000,000 |
&n=
bsp; |
$3=
16,350,000
|
31=
-Mar-08 |
Appendix B
=
Appendix C
|
iPath DJ AIG Natural Gas TR Sub-Idx ETN (GAZ=
) |
At 11:56AM ET: 74.35 2.09 (2.73%) |
||||||
|
RICES |
|||||||
|
Da=
te |
Op=
en |
Hi=
gh |
Lo=
w |
Cl=
ose |
Vo=
lume |
Adj
Close* |
|
|
Th=
ursday,
July 10, 2008 |
74=
.79 |
76=
.44 |
73=
.4 |
76=
.44 |
39=
,100 |
76=
.44 |
1<= o:p> |
|
We=
dnesday,
July 09, 2008 |
75=
.59 |
76=
.74 |
73=
.24 |
73=
.31 |
67=
,800 |
73=
.31 |
2<= o:p> |
|
Tu=
esday,
July 08, 2008 |
77=
.27 |
77=
.64 |
75=
.66 |
75=
.72 |
13=
5,600 |
75=
.72 |
3<= o:p> |
|
Mo=
nday,
July 07, 2008 |
80=
.69 |
82=
.24 |
79=
.38 |
79=
.72 |
61=
,600 |
79=
.72 |
4<= o:p> |
|
Th=
ursday,
July 03, 2008 |
82=
.16 |
82=
.93 |
81=
.88 |
82=
.85 |
33=
,000 |
82=
.85 |
5<= o:p> |
|
We=
dnesday,
July 02, 2008 |
83=
|
83=
.38 |
81=
.14 |
82=
.52 |
52=
,300 |
82=
.52 |
6<= o:p> |
|
Tu=
esday,
July 01, 2008 |
83=
.44 |
83=
.64 |
82=
.77 |
83=
.24 |
40=
,300 |
83=
.24 |
7<= o:p> |
|
Mo=
nday, June
30, 2008 |
82=
.29 |
82=
.4 |
81=
.24 |
82=
.3 |
39=
,000 |
82=
.3 |
8<= o:p> |
|
Fr=
iday,
June 27, 2008 |
82=
.06 |
82=
.25 |
81=
|
81=
.52 |
42=
,200 |
81=
.52 |
9<= o:p> |
|
Th=
ursday,
June 26, 2008 |
78=
.74 |
81=
.63 |
77=
.62 |
81=
.3 |
73=
,700 |
81=
.3 |
10=
|
|
We=
dnesday,
June 25, 2008 |
79=
.55 |
79=
.61 |
78=
.28 |
78=
.7 |
31=
,200 |
78=
.7 |
11=
|
|
Tu=
esday,
June 24, 2008 |
80=
.75 |
81=
.44 |
80=
.05 |
80=
.64 |
28=
,000 |
80=
.64 |
12=
|
|
Mo=
nday,
June 23, 2008 |
81=
.13 |
82=
.1 |
81=
.11 |
81=
.95 |
45=
,800 |
81=
.95 |
13=
|
|
Fr=
iday,
June 20, 2008 |
81=
.24 |
81=
.57 |
80=
.43 |
80=
.55 |
43=
,700 |
80=
.55 |
14=
|
|
Th=
ursday,
June 19, 2008 |
82=
.2 |
82=
.33 |
78=
.32 |
79=
.44 |
48=
,100 |
79=
.44 |
15=
|
|
We=
dnesday,
June 18, 2008 |
80=
.88 |
81=
.99 |
80=
.67 |
81=
.96 |
27=
,400 |
81=
.96 |
16=
|
|
Tu=
esday,
June 17, 2008 |
80=
.22 |
80=
.51 |
79=
.44 |
80=
.11 |
20=
,600 |
80=
.11 |
17=
|
|
Mo=
nday,
June 16, 2008 |
79=
.33 |
80=
.09 |
79=
.33 |
79=
.77 |
19=
,500 |
79=
.77 |
18=
|
|
Fr=
iday,
June 13, 2008 |
78=
|
78=
.39 |
77=
.76 |
78=
.13 |
19=
,000 |
78=
.13 |
19=
|
|
Th=
ursday,
June 12, 2008 |
77=
.57 |
80=
|
77=
.42 |
79=
.1 |
26=
,500 |
79=
.1 |
20=
|
|
We=
dnesday,
June 11, 2008 |
77=
.87 |
78=
.61 |
77=
.8 |
78=
.54 |
44=
,100 |
78=
.54 |
21=
|
|
Tu=
esday,
June 10, 2008 |
77=
.91 |
78=
.38 |
75=
.93 |
76=
.78 |
22=
,700 |
76=
.78 |
22=
|
|
Mo=
nday,
June 09, 2008 |
77=
.68 |
78=
.84 |
77=
.48 |
77=
.84 |
18=
,600 |
77=
.84 |
23=
|
|
Fr=
iday,
June 06, 2008 |
78=
.99 |
78=
.99 |
77=
.94 |
78=
.21 |
25=
,000 |
78=
.21 |
24=
|
|
Th=
ursday,
June 05, 2008 |
77=
.01 |
77=
.22 |
75=
.91 |
77=
.19 |
27=
,500 |
77=
.19 |
25=
|
|
We=
dnesday,
June 04, 2008 |
74=
.96 |
76=
.8 |
74=
.7 |
76=
.64 |
27=
,200 |
76=
.64 |
26=
|
|
Tu=
esday,
June 03, 2008 |
76=
.46 |
76=
.46 |
75=
.09 |
75=
.54 |
43=
,800 |
75=
.54 |
27=
|
|
Mo=
nday,
June 02, 2008 |
77=
|
77=
|
72=
.86 |
74=
.3 |
79=
,100 |
74=
.3 |
28=
|
|
Fr=
iday,
May 30, 2008 |
71=
.6 |
72=
.51 |
71=
.31 |
72=
.51 |
11=
,500 |
72=
.51 |
29=
|
|
Th=
ursday,
May 29, 2008 |
72=
.93 |
74=
.65 |
70=
.65 |
70=
.65 |
23=
,700 |
70=
.65 |
30=
|
|
We=
dnesday,
May 28, 2008 |
73=
.01 |
74=
.6 |
72=
.87 |
74=
.06 |
11=
,500 |
74=
.06 |
31=
|
|
Tu=
esday,
May 27, 2008 |
74=
.2 |
75=
.4 |
73=
.33 |
73=
.33 |
33=
,200 |
73=
.33 |
32=
|
|
Fr=
iday,
May 23, 2008 |
73=
.72 |
74=
.14 |
72=
.76 |
74=
.14 |
7,=
900 |
74=
.14 |
33=
|
|
Th=
ursday,
May 22, 2008 |
72=
.35 |
73=
.62 |
71=
.78 |
72=
.62 |
25=
,000 |
72=
.62 |
34=
|
|
We=
dnesday,
May 21, 2008 |
71=
.41 |
73=
.1 |
71=
.1 |
73=
.05 |
37=
,100 |
73=
.05 |
35=
|
|
Tu=
esday,
May 20, 2008 |
69=
.67 |
71=
.18 |
69=
.55 |
71=
.05 |
34=
,200 |
71=
.05 |
36=
|
|
Mo=
nday, May
19, 2008 |
69=
.6 |
70=
.34 |
67=
.69 |
68=
.24 |
32=
,200 |
68=
.24 |
37=
|
|
Fr=
iday,
May 16, 2008 |
71=
.88 |
72=
.14 |
69=
.1 |
69=
.2 |
29=
,900 |
69=
.2 |
38=
|
|
Th=
ursday,
May 15, 2008 |
72=
.73 |
72=
.73 |
69=
.75 |
71=
.14 |
29=
,000 |
71=
.14 |
39=
|
|
We=
dnesday,
May 14, 2008 |
72=
.9 |
73=
|
72=
.03 |
72=
.09 |
18=
,600 |
72=
.09 |
40=
|
|
Tu=
esday,
May 13, 2008 |
71=
.99 |
72=
.41 |
70=
.36 |
71=
.18 |
17=
,600 |
71=
.18 |
41=
|
|
Mo=
nday,
May 12, 2008 |
71=
.46 |
72=
.14 |
70=
.16 |
70=
.36 |
32=
,900 |
70=
.36 |
42=
|
|
Fr=
iday,
May 09, 2008 |
71=
.18 |
72=
.12 |
70=
.64 |
71=
.92 |
24=
,500 |
71=
.92 |
43=
|
|
Th=
ursday,
May 08, 2008 |
70=
.74 |
71=
.02 |
69=
.8 |
70=
.24 |
27=
,400 |
70=
.24 |
44=
|
|
We=
dnesday,
May 07, 2008 |
69=
.43 |
71=
.15 |
69=
|
70=
.51 |
38=
,100 |
70=
.51 |
45=
|
|
Tu=
esday,
May 06, 2008 |
70=
.13 |
70=
.74 |
69=
.08 |
69=
.15 |
30=
,200 |
69=
.15 |
46=
|
|
Mo=
nday,
May 05, 2008 |
68=
.37 |
69=
.84 |
68=
.3 |
69=
.65 |
19=
,400 |
69=
.65 |
47=
|
|
Fr=
iday,
May 02, 2008 |
65=
.75 |
67=
.08 |
65=
.54 |
66=
.9 |
18=
,200 |
66=
.9 |
48=
|
|
Th=
ursday,
May 01, 2008 |
67=
.09 |
67=
.1 |
65=
.51 |
65=
.91 |
47=
,500 |
65=
.91 |
49=
|
|
We=
dnesday,
April 30, 2008 |
67=
.77 |
68=
.5 |
66=
.59 |
67=
.99 |
33=
,300 |
67=
.99 |
50=
|
|
Tu=
esday,
April 29, 2008 |
70=
.38 |
70=
.38 |
67=
.23 |
67=
.38 |
25=
,600 |
67=
.38 |
51=
|
|
Mo=
nday,
April 28, 2008 |
70=
.75 |
71=
.2 |
69=
.75 |
70=
.32 |
34=
,900 |
70=
.32 |
52=
|
|
Fr=
iday,
April 25, 2008 |
68=
.93 |
69=
.49 |
68=
.75 |
69=
.49 |
11=
,200 |
69=
.49 |
53=
|
|
Th=
ursday,
April 24, 2008 |
67=
.71 |
69=
.29 |
67=
.15 |
68=
.21 |
28=
,400 |
68=
.21 |
54=
|
|
We=
dnesday,
April 23, 2008 |
66=
.26 |
68=
.69 |
65=
.92 |
68=
.65 |
13=
,400 |
68=
.65 |
55=
|
|
Tu=
esday,
April 22, 2008 |
67=
.35 |
68=
.03 |
66=
.88 |
67=
.68 |
23=
,600 |
67=
.68 |
56=
|
|
Mo=
nday,
April 21, 2008 |
66=
.61 |
67=
.75 |
66=
.36 |
67=
.6 |
17=
,800 |
67=
.6 |
57=
|
|
Fr=
iday,
April 18, 2008 |
64=
.74 |
66=
.78 |
64=
.52 |
66=
.78 |
38=
,800 |
66=
.78 |
58=
|
|
Th=
ursday,
April 17, 2008 |
65=
.25 |
66=
|
64=
.88 |
65=
.05 |
14=
,000 |
65=
.05 |
59=
|
|
We=
dnesday,
April 16, 2008 |
63=
.96 |
65=
.76 |
63=
.21 |
65=
.28 |
19=
,700 |
65=
.28 |
60=
|
|
Tu=
esday,
April 15, 2008 |
63=
.9 |
64=
.26 |
63=
.68 |
64=
.26 |
10=
,500 |
64=
.26 |
61=
|
|
Mo=
nday,
April 14, 2008 |
62=
.55 |
63=
.12 |
61=
.98 |
63=
.12 |
5,=
300 |
63=
.12 |
62=
|
|
Fr=
iday,
April 11, 2008 |
62=
.64 |
62=
.64 |
61=
.77 |
62=
.17 |
25=
,400 |
62=
.17 |
63=
|
|
Th=
ursday,
April 10, 2008 |
63=
.99 |
64=
.34 |
62=
.75 |
62=
.95 |
22=
,400 |
62=
.95 |
64=
|
|
We=
dnesday,
April 09, 2008 |
62=
.69 |
63=
.58 |
62=
.69 |
63=
.44 |
36=
,600 |
63=
.44 |
65=
|
|
Tu=
esday,
April 08, 2008 |
61=
.78 |
62=
.13 |
60=
.7 |
60=
.95 |
4,=
000 |
60=
.9 |
66=
|