7-20-8_DOC_G=
AS Performance Evaluation- GAS
ETN ROI LOOK AHEAD MULTIPLE REGRESSION HOLDOUT SAMPLE BUDGET FORECAST VARIA=
NCE
ANALYSIS
PERFORMANCE EVALUATION- GAS ETN ROI LOOK AHEAD LAGGED MULTIPLE REGRESSION BUDGET FORECAST ANOVA & VARIANCE ANALYSIS HOLDOUT SAMPLE BACKTESTING
= ;
Avi and Sara Rushinek, University of M= iami, arush@miami.edu arushine@aol.com
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
Abstract
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 test the mont= hly linear model and assume that the statistical significance of the monthly linear mo= del also applies to the semiannual model.
This study
develops Gas ETN Trading Rules using Linear & Polynomial Daily Open
Regression models. It forecas=
ts
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 A=
ccounting,"(March
1984) dedicate sufficient resources to setup a Management Accounting
Information Systems to evaluate the process for cash management, as Rushine=
k,
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
Investments: An Empirical Ana=
lysis
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 t=
he
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
investment 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 autom=
ated
trading programs.=
=
Much
like Rushinek. and Rushinek explain in "Project Management Software Fe=
ature
Profitability: Windows, Networks, Mainframes, Filtered Task Diagrams,
Schedules, and Calendars,” ( Summer 1997). An automated trading program is
basically a project management scheduling program. The traders are scheduling entry, =
exit,
and alternative courses of trading actions in the stock market. Thus they have to apply similar co=
ntrols
and due diligence. Like the c=
ase of
Rushinek. and Rushinek
of “Internet Fraud Auditing: A Simulated Health Care In=
dustry
Case Study”( 2000), trading has become an internet dependen=
t occupation
base on gathering information as well as executing trades, and avoiding fra=
uds
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 litigat=
ion purposes.
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 microcomput=
er-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 forecas=
ting
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 characteristics of the latter. Similar to equitie= s, they are traded on an exchange and can be shorted. Similar to index fund, they are li= nked to the return of a benchmark index. But as debt securities, ETNs don't actu= ally 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, add= itional issuers entered the market with their own offerings; these include 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 rate 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 increase 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 Large Cap U.S. Sector Momentum Index, is to take advantage of the varied performances of the 10 sub-indexes of the S&= ;P 500 Total Return IndexSM (SPTR) relative to each other and to the SPTR. The wei= ghts of the 10 sub-indexes are computed each day based on performance and correlation. This makes SPECTRUM Large Cap U.S. Sector Momentum Index diffi= cult to track through ETF. On the contrary, ETN provides opportunities to gain exposure to these types of investment strategies 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 issui= ng 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 d= etermine the relationship between the overall satisfactions of computer users, this study uses regression to determine the overall impact on the Open stock mar= ket values (Communications of the ACM, July 1986). Another similar example is “= forecasting sales, expenses and stock market values by quarterly financial statement ra= tio analysis: a microcomputer software development model.” Such study of “Forecasting 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 fin= ancial statement ratio analysis (FSRA). This analysis matches company to industry = data and builds sales forecasting models. FSRA imputes forecast standards of sal= es and costs, and applies them to a budgeted financial statement variance anal= ysis for the EE (electronic and electrical) industry. The present study is similar= in dealing with an industry, except that the current industry is the Gas and G= as industry (Gas). Likewise, this study demonstrates a financial statement ratio that is the daily growth rat= e 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 exceptions. Likewise, the cur= rent study does the same except that it uses new software techniques that were n= ot available before. Instead of forecasting an individual stock market value t= he 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.&nb= sp; The previous study “uses a multivariate linear trend regression analysis for the sales forecasting model.” This study is using a Univariate (1 independent variable, the Julian date) instead of a multivariate (more than= 1 independent agruement variables). The previous study used only linear regression; the current study ad= ds non-linear (Polynomial) regression, to the 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 financia= l ratio of ETN daily growth rate and builds forecasting models, to forecast its 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 suc= h 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 imp= act 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
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 “Foren= sic Audits of Stock Market Forecasts.”&n= bsp; In this case they applied the model to “Texaco & the International Gas and Gas Industry.”= Using “Financial Models for Online Broker Litigation (2003),” 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. and Rushinek S. show = the “Optimal Forecasting Models for the Gas & Gas Industry” will take into consideration some problems and deal with them effectively. “A Study of the Daily Dow Jo= nes U.S. Gas & Gas Index and ConocoPhillips” is similar 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 mathematical 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
|
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 |
|
|||||||||||||||||
|
Multiple R |
0.97369 <= o:p> |
|
||||||||||||||||
|
R Square |
94.81% |
|
||||||||||||||||
|
Adjusted R Square |
94.62% |
|
||||||||||||||||
|
Standard Error |
2.64346 <= o:p> |
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||||||||||||||||
|
Observations |
177 |
|
||||||||||||||||
Table 0 shows the “Linear Models of Regressions of Open on Date of a Month Semi Ann= ual models. We want to find out which time per= iod is better. The R Square measures= the quality of the regression line the highest possible value is 100%, a perfect predictor, and the lowest possible value is zero, which means no predictive abilities. The tables show se= veral 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). It describes the Date, Open, and t= he rest of the data that this program ignores including: High, Low, Close, Vol= ume, 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 variables. &nb= sp; = &nb= sp; =
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 |