The information that FastGraph provides is only part of the information needed for a
good investment program. Consult your mutual fund representative before buying or
selling any fund. Read the prospectus to determine whether an investment meets your
objectives.
EDGE WARE, INC. DOES NOT RECOMMEND SPECIFIC INVESTMENTS
SUITABLE FOR YOUR PERSONAL OBJECTIVES BUT IS LIMITED TO PROVIDING INFORMATION FROM THE BEST AVAILABLE SOURCES. HOWEVER, THESE SOURCES ARE KNOWN TO CONTAIN ERRORS, AND EDGE
WARE, INC. DOES NOT ASSUME LIABILITY FOR ERRORS IN INFORMATION. THIS PRODUCT IS DISTRIBUTED “AS IS” WITHOUT WARRANTIES
OF ANY KIND, EITHER EXPRESSED OR IMPLIED. NEITHER EDGE WARE,
INC. NOR ANYONE ELSE INVOLVED IN CREATING, PRODUCING, OR DISTRIBUTING THIS PRODUCT SHALL BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL OR CONSEQUENTIAL DAMAGES ARISING
FROM THE USE OF THIS PRODUCT.
Program and documentation copyright 1998 by Edge Ware, Inc. All rights are reserved.
The software packaged with this manual is not copy-protected. Duplication of this software is limited to one backup copy. No part of this manual may be reproduced or transmitted in any form without written consent from Edge Ware, Inc.
FastGraph, FastBreak, and Edge Ware logos are trademarks of Edge Ware, Inc.
FastTrack and AccuTrack are trademarks of Investors FastTrack.
FastWays is a trademark of Software Support Products, LLC
Appendix A - Technical Discussion ................................. 55
3
1.0 Introduction
First, a little background. FastGraph is a product of Edge Ware, Inc. which was founded
by brothers, Ken and Nelson Huck. Ken is an engineer with 20 years of experience in
technical analysis and computer simulation in the aerospace industry. Nelson is a programmer/MBA with 10 years experience in financial programming.
After developing an investment software tool called FastBreak*, Edge Ware found a need
for graphical tools that were not readily available in other programs. It was with this
need that FastGraph was developed. The initial version of FastGraph was oriented toward visual aids to determine stable/robust trading parameters using output from FastBreak, and FastTrack. This latest version of contains some of the most advanced technical analysis features you will find in any investment software package.
Kenneth L. Huck
Nelson R. Huck
*Visit the Edge Ware Internet web site (www.edge-ware.com) for additional information
on all these products. FastBreak is a Windows based strategy testing and trading program. FastBreak relies on the FastTrack database. For those not familiar with FastTrack,
it is a mutual fund & stock database and software analysis package. The database is updated by modem each day the market is open with the closing prices of thousands of mutual funds, stocks and indexes. Users of FastBreak must be subscribers of FastTrack (call
800-749-1348 to subscribe) to access the required data.Do not call FastTrack for
information relating to FastBreak or FastGraph.
4
2.0 Upgrade Notes
Below are a few changes to the manual that reflect the enhancements made with Version
3.0 of FastGraph.
FastGraph now loads all the FastTrack mutual fund and stock databases at the same time
when “FastTrack Funds, Stocks & FNU files” is selected in the following menu:
Starting with Standard FastBreak 4.0 and FastBreak Pro 4.0 three new data fields were
added in the Summary output: Beta, Correlation, and Alpha. If you are using these versions of FastBreak you can graph these new parameters because they are now available in
the Data Field pull down menu:
Clarification Issues
FastGraph only reads the output files from the DOS version of FastWays.
We have a place holder in the Data Types menu for FastTools but don’t currently read
any FastTools file types.
5
3.0 Technical Support and Upgrades
Note: Do not call Investors FastTrack for technical support.
Do not use the 800 order line number for technical support. This is a commercial
order line that only takes orders and they are not equipped to answer any questions.
Any messages left with the order line will not be returned.
Please read this entire manual and check the FAQ chapter before calling for support.
We have tried to make this software and documentation as user-friendly as possible. You
should have a basic working knowledge of Windows, i.e., how to copy and move files,
change directories, select drives, etc.
Technical support is provided by email. You will usually receive a response within 24
hours. We encourage you to post questions of general interest on the FastBreak/FastGraph discussion area on the site www.ft-talk.com. This allows us to help
several users at once. If you post a question on the web site, email us to let us know you
posted the note.
We can be contacted at email2ew@edge-ware.com. This address will send your note to
both Ken and Nelson and will help you receive a timely response. We recommend that
you always use this address. If one of us is traveling or otherwise unavailable your note
is likely to be answered sooner if it is sent to both of us.
If your support issue can’t be handled by email, we will arrange for telephone support.
We charge $25 for replacement installation CDs.
There is no charge for most technical support. Problems with reinstalling FastGraph is
our number one tech support problem. We receive a large number of support requests
from users reinstalling FastGraph because of hard drive failures, purchase of new computers, etc. We reserve the right to charge $25 to assist in reinstallation of the product,
starting six months after purchase. If you follow the following steps you shouldn’t have
any problem reinstalling.
Reinstalling FastBreak
You MUST use the installation CD to reinstall. We have had a number of users just try
to copy files to the new computer or hard drive. This will not work. Here are the steps:
Install FastTrack first
Do at least one download and update of FastTrack data
Verify that the FastTrack account number on this computer matches the account
number on the FastGraph CD
Install FastGraph using the installation CD
6
Go to our web site and download the latest upgrade, if one exists
Upgrades
We provide minor upgrades to FastGraph on our web site, and if you encounter an error,
we suggest you download the latest version of the software because this will often solve
the problem. The Edge Ware Internet Web site (www.edge-ware.com) always has the
latest version for download.
7
4.0 Installing FastGraph
Note: We have found that FastGraph installs with the least number of problems when
the installation is made just after booting your computer. Also, before you start the
installation make a backup copy of the installation disks.
To install FastGraph:
Minimum of 5 MB free on your hard drive
Windows operating system
Note: FastGraph will not run under Windows 3.1
16 MB RAM
Pentium class processor
1) Start Windows
2) Stop any application that may be running. Note: We have had a number of users call
with installation problems because Microsoft Office was running in the background.
3) Insert the installation CD
4) From the Start menu, choose Run. Type A:\SETUP (or B:\SETUP depending on your
drive.) The first screen you will see is:
This is a warning to close any applications you may have running. The various versions
of Windows have different methods for determining applications that are running. Consult your Windows manual to determine how your version works. If you don’t have applications running select OK otherwise, exit Setup and close the applications.
8
5) The second screen you will see is:
The setup program is asking the name of the drive and directory where FastGraph is to be
installed. The default is C:\FTGRAPH, and we suggest that you use the default directory
name. If the default is acceptable click on the button that resembles a computer and skip
to step 8.
6) If you need to change the drive letter or directory path click the Change Directory button and the following screen will appear:
This screen allows you to change the drive and or the path and directory. If you need to
change the drive, click on the Drives pull down arrow button to get a list of your drives to
select from. Once you have selected a drive, click on the drive folder to see a list of existing directories for installation or type a directory name in the Path box then click the
OK button.
9
A FastGraph run icon will be created in your Windows Programs environment. Click the
FastGraph icon as you would to launch any application.
Reinstalling FastGraph
Reinstalling FastGraph is our number one tech support problem. Users crash hard drives,
buy new computers, new laptops, etc. You MUST use the installation CD to reinstall.
We have had a number of users just try to copy files to the new computer or hard drive.
This will not work. Here are the steps:
Install FastTrack first
Do at least one download and update of FastTrack data
Verify that the FastTrack account number on this computer matches the account num-
ber on the FastGraph CD
Install FastGraph using the installation CD
Go to our web site and download the latest upgrade, if one exists
10
5.0 FastGraph Quick Start
FastGraph is run from the Windows environment and your installation should have created an icon under Programs when you use the Start button. Click the icon as you would
to launch any application.
When FastGraph is launched the main menu will appear:
The menu may initially look very complicated but is quite logical and user friendly. We
will step through each menu and describe each feature. FastGraph uses the very common
Windows Tool Bar method of presenting functions and data.
Main Screen
When FastGraph launches the Main Screen is on top. See the above figure. This screen
is used to select the type of file to import and the settings for the graph to be plotted.
Data Type
The type of data file must first be selected before loading data. The Data Type pull down
menu allows selection of FastBreak, FastTrack, FastWays, and eventually FastTools data
files.
11
File Name
When the File Name button is selected the following menu will appear:
This menu allows you to find and load the appropriate file. Use the Drive and Directories boxes to find the data files. Select the file from the left side of the screen and click
the OK button.
Graph Parameter Settings
These pulldown menus allow you to change the graph parameter settings and are self explanatory.
% of data to graph
This menu item allows for graphing only part of the loaded data. For example, if a FastBreak Summary file has been loaded with 500 test cases, selecting 40% will graph only
the first 200 test cases. This menu item will be demonstrated in a later chapter.
Shifting Screens
Use the above icons to shift between screens. The first icon will bring up the Main
Screen, the next icon shifts to the Data Screen, the next icon brings up the Graph Screen,
12
and the far right icon brings up the Calculations Screen. These icons will be described
later in the chapter.
Loading FastTrack Data
Note: When you select FastTrack as the data type a large number of new items appear
on the main screen. Some of these will be explained now, others will be explained in
Chapter 7.
If the user selects FastTrack Funds & FNU Files as the Data Type data on the Graph Settings Tab the following menu will appear (If FastTrack Stocks is selected as the Data
Type, a very similar menu will appear):
This menu contains FastTrack trading family names or Fund names. The default is to
load the family names. Put the cursor in the empty line just above the first family name
and start to type the name of the family to be evaluated. FastGraph will find the family
as the name is typed. Note: The indexing may have problems if you have family names starting with unusual characters such as ~,@ etc. You can use the slider bar on the
right of the family names to find the family of interest. Once the family is located, use
the cursor and left mouse button to click the family. It will highlight as in the above
screen. Note: The highlighted family will NOT appear in the box where you started to
type the name.
Family or Fund Selection
The box marked Selections allows loading data of individual funds. Selecting the Funds
button will load all individual fund names into the scroll box:
13
A fund can be found by typing the fund symbol as you did the family name. To select
multiple fund names FastGraph uses the standard Windows selection method: hold the
Control key on your keyboard and “click” the left mouse button to select additional
funds. In the above example both FSELX and FSESX have been selected.
Note: FastGraph will read all your FNU files. When these files are made part of your
trading family, FastGraph will include them in the graph. See the FastTrack manual
for information on FNU files.
Load Data
After the appropriate FastTrack family or fund(s) have been selected click the Load Data
button to load the data into the spread sheet.
Graphing FastTrack Data
When FastTrack is selected as the Data Type the following menu item appears on the
Graph Setting Tab:
This menu item allows you to graph all the selected funds on a single screen or graphed
one at a time. If the One at a time option is selected the following icons appear on the
FastGraph tool bar:
These arrow icons will allow you to move forward or backward through all the selected
funds one at a time.
Data Screen
14
After loading data from the select file, the data can be reviewed in a spread sheet by selecting the Data screen icon. Going to the Data screen icon the data will resemble the following:
Different parts of the data can be reviewed by using the slide bars or page up and page
down keys. This screen will be covered in more detail later.
The data is loaded on a distribution included basis, i.e., the fund distributions have been
included into the fund NAV, and therefore, the NAV values may not be the same as the
actual fund NAV. This is equivalent to exporting the “red” line in FastTrack.
Note: A minus one ( -1) is used to denote a fund was not yet available.
Before FastGraph can plot FastTrack data the specific data to be plotted needs to be selected. This is done by going to the Data Screen and highlighting the column of data to
be plotted. This is done by clicking on the column heading, i.e., B, C, etc. The entire
column of data will become highlighted or shaded. Different columns of data can be selected at the same time by using the standard Windows Shift and Ctrl keys in combination with the left mouse keys. In this manner many funds can be chosen from a loaded
family. The next chart shows four columns of NAV data that are selected:
15
Graph
This tool bar icon allows the user to produce a graph. When the icon item is selected
FastGraph will go into a graphing mode and bring up the Graph Screen.
16
Changing the Time Period Displayed
The slide bar at the bottom of the graph can be used to view different graph start and stop
times.
Changing the Graph Time Period
When FastTrack data has been selected the time period of the graph can be changed by
using the Time Period pulldown menu. A variety of time periods can be selected.
Printing the Graph and Other Options
Placed the cursor on the FastGraph Graph Tab screen and click the right mouse button.
The above menu is displayed. These options allow the graph to be printed as well as customizing the graph. The graph can also be saved or a saved graph reloaded. The menu is
mostly self explanatory. One item that may deserve special note is the Edit Chart Data
option. This item will allow you to edit the data displayed on the chart.
17
6.0 Analyzing FastBreak Output
FastBreak summary files can be analyzed using FastGraph, and this is where the real
power of FastBreak can be realized. This example will compare the effect of changing a
single parameter on return results of a trading strategy.
Start by making two FastBreak back testing runs using the following parameters:
Run #1 - Trade using the Select family, date start 1/1/89, end date 12/31/95, Buy and
Sell using Rank, Set Buy rank = Sell rank, with a minimum ranking period of 5 days and
a maximum of 50 days, Delta=1 day, Top%=50 , Min hold 30 days, Delay =1 day, Short
loss=.75, and #funds set to 1.
Run #2 - Same settings as Run #1 except hold three funds rather than one. Be sure you
change the summary file name when making the two runs.
Go to the FastGraph main screen and select FastBreak Summary file as the import file
type and import the Summary file data into FastGraph using the File Name button. Note:
You can load several files at a time. When the file selection menu is open select all the
files you want to load by using the standard Windows left mouse button clicking
method (including Shift and Ctrl key methods to select several files)
Select Scatter as the Graph Type, Test Case as the X Parameter, and Avg Annual % as
the Y Parameter. Now use the graph icon to create the following graph:
18
In this example, the + symbols represent test cases holding one fund, and the * symbols
represent three funds. The first thing to notice is the large variation in annual performance when holding one fund.
It is rather difficult to determine the average effect on return by holding one fund vs.
three funds. However, there is a solution.
Sort
When the Sort icon is selected the following menu appears:
This menu allows you to sort the data in the spread sheet by a variety of criteria. Each of
the sort keys is a pulldown menu. The Sort Keys allow a hierarchy for sorting. In the
above example, the data will be sorted by Avg Annual% first. If two records (test cases)
have the same Avg Annual% then Sort Key 2, Ulcer Perf Index, is used to discriminate
the test cases. Finally, Max Drawdown% is the final sort criteria. You can also sort the
date in Ascending or Descending Order.
Sort All
This icon allows all the spread sheet pages (if multiple files are loaded) to be sorted at the
same time. For example, you may have five different FastBreak Summary files loaded
and want to sort all the sheets of the spread sheet at the same time. This icon will bring
up the same sort menu as shown above.
Select the Sort All icon and sort on Avg Annual % in Descending order. Go to the Main
screen and select XY Line as the Graph Type. Now, graph the sorted data using the
graph icon. You will see the following:
19
Now it becomes clear that holding one fund can have a return of more than 5% per year
when compared to holding three funds. However, it is also clear that holding three funds
can give more consistent performance regardless of ranking period.
If you want to look closer at the best test cases go to the Graph main screen and select
50% in the “% data to graph” menu. Now, re-graph the data:
Now only the best half of the test cases are shown but in greater detail. Other parameters
in the FastBreak Summary file can be charted in a similar manner.
20
Finally, what are the best parameters to use for buy and sell ranking? The values that
gave the best annual return may not be the best choice because that combination may
have undesirable characteristics, i.e., high drawn down, too many switches per year, etc.
The most significant problem - the parameters may not be a good “robust solution” and
only a “statistical fluke.” Stability is a requirement in your parameter choice. In other
words, if the parameters are changed slightly, there shouldn’t be a large change in annual
trading performance. You do not want to “curve fit” the past. In the above example
holding three funds may have resulted in a slightly lower return, but the return was quite
consistent and peaked in the 25-30 day ranking period. Holding a single fund shows considerable variation in performance, For example, ranking over 24 days has over a 35%
annual return but ranking over 16 days results in less than 20% annual return.
Using FastBreak with different ranking periods for buying and selling the problem becomes a little more difficult because there are now two independent parameters and many
more combinations. Contour plots can be used to help select “optimum” parameters. For
example, make a FastBreak run the same as Run #1 earlier with the following exceptions:
Buy min and Sell min set to 10, and Buy max and Sell max set to 50.
Import the file in FastGraph, select contour as the graph type, and Avg Annual % as the
Date Field. You get the following graph:
Note: The graph will be in color on the computer monitor.
The annual return is shown as a different color and is a function of buy and sell ranking
periods. It appears there are large regions of stable/robust parameters. Parameters are
considered robust when by changing them by a moderate amount the results stay consistent.
21
The areas can be further evaluated by looking at UPI, UI, S/Y etc. The following graph
was made by selecting UPI as the Data Field:
All regions still look reasonable, but the buy 16/sell 45 does a little better.
There are no guarantees the ranking period that tested well in the past will work well in
the future. However, looking at the past performance may give an indication of what will
work in the future, and you certainly don’t want to choose a parameter set that performed
poorly in the past.
22
7.0 Analyzing FastWays Output
FastWays is a FastTrack add-on product (see Resources Chapter for more information)
that can evaluate a variety of FastTrack functions: AccuTrack, Stochastic, Moving Average, and MACD. FastWays output can be analyzed in a graphical manner to help select
optimum/robust parameters. Note: When running FastWays select the “Fixed length”
type for file output.
FastWays Example #1 - AccuTrack
One popular FastTrack trading strategy is to switch between energy funds and transportation funds using AccuTrack. These two sectors of the market often move opposite to
each other and it is often better to be in one or the other. One question the investor may
have is it better to switch between Fidelity Select Energy and Select Transportation, or
switch between Select Energy Service and Select Transportation? With this in mind
make two FastWays runs: Run #1 will use AccuTrack switching between Select Energy
and Transportation, and Run #2 will switch between Select Energy Service and Transportation. Make both FastWays runs with a range from 5 to 50 on AccuTrack parameter one
and parameter two. The time period for this example is 12/30/88 - 12/21/96.
Once the two FastWays runs have been made load the data into FastGraph. Next, select
the “Sort All” icon and sort based on Ra in decreasing order. Now use the “Graph” icon
to get the following graph:
23
Note: If you have any doubt about the effectiveness of this AccuTrack strategy here are
the buy and hold values for each fund and the S&P 500 index over the same time period:
FSENX 156%
FSESX 227%
FSRFX 225%
S&P 500 197%
The AccuTrack system easily beats these values using ANY set of parameters. It is also
clear that trading Transportation with Energy Service is the preferred pair. The next step
is to determine the AccuTrack parameters that give a good robust strategy. Go to the
FastGraph Data Tab and bring the FSESX/FSRFX data to the top. Go to the main screen
and select Contour as the graph type and Ra as the Data field. Here is the graph:
The set of parameters that result in the best Ra (600% or greater) form a wide band centered in the area of 15/22. Other FastWays output parameters such as switches per year
could be used to further refine the parameter choices.
Here are other studies to consider:
Rather than using Select Transportation, perhaps Select Air Transportation would have
been a better choice. Run FastWays switching between Air Transportation and the two
energy funds. Import these two FastWays files into FastGraph, sort the data and compare
all four line graphs.
Some AccuTrack users trade between a mutual fund and a common index, i.e., DJ-30,
S&P 500, OTC, etc. A good question is which index should be used because different
equity funds respond differently to the different market indexes. Make different Fast-
24
Ways runs using your fund of choice and switch between different indexes. Next, load
these FastWays files into FastGraph, sort, and compare the different line graphs. It
should make the selection of an index more obvious.
FastWays Example #2 - Moving Average
FastWays/FastGraph can be used to find robust parameters for a moving average. Make
a FastWays run using the OTC-C index as the fund and Vanguard Money Market fund
(VMMXX) as the index. Run with a moving average range of 10 days to 250 days. The
time period evaluated was 12/30/88 - 12/31/96.
Import the resulting FastWays file into FastGraph. Select XY Line as the graph type and
you will get the following graph:
Note that the X axis is case number and not the moving average value (case#1 = 10 days,
case #2 = 11 days, etc.).
Buy and hold had a return or 238% over this test period. It can be seen that a moving
average between 50 and 100 days is optimum for Mr.
25
Selecting Switches per Year give the following graph:
The number of switches is a reasonable 2-4 per year for the most favorable Ma.
Finally, charting risk:
The risk (percent time invested in the OTC index) for the most favorable moving average
values is in the range of 70-75%
Maximum Draw Down (MDD) could be examined to determine the benefit of using the
moving average vs. buy and hold.
26
FastWays Example #3 - MACD
Since the functions that FastWays evaluates have different number of parameters FastGraph changes the graph selection parameters depending on the type of file imported.
For example, AccuTrack has two parameters but MACD has three. There is also the issue of how to determine parameters if the function has more than two independent variables. MACD is an example since it has three parameters. Here is a method to help determine good parameter ranges.
First, make a FastWays run on a fund over a wide range of MACD parameters. Import
this file into FastGraph. What we want to see are those parameters that give the best Mr
return. Sort the FastWays file by Mr in descending order. Next, set 10% as the % of data
to graph. Now graph the data:
In this case the MACD parameter 1 and 2 were varied from 10 to 50. Parameter 3 was
varied from 2 through 15. This graph only shows the results of the “best” 10% of the test
cases. The results indicate that good Parm1 values are in the 25-50 range, Parm 2 is in
the 10-30 range, and finally, the best Parm 3 values are in the 2-4 range.
Again, the values can be further refined by looking at switches per year, Mr, Risk etc.
27
8.0 Analyzing FastTrack Data
The FastGraph Main screen changes dramatically when FastTrack Funds & FNU Files is
selected as the Data Type:
Several options become available and we will step through each with an example.
FastTrack Example #1 - Multiple Funds
The FastTrack DOS has a limitation of comparing only two funds or indexes at once.
FastGraph can put many sets of data on a single graph. Here is an example comparing
the DJ-30, OTC-C, Fidelity Select Electronics, and Select Air Transportation. Note:
Once the FastTrack data has been imported you must select the funds to be graphed by
“selecting” the data columns in the Data screen spreadsheet.
28
This graph makes it much easier to compare multiple funds and indexes.
FastTrack Example #2 - Exponential Moving Average/Adaptive Moving Average
Exponential moving average (EMA) analysis is one of the most common techniques in
technical analysis. See your FastTrack manual for a description how exponential moving
averages are calculated.
To display a fund with it’s EMA, first load a FastTrack family or individual funds. Next,
go to the Data screen and highlight the fund(s) you want to display, go to the FastGraph
main screen and select Show Exp Moving Avg and enter a period over which to calculate
the EMA. Determine if you want to show all the selected funds at once or one at a time.
Finally, click the graph icon.
29
The following graph was made with a 50 day EMA and is displayed for a period of two
years:
The Adaptive Moving Average (AMA) can be displayed in the same way. See the Appendix for a description of AMA calculation.
FastTrack Example #3 - Parabolic
The Wilder parabolic is a very common technique to set a stop in trading. See Appendix
A for a description of how a parabolic is calculated.
To display a fund with its parabolic, first load a FastTrack family or individual funds.
Next, go to the Data screen spreadsheet and highlight the funds you want to display, go to
the main FastGraph screen and select Show Parabolic and enter the parameters to use in
the calculation. Determine if you want to show all the selected funds at once or one at a
time. Finally, click the graph icon.
The following graph was made with a starting acceleration value of 0.02, maximum value
of 0.2, and delta acceleration value of 0.0003 for a period of two years:
30
FastTrack Example #4 - Bollinger Bands
Bollinger Bands are used by many technical analysts. See Appendix A for an explanation of how Bollinger Bands are calculated.
To display a fund with its Bollinger Bands, first load a FastTrack family or individual
funds. Next, go to the Data screen and highlight the funds you want to display, go to the
main FastGraph screen and select Show Bollinger Bands and enter the number of trading
days to use in the calculation - the typical value is 20 days. Determine if you want to
show all the selected funds at once or one at a time. Finally, click the graph icon.
FastGraph shows the NAV of the fund, the upper and lower Bollinger Band, and the
moving average for the period used in the Bollinger Band calculation. The Bands are +/2 standard deviations from the average.
31
FastTrack Example #5 - Candlestick Charts
Many traders use Candlestick charts to make trades. Candlestick charts are built using
daily open, high, low and close values. With mutual funds the only data available is the
daily closing. Some users have found that a “synthetic” Candlestick chart can be useful
using weekly data to determine the “open, high, low and closing” values. This is the approach FastGraph uses. After importing FastTrack data, and selecting the columns of
data to graph, select Candlestick Bar as the chart type. The following chart was built
using Fidelity Select Electronics:
The interpretation of Candlestick charts is well beyond the scope of this manual. Please
check your local bookstore for books on this subject.
FastGraph has the capability to graph Candlestick Line chart that will show weekly open,
range and closing values for your funds:
32
FastTrack Example #6 - Point & Figure Charts
Point & Figure (P&F) charting is a technique that has been around for a century. Recently this method of analysis has been making a strong resurgence. Interpretation of
P&F charts is beyond the scope of this manual, but see the Resources chapter for a list of
books on the subject.
To make a P&F chart in FastGraph you first need to import FastTrack data. Next, select
Point & Figure as the Graph Type. You will see the following button appear on the
screen:
Clicking this button will bring up the following screen:
33
This menu will allow you to change the box size values (the defaults are from the Dorsy
book which is listed in the Resource chapter) and the Box Reversal values.
The next step is to select a time period range. The final step is to use the Graph icon to
see the chart:
To move through a family of funds, first load the family into FastGraph. Next, go to the
Data screen and “select” the columns for those funds you want to view. You can select
the entire family by quickly by clicking in the blank cell in the upper left corner (cell
A:1).
Select the Graph icon to chart the first P&F chart. Now you can review each of the funds
by using the:
icons to move forward and back through the funds you selected.
If you get the following message:
The time period selected contains too many columns of X&O’s. Select a shorter time
period using the Time Period menu.
34
FastTrack Example #7 - Correlation Analysis
Correlation Analysis allows the comparison of funds and indexes to determine how
closely related they may be. FastGraph uses the common Pearson’s correlation to do this
analysis. Maximum correlation has a value of 1.0 and negative correlation has a value of
-1.0
If an investor is trying to be diversified by holding more than one fund it may be a good
idea to hold two funds that have a low correlation. Correlation can also be used for intermarket analysis.
To display the correlation between two funds, first load a FastTrack family or individual
funds. Next, go to the Data screen and highlight the two funds you want to analyze (only
two funds at a time), go to the main FastGraph screen and select Show Correlation and
enter the number of trading days to use in the calculation, a minimum value of 50 trading
days is recommended. Finally, click the graph icon.
FastGraph shows the NAV of the funds (or indexes) in the upper part of the screen, the
lower part of the screen shows the correlation value.
The following chart shows the correlation is very high between Fidelity Select Regional
Banks and Select Home Finance, as would be expected. However, notice that there are
periods when the correlation does change dramatically. The chart is for a total of five
years.
35
The following chart shows the low, even negative correlation between Fidelity Select Air
Transportation and Select Energy Service. The type of correlation shows why the pairing
of these two funds using AccuTrack has been a very successful trading strategy.
Correlation analysis can be used to show inter-market relationships. The following graph
shows the relationship between the Dollar Index and the price of gold:
36
This chart shows the low to very negative correlation between the value of the dollar and
the price of gold. This would tend to support the common notion that when the dollar is
strong, the price of gold (denominated in dollars) declines.
FastTrack Example #8 - Hurst Exponent Analysis
Hurst Exponent (HE) calculations are quite involved. See Appendix A for a description
of the calculation.
The HE is of interest because it can be used to determine if an index or fund has strong
trending properties. The HE can have a value between 0 and 1. Values less than 0.5 indicate a fund is antipersistent, i.e., trading range, values greater than 0.5 indicate trending.
Show Hurst Exponent
The option to display the HE appears when FastTrack data is selected as the data file
type. Two values are required when the option is selected. See Appendix A for a description.
The HE can be used to compare the trending characteristics of different funds. The following chart shows that Fidelity Select Home Finance historically has a higher HE than
Select Electronics. The chart was made with a HE period of 500 days and 10 periods:
37
38
9.0 MEM for Cycle Analysis
A larger number of market technicians use cycle analysis in their trading. Proponents of
cycle analysis will claim that the market moves in somewhat repeatable cycles and if the
period(s) of these cycles can be determined then it may be possible to make predictions
of short term price movements. Just knowing if the market is in a cycle mode or trending
mode can be very important to an investor. If the market is in a trending mode then the
investor should use trend following methods such as moving averages, and if the market
is in a cyclic mode then trading methods such as stochastic are better tools to use.
The method FastGraph uses to determine cycle information is called the Maximum Entropy Method (MEM) that has been popularized by John F. Ehlers. For an excellent book
on the subject see Mr. Ehlers’s MESA and Trading Market Cycles. The mathematics of
the MEM are quite involved and beyond the scope of this manual. We will concentrate
on how to interpret the charts in FastGraph.
Note: The color charts do not reproduce well in black & white. It may be a good idea
to bring the following examples up on your color monitor as you walk through this section.
To activate the MEM control options you must have selected and loaded the FastTrack
families or funds. Once this is done the following options can be found on the main FastGraph screen:
The two MEM control parameters will be explained later in the chapter. For now, load
the FastTrack funds, find and load the NASDAQ composite index (OTC-C), select the
Show MEM option, go to the FastGraph Data screen and select this column of data that
has been loaded., and click on the graph icon. You will see a chart similar to the following which was made for a period of six months with an ending date of October 1996:
39
This is a very busy screen. The top half of the screen has the NAV of the index and a
moving average line. The bottom half of the screen contains information about the dominant cycles, and finally, the upper right part of the screen has the spectrum of a specific
day.
Starting with the lower half of the screen there is a solid line (red) that starts at 50 on the
left of the screen and cycles between 8 and 50 as it moves from left to right. This line is
the period of the dominant cycle period. When the line is at or near 50 the NAV (the
OTC-C in this case) is considered to be in a trend mode. The value of this period is used
to calculate the trend line (green) in the upper half of the chart. The trend line is a simple
moving average using this dominant period. Notice that as we move toward the right in
time, the dominate period drops toward 20 days and you can see the moving average in
the upper part of the chart respond by moving much closer to the NAV line (red). When
the NAV line crosses below the trend line this is considered a sell. The NAV continues
below the trend line into the center of the chart with the dominant period falling between
20 and 40 days. Near the center of the chart, in time, the dominant period again goes to
50 days. The MEM is now saying that the index is in trending mode, but it is a down-ward trend. The dominant period starts to move toward 50 days and the NAV jumps
above the trend line. Note: Using the criteria outlined in Ehlers’s book, a fund would
not be purchased until it had traded above the trendline for one-half the dominant period. We have found this to introduce too long a delay. For mutual funds a better buy
40
point may be when the NAV trades above the trendline and the dominant period goes
to 50 days.
Spectrum
The spectrum in the upper right portion of the screen shows the “power” of each period
in the cycle. In the above example the maximum power is in the 50 day period and indicates a high quality trend mode. The following spectrum is characteristic of a cycle
mode:
This spectrum shows that the dominant cycle is 28 days long and a
second, less powerful cycle, at 12 days. The minimum period that FastGraph will allow
is 8 days.
To see the spectrum of different days use the following icons:
These icons will move you left and right to show the spectrum of different days. The day
you are showing is indicated on the charts by the large red and green asterisks:
41
These move along the graph lines as you click the icons.
In the lower right corner of the MEM screen you will see:
This is the legend for various peaks in the spectrum. In a trending mode only the red
dominate period will be displayed on the bottom Power chart. As other peaks appear in
the spectrum these will be indicated on the Power chart. For example:
This portion of the Power chart shows the red line indicating what the dominant period is
doing. There are also a few green and red + symbols to indicate that other peaks are present in the spectrum but are of lesser power, and hence lesser importance, than the dominate period. When additional peaks start to show on the Power chart it is an indication of
a stronger cycling vs. trending mode. As the spectrum moves toward a trending mode the
extra peaks will start to disappear and finally only the dominant period red line will remain.
Price Prediction
The MEM has the ability to make a short term price prediction. FastGraph always shows
a ten day price prediction at the far right of the NAV chart:
42
The red NAV line to the right of the * is a 10 day price prediction based on the current
spectrum analysis. You can look at past price predictions by moving the mouse cursor to
any point along the red NAV line and clicking the left mouse button. The ten day price
prediction will appear as a blue line. Here are some examples (in black/white):
Note: When trying to make price predictions the placement of the cursor is very sensitive. Often when you click you may bring up the option to change the NAV line characteristics. We suggest that you only show short time periods, a month is good, when
checking price prediction accuracy. With a little practice you can determine the best
area on the NAV to place the cursor.
You will find that the predictions are poor when the mode is a transition, switching from
cyclic to trending, and from trending to cyclic. Such short term predictions are of limited
use in mutual fund trading.
Using MEM - Summary
Should the NAV moving above or below the trend line be used as specific trading signal?
The answer is an emphatic NO! What the MEM charts can help tell you is if a fund or
index in a trend mode is starting to break down into a cycle mode and may be an indication to start watching closer if you are in the fund or index. On the other hand, if a fund
or index has been in a trading mode and now the spectrum and Power charts start to move
toward longer dominant periods then you may want to start to consider an entry into a
long position.
The Power and spectrum chart can help determine the quality of a trend. If the dominant
period is at fifty days but you start to see other peaks appear then a change MAY be starting.
Here is another example using Fidelity Select Electronics for nine months ending in October 1997:
43
When the chart starts on the left the dominant period is fifty days, and therefore a trend
mode. In this case it is a down trend and the NAV drops below the trend line shortly after the chart begins. Approximately three months into the chart the dominant period
drops to a cyclic mode with a period of about 18 days, however, the length of the dominant period turns up almost instantly and the NAV goes above the trend line. An aggressive trader may want to buy the fund at this point. A more conservative trader would
wait until the trend is more obvious. This happens when the dominate period goes to 50
days. The upward trend continues with little indication of changing until the dominate
period drops to about 12 days and the trend line moves toward the NAV quite dramatically. This is an indication that the upward trend may be ending and the fund is entering
a cyclic mode. Other indicators should be looked at to help make a trading decision.
In this particular case the upward trend was ending and the fund dropped significantly.
Will this happen in every case? NO! There are no perfect indicators or guarantees. This
is another tool to put in your tool box.
A Note on Picking MEM Parameters
We recommend that the Max Period parameter be left to the default of 50 days. This is
the value recommended by Ehlers. The selection of the # of Poles parameter is a little
more difficult. The higher this number the more “spikes” that will appear in the spectrum. A recommend value is 40% of the Max Period parameter. Therefore, if using 50
days then 20 poles is a good starting point. We have very little experience with using the
MEM and are in an experimental mode ourselves.
44
10.0 Making Simulated Index Funds
Index fund investing has become very popular and some of the new index fund products
actually leverage the index. For example, the Rydex Nova fund actually attempts to beat
the S&P 500 Index by 50%. Other funds actually take an inverse approach to the index,
for example, the Rydex Ursa fund rises when the S&P 500 Index drops and declines in
price when the S&P 500 Index increases.
The problem for investors is that there is a limited amount of data because these funds are
relatively new. This lack of historical data prevents developing strategies in FastBreak
(and other products) that can be tested back to 9/1/88.
FastGraph allows you to create a simulated index fund that has the same length of history as the index you are using in the simulation. Note: This will be an approximation
that may be very good or very bad depending on a number of issues. You need to be
very careful in how you use this feature. Trading systems that spend a short time in
the simulated index fund will be affected much less than strategies that hold the simulated index for very long periods of time because errors tend to compound over time.
FastGraph calculates the daily percentage change in the index to be matched, then multiplies this change a “beta” and applies the result to the simulated fund. For example, if
the S&P 500 increases by 1% on a given day and a beta of 1.5 is used the simulated fund
will increase by 1.5% on that same day.
To use the new feature first load the fund or index you want to "clone" into FastGraph.
For example, if you want to create a simulated Rydex Nova fund load the S&P500 (SPCP) from the FastTrack data base. Go to the Data Screen and select (highlight) the SPCP data column.
Calculations Screen
When you click this icon a new screen appears:
There is a small button on this screen that when clicked a menu appears that asks for the
name of the FNU file. Once you enter the file name and click OK, screens appear to input a title description and symbol. You need to input a Beta factor that will be applied to
the imported index. For example, to make a Nova "like" fund use 1.5 as the beta multi-
45
plier. The last issue is to input a starting NAV value for you simulated index. This value
isn't very critical because FastTrack and FastBreak work off changes in NAV not the actual value. However, if you build a simulated index fund that declines dramatically over
time then this value needs to be made large enough to prevent round off errors as the
NAV gets smaller. A good starting value is 100.
The last step is to click the Calculate button. The FNU file will be created and the data
will be loaded into the Data Screen.
The file produced by FastGraph will be perfectly correlated (correlation coefficient of
1.0) with the imported index. This usually isn't the case for the real index funds even
though this may be their stated goal. Also, the simulated fund will not be updated automatically each day.
Again, be careful how you apply the results and let us know how we can make this a better feature.
46
11.0 Calculate Advance/Decline Lines
FastGraph can calculate the Advance/Decline (A/D) line for both the New York Stock
Exchange (NYSE) and a user specified family. These data are put in a FNU format that
can be loaded into FastTrack or FastGraph for viewing.
Go to the Calculation screen and you will see the following area:
This option will calculate the A/D line for the NYSE. If all the inputs fields are loaded
with acceptable values click the “Calc FNU” button. If you want to change the fields
click the button next to “FNU File” and a series of screens will ask for the name of the
FNU file, title, and symbol. After you input these values click the Calc FNU button.
You can load and view the A/D line in FastTrack or FastGraph.
To calculate the A/D for a user specified family use the following screen area:
This option is very similar to the NYSE option. The only difference is you need to input
the family that you want to analyze first. This is accomplished by clicking the Family
button to select the FastTrack family.
47
12.0 Composite Timing Signal Analysis
There are no perfect market timing signals. Some users have found that better results are
obtained by using combinations or composites of several signals. For example, a strategy
could use five separate signals, and the investor would buy into the market when any
three or more signals are on a buy, and sell out of the market when two of fewer signals
are on buy. The question is should the investor use two of five signals, four of five …?
Also, what results can be expected; Annual return, MDD, Switches per year, etc. FastGraph allows you to build and test composite signals.
Calculations Screen
Clicking on this icon will bring up the following screen:
Note: This screen takes some time in loading because FastTrack data is being loaded.
There are several steps in analyzing a composite of signals. The first step is to select the
signals from your FastTrack signals directory that you want to combine. This is simply
done by clicking on a signal file name from the list on the left part of the screen. Clicking the Add button will add this signal to the box on the right half of the screen. If you
make a mistake you can use the Remove button.
Once you have built your list of signals you can save it by clicking on this button:
48
We suggest you use the default suffix. Then click on the save button.
Next, enter the starting and ending dates for the period to be analyzed. In addition, add
the delay, in days, for the signal. If the signal is to executed the same day it occurs, the
delay is zero, and if the signal is executed the next day (most typical for FastTrack users)
enter a one day delay.
The next step is to select the fund or index to be invested in when you are “in” the market
and the fund or index when “out” of the market. This example will be invested in the
S&P index when long and into the FDRXX money market when out of the market.
We now need to create a place to save our results. Click on the Make Sig Sum File box:
A menu will pop up to enter a file name. Note: Do not confuse this file with the Signal
Family File which was created a few steps back.
For the next step we will skip toward the bottom of the screen to this line:
FastGraph has a choice of two types of analysis. The simple strategy is what we call a
One Dimensional test. This method uses the same number of separate signal buys and
sell for the composite signal. For example, a strategy that goes long on three signal buys
will exit the market if there are only two signals in the market. The Buy and Sell Range
will test all combinations of the separate signals. In our five signal example we will look
at the results when one or more signals are on a buy, two or more, three or more …. Up
to five or more. Any time that fewer signals are in the market then the composite will
sell out of the market.
The next step is to save the setting we have just made using:
Clicking this button will bring up a menu to save a parameters file that you can reload
later using this button:
Finally, we can start the analysis with this button:
When the execution is complete go to the FastGraph Main screen and select XY Line as
the Graph Type since this is 1 dimensional analysis. The Summary data is loaded to the
Data screen during execution so the Summary File (SSM) does not need loaded before
graphing. The file can be reloaded at a later time by selecting FastGraph Summary File
as the Data Type. When we click the Graph icon we get the following graph:
49
From this graph we see that we get the best annual return when we “Buy” with any three
of the four signals in the market. We would sell if there are less than three separate signals on a buy.
You can also examine MDD, UI, UPI and switches per year in the same manner if you
select a different Y Parameter.
To make a Two Dimensional analysis (2D) go back to the Calculations Screen. Now,
select:
Notice that we now have separate fields for Buy Range and Sell Range. FastGraph can
now use or have a different number of “buy” signals to go long the market than the number of “buy” signals to leave the market. For example, a strategy may enter the market
when four of five separate signals are on a buy but not sell until there are only two signals still on a buy. Note: FastGraph always looks at the direction of the last change in signals. This will be explained in the following example.
Create a Sig Summary File by clicking the Calc Sig Sum button. When the calculation is
complete go the Main Screen and load the file. Since we have made a 2D run we can use
Contour as the Graph Type. Here are the results:
50
This graph needs some explanation. This graph indicates the best results are obtained
when a Buy is made when any 3 OR MORE signals are on a buy. A sell is made when
only 2, 3, 4, 5 OR FEWER signals remain on a buy. At first this may not make sense, but
remember FastGraph looks at the direction of the most recent change in the number of
signals in the market. The above graph has the best results centered about the point 3/3.
This means that the best results were obtained when 3 or more signals were a Buy (Buy
when going from 2 to 3 signals on a Buy), and the market was Sold when 3 or fewer signals were on a Buy (Sell when 3 or fewer signals were on a buy with the last change in
direction is a sell signal). Here is an example of how a series of trades would look as different signals go in and out of the market:
Date Number of Signals on a Buy Position
2/10/90 2 on sell
2/11/90 3 Buy
2/17/90 4 on buy
2/18/90 5 on buy
4/11/90 3 Sell
Notice that the same number of signals (3) on a buy is used for both Buying and Selling.
The difference is the direction of the last change (go from 2 to 3 to buy and go from 5 to
3 to sell).
Now that we have determined a specific strategy we can create an FNU file that FastTrack can use to display the equity curve for this strategy. Enter the optimum parameters
in the Buy and Sell Ranges:
51
Now click on the Make Signal FNU box which will bring up menus that allows you to fill
in the file name, title and symbol name:
We can also make a Detail file by selecting the following menu:
The Detail file contains the information on each trade and can be loaded into the FastBreak Data Screen.
We can also create a Composite signal file that FastTrack can use. This file will be a
standard FastTrack signal file that can be placed in the FastTrack Sig directory. This file
is created and named by using the following menu item:
At this point the composite strategy can be executed by using the Calc Sig Sum button.
Here are some of the details that can be viewed in the Data Screen:
52
13.0 Frequently Asked Questions
Q) Just because a particular strategy works well in back testing, what guarantee is there
that that is will work well in the future?
A) We are all looking for the perfect trading strategy or tool. There are no guarantees
any strategy or indicator will work well in the future. An investor needs to look at his
strategy(s) over a variety of market conditions and try to determine if it is a good
general solution.
Q) What trading parameters have you found that work best?
A) There is more than one answer here. Depending on the account there are different
strategies. Each investor has different objectives. FastTrack is operated under the
rules that the individual investor take active involvement in investment decisions and
the authors of FastGraph have the same rule.
Note: Even with this answer we still receive many calls asking us to help, and we have
spent countless hours on the phone. Therefore, we have a new policy. We will help
develop and modify strategies, but our fee is $100 per hour for this support.
Q) File not found error?
A) One of the file names you used is not valid. File names need to start with a letter of
the alphabet, have up to eight characters before the period, and up to three characters after the period.
Q) Can I use the spread sheet capability in FastGraph?
A) You may have noticed the Data screen can become an active spreadsheet if you dou-
ble click on the page. We have not fully evaluated this capability of the spreadsheet
and do not support spreadsheet functions at this time.
Q) Can I suggest enhancements to future versions of FastGraph?
A) We always welcome user suggestions. Some of our best enhancements to FastBreak
came from users. However, we receive numerous suggestions and try to incorporate
the most frequently requested items.
53
14.0 Resources
The Edge Ware Internet web site (www.edge-ware.com) is a good place to visit. Other
items of interest will be posted as they become available.
FastWays is a product of Software Support Products, LLC. Edge Ware has no financial
interest in this product, but we believe it to be a very powerful add-on to FastTrack and
have used it for years. See FastTrack commentary number 8100 for additional information.
Traders Press is a good source of books on technical analysis. Call them at 800-9278222 and ask for a copy of their catalog.
These are the books that Edge Ware used in researching Point & Figure Charting:
Point & Figure Charting: The Complete Guide by Carroll Aby
Study Helps in Pint & Figure Technique by Alexander Wheelan
Point & Figure Charting by Tom Dorsey
The reference used for research in cycle analysis :
MESA and Trading Market Cycles by John F. Ehlers
The reference used for the Hurst Exponent:
Fractal Market Analysis by Edgar Peters
54
Appendix A - Technical Discussion
Parabolic Stop
The parabolic stop system was developed by Welles Wilder and is documented in many
books on technical analysis.
The parabolic formula can be summarized as follows:
Par2 = Par1 + Acc_fac x {high_of_trade - Par1}
Where:
Par2 = Tomorrow’s parabolic value
Par1 = Today’s parabolic value
Acc_fac = Acceleration factor
high_of_trade = Highest price since the trade was established
The fund is held until the mutual fund NAV becomes equal to, or drops below the Par
value. The initial value of the parabolic for a long trade is set to the lowest price reached
while the fund was trading below the parabolic.
Wilder suggested setting the initial value of the acceleration factor to 0.02 and increased
by 0.02 each time the trading vehicle (stock, commodity, etc.) hit a new high during the
trade. He also suggested a maximum value of 0.2 Traders using this function for mutual
funds have found the 0.02 increase for each new high to be too large a value. A more
reasonable value is in the 0.001-0.0001 range. FastGraph allows the user to set the starting, maximum, delta increase.
Bollinger Bands
Bollinger Bands were developed by technical analyst John Bollinger. See a good book
on market technical analysis for an explanation on how to best use this indicator.
Bollinger Bands are plotted two standard deviation above and below a simple moving
average. The data used to calculate the standard deviation are the same data as those
used for the simple moving average.
Upper band = X + 2*σ
Lower band = X - 2*σ
55
Where:
X = A simple moving average = ΣX
i
/ N
X
= The daily NAV for days = 1, N
i
N = Total number of days for the calculation. The recommended value is 20 days.
σ = Standard Deviation = [Σ(Xi - X) / N]
0.5
Adaptive Moving Average (AMA)
There are a number of different methods to calculate adaptive moving averages. FastGraph uses the following equation:
AMA(day) = EMA ( N x EMA(day) - (N-1) x EMA(day-1))
Where:
day = current point in time series
day-1=current point in time series minus one
EMA = Exponential Moving Average
N = number of periods in the time series to use for smoothing
Hurst Exponent
A good book on the subject of the Hurst Exponent (HE) is Fractal Market Analysis by
Edgar E. Peters.
Interestingly, the HE development grew out of work by Einstein who found that the distance a random particle covers increases with the square root of time:
0.5
R = T
Where R = the distance covered
T = a time index
A process that changes with an exponent greater than 0.5 is said to be persistent or in
market terms, trending. A process that changes with an exponent less than 0.5 is antipersistent or in market terms, trading range.
H.E. Hurst (1900-1978) studied river flows in his work as a dam builder. He noticed that
flood years tended to be followed by other flood years, i.e., not a random occurrence. He
developed a method to measure how persistent a process may be. The method is very
56
data intensive and this chapter will give a brief overview. Anyone with a deeper interest
is directed toward the Edgars book.
The HE works with “time series data” which for our purpose will be the daily NAV of a
fund or index. The first step is to take the logarithm of the ratio of each daily NAV divided by the previous day’s NAV.
The result of the first step is divided into a number of time series. If working with 100
days of daily data, for example, you may divide it into four periods of 25 days each. The
average value is calculated for each of these four periods.
The next step is to find the “accumulated departures” from the average for each of the
four periods. Accumulated departures are calculated by taking the sum of each value in
the period minus the mean value of the period.
Next, a range is calculated for each period which is simply the maximum value minus the
minimum value for each period.
A standard deviation is calculated for each of the four periods, and the range for each of
the four periods is divided by the standard deviation of each period. This result is called
R/S. An average R/S value is calculated by summing the R/S for each of the four periods
and dividing the sum by four.
We are almost finished. The above result gives one value of R/S for a single period of
time, i.e., number of days, in this case 25 days. To calculate the HE we need to find an
R/S value for several different number of days, i.e., 20, 30 40 etc. The R/S values can be
plotted vs. the different number of days on log/log paper and the HE will be the slope of
the line. FastGraph calculates the HE by a mathematical curve fitting routine.
FastGraph requires two values when it calculates the HE. The Period is the maximum
number of market days used to calculate the HE. The number of sub periods is the number of different values of time to curve fit. If you see values of HE less than zero or
greater than 1, increase the number of sub periods to get a better curve-fit. The suggested
number of sub-periods is five. The number of days to use should be one hundred or
more.
57
Loading...
+ hidden pages
You need points to download manuals.
1 point = 1 manual.
You can buy points or you can get point for every manual you upload.