1. Statistical Study of Multi Dimensional Arbitrage Model
Apogee Fund Management
November 26, 2004

2. 2
Table of Contents
Introduction
Apogee Simulation
Statistical Analysis
Profit and loss 1, 5, 10, 20 days forward
Probability 1, 5, 10, 20 days forward
Conclusion
Appendix
2002
2003
2004

3. 3
Introduction
This presentation will show the reader selected tools Apogee Fund
Management uses for researching and validating trading strategies.
The first section presents the results from Apogee Simulation going
back to 2002, comparing Statistical Arbitrage with just equity data to
Multi Dimensional Statistical Arbitrage.
The second section provides a statistical study which will work as a
supplement to our Apogee Simulation in understanding the added
benefit of looking across asset classes as opposed to a equity only
driven Statistical Arbitrage model.

4. 4
Apogee Simulation
Apogee Fund Management’s primarily research and production
environment is a sophisticated simulation and production trading
system developed in C++ and Matlab,
The graph on the following slide shows three graphs of two different
strategies from March 2002 to October 2004 (simulation).
The top graph shows the dollar amount ($) made by the two strategies
The middle graph shows market value (MV) and the fluctuations in
market value
The bottom graph shows the percentage (%) return
The two strategies are:
Statistical Arbitrage model ---- (Stat Arb Model) which is driven by equity
price deviations
Multi Dimensional Arbitrage model ---- (MultiDimen Arb Model) which is
driven by equity price deviations, credit information, and option
information

5. 5
Apogee Simulation Graph

6. 6
Apogee Simulation (continued)
The graph shows clearly the advantages of looking across asset classes for
information.
The market value is very similar, but the dollars made and therefore also the
percentage return is significantly higher for the Multi Dimensional Arbitrage model.
Also, the Sharpe ratio enjoys a nice boost from 1.48 to 2.40 (the risk free rate has
not been taken out for either strategy which would lower both ratios slightly).
The leverage used is one dollar long and one dollar short for every one dollar
under management.
Transaction cost and slippage are accounted for.
Our simulation approach makes every attempt to avoid possible path
dependencies, over fitting, data mining and other types of errors, but doubt
about these problems may still exist. This is why the second part of this
presentation will examine our signals from a pure statistical point of view.
The statistical analysis is meant to be looked at as a complement to the
simulation study.

7. 7
Statistical Analysis
The methodology for the statistical analysis section is as follows.
All stocks that Apogee trade will be gathered in a database from March
2002 to August 2004 on daily basis with: equity signal, credit signal,
option signal and future return for 1, 5, 10, and 20 days.
A filter will then condition the data and average the future profit/loss as
well as the probability of a profitable return.
For example, if the option signal is filtered as being > 0 , half of the data will be
displayed (total data points is 125,000 for 2002, 150,000 for 2003, and 92,000 for
2004). For example, 600 stocks * 255 trading days = around 150,000 data points.
Furthermore, since the equity data around 0 will be noisy an equity filter
will be above or below the “noise level” which in this study will be 1
standard deviation (Stdev).
Credit and Option information will then be added and the future return and
probability of a profitable return will be calculated. The Credit and Option data will
be used at a level far below our triggers and simple cut the data in half by using < 0
for long signals and > 0 for short signals.

8. 8
Statistical Analysis
The graph on the following slide shows a bar graph outlining the
One, Five, Ten, and Twenty day forward PL for (1) equity, (2) equity
plus bond information, (3) equity plus option information, and (4)
equity plus bond and option information in the time period 2002-
2004.
Note, the bond information is making its biggest impact on the longer
time horizons (Ten and Twenty Days), meanwhile the option information
is making an impact across all the sampling periods.
Also, observe the added benefit in all time periods for adding information
from both the bond and option universe.

9. 9
Statistical Analysis (PL graph)
0.00%
0.20%
0.40%
0.60%
0.80%
1.00%
1.20%
1.40%
1.60%
1.80%
2.00%
2002-2004 Future Returns on fixed time intervals using multi dimensional data
Equity 0.15% 0.53% 0.77% 1.15%
Equity plus Bond 0.15% 0.55% 0.83% 1.49%
Equity plus Option 0.21% 0.74% 1.11% 1.74%
Equity plus Bond, Option 0.20% 0.75% 1.14% 1.96%
OneDay PL Five Day PL Ten Day PL Twenty Day PL

10. 10
Statistical Analysis (Probability Graph)
The slide below is looking at probabilities of a successful trade and is
peaking for a twenty day forward “trade” around 60% when looking at
equity, bond and options meanwhile the success rate for a pure equity
derived “trade” is 55% for the same time period.
50.00%
51.00%
52.00%
53.00%
54.00%
55.00%
56.00%
57.00%
58.00%
59.00%
60.00%
61.00%
2002-2004 Probability on fixed time intervals using multi dimensional data
Equity 53.58% 54.81% 55.10% 55.36%
Equity plus Bond 53.71% 55.14% 56.16% 57.55%
Equity plus Option 54.81% 57.34% 57.98% 58.75%
Equity plus Bond, Option 54.98% 56.87% 58.23% 60.18%
OneDay Probability Five Day Probability Ten Day Probability Twenty Day Probability

11. 11
Statistical Analysis (Sample Size Graph)
The slide below shows the sample size for the different strategies. The
total sample size is around 367,000 data points.
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
Sample size 2002-2004
Data points 2002-2004 120,379 54,417 78,507 37,782
Equity Equity plus Bond Equity plus Option
Equity plus Bond,
Option

12. 12
Summary
Even though the statistics methodology with fixed time intervals and
“above noise” filters are different from our trading rules displayed in
the Apogee Simulation (and especially our exit logic has been
ignored in the statistical analysis section), the results are in line and
shows a boost when looking across asset classes for added
information.
The PL is in the range of 1-2 % for twenty days forward period which is a
common holding time for Apogee’s actual trading and will annualized by
similar to our target of 12-18%.
The probabilities of success per trade are similarly accurate for our
strategy and is in the range of 55-58%.
The Apogee Simulation and the statistical study, will work as
complements to each other for the reader who wants to learn more
about Apogee Fund Management’s edge in today’s competitive
market-neutral arena.

13. 13
Appendix
The following slides breaks down the PL and probabilities by year.

14. 14
2002 Forward Returns/Win-Loss Probabilities
2002 has the same overall pattern as the summary graphs
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
4.00%
2002 Future Returns on fixed time intervals using multi
dimensional data
Equity 0.19% 0.66% 0.73% 1.89%
Equity plus Bond 0.16% 0.74% 0.96% 2.76%
Equity plus Option 0.25% 0.97% 1.24% 2.84%
Equity plus Bond, Option 0.23% 1.07% 1.54% 3.64%
OneDay PL Five Day PL Ten Day PL
Twenty Day
PL
50.00%
52.00%
54.00%
56.00%
58.00%
60.00%
62.00%
64.00%
66.00%
2002 Probability on fixed time intervals using multi dimensional data
Equity 53.03% 53.62% 53.86% 57.34%
Equity plus Bond 52.08% 55.02% 55.96% 61.91%
Equity plus Option 53.64% 55.82% 57.08% 61.45%
Equity plus Bond,Option 53.01% 57.48% 59.60% 65.74%
OneDay
Probability
Five Day
Probability
Ten Day
Probability
Twenty Day
Probability

15. 15
2003 Forward Returns/Win-Loss Probabilities
2003 has a very different shape than the summary graphs and indicates better performance in the
short-term and the long-term time periods [is not mean-reverting]. 2003 was also a weaker than normal
year for our simulation (9 % return).
-0.60 %
-0.40 %
-0.20 %
0.00 %
0.20 %
0.40 %
0.60 %
0.80 %
2003 Future Returns on fixed time intervals using multi dimensional data
Equity 0.15% 0.43% 0.57% -0.40%
Equity plus Bo nd 0.16% 0.33% 0.30% -0.52%
Equity plus Option 0.23% 0.62% 0.68% -0.24%
Equity plus Bo nd, Option 0.22% 0.52% 0.36% -0.43%
OneDay PL Five Day P L Ten Day P L Twenty Day PL
44.00%
46.00%
48.00%
50.00%
52.00%
54.00%
56.00%
2003 Probability on fixed time intervals using multi dimensional data
Equity 53.51% 53.46% 52.12% 46.49%
Equity plus Bond 54.10% 51.66% 50.12% 46.35%
Equity plus Option 54.72% 55.91% 53.19% 47.89%
Equity plus Bond, Option 55.58% 53.28% 50.39% 46.93%
OneDay Probability Five Day Probability Ten Day Probability
Twenty Day
Probability

16. 16
2004 Forward Returns/Win-Loss Probabilities
2004 has the same overall pattern as the summary graphs
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
2004 Future Returns on fixed time intervals using multi dimensional
data
Equity 0.11% 0.49% 1.00% 1.95%
Equity plus Bond 0.13% 0.57% 1.24% 2.23%
Equity plus Option 0.16% 0.64% 1.42% 2.61%
Equity plus Bond, Option 0.15% 0.65% 1.50% 2.66%
OneDay PL Five Day PL Ten Day PL Twenty Day PL
50.00%
52.00%
54.00%
56.00%
58.00%
60.00%
62.00%
64.00%
66.00%
68.00%
2004 Probability on
fixed time intervals using multi dimensional data
Equity 54.21% 57.34% 59.32% 62.25%
Equityplus Bond 54.95% 58.74% 62.40% 64.39%
Equityplus Option 56.08% 60.28% 63.68% 66.90%
Equityplus Bond,Option 56.35% 59.85% 64.71% 67.87%
OneDay
Probability
Five Day
Probability
Ten Day
Probability
TwentyDay
Probability