Etf Portfolio Optimization

ETF Portfolio Optimization
January 20xx

Copyright © etftopportfolios.com Page 1
Table of Contents
1. Legal Considerations........................................................................................................................2
2. Target audience...............................................................................................................................3
3. Underlying principles.......................................................................................................................4
4. Imposed constraints ........................................................................................................................5
5. Detailed approach ...........................................................................................................................6
6. Findings...........................................................................................................................................8
Summary.........................................................................................................................................8
Target annual return = 4% .............................................................................................................10
Target annual return = 10% ...........................................................................................................16
7. Next steps......................................................................................................................................26
Attachments..........................................................................................................................................27

1. Legal Considerations
Seller’s Disclaimers
 All investments entail risks.
 Past performance of an investment security or portfolio may not provide an accurate estimate
of future performance.
 Opinions expressed herein are current opinions as of the date appearing in this material only
and are subject to change without notice.
 Reasonable people may disagree about the opinions expressed herein.
 In the event any of the assumptions used herein do not prove to be true, results are likely to
vary substantially.
 There is no guarantee that investment strategies will achieve the desired results under all
market conditions. Every investor should evaluate his/her ability to invest for a long term,
especially during periods of a market downturn.
 We make no representation that strategies identified herein will or are likely to achieve profits,
losses, or results similar to those discussed, if any.
 No part of this document may be reproduced in any manner, in whole or in part, without our
prior written permission.
 This information is provided with the understanding that you will make your own independent
decision with respect to any course of action in connection herewith and as to whether such
course of action is appropriate or proper based on your own judgment, and that you are capable
of understanding and assessing the merits of a course of action.
 We do purport not to provide broker/dealer, consulting or any related services.
 You may not rely on the statements contained herein.
 We shall have no liability for any damages of any kind whatsoever relating to this material.
 You should consult your advisors with respect to these areas. By accepting this material, you
acknowledge, understand and accept the foregoing.
Purchaser’s Rights
 Neither this report, its contents nor the corresponding source data may be distributed or resold
without the express written consent of etftopportfolios.com.

2. Target audience
The purpose of this report is to provide objective guidance to those investors who:
 understand successful investing requires tradeoffs between risk and reward
 subscribe to the key tenets of modern portfolio theory
 want to avoid bad investment choices based on emotion or slick marketing pitches
 seek to maximize their long term investment performance by minimizing unnecessary
investment risk and unnecessary investment cost
This report is definitely not intended for speculative investors who:
 believe guaranteed returns are achievable in financial markets
 seek to “time the market”
 seek to get rich quick
 believe they can “beat the market” over sustained periods

3. Underlying principles
Our approach is grounded in the following principles. If you disagree or are uncomfortable with any of
these assumptions, then this report will be of little to no use for you. However, if you are comfortable
with these assumptions, then the findings herein are likely to be highly useful in building your
investment portfolio.
Please review these assumptions and ensure you are comfortable with each of them before proceeding.
 Financial markets are generally efficient. There are no “free lunches” and no “can’t lose”
opportunities in efficient financial markets.
 Institutional investors have the benefit of formal training, years of professional experience, 40+
hours every week of attention, and staffs of research analysts. As a result, it is highly unlikely
that an individual investor, lacking such advantages, can outperform institutional investors over
time.
 The performance of most institutional investors will lag passive market benchmarks over time.
 Individual investors can maximize their net investment gain by eliminating unnecessary
investment costs and eliminating “diversifiable” investment risks.
 Individual investors can dilute their risk exposure to individual securities (stocks, bonds, etc.) by
utilizing “security baskets” versus individual securities.
 Individual investors can minimize investment costs by utilizing passively managed, index-based
security baskets versus actively managed security baskets. More specifically, individual investors
can avoid the management fees and load fees associated with mutual funds by utilizing
Exchange Traded Products (primarily ETF’s, but including other exchange traded products such
as ETN’s).
 As financial markets are generally efficient, the historic performance of market indices and
passively managed security baskets provides a reasonable proxy for their future performance.
 Correlations of historic returns for distinct security classes can be used as reasonable proxies to
predict future correlations. Correlations across securities can then be used to reduce the overall
volatility of candidate security portfolios (i.e. to minimize “diversifiable risk”).

4. Imposed constraints
For reasons of practicality and/or to control investment risk, we have imposed the following constraints
upon our analysis:
 Limited securities considered to Exchange Traded Products (ETF’s, ETN’s, Commodity Pools, etc.)
only. Individual stocks, individual bonds and mutual funds, among other security classes, have
been excluded from consideration.
 Ignored consideration of income tax efficiency. For example, we’ve ignored the potential
impacts of differential tax treatment for dividend distributions versus share price gains. We’ve
also ignored the potential impacts of differential tax treatment for municipal bond funds.
 Limited the maximum size of a portfolio to seven member securities.
 Limited allocation of any portfolio member to a minimum of 5% of the total portfolio.
 Limited allocation of any portfolio member to a maximum of 20% of the total portfolio.
 Limited allocation of any single commodity-based security to a maximum of 5% of a portfolio.
 Excluded all leveraged and derivative-based securities from consideration.
 Excluded all securities without at least six years of history to assess performance.
Note we have attached text files containing our underlying security performance data should you wish
to perform your own analyses without these constraints.

5. Detailed approach
Our analysis was structured as the following sequence of steps:
 We began by compiling a list of over 1500 Exchange Traded Products (ETF’s, ETN’s, Commodity
Pools, Grantor Trusts, Unit Investment Trusts) listed on publicly traded US exchanges.
 For each of these securities, we gathered end-of-day prices for the past several years. For
securities with limited history, we augmented the security’s history with the price history of an
associated market index in cases where such an index was specified and available.
 We adjusted these historical prices to incorporate the effects of share splits, dividends, etc.
 For each security, we computed key historical performance metrics, namely average total return
and return variation (variance), over short, medium and long term periods.
 We computed the covariations (covariances) of total returns for all 1500 x 1500 = 2.2 million
security pairs over the same short, medium and long term periods.
 We then excluded from further consideration all securities lacking a minimum of six years of
augmented, adjusted historical prices.
 To limit investment risk, we also excluded leverage-based securities or securities based on
underlying derivatives, reducing our list of securities to approximately 1300.
 As an additional risk control, we also applied strict allocation limits on commodity-based
securities still in our list.
 For each of a set of explicit target returns, we identified the optimal portfolio of securities from
our list of 1300 candidate securities.
Note for a seven member portfolio there are approximately 13007
= 6.3 x 1021
possible security
combinations to consider. Furthermore, for each of these possible portfolios, the optimum
allocation of investment funds between portfolio members must next be found. To illustrate this
point, imagine we have $500,000 to invest. We could simply split this $500,000 evenly between
the seven members of our portfolio. In such case, we’d allocate 1/7 x $500,000 = $71,428 to
each security. Unfortunately, this simplistic allocation scheme is unlikely to maximize the
portfolio’s performance while minimizing its risk. It probably makes sense to overweight some
portfolio members and underweight others, based on your risk tolerance and target rate of
return. Consequently, all possible investment allocation possibilities must be considered to find
the optimum allocation scheme (maximizing return while minimizing variance) for a portfolio.
As you can probably see, this leads to an essentially infinite number of possible solutions to
consider. Finding an optimum portfolio is too big a task for even the most powerful
supercomputers using conventional “brute force” approaches. However, by combining elements
of artificial intelligence and advanced numerical analysis, we have developed the means to
complete this analysis on highly scalable, low cost public cloud computer networks.
 For each target return scenario we analyzed, we documented the portfolio composition and
optimum allocation of funds across portfolio members, computed the projected variation in the

portfolio’s return, and back computed the portfolio’s performance over the previous several
years. Our latest findings are documented in this report.
 As a final qualitative check, we then reviewed each portfolio’s diversification across geographic
region and asset class.

6. Findings
Note the findings reported here are based on input data through month end December 20xx.
Summary
The following chart summarizes total return and corresponding lowest variation of return for each
target return assessed in this report. Note variation of return (as measured here by standard
deviation) increases sharply as target return increases—this variation reflects the increased risk an
investor must incur in exchange for the opportunity for higher gain.
0%
1%
2%
3%
4%
5%
6%
7%
4% 6% 8% 10% 12% 14% 16% 18%
StdDeviation(Yearly)
Average Return (Yearly)

Assuming a normal distribution, the probability densities of expected returns for these portfolios are
then as follows:
0
5
10
15
20
25
30
-10.0%
-8.5%
-7.0%
-5.5%
-4.0%
-2.5%
-1.0%
0.5%
2.0%
3.5%
5.0%
6.5%
8.0%
9.5%
11.0%
12.5%
14.0%
15.5%
17.0%
18.5%
20.0%
21.5%
23.0%
24.5%
26.0%
27.5%
29.0%
30.5%
32.0%
33.5%
35.0%
36.5%
38.0%
39.5%
ProababilityDensity
Actual Return (Yearly)
4%
6%
8%
10%
12%
14%
16%
18%
Target Return

Target annual return = 4%
The following portfolio returned an average of 4% annually over the previous six year period with
the lowest volatility:
Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
Vanguard Muni Bond Fund ETF ABC 20.00% 3.98% 3.00%
iShares Lehman 10-Year Treasury Note ETN BUG 19.97% 4.06% 6.37%
iShares Morningstar Large Growth Index Fund ETF CID 5.00% 20.81% 14.83%
JP Morgan 1-30 Laddered Treasury Portfolio ETF DMN 18.77% 4.36% 8.59%
PowerShares Emerging Market ETF ETF EAT 20.00% 0.31% 0.20%
CBOE Interest Rate 2-Year Treasury Fund ETF FIG 9.23% 5.20% 34.17%
PowerShares DB US Dollar Index Bullish Fund ETF UUP 7.03% -0.12% 8.71%
Return correlations () for these securities over the previous six year period were as follows:
ABC BUG CID DMN EAT FIG UUP
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%
Combining these individual performances led to the following portfolio-level performance:
Por olio return = 4.0%
Por olio standard devia on = 0.86%

Actual monthly performance of this portfolio over the previous six plus years is as follows:
The diversification profile for this portfolio is as follows:
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%ActualReturn(Monthly)
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Asset Class Diversity
Fixed Income - Government Asset Backed
Fixed Income - Municipal Investment Grade
Fixed Income - Municipal Floating Rate
Fixed Income - Government Medium Term
Equities - Health Care
Equities - Energy
Commodities- Agriculture
100.0%
Geographic Diversity
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%

-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
2.5%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%

-1.5%
-1.0%
-0.5%
0.0%
0.5%
1.0%
1.5%
2.0%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%

-6.00%
-5.00%
-4.00%
-3.00%
-2.00%
-1.00%
0.00%
1.00%
2.00%
3.00%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%
Por olio standard devia on =3.26%

-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%

-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%

-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

Security Type
Trading
Symbol
Allocation
(w)
Avg Return
Yearly
(r)
Std Dev
Yearly
()
ABC 100.0% 87.6% -1.8% 81.7% 4.1% -85.5% -18.1%
BUG 87.6% 100.0% -29.0% 94.7% -1.4% -96.1% 6.3%
CID -1.8% -29.0% 100.0% -37.0% -0.2% 29.7% -65.8%
DMN 81.7% 94.7% -37.0% 100.0% 1.6% -96.1% 14.9%
EAT 4.1% -1.4% -0.2% 1.6% 100.0% 1.2% -12.9%
FIG -85.5% -96.1% 29.7% -96.1% 1.2% 100.0% -10.1%
UUP -18.1% 6.3% -65.8% 14.9% -12.9% -10.1% 100.0%

-10.00%
-8.00%
-6.00%
-4.00%
-2.00%
0.00%
2.00%
4.00%
6.00%
20.0%
19.7%
18.2%
18.1%
12.3%
6.6% 5.0%
Equities - Energy
100.0%
US

7. Next steps
Now that you’ve reviewed this entire report, we suggest you proceed as follows:
 Re-read the “Disclaimers” section of this report.
 Carefully study the detailed findings presented in this report.
 Compare the projected variance in each portfolio versus its targeted return.
 Identify the portfolio delivering the highest return for the maximum return variance you can
accept. Remember, as a general rule, the shorter your investment time horizon, the less
variance (risk in your portfolio return) you should be willing to accommodate.
 Perform your own research. Recall we’ve attached raw ETF performance data to aid you in such
research.
 Based on your research, adjust your portfolio.
 Once you’ve invested, implement a practice of rebalancing your portfolio on a recurring basis.
Based on our backward analyses, rebalancing monthly provides little advantage versus
rebalancing quarterly but increases your trading costs. Unless your investment portfolio is very
large, it probably makes sense to rebalance quarterly.

Attachments
1. Text file – security listing
2. Text file – monthly historical performance (adjusted) by security

Etf Portfolio Optimization

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