Engineering Returns With Multi Asset Universes

Before the engineering starts: Only four months ago, the pageview counter passed the 100,000 milestone. In all likelihood the 200,000 mark will be hit today. Thank you very much for your interest.

The series about Harvesting Momentum (see part I, part II and part III) largely covered pairwise strategies. Now it is time to investigate the performance of more diversified universes to generate returns.

A recent post on CSSA presented Momentum Score Matrices as a tool for predicting the profitability of a given asset universe. Assuming a random walk, the momentum profitability depends on the degree in dispersion of mean returns between the assets in a portfolio. David Varadi states: "A heterogeneous universe of assets such as one containing diverse asset classes will have different sources of returns- and hence greater dispersion- than a homogeneous universe such as sectors within a stock index."

Following a similar, but simplified approach to the cross-sectional dispersion of mean returns, the pairwise momentum score can be calculated as the population average of the squared difference between the momentum values of asset ABC against asset XYZ. Or in "R":

Dispersion (D) for $IEF - $TIP based on 3 month returns during 2001 - 2014. Average = 8

For an asset collection consisting of 14 assets, this approach results in the below matrix. The calculations can be performed using "R", Excel or AmiBroker. Examples of each are available on the Google Drive connected to this post. AmiBroker has the benefit of exporting the momentum matrix as html-file, which then can be imported into Excel for analysis (and prettifying).

Dispersion matix based on 3 month returns using synthetic $ETF's

Harvesting Momentum: Let's Kick Tires With AmiBroker [ Part III - Final ]

The previous posts in this series covered a basic Tactical Asset Allocation approach with with signals taken from the daily and the weekly time frames. This final post will be dedicated to portfolio rotation based on monthly and quarterly time frame. Only two asset class universes will be covered. Multi asset class universes are going to be the subject of a future post.

Taking the monthly time frame into consideration basically means rotation decisions are made once a month, after the close of the month. For the quarterly time frames this comes to only 4 re-balancing opportunities per year: at the end of each quarter. However, usually the re-balancing frequency is way lower.

For backtesting once again the source code provided in the opening post will be used, basically allowing the DIY retail investor to engineer his own alpha. Even if you don't have access to thinkorswim or Amibroker, the strategy at hand can be fairly easy implemented using Excel, since momentum is the only metric taken into consideration for re-balancing decisions.

Monthly Periodicity

The typical US stock market year has 252 trading days (= 12 months with 21 days on average). So for the previously used 85 days/17 weeks lookback period, momentum calculated over a 4 month period (= 4 x 21 days) is suitable. Applied to the base pair (SPY-TLT) this 4 month lookback period renders the following results.

Portfolio Equity SPY - TLT (4 months), drawdown periods in red

Harvesting Momentum: Let's Kick Tires With AmiBroker [ Part II ]

In Part I of this series the frame work for a basic Tactical Asset Allocation strategy was discussed using two ETF's representing stocks (first SPY, later MDY) and bonds (TLT). Following on the daily signals of the first post, the continuation of this series will be all about the higher time frames, starting with weekly signals.

Engaging a strategy based on weekly signals might be the way to go for anybody who does not want to be in synch with the crowd, since everyone and his uncle is doing momentum on monthly basis these days. And as it happens, the AFL-code provided in the previous post is just as suitable for weekend traders too.

Weekly Periodicity

As a starting point, the weekly equivalent of 85 days for the momentum calculation is used: 17 weeks without any smoothing.

Portfolio Equity SPY - TLT (17 weeks), draw down periods in red

Profit table SPY - TLT (17 weeks)

SPY-TLT (17w)		2004 - 2013
Total Profit		211	%
CAR		12.05	%
MDD (trades)		-16.16	%
MDD (system)		-16.16	%
Calmar (0%)		0.75
Sharpe (0%)		0.76
Trades		43
Winners		58.14	%

Harvesting Momentum: Let's Kick Tires With AmiBroker [ Part I ]

Developing indicators and strategies is great, putting them to a stress test by mr. Market is better. But how? As we speak, thinkDesktop does not have the nuts and bolts to perform proper backtesting. After much consideration I decided to invest nearly $500 by buying the AmiBroker Professional suite at the turn of the year. Next I found myself back in primary school, learning to write again ...

Over the last couple of weeks I have been studying AmiBroker’s Formula Language (AFL) like there is no tomorrow. Luckily the "Introduction to AmiBroker" by Howard Bandy (free download) is a great read and AFL has a huge and generous user base, gathered in the AmiBroker User’s List on Yahoo. Last but not least there is Tomasz Janeczko’s extensive UsersGuide with an overwhelming amount of examples.

So this post is all about backtesting. Actually it probably will be the first in a series for presenting some of the backtesting possibilities AmiBroker has to offer. And while we are discovering the AmiBroker Backtester, chances are we might come across some pretty neat portfolio strategies along the way. Stay tuned!

Harvesting Momentum

As stated in previous posts, the "momentum anomaly" is known for centuries. The gist of the momentum anomaly is that assets often continue their price momentum, defined as the change in price over a given lookback period. Momentum works well across asset classes as well as within them. So harvesting momentum really is all about follow the money.

On Seeking Alpha contributor Marc Cohn has published various strategies involving momentum based trading. One of them, "Return Like A Stock, Risk Like A Bond: 15.5% CAGR With 17% Drawdown" utilizes so called "Paired Switching" (see here for SSRN paper) between two exchange traded funds: SPY and TLT. Marc's comprehensive system actually is a TAA strategy in its simplest appearance.

Flexibile Asset Allocation With C(r)ash Protection

The "Conceptual sketch" posting presented a survey for designing a portfolio that generates stable profits during every type of economic environment the investor is faced with. Stimulating as well as  challenging comments were made providing food for thought on the building blocks for such a model. During our research we came across a paper published in late 2012 by Keller and Van Putten: "Generalized Momentum and Flexible Asset Allocation (FAA), An Heuristic Approach". The interested reader is encouraged to get acquainted with the elements of FAA.

Common asset allocation strategies (like the TAA strategy) are based on the so-called "momentum anomaly", which is known for centuries. The gist of the momentum anomaly is that assets often continue their price momentum, defined as the change in price over a given lookback period. Therefore one should buy assets with the highest momentum and sell assets with the lowest momentum.

FAA incorporates new momentum factors into risk regime determination. Next to the traditional momentum factor (R) based on the Relative returns among assets, Keller and Van Putten introduced Generalized Momentum by adding these new factors: Absolute momentum (A), Volatility momentum (V) and Correlation momentum (C). In their paper Keller and Van Putten demonstrated that by expanding the traditional momentum approach, portfolio performance increases compared to the buy and hold benchmark, both in terms of return as well as risk.

Summarizing FAA, Keller and Van Putten present their strategy with an example universe of 7 index funds. Applying a 4 month lookback, from this universe at the end of each month the top 3 assets are selected through a nested ranking process of these 7 assets based on relative momentum (higher is better), volatility (lower is better) and correlations (lower is better). Last, each of the top 3 assets chosen, has to pass the absolute momentum test: if their absolute momentum is negative, just go into cash. Capital is equally allocated over the top 3 assets or if applicable into cash.

FAA was scrutinized by Empiritrage. In their full report following findings are reached:
FAA has significantly higher risk-adjusted return than an equal weight portfolio. FAA decreases maximum drawdown dramatically. FAA is robust when adjusting look-back periods. Absolute momentum can directly add value on identifying down side risk regimes and decrease maximum drawdown.

Source: Empiritrage