DARWIN Filters: A Practical Alternative to Markowitz Portfolio Theory

In 1952 [1], the great Harry Markowitz published a paper on portfolio selection that essentially set the stage for modern portfolio theory in a mathematical context.

Harry Markowitz

Harry Markowitz – Nobel Prize Winning Economist

For those not familiar with this Nobel Prize winning economist [2], he devised a methodology whereby investors could mathematically evaluate the proportion of total available capital to allocate, to each constituent asset in a portfolio of assets.

His method was based on just the means and variances of asset returns.

For different choices of capital allocation per asset in a portfolio, different combinations of mean (μ) and variance (σ²) would materialize, collectively referred to as the attainable set.

As investors always want the highest possible return for the lowest possible risk, Markowitz termed all those combinations of μ and σ² where either:

1) σ² was the minimum possible value for a given μ, or

2) μ was the maximum possible value for a given σ²,

.. as the efficient set, or “efficient frontier” as it’s more popularly known.

Harry Markowitz - Efficient Frontier ModelHow did it benefit investors?

Markowitz Portfolio Theory (MPT) stated that investors should select a portfolio from the efficient set, depending on their risk appetite.


The variances of asset returns in a portfolio do not fully explain the risk taken by an investor, and MPT is therefore not entirely applicable in practice.

For instance, MPT does not reveal the Value-at-Risk (VaR), extreme variations in an asset’s risk profile during times of high volatility, nor the Capacity of a given portfolio.

Darwinex’ Solution to Markowitz Portfolio Selection

Years of proprietary R&D at Darwinex, reliably addresses some of the inherent problems in traditional mean-variance portfolio construction & optimization.

All DARWIN (Dynamic Asset & Risk Weighted INvestment) assets listed on The Darwin Exchange are measured in terms of 12 Core Investment Attributes that go far beyond mean and variance.

These are:

  1. Experience
  2. Market Correlation
  3. Risk Stability (in terms of VaR)
  4. Risk Adjustment (in terms of intervention to stabilize VaR)
  5. Open Strategy
  6. Close Strategy
  7. Positive Return Consistency
  8. Negative Return Consistency
  9. Duration Consistency
  10. Loss Aversion
  11. Performance
  12. Capacity

With these robust behavioral analytics, DARWIN investors are able to iteratively filter assets in order to maximize expected returns and minimize standard deviation (risk), with zero mathematical optimization necessary to achieve desired allocations.

In fact, even an equally-weighted portfolio arrived at using DARWIN Filters presents a more statistically robust set of portfolio allocations, than mean-variance optimization where the possibility of overfitting to asset returns is a hidden risk.

DARWIN Filters

Creating custom combinations of the 12 investment attributes allows investors to analyse the behavioral machinery of assets they wish to include in their portfolios.

As Value-at-Risk (VaR), Excursion Analysis (+/- return consistency) and Capacity among others, become integral components of an investor’s selection criteria, the risks presented by traditional MPT (as discussed earlier), are effectively mitigated.

Perhaps the best way to demonstrate the effectiveness of this approach to portfolio construction, is through an example.

EXAMPLE: Real portfolio constructed using DARWIN Filters

A portfolio of 15 highly uncorrelated DARWIN assets (with an impressive Sharpe Ratio) was built using just DARWIN filters and zero mathematical optimization.

For inspiration, here are the actual realised returns of this portfolio between June 2014 and March 2017, both gross and net of performance fees:

DARWIN Portfolio Returns (June 2014 - March 2017)

DARWIN Portfolio Returns (June 2014 – March 2017)

And here is this DARWIN Portfolio’s performance against the S&P500 over the same time period:

DARWIN Portfolio vs. S&P500 (June 2014 - March 2017)

DARWIN Portfolio vs. S&P500 (June 2014 – March 2017)

Steps used in portfolio construction:

1) DARWIN Filters were first created using a combination of the 12 available Investment Attributes (as listed earlier), to define the investment criteria.

Create DARWIN Investment Attribute Filters

Create DARWIN Investment Attribute Filters

This filtered the initial full list of over 1,000 listed DARWIN assets, down to 15.


2) Monthly Returns listed publicly on each of the 15 DARWINs’ pages, were then used to construct a Variance-Covariance Matrix.

DARWIN Asset Returns

DARWIN Asset Returns


DARWIN Variance-Covariance Matrix

DARWIN Variance-Covariance Matrix


3) Assigning equal weights of 6.67% to all 15 assets, Expected Portfolio Returns and Standard Deviation were then duly calculated.

This led to a DARWIN portfolio with the following features:

DARWIN Portfolio Backtest Statistics

DARWIN Portfolio Backtest Statistics





4) For sake of exercise, here is a comparison of what MPT optimized allocations would be for the same portfolio:

Equal vs. MPT Optimized Portfolio Weights

Equal vs. MPT Optimized Portfolio Weights













MPT Optimized Portfolio Backtest Statistics

MPT Optimized Portfolio Backtest Statistics





An MPT optimized DARWIN portfolio would indeed have lead to a higher Sharpe Ratio (5.92 vs. 4.17), higher Expected Return (38.80% vs 28.61%), and a slightly higher Standard Deviation (5.71% vs. 5.66%)..

.. but at the risk of allocating a majority of available capital to only 4 out of 15 assets in the portfolio.

In this scenario – and as per Markowitz Portfolio Theory – a conservative investor would likely have opted for the equally-weighted portfolio, while a more aggressive investor may have opted for the MPT-optimized portfolio.

In both cases however, DARWIN Filters enabled both profiles of investor to consider the important attributes of Value-at-Risk (VaR), Capacity, Risk Stability and Consistency..

.. as opposed to traditional MPT mean-variance analysis where these would have been overlooked.


[1] Markowitz, H. (1952) Portfolio Selection. The Journal of Finance, Vol. 7, No. 1, 77-91. March. 1952.
www.jstor.org.proxy.lib.chalmers.se/stable/10.2307/2975974?origin=api (2012-10-30)

[2] The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 1990.

Watch this video to learn more about a DARWIN’s Investable Attributes:
* please activate CC mode to view subtitles.

Do you have what it takes? – Join the Darwinex Trader Movement!

Darwinex - The Open Trader Exchange

Darwinex – The Open Trader Exchange

Quantitative Trader

Why Quantitative? – Serious Algorithmic Trading Series (Part 2)

Quantitative Trading

Quantitative Trading

In case you haven’t already, you may wish to read the first two posts of the Serious Algorithmic Trading Series, here and here.

Many individual traders will often hear the term “Quant” and may visualize either:

  1. A sharply dressed City trader working in a hedge fund, sat in front of his Bloomberg or Thomson Reuters Eikon terminals, or
  2. A stocky chap wearing a Batman t-shirt, with telescopes for specs (and possibly a doctorate in Nuclear Physics), sat in his basement trading room pouring over mathematical models, following a staple fast food diet.

For the avoidance of doubt: you do NOT need a university degree to become a Quantitative Trader (though having one does come in very handy, IF you were paying attention in class!)

Now, both these individuals above likely followed a similar academic (or independent learning) path to their current disposition.

It’s even possible that the City trader was once a frequent visitor to his own basement trading room, before being spotted by a financial recruiter and beamed up to the 39th floor.

This prompts a few questions:

Why do Quants become Quants in the first place?

Quantitative Trader

Quantitative Trader

There are numerous advantages to quantitative trading, advantages that not only reduce the financial impact of discretionary decision-making going wrong, but also help measure performance in a manner that permits efficient future learning.

For the purpose of distinction, it must be noted that unlike algorithmic trading that employs technical analysis, the quantitative approach to algorithmic trading involves primarily Bayesian Statistics and Time Series Analysis.

These are more effective methods of generating uncorrelated risk-adjusted returns, all too often ignored by the retail fundamental or technical analyst. Those who recognize their advantages, naturally progress down a path to becoming Quants.

Is Quantitative Trading reserved for just institutions?

In short, no it isn’t. Find out why in part 1 of this series here.

Why should this interest retail traders?

The world of quantitative trading extends far beyond that of technical moving average crossovers, candlestick patterns, martingales, grids, and off-the-shelf trading systems celebrating their latest and greatest “trading secrets” that resulted in their most sensationally overfitted backtests to date.

It does so because the markets are a much more complex phenomenon than we think, and undergo several micro-structure and regime changes frequently.

Darwinex - The Open Trader Exchange

Darwinex – The Open Trader Exchange

Note: To protect investors from overfitted systems, all strategies listed as DARWINS on the Darwin Exchange are analyzed for proficiency in 12 investment attributes. Investors therefore have the ability to immediately assess whether a strategy’s current equity curve is likely to persist in future or not, something standard backtest results cannot reveal.

Indeed one could go as far as to say that the market is a stochastic process in and of itself.

Generating uncorrelated risk-adjusted returns in as seemingly stochastic an environment as this, is therefore a mammoth task.

Why more retail traders haven’t then embraced quantitative methods (that enable the discovery and subsequent exploitation of inefficiencies in stochastic processes) can only be attributed to a lack of awareness and “approachable” learning resources.

We will aim to address this in Part 3 of this series, “The Quantitative Approach to Algorithmic Trading”, and all subsequent posts that fall in the same category.

Advantages of Quantitative Trading

  1. Alpha is an elusive beast.

    Alpha is difficult to discover, gradually loses its profitability as more capital is allocated to its exploitation, and inevitably transitions from a source of risk-adjusted profitability to a source of risk.

    Quantitative methods allow traders to not only discover and exploit alpha, but to do so in a manner that maximises its profitability horizon and minimizes risk of decay.

    Quantitative analysis also facilitates the creation of statistical testing frameworks that can forecast risk of alpha decay in advance.

    Note: DARWIN investors benefit from a Scalability/Capacity investment attribute  displayed on each asset listed on the Darwin Exchange. It is a score ranging from 1 to 10 that indicates how much capital the underlying strategy can support without decay. The higher the score, the more assets under management (AuM) it can attract.

  2. Statistically Robust vs. Regular Backtesting

    Quantitative traders can make use of statistical tools that add another layer of validity to backtests.

    In simple terms, if you’re currently examining a backtest and taking its results with a “grain of salt”, substitute the latter with some rigorous quantitative testing and you have a much more credible (or not) backtest on your hands.

  3. Quantitative Trading encourages thinking in “Portfolios”

    Common behaviours among a large segment of individual traders include deploying a single trading strategy on a single asset, or deploying the same strategy on a mix of assets, without careful consideration given to weighted allocation as would be the case in an institutional setting.

    In the former’s case, the trader has put all his/her eggs in one basket.

    In the latter’s case, the trader has employed logic that goes something like “if it’s a robust strategy, it will perform well in all markets, under all market conditions.”

    Unfortunately, this logic is prone to leading traders into intractable situations where the lack of an appropriate risk-adjusted allocation matrix may lead to unexplained underperformance.

    Construct DARWIN Portfolios

    Construct DARWIN Portfolios

    Quantitative analysis allows traders to construct portfolios of assets or strategies (or both), such as to maximize their aggregate profitability while minimizing their aggregate risk. This is simply not possible to achieve without quantitative methods being employed.

    Note: Investors on the Darwin Exchange can construct uncorrelated portfolios of DARWINS using our proprietary diagnostics toolkit. Twelve investment attributes (as of Darwinex Reloaded) allow investors to not only select DARWINS that match their criteria for investment, but also reduce overall portfolio risk through adequate diversification. As of Darwinex Reloaded, investors are even rewarded for diversifying their DARWIN portfolios, through the introduction of Diversification Rebates.

One of the most commonly voiced disadvantages of Quantitative Trading is that it’s a complex discipline to master.

So is learning to drive a car for the very first time. The right instructor can be the difference between a confident future driver and a jittery one.

Quantitative trading is no different. Over the course of these posts (that aim to make the complex simple), the best most approachable educational material will always be referenced for the reader’s benefit.

The fruits of a Quant’s labour are far sweeter than one can imagine. You will be well served by visiting the Darwin Exchange Leaderboard for inspiration.

The next post will begin our journey into the Quantitative Approach to Algorithmic Trading.

Trade safe,
The Darwinex Team

Do you have what it takes? – Join the Darwinex Trader Movement!

Darwinex - The Open Trader Exchange

Darwinex – The Open Trader Exchange