# 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.

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.

## How did it benefit investors?

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

### However,

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 (**D**ynamic **A**sset & **R**isk **W**eighted **IN**vestment) assets listed on **The Darwin Exchange** are measured in terms of **12 Core Investment Attributes** that go far beyond mean and variance. These are:

- Experience
- Market Correlation
- Risk Stability
*(in terms of VaR)* - Risk Adjustment
*(in terms of intervention to stabilize VaR)* - Open Strategy
- Close Strategy
- Positive Return Consistency
- Negative Return Consistency
- Duration Consistency
- Loss Aversion
- Performance
- 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:

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

### 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.

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.**

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:

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

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. — **References** [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. http://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/1990/markowitz-facts.html — *Do you have what it takes? –* *Join the Darwinex Trader Movement!*