WIDEALPHA ANALYTICS

Back-testing WideAlpha’s Portfolio Optimisation Algorithm

Copyright WideAlpha Ltd. 2017
MSc. Sergio Garcia de Alba
Correspondence: investors@widealpha.com

Abstract

The objective of this set of tests is to evaluate the WideAlpha optimisation algorithm on four ETF portfolios. Each of the tested portfolios was constructed using the most liquid and low-cost ETFs with the longest trading histories. We offer optimisation services based on these and other customised portfolios to institutional investors.

Keywords: ETF Portfolios; Kelly criterion; Optimal asset allocation; Growth-optimal portfolios; Machine Learning Portfolio Optimisation

Introduction

It is generally accepted that diversification is important when building a portfolio, however how diverse should a portfolio be and how can we predict which investments will be the more profitable ones and therefore become a focus?

The best a smart investor can do is model the return probabilities to the best of his knowledge and ability, and use this information to maximise the expected returns for the amount of risk he or she is willing to assume.

The problem of course is that doing a good job in this regard is no easy task. Dr. Harry Markowitz tackled this complex problem in his 1952 paper ”Portfolio Selection”, and was awarded a Nobel prize for this research that served as the basis for what later became known as Modern Portfolio Theory. To this day most of finance theory continues to rest on this foundation.

The theory is mathematically elegant and was a great first approach to tackling this very difficult problem. It has nonetheless several weaknesses that limit its usefulness when investing in real life. Chief among these are that the theory assumes returns are normally distributed, correlations and volatilities are static over time, and that the investor knows what the exact values for volatility and expected returns are. These assumptions have been proven incorrect in the market, especially during market melt-downs.

What we have done at WideAlpha is develop a machine learning algorithm that uses economic and market indicators to better model these variables. We then use a stochastic approach to find the optimal portfolio. With these improvements we are able to make better allocation decisions that generate alpha.

Underlying Philosophy

Another shortcoming we find with the Markowitz approach to portfolio selection is that it favours the maximisation of the arithmetic average of the expected return.

This is far from ideal for medium to long term market investors. Optimising the geometric growth rate delivers much better results for investors. The best way to accomplish this is by employing the Kelly criterion.

A benefit of growth-optimal Kelly inspired portfolios is that they are not adverse to positive volatility. Investors should aim to avoid loss, but there is no good reason why they should try to avoid big increases in the value of their holdings.

Following a Kelly sizing approach has a number of additional benefits, including being proven to eventually outperform every other allocation strategy. This is thanks to the Kelly allocation approach providing just the right amount of diversification. To be able to follow a Kelly strategy it is necessary to correctly model the return probabilities of investments. The better securities are modelled, the better the results from the Kelly optimisation. This is where our algorithm adds significant value.

Risk Management Approach

When using the growth-optimal Kelly approach the allocation strategy is focused on obtaining the highest compounded growth-rate, and should therefore not be relied upon to dial risk appetite.

We therefore propose managing the risk of the portfolio at the securities selection stage. This can be seen by how the four WideAlpha Indexes we will maintain were affected by the financial crisis. While they all use the same optimisation algorithm, the maximum draw-downs differed significantly depending on their ETF components.

Algorithm Description

The algorithm developed at WideAlpha uses proprietary machine learning techniques to model the return probability distribution of public market investments. This means that the algorithm can learn, for example, that an investment has a higher return on average when interest rates are increasing.

The second part of the optimisation algorithm deals with finding the growth-optimal allocation. This is a complex endeavour given how the number of possible investment combinations to evaluate grows exponentially with the number of investment options. For this we developed a proprietary stochastic simulation yielding very satisfactory results while being time and resource efficient.

The algorithm is able to generate alpha through better security modelling, smart rebalancing, and embracing the benefits of uncorrelated assets. The last point has been one of the fundamental strengths of portfolios such as Bridgewater’s All-weather portfolio and other risk-parity approaches.

Back-test Results

The back-test results for our flagship WideAlpha ETF portfolios are shown in the following pages. It is worth mentioning that the same algorithm was used for all the portfolios, which is reassuring given that most quantitative algorithms fail in live tests due to over-fitting.

In the following figures the back-testing results for the last ten years can be seen for four portfolios. One portfolio is focused on the U.S. market, one is a multi-asset portfolio, one is an investment grade bond portfolio, and the other is an international equity portfolio. All of them built with ETFs. They all outperformed their benchmark after adjusting for their β.