A New Dimension
My good friend and colleague, Michael Wood recently reminded me how clients of his firm appreciated his articles on investment matters, which prompted me to write the following.
Michael was a great advocate of Dimensional, a firm of fund managers using the principles of passive fund management established by Eugene Fama. Hence, many of his clients were recommended to invest in those funds and still do.
The Dimensional philosophy can be expressed as the chances of successfully picking stock are fewer than you’d expect. So why even play the game? Instead, Dimensional invest across massive numbers of different stock with a view to extracting the market return, ie the market average. To be fair, it’s a little more complex than that and based around the idea that everything you need to know about a stock is in its price. As such, Dimensional can be set to follow broadly within what is referred to as modern portfolio theory (MPT).
The idea of MPT was developed by Harry Markowitz as an undergraduate dissertation back in 1952 and is still the prevailing theory for many in the investment world. It’s an elegant and mathematically appealing solution to the problem of where and how much to invest using historical pricing as a basis. What it provides is a basis for spreading the risk of investing in any single stock by diversifying holdings across different markets that, in combination, provide an optimum ratio of risk to reward.
When you do the maths, it’s interesting to note that the relationship between risk and reward is not linear but a curve. In effect, you can increase risk as much as you like but, at a certain point, expected returns flattens. At a certain point of the curve lies a point (referred to as the tangency) which describes the theoretical portfolio providing the highest return for the lowest exposure to risk. Interestingly, the maths also determines that such a portfolio will also have the maximum amount of diversification of stock – something that links Dimensional with the wider school of MPT.
However, herein lies a problem. After the tangency, classic MPT requires you to decrease diversification until you end up increasingly in the realms of placing bets on single stocks. Typically, investment practitioners get around this by applying constraints to the upper and lower bounds of the various asset classes thereby artificially forcing diversification into the equation. However, no matter how we try and justify this, it effectively places us back in the land of stock picking. However, the problem isn’t really with MPT but in the specific nature of the maths.
MPT uses quadratic analysis of bivariates, a fancy way of saying that it uses a form of the quadratic equation you learned at school. The data it uses is the historic periodic returns on different asset classes, the more granular the better. From this you extract covariances between each asset class using a form of maths similar to the quadratic equations taught in secondary schools, which you then mangle with returns to extract a data point on a graph. Replay this thousands of times and the data points describe an arc known as the ‘efficient frontier’, or rather the curve we were talking about earlier.
At Leabold, being technical purists, we take this to extremes, using weekly returns for the last fifteen years on up to nineteen different asset classes. Not being satisfied with anything we could buy off the shelf, we wrote our own software to do this, pfOptimize. It’s a master class in how to apply modern portfolio theory taking up to twenty minutes to complete an entire calculation. However, the problem with being technical purists who make a point of understanding the maths in all its grisly details is that we also get to see the flaws in it. Something that drives us towards constant attempts to improve upon it.
Currently, we are working with a concept developed by Professor Lopez de Prado in 2016 called hierarchical risk parity’ (HRP), which combines graph theory and machine learning to produce portfolios that produces better out-of-sample performances while maintaining diversification.
The challenge with HRP is that it’s sufficiently complex to render spreadsheets unusable. Coding your own software therefore requires you to use dedicated data analysis languages such as Python, R or Matlab. However, what you get out is astounding and quite beautiful (if you like maths). Here’s a picture of one of the outputs, called a dendrogram, describing the relationship between, in this case, a few simple ticker stocks.
The above describes the relationship between the elements of portfolio in terms of risk contribution (variance) as opposed to the difference in risk (covariance). Not only does it preserve diversification, using all available asset classes, but it removes another problem of classic MPT, sensitivity to outlying data that tends to over/underweight allocations.
It’s reasonable, given previous mention of Dimensional to ask whether they do something similar, to which the answer is no. Put analogously, a passive fund manager is a baker of bricks, whereas it’s the financial adviser that builds the house. How Leabold uses Dimensional funds is something that has evolved over the years. We started off fairly simply, where most advisers do and most still remain. However, approach developed when we came to appreciate that the efficiency of investment is key to the outcome the client needs to achieve. Simple strategies using single funds, or just a few funds will suffice when the portfolio is small but, the weaknesses in that approach begin to become clear where larger amounts are involved. These weaknesses convert into excess risk and cost. However, much of the complexity of what we do is left under the bonnet, except in occasions such as this.
By Derek Lavington
Senior Director and Compliance Officer at Leabold Financial Management.