## Are we in a Hedgie winter?

Modern finance is built on linear regression, the statistical method that allows summarization and study of relationships between dependent and independent variables. Hence Asness’s textbook use of linear regression is brilliant because simplicity is beautiful. He uses Aristotelian logic to elegantly bring out the information content buried in hedge fund performance.

The industry indeed needs assistance in knowing how to measure true alpha and how an apple to apple comparison can be done between active managers and hedge funds. Asness systematically proves that he is not only true to his vocation, but also that his views are inextricable from the Fama and French linear regression ecosystem.

In the world of data science, quantum computing, black holes and space X flights, investors, journalists, the public at large, and presumably asset managers should be more open to Asness's approach. For the few who are on the fence and struggling to understand how the quants are changing everything from finance to the cryptographic world, the following represents a sequential summary of Asness’s regression logical steps.

In very simple words, consider the data you have to study as a set of points across Y and X-axis. Regression is the approach to fit a straight line between the data points so that it represents the closest distance from all the points. But why do we fit a line? Because the objective is to find meaning, behavior, causality in the data.

The better you understand your data, the better you can drive meaning from that data. The line and its slant provide a snapshot of what happened in the past to the data and potentially an insight into the future. This line fitting is at the heart of many quant systems today. Line fitting is at the heart of two Nobel prizes (1990 [1] and 2013 [2]). Success in the quantitative asset management business is believed to be a function of better line fitting.

Sequentially this is what Asness does...

First

He plots a chart of hedge fund returns data as y and market returns of the S&P 500 Index as x data point and then fits a line, which results in the angle of the line and where it starts. Because the slant in the line (sensitivity or coefficient) is less than what is generally assumed by the industry, Asness proves that the one to one comparison between the hedge fund and the market (S&P 500 Index) is incorrect. The relationship should be more like 0.46 to 1.

Second

Eugene Fama earned his fame and Nobel prize based on his 1960's work on market theories which included studying the slant. Fama also focused on extracting information content out of data and studying market returns. He found that the market was important, but there was more than one robust behavior inside the market. Fama is well known for enhancing the market factor by two more factors, ‘Size’ and ‘Value’.

Fama’s size factor that Asness uses in his article suggests that a portfolio return would be higher if it had more small size companies than large size companies. Technical jargon refers to this as ‘Size bias’. This meant that a portfolio manager’s skill could only be judged net of the size factor as making a portfolio with small-sized companies required zero skill.

Here Asness shows that the hedge fund stripped of the size premium using the slanting line technique has a different look. With a new factor added, a new dimension is achieved converting the line to a plane.

Y = C + Sensitivity (mkt factor) + Sensitivity ’ (Size factor)

Third

Next, Asness shifts focus to the traditional active manager and repeats the slanting line method to strip the luck from the hedge fund manager’s skill (alpha) and proves that hedge funds have done better compared to active funds while active managers have witnessed a secular underperformance.

Fourth

Finally, Asness give an apples to apples comparison by comparing the correlation of hedge funds vs. active managers.

His conclusion, hedge funds really do not add value vs. active managers, there is limited differentiation and hence are “perhaps less special”.

Slanting line education has become an important part in the world of advanced science in finance. Financial professions have fallen in love with the line and refuse to let go. The slanting line was a start. Science has moved ahead beyond regression. The science was started back in 1886 by Francis Galton who saw that natural data tended to fall back to the mean.  In the slanting line case, it means that the line finds the “middle” of the data. Jules Regnault talked about it even before Galton in the mean deviation of returns resulting in early statistical and probabilistic analysis.

For every claim about the effectiveness of the slanting line approach, there are a host of other claims which suggests that the slanting line methodology is actually weak science. The Nobel prizes of 2002 [3] and 2017 [4] have been awarded to academicians who opined that the line works not because of the data by itself, but because human psychology (bias) is embedded in the data.  A few of the challengers have showcased that the risk and return equation is broken proving that low risk does not always lead to low returns and vice versa. This means that the slanting line can move from a positive slope to a negative slope and hence can impact our metrics and consequently our understanding of alpha.

This is why Nobel Prize-winning theories have failed to translate into robust alpha. Slanting line methodology and many other linear modeling approaches are textbook models that can’t compete with well designed computational heavy new age quant models which don’t rely on linear models but do consider that markets are non-linear and complex by nature.

The world today has moved beyond the assumption that psychology drives data to understand that a better approach to discover robust behavior in data is to not assume causality. Reinforcement learning, deep learning, lazy learning etc. offer a logical and sound shot at moving beyond simplistic extrapolation of the past data to anticipate with likelihood the future. While such new models are not free of their biases, at least they are not used to gather assets under management and the building of businesses on old assumptions from a physical tape reading world which is long dead. We are entering the world of alpha bots which don’t need to be trained for linear regression, they learn, adapt and learn again. The new manager you may hire may not be a human, it might be a bot named 01101111 and it may very well understand that naive diversification can work better than assuming specific factor exposure. It may know when size factor can fail and when it may continue to work.

In an industry that suffers from underperformance, teaching the world about the history of regression-based metrics, though important, distracts us away from the fact that it's the same “old” slanting line approach that has caused this underperformance in the first place. When you build models on somebody else's assumptions, you are operating a risky business. The market was never linear, it was always non-linear and size is a proxy which works and fails alternatively. The technology 40 years back was weak, but simplification was a necessity. That said, to talk about linear regression as an alpha measurement or alpha generation process is dangerous. Moreover, understanding inefficiencies do not automatically lead to model robustness. If Fama can himself admit that he doesn't know why the Size premium works, adjusting everything for size factor is an objective measurement, but it's not enough to take the industry out of its innovation less state.

We have a real problem not just for investors who have rightly decided to not pay for underperformance, but for asset managers who will be forced to innovate once the new wave of systematic, scientific and replicable models start delivering sustainable and robust alpha. The next generation hedge funds are already reworking on new processes which from outside might still look like a wretched winter.

Bibliography

[1] Harry M. Markowitz, Merton H. Miller, William F. Sharpe
[2] Eugene Fama, Robert Shiller
[3] Daniel Kahneman, Vernon L. Smith
[4] Richard Thaler