Our last post finished up examining the three different methods used to predict market regimes in the Gold Miners ETF, GDX – namely, clustering, Gaussian Mixture Methods (GMMs), and Hidden Markov Models (HMMs). We found GMMs performed the best in terms of proof-of-concept. But there was a lot of work to do to go from backtest to viable trading strategy.
In the next few posts, we’ll look at some of the ways we can improve our backtests.
We conclude our discussion of market regime detection by examining Hidden Markov Models (HMMs). Recall this series was inspired by a post from PyQuant News that highlighted a longer article from the London Stock Exchange Group (LSEG).
Those who took the CFA exams probably forgot using HMMs in the quant section. Whatever the case, the intuition behind them is clever. HMMs use observable data to infer non-observable data, or hidden states.
Our previous post, used hierarchical clustering to identify market regimes in the gold miners ETF, GDX. This was inspired by a post from PyQuant News that highlighted a longer article from the London Stock Exchange Group (LSEG). In this post, we’ll continue looking at identifying market regimes and using those predictions as signals for a simple trading strategy.
As noted, the LSEG article showed three different machine learning methods to segregate regimes: clustering, Gaussian Mixture Models (GMMs), and Hidden Markov Models (HMMs).
We recently saw a post from PyQuant News that piqued our interest, compelling us to dust off the old blog files and get back into the saddle. The post highlights a longer article from the London Stock Exchange Group (LSEG) on how to use different machine learning models to identify and forecast market regimes. That article uses Refinitiv, a market data service like Bloomberg, which we don’t have access to.
For fundamental equity investors, the financial statement is the launchpad for the search for value. True, quants use financial statements too. But they spend less time on what the numbers mean, than on what they are. To produce a financial statement that adequately captures the economic (not GAAP or IFRS) position of a company is no mean feet and draws upon accounting, domain knowledge, and artistry. Data scientists and machine learning engineers are more than acutely aware of the chore of data processing and cleaning.
Our last post examined the correspondence between a logistic regression and a simple neural network using a sigmoid activation function. The downside with such models is that they only produce binary outcomes. While we argued (not very forcefully) that if investing is about assessing the probability of achieving an attractive risk-adjusted return, then it makes sense to model investment decisions as probability functions. Moreover, most practitioners would probably prefer to know whether next month’s return is likely to be positive and how confident they should be in that prediction.
In our last post, we introduced neural networks and formulated some of the questions we want to explore over this series. We explained the underlying architecture, the basics of the algorithm, and showed how a simple neural network could approximate the results and parameters of a linear regression. In this post, we’ll show how a neural network can also approximate a logistic regression and extend our toy example.
What’s the motivation behind showing the link with logistic regression?
Our last post parsed portfolio optimization outputs and examined some of the nuances around the efficient frontier. We noted that when you start building portfolios with a large number of assets, brute force simulation can miss the optimal weighting scheme for a given return or risk profile. While optimization finds those weights (it should!), the output can lead to infinitesimal contributions from many assets, which is impractical or silly. Placing a minimum on the weights helps a bit.
Our last few posts on risk factor models haven’t discussed how we might use such a model in the portfolio optimization process. Indeed, although we’ve touched on mean-variance optimization, efficient frontiers, and maximum Sharpe ratios in this portfolio series, we haven’t discussed portfolio optimization and its outputs in great detail. If we mean to discuss ways to limit our exposure to certain risks (presumably identified in the risk factor model) while still shooting for a satisfactory (or optimal) risk-adjusted return, we’ll need to investigate optimization in more detail.
In our last post, we took our analysis of rolling average pairwise correlations on the constituents of the XLI ETF one step further by applying kernel regressions to the data and comparing those results with linear regressions. Using a cross-validation approach to analyze prediction error and overfitting potential, we found that kernel regressions saw average error increase between training and validation sets, while the linear models saw it decrease. We reasoned that the decrease was due to the idiosyncrasies of the time series data: models trained on volatile markets, validating on less choppy ones.