# Category: Quant Finance

### Black-Litterman allocation in algorithmic trading

In December 2019, I released a major update to PyPortfolioOpt, my python portfolio optimisation package. The most significant addition was an implementation of the Black-Litterman (BL) method. Although BL optimisation is commonly used as part of a pipeline to optimise a multiasset/equity portfolio, in this post I argue that BL is particularly well suited to the problem of optimally weighting signals in an algorithmic trading context.

### How predictive is the historical volatility?

One of the things that makes markets exciting (or frightening) is that prices move around a lot. It is important to be able to describe and predict the range of possible price movements over a given time horizon since some investors might desire assets whose prices don’t move up and down too much. We can quantify this by computing the volatility, which is commonly defined to be the standard deviation of the asset’s (log) returns. This post examines how well we can predict future volatility and why that matters.

### Graph algorithms and currency arbitrage, part 2

In the previous post (which should definitely be read first!) we explored how graphs can be used to represent a currency market, and how we might use shortest-path algorithms to discover arbitrage opportunities. Today, we will apply this to real-world data. It should be noted that we are not attempting to build a functional arbitrage bot, but rather to explore how graphs could potentially be used to tackle the problem. Later on we’ll discuss why our methodology is unlikely to result in actionable arbitrage.

### Graph algorithms and currency arbitrage, part 1

In this post we briefly outline how graph theory can be used to systematically find arbitrage opportunities in foreign exchange markets. Read more...

### Portfolio optimisation: lessons learnt

Over the past few months I have been busy doing a mixture of blockchain consulting and quantitative finance work for a couple of companies in South East Asia. In particular, I have had the opportunity to investigate the interesting problem of portfolio management for cryptoassets – it was not my first experience with portfolio optimisation, having implemented efficient frontier portfolios at a roboadvisor startup, but this time I took the opportunity to do a deep dive into the subject.

### Exponential Covariance

In this post, I describe a method of computing covariance matrices that gives additional weight to recent observations. This is particularly important in the field of financial portfolio optimisation, wherein a better estimate of future covariance can create significant value. Read more...

### Classifying financial time series using Discrete Fourier Transforms

A financial time series represents the collective decisions of many individual traders; it seems reasonable to me that the nature of these decisions may differ based on the underlying asset. For example, a company with a higher market cap may be more liquid, and subject to larger individual buy/sell orders including institutional investment. Thus, there is a case to be made that information such as the market cap of a company should be ‘encoded’ into its price movements. While these characteristics may be difficult to pinpoint on a chart, in principle it may be possible for a machine learning algorithm to find statistical relationships between the time series and the market cap of the company. This post will investigate that claim.

Yahoo Finance has long been an excellent free financial resource with a wealth of data and a convenient API, allowing open source programming libraries to access stock data. But not any more. As of May 2017, they have discontinued their API, probably as a result of Yahoo’s pending acquisition by Verizon. This means that excellent tools like pandas-datareader are now broken, much to the dismay of many amateur algorithmic traders or analysts. It turns out that there is a rather hackish workaround which allows us to download the data as CSV (i.e spreadsheet) files, which of course can then be read into excel, pandas dataframes etc.