This article completes the three part-series of book reviews for Quantitative Trading. The Software Development and Statistics knowledge you gained from the previous two articles will be applied specifically to solve the problems that arise when developing algorithmic trading strategies.
The basics of how the Finance Industry operates will be surveyed. Next, we construct a framework for systematically making trading decisions based on objective criteria. Finally, insight on how to successfully wield this framework is gained by learning from the experience and mistakes of others.
Finance Fundamentals
An appreciation of the Finance Industry involves acquiring a wide breadth of knowledge. A non-exhaustive list includes understanding: the range of different asset classes traded, their derivatives and how they’re priced; the composition of market participants and the respective roles they play; the selection of venues in which trading can take place in a fragmented market and the intended function of each trading venue; and the regulations governing financial markets and the market microstructure describing their inner workings.
With the Finance domain knowledge grasped, we can begin to construct a framework for developing algorithmic trading strategies. The notion of risk is defined concretely as the standard deviation of the annualised returns of any portfolio of assets. The risk-adjusted expected excess return is adopted as a quantity that we seek to maximise. Given any specific risk-tolerance, it can be shown that there exists a unique portfolio that maximises the risk-adjusted expected return up to an additive multiple of the benchmark portfolio. Equipped with this objective we’re therefore able to make decisions systematically without subjective influences.
The role of a Portfolio Manager is to allocate capital “”optimally”” across a universe of assets. A notion of optimal must therefore be established. There are two main contenders: (i) maximal expected risk-adjusted residual return minus transaction costs (ii) maximal expected long-term wealth. In this article we consider maximal expected risk-adjusted residual return. Here the return is over the period starting from the present moment in time and ending at the time that the optimal allocation of capital is re-evaluated. The optimal allocation of capital should be re-evaluated whenever new information is received.
The Information Ratio of a Portfolio is defined as the ratio of the Portfolio’s residual return and residual risk. The Information Ratio is defined as the maximal Information Ratio of any Portfolio. We assume that the Information Ratio for a particular Portfolio Manager is known and therefore defines the set of opportunities available to a given Portfolio Manager.
A problem with the optimal solution of the utility function is that there are errors in the estimates of alpha and covariance-variance matrices. These errors can cause the optimal allocation to be far from the true optimal allocation. For example if the estimated alpha of particular asset is far greater than reality then too much capital will be allocated to it. All these freak noise will be picked up by the optimiser and ruin everything.
To fulfil the objective of maximising the the risk-adjusted expected return operationally there are a number of steps to complete. First, we must establish a list (or universe) of assets that we’re willing and able to trade. Our goal is to determine the optimal allocation of capital among these assets. Next, we must forecast the annualised returns of these assets, together with an estimate of their covariance-variance matrix. Finally, after specifying a risk-tolerance and any additional constraints, the optimal capital allocation can be determined by maximising the objective subject to the constraints.
Building on top of this broad financial underpinning, a deeper knowledge of Trading Strategies must then be developed. The statistical concepts grasped from the previous article grants you the ability to formulate and rigorously test trading strategies using historical data (backtesting). Moreover, it lends the statistical intuition necessary to instantly evaluate trading ideas without implementation and leads to a preference for parsimonious models over unnecessarily complex models. Combined with the programming knowledge developed in the first article, yields the ability to completely automate trading strategies, minimise the run-time of backtests and exercise full control of the trading system’s infrastructure.
We start the reviews with a book that requires no prerequisite financial knowledge and starts by introducing a host of important financial terms and concepts.
The Concepts and Practice of Financial Mathematics
The Concepts and Practice of Financial Mathematics by Mark Joshi presents the theory of pricing financial products. Each theorem presented is carefully stated and proven, with occasional details being relegated to references or the appendix.
The first half of the book, comprised of Chapters One to Seven, deals with the pricing of Options. An Option on a particular stock is a contract providing the owner with the right but not the obligation to buy the stock at a predetermined price (the Strike Price) at some later point in time (the Maturity Date). Consequently, the value of an Option is derived from the properties of the underlying stock. Options are part of a class of financial products known as Derivatives.
It’s possible to deduce the correct price of an option given a set of simple assumptions. The price of an option is expressed in terms of a collection of quantities known as The Greeks, which includes Delta, Gamma and Vega. These are partial derivatives of the underlying’s price with respect to different quantities.
The price of an Option is deduced in two distinct ways. The approach of Chapter Five constructs and solves the infamous Black-Scholes partial differential equation. There are assumed to be no arbitrage opportunities, the underlying price is assumed to follow Geometric Brownian Motion and Ito’s Lemma is applied. The second approach presented in Chapter Six uses Martingale Pricing Theory.
Quantitative Trading: How to Build Your Own Algorithmic Trading Business
The focus of Quantitative Trading: How to Build Your Own Algorithmic Trading Business by Ernie Chan is on the infrastructural components of a trading system and how everything pieces together.
Algorithmic Trading: Winning Strategies and Their Rationale
In Ernie Chan’s second book, Algorithmic Trading: Winning Strategies and Their Rationale, the process of generating alpha takes the spotlight with less emphasis on the overarching trading system.
Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Selecting Superior Money Managers
Active Portfolio Management by Richard Grinold and Ronald Kahn is regarded by many Portfolio Managers as the foundational book of Quantitative Investment. Definitions are established and well-formulated, objective functions are adopted and a structure for Quantitative Trading is constructed. From within this structural framework, guiding principles and closed-form equations that answer pertinent real-world questions can and are deduced.
As to not disturb the flow of the main text, many of the mathematical statements and proofs are relegated to the Technical Appendix found at the end of each Chapter.
Further Resources
Aaron Fifield’s Chat With Traders PodCast
On the ChatWithTraders Podcast, Aaron Fifield interviews a broad range of Quantitative Researchers, Discretionary Traders and University Lecturers including the Edward Thorp, Ernie Chan, Michael Halls-Moore of QuantStart.com and Dr Yves Hilpisch. In addition, a six episode series on Systematic Trading was produced as part of a collaboration with Quantopian.com.
The Podcast can be listened to on YouTube, SoundCloud or the ChatWithTraders.com website. For those as eager as me, I’ve noticed that the podcasts are uploaded to SoundCloud first before either of the other two distribution channels. For those who are also as impatient as me, you can listen to these podcasts on 2x speed on YouTube by adjusting the speed setting.
In addition to the episodes already mentioned, some of my favourites were: Kevin Daley’s, Bert Mouler’s and Dave Lauer’s.
Ernie Chan
Michael-Halls Moore
Bert Mouler