Wonder of Residuals
Some mathematical constructs appear so repeatedly across trading strategies that they evolve into mental models for quantitative trading. Each of these constructs deserve their own post, given their fundamental role in algorithmic trading.
Residuals are one of these wonderful constructs.
Many market-neutral strategies are derived from residuals, particularly the arbitrage family: volatility arbitrage, dispersion arbitrage, index arbitrage, basket arbitrage, correlation arbitrage, etc. Residuals also open for trading an infinite-sized universe of investable assets, rather than just the instruments for which quotes are available from Yahoo or Bloomberg.
Levered ETFs and Market Close
Cheng and Madhavan from BGI recently published a research article entitled “The Dynamics of Leveraged and Inverse Exchange-Traded Funds”. This article models and analyzes numerous dynamics of levered ETF, for which traders may be unaware: daily returns, return divergence, path dependency, tracking errors vs underlying, rebalancing, and hedging.
Their results motivate a seemingly-contradictory (and a priori unexpected) hypothesis: side effects of levered ETF will influence behavior of quantitative strategies which do not trade the corresponding ETFs. To use a quantum mechanics analogy: levered ETFs will have action at a distance effect on wholly-unrelated strategies.
Flash Orders
High-frequency trading (HFT) has been the subject of much hubbub across the blogosphere (and just recently mainstream media) lately, stoked by the combo of Tyler Durden from Zero Hedge on the investigative side and Joseph Saluzzi from Themis Trading on the institutional agency broker side. No doubt buy-side agency brokers and their their NBBO– and VWAP-pegged execution algos are getting killed by the HFT guys.
A fascinating development along this thread are flash orders, originated by Direct Edge‘s ELP.
Three Horsemen
Conventional wisdom tells us quantitative trading is hard. Yet, few know specifically why it is difficult. Moreover, different types of quantitative trading suffer from differing complexities, such as: mathematical modeling, information access (e.g. tick-level data), computational facilities, execution facilities (e.g. low latency), risk management (e.g. real-time VaR), and leverage (e.g. RegT vs portfolio margin).
Amongst all complexity, much is due to the three horsemen of quantitative trading: bias, stationarity, and ergodicity.
Mean Reversion
Continuing introduction of fundamental phenomena, or stylized facts of financial markets, underlying quantitative trading.
Mean reversion is the second, of two, force driving prices:
“A price will tend to average over time.” (Wikipedia)
One intellectual challenge in understanding financial markets is internalizing, what appears at first to be, fundamental contradiction: prices are simultaneously driven by the counteracting forces of both momentum and mean reversion. Up is down, and left is right.
Mean reversion is one of the most generic phenomena, manifesting in myriad beautiful ways across diverse subjects. For example, Ornstein–Uhlenbeck processes are continuous-time stochastic processes for modeling mean-reversion. Cointegration from time-series econometrics is a stationarity property of linear combinations of series. The Bollinger Bands is a technical indicator formed by bracketed upper and lower bounds based upon standard deviation. Mean reversion also forms the basis for entire trading disciplines such as statistical arbitrage and volatility arbitrage.
Mean reversion is nicely illustrated via pairs trading, a classic statistical arbitrage trading strategy. For simplicity, consider closing prices of SPY and PRF during 2007 – 2008. This relationship is potentially interesting, as both are large-cap indices; their difference lies in weighting: PRF is weighted by fundamentals, while SPY is weighted by market capitalization. Price graph over this period is:
Momentum
Successful algorithms tend to be elegant: conceptually simple, built upon crisp intuition. Towards this end, summarizing a handful of fundamental phenomena which underlie much of quantitative trading is worthwhile.
Basic trading experience informs us that prices are systemically driven by one of two counteracting forces. The first force is momentum:
“Momentum is the empirically observed tendency for rising asset prices to raise further.” (Wikipedia)
Momentum manifests in many algorithmic and technical guises. For example, follow through is a classic measure originating from technical analysis. As illustration, consider the closing prices for an arbitrary heavily-traded ETF (IWM) during 2007 – 2008:
The corresponding cumulative daily change in close prices, measured in percentage over the same period, is illustrated below.
Impetus
A journal of quantitative trading strategies, algorithms, and related analysis. Emphasis is intuition and practical use in trading, over rigor (expect no proofs).
Focus is strategies tradable on public exchanges by automated systems; instruments include equities, equity derivatives, and volatility derivatives; frequency ranges from daily to tick. Posted strategies will either have no proven alpha (for instrument(s)/market(s) analyzed) or already ran their course.
Primary background topics include computational finance, financial economics, applied mathematics, financial engineering, and programming (Excel, R, and Java).
All content on this site is provided for informational purposes only. It is not intended as advice to buy or sell any securities. Stocks are difficult to trade; quantitative strategies are much more difficult to trade. Please do your own homework and accept full responsibility for any investment decisions you make.
Quantivity 