This blog article is taken from our book [1]. In most entry-level materials on pairs trading such as in [2],  a mean reverting basket is usually constructed by this relationship: $$P_t – \gamma Q_t = Z_t, \textrm{(eq. 1)}$$ , where $$P_t$$ is the price of asset $$P$$ at time t, $$Q_t$$ the price of asset $$Q$$ …

Solving the “Corner Solution Problem” of Portfolio Optimization

Many portfolio optimization methods (e.g., Markowitz/Modern Portfolio Theory in 1952) face the well-known predicament called the “corner portfolio problem”. When short selling is allowed, they usually give efficient allocation weighting that is highly concentrated in only a few assets in the portfolio. This means that the portfolio is not as diversified as we would like, which …

Mean-Variance Portfolio Optimization When Means And Covariances Are Unknown

[Lai, Xing and Chen, 2010], in the paper “Mean-Variance Portfolio Optimization When Means And Covariances Are Unknown”, proposed a ground breaking method to do portfolio optimization. In what follows we summarize their idea and use it to implement a periodic rebalancing strategy based on the AlgoQuant framework. Harry Markowitz won the Nobel prize for his …

Trading and Investment as a Science

Here is the synopsis of my presentation at HKSFA, September 2012. The presentation can be downloaded from here. 1. Many people lose money playing the stock market. The strategies they use are nothing but superstitions. There is no scientific reason why, for example, buying on a breakout of the 250-day-moving average, would make money. Trading …

Data Mining

The good quant trading models reveal the nature of the market; the bad ones are merely statistical artifacts. One most popular way to create spurious trading model is data snooping or data mining. Suppose we want to create a model to trade AAPL daily. We download some data of, e.g., 100 days of AAPL, from …

The Role of Technology in Quantitative Trading Research

I posted my presentation titled “The Role of Technology in Quantitative Trading Research” presented in HKU-HKUST-Stanford Conference in Quantitative Finance. Dec 9, 2011. Workshop On Recent Developments Of Financial Mathematics (REDFIN2011). Dec 13, 2011. You can find the powerpoint here. Abstract: There needs a technology to streamline the quantitative trading research process. Typically, quants/traders, from …

Mean Reversion vs. Trend Following

AlgoQuant 0.0.5 just got released! This release is particularly exciting because you no longer need a license to use AlgoQuant. AlgoQuantCore now disappears forever. The source of the entire AlgoQuant project is now available: http://www.numericalmethod.com/trac/numericalmethod/browser/algoquant Maybe even more exciting is that we ship this release with two quantitative trading strategies: one mean reversion strategy and …

On White’s (2000) Reality Check

I was asked the following question the other day on White’s reality check. QUESTION: I was reading White’s (2000) paper (http://www.ssc.wisc.edu/~bhansen/718/White2000.pdf). It seems to suggest that to examine the pnl characteristic of a strategy, we should do bootstrapping on the P&L. I am wondering why this makes sense. Why scramble the P&L time series? Why …

Quantitative Trading: Economist Approach vs. Mathematician Approach

Thank you Lewis for introducing me to the field of “Quantitative Equity Portfolio Management”. It opens my eyes to the other spectrum of “Quantitative Trading.” Apparently what Lewis considers quantitative trading is very different from what I consider quantitative trading. I call the former an economist approach and the latter a mathematician approach. This blog …

Open Source Trading Software Or Not?

I have built a few trading systems from scratch during my years with investment banks. So, I have learnt from the many mistakes made. I am recently reviewing some open source system, and would like to share some thoughts. In general, I am against building software in house. Funds and banks are not software firms. …