Correlation: using time weights

Most correlation calculators use an ‘equal weights’ formula: each data point is given the same weight, whether they are recent or long past. This is an easy calculation that is used for example in the CORREL function in Excel.

In the ‘exponential weights’ formula, the more recent data points are given more weight in the calculation, making it more responsive to recent events and less sensitive to past ones.

The Microsoft and Yahoo stocks recently provided an example of the advantage of the exponentially weighted formula over the equally weighted formula. On Feb 1st, 2008, Microsoft announced a bid over Yahoo stock. Immediately, the daily correlation of returns became negative as the two stocks started moving in opposite directions.

The equally weighted calculation (in the example above, based on 50 days window) takes longer to register the shock, and it has a major flaw: on Apr 14th the the Feb 1st data point is no longer part of the 50 days window, and the correlation surges upwards.

The exponentially weighted calculation on the other hand, is able to better incorporate the Feb 1st shock, because it assigns higher weights to the more recent data points. It reacts more promptly, then absorbs the shock gradually, avoiding any artificial surge.

The above is meant to illustrate the correlation calculation formulas; it does not suggest any trading idea. As a matter of fact, correlation is only a starting point for pairs trading. Cointegration is preferred (and the two stocks have indeed been cointegrated in the last 90 days).

Pairs trading (Ganapathy Vidyamurthy)

Pairs trading attempts to profit from the relative mispricing of a pair of stocks by buying one stock in the pair and shorting the other, and holding these positions until the prices converge. This book explains two approaches to pairs trading: statistical arbitrage (identify the mispricing by analyzing historical data) and risk arbitrage (when a corporate event such as a merger, is expected). A minimal mathematical background is required; the math is not hard, but it is essential.

The first part of the book is a gentle introduction to timeseries analysis and arbitrage pricing theory – topics of importance in quantitative finance – that many readers will find accessible. In other books, the treatment of these subjects is often academic and dry.

For the arbitrage pairs, the author uses a factor model and cointegration tests to determine the pairs. He proposes a way to estimate the holding time for pairs and details an approach to calculate the trading bands, however don’t expect a ‘ready to trade’ recipe. The method requires tools which are not readily available to individual traders (factor models, cointegration). In addition, choosing crucial model and trading parameters (the time window to identify the pairs for example, or the choice of time-based stops) is left as an exercise for the reader.

The third and last part explores pairs trading in the context of an announced merger, using a Kalman filter to separate in the spread dynamics, the deal risk component from the noise.

Despite the shortcomings, this book is an interesting read. It provides an insight on how the pros approach the topic. Contrast this with the easier but ad-hoc approaches, such as trading correlated pairs.

Common sense on mutual funds (John Bogle)

John Bogle – a Wall Street legend and founder of the Vanguard family of funds – exposes simple and wise precepts: take a long term view; diversify to lower risk; pay attention to costs; prefer passively managed funds (i.e. index funds) to actively managed funds.

In particular, he details the effects of costs (expense ratio, fees such as 12-b1, taxes). Essential concepts such as compounding and tax deferral are explained. A well covered topic is the reversion to the mean; no manager or asset class can stay on top of the game forever. Also explained is the important rule that past performance is no guarantee of future returns.

One of Bogle’s most famous quotes: “Investors have two enemies: expenses and emotions”.