Table 12.9: Optimal parameter choices for S&P 100

In fact with these choices the long portfolio underperformed and the short portfolio outperformed the index!

Since the parameter choice for the current month is made on the basis of last months performance, this autocorrelation in information ratios is a crucial performance indicator

The point of this exercise is to check the robustness of the portfolio over time, as this is fundamental to cointegration. The most important property to look for is consistency between the 1-, 2- and 3-month information ratios. Table 12.10 indicates that if the 1-month information ratio is high so also, on the whole, are the 2- and 3-month information ratios. So if a portfolio starts well for the first month, it tends to perform well over several months. Similarly, if the portfolio does not perform well during the first month, this tends to continue for subsequent months. Since the parameter choice for the current month is made on the basis of last months performance, this autocorrelation

in information ratios is a crucial performance indicator. A similar robustness check that can be done from Table 12.10 is to ensure high ADFs and relatively low turnover projections when the portfolio is rebalanced using the same fixed parameters each month.

It is evident from Table 12.9 that the same parameter selection is not generally going to be optimal for two consecutive months. In fact, the real test of the model is its actual performance, using returns that are obtained when the alpha and training periods are reoptimized every month. Table 12.11a reports the consolidated returns from applying the long-short hedge strategy to the S&P 100 during three years that have been chosen as representative of difficult market conditions: 1987, 1993 and 1998.11

As should be expected from a successful hedge fund, the long-short strategy performs relatively well during the market crashes of October 1987 and August 1998. The returns are also much less volatile than the S&P 100 index returns, and during each of these years the fund outperformed the index.

A summary of returns, including execution costs, between 1995 and 1999 is shown in Table 12.1 lb. In the earlier years absolute returns were lower and less volatile than in 1998 and 1999, but the average annual return for all five years was approximately 35%.The average leverage was approximately 1.5 on both the long and the short legs of the hedge.

The real test of the model is the validation of its actual performance, by analysing the returns that are obtained when the alpha and training periods are reoptimized every month

Barra have performed an analysis of the 1999 returns, so that the hedge strategy could be described in terms to which the market is already accustomed. It shows that the strategy derives its excess returns primarily from risk assessment items such as earnings yield, earnings variation, momentum, size, and, as one would expect, some leverage. Both value and growth assessment are not contributing to the return, which somewhat distinguishes the strategy from the status quo.

12.6 Common Features

When time series are cointegrated they have a common stochastic trend. The many papers cited in §12.4 demonstrate that integration is a common feature that is prevalent in many financial markets. A common trend is just one of many common features that multivariate time series may possess. This section examines the evidence for and against the existence of other common features in financial markets. In particular, the possibility of common autocorrelation and common volatility in financial markets is examined.12

"The returns stated include transactions costs but no other fees.

12Thus the time series that are analysed will be returns, rather than the prices or log prices that are analysed for cointegration.

Long Short

Continued

Table 12.10: Backtesting the October 2000 parameter choices