Introduction:

 The performance measures of the risk models considered in this paper are presented in 2 ways:

Univariate: As an average performance over the 10 trivial portfolios that are defined by the 10 risk factors k - as being the sole asset in the portfolio.

Multivariate: In conjunction with a candidate portfolio P of 10 risk factors itemized in section  and having equal weights.

We shall hereafter use univariate and multivariate to describe the context of the performance measures as defined above.

The entire analysis is done assuming zero mean price change - but to account for any bias due to long term increases or decreases in one or more of the time series - the performance information is symmetrized by taking the mean performance over the 2 portfolio position vectors defined by:

Long on the US dollar with equal investment in each risk factor.

Short on the US dollar with equal investment in each risk factor.

The above symmetrization procedure applies equally to the univariate as well as the multivariate presentations.