Readers of yesterday’s posting on Gordon Johnson’s 130/30 paper will remember that he took inspiration from the earlier work of Roger Clarke, Harindra de Silva and Steven Sapra. Well it turns out this prolific trio (plus fourth bandmember Steven Thorley) have just published a new paper of their own on 1X0/X0.

Many regard these four as being the originators of the craze we now know as 130/30. In an article last spring on the website of UK-based consultancy bfinance, AllAboutAlpha.com Hall of Famer Tris Lett observed that, like so many mega-trends, 130/30 was originally cooked up on the sunny shores of Southern California:

“While some may say that they were running strategies in the short enabled structure before Analytic Investors, I can find no one who precedes them. Harindra de Silva, Roger Clarke and Steve Sapra of Analytic Investors earn the credit for naming the process and operating the first real time portfolio. On July 1, 2002, Analytic [of Los Angeles] launched its Core Plus Equity Composite (120/20) strategy.”

Clarke, de Silva, Thorley and Sapra have since achieved stardom by producing several papers on the topic of 130/30. Their newest production, *“Long/Short Extensions: How Much is Enough?”* has now been revised after a limited release over the summer at a screen near you.

Like the Citigroup 130/30 study led by Manolis Liodakis (see posting, “New Research Explores Whether 130/30 is Actually Optimal“), Clarke et al say that many factors determine what they call the “expected short extension”. However, in this paper they focus only on the exogenous factors, not the “discretionary parameters” that are within the manager’s control. These exogenous factors are:

**Security Risk:**represented by “a trailing 60-month sample covariance matrix for the largest 500 common stocks”.**Security Correlation:**represented by “the average pair-wise security correlation using the covariance matrix calculated from the trailing 60 months”.**Benchmark Concentration:**represented by “Effective N”, or “the number of equal-weighted securities that would have the same diversification implications as the N actual benchmark weights”.

When they look for historical proof that these variables actually inform the optimal leverage for a 1X0/X0 fund, they find that security risk trumps the other two parameters handily. For each year between 1967 and 2006, they calculate the “expected short extension” with 2 of the 3 factors held constant. This allowed them to view the effect of each factor independently. Here’s what they found:

Security risk is negatively correlated to the expected short extension…

Security *correlation* was not a particularly strong determinant of the expected short extension…

And benchmark concentration barely had an impact on the expected short extension…

The authors caution that their results are pretty high (like, closer to 160/60 than 130/30) because they assume the portfolios are totally unconstrained (i.e. there are no discretionary parameters). In the presence of the additional constraints – which are common in many analyses – the numbers would be much lower. In their words:

“Discretionary constraints, a lower assumed information coefficient, and higher costs, all reduce the desirable level of shorting for a given strategy.”

But the fact remains that 130/30 managers don’t operate in a vacuum. Exogenous variables like market volatility, benchmark concentration, and security correlation mean that the most desirable level of “X” in “1X0/X0” is actually a moving target. As the stars from Los Angeles say in their paper:

“One major implication of our analysis is that because relevant market parameters change over time, managers should allow the short extension to vary with market conditions even though the targeted level of active risk is held constant.”