New research explores whether 130/30 is actually “optimal”

130/30 01 Aug 2007

In late June, Citigroup released a comprehensive 36 page quantitative analysis of 1X0/X0 strategies.  We found that the report went beyond similar studies and reached a number of useful conclusions about the optimal X in 1X0/X0.  The paper’s lead author, London-based Citigroup MD Manolis Liodakis has written this summary exclusively for  We have divided it into two postings.  The second half will be posted tomorrow.

Special to by: Manolis Liodakis, PhD, Managing Director and Head of Global Quantitative Equity Research, Citigroup Investment Research

Fund managers are always looking for ways to improve their performance. The success and growth of the hedge fund industry has highlighted the potential benefits from shorting stocks and investing with leverage.Short extensions are also an increasingly popular method of performance enhancement for fund managers.  Their main benefit comes from enabling negative plays to be made on stocks, even when their weight in the benchmark is small.  Unfortunately, most managers face some sort of active risk constraint such as a tracking error target.  (Adding new long and short positions to an existing portfolio usually increases tracking error unless it is controlled in some way.) 

Motivations for the use of short extension strategies

Long-only portfolios are constrained in the negative plays that they can make on small-cap stocks. Managers can make a positive play on a stock by overweighting it in relation to the benchmark. They can also make negative plays by under-weighting a stock they don’t like. With these negative plays however there is an obvious limit to the size of the play they can make; it is not possible to under-weight a stock by more than its weight in the benchmark. The distribution of weights in large and small-cap stocks varies considerably between different types of benchmark.


Why 130/30?

There is no requirement to use exactly 30% leverage though. (Indeed, this website often uses the term 1X0/X0 to avoid erroneously committing to any one form of the strategy).  The level of leverage at which expected returns are maximized can be thought of as the “optimal leverage” for a particular fund. 

The factors that determine optimal leverage can be split into two groups – factors related to the characteristics of the fund itself (endogenous) and factors that are outside the control of the manager (exogenous). The first group includes the tracking error of the fund, the type of benchmark used, the number and size of stocks that a fund manager has views on (especially on the downside), the type of alpha model used, and the risk characteristics of these stocks. The exogenous factors include the symmetry of the fund manager’s skill (is he equally good at picking both winners and losers?), market conditions and the costs of trading and maintaining short positions.

Let us consider a fictional portfolio manager who manages a fund benchmarked to the MSCI Europe index.  Our fictional portfolio manager has a buy list and a sell list, each containing 100 stocks.  First, he creates a 3% tracking error portfolio using only stocks from his buy list.

Optimized with no short selling, his portfolio would look like this:


Taking overweight positions in stocks he favours and underweight positions in stocks he dislikes are both potentially profitable assuming that he is skilled at picking stocks. We will call the sum of these two the useful active weight.   (Active weight taken in the neutral stocks will on average be a zero sum activity and represent a “waste” or “dead active weight”.)  As you can see, with no short-selling the portfolio’s useful active money is naturally skewed in favour of the stocks from the buy list.

Introducing a short extension (as below) reduces this skew and now enables more active positions to be taken based on sell ideas.  With the relaxation of the short constraint, overweight positions in stocks from the buy list sum to 88% and underweights in stocks from the sell list sum to 52.9%.


Adding a short extension can also help address size biases in a portfolio.  Figure 5 shows the distribution of underweight and overweight positions in the long-only portfolio we just focused on.


Naturally, adding the ability to take short positions in size quintiles 2 to 5, would allow the manager to express more of his (negative) opinions and thus increase the optimal amount of active weight in the fund.

Additional Benefits

When adding a short extension to a portfolio, the additional long/short portfolio does not have to be based on the same alpha model as the long-only portfolio. It could use a different model or be a blend of several models. In this way a long/short portfolio could reduce the risk of the overall portfolio rather than contributing to a higher tracking error. In addition, there may be more stock-specific or country-specific benefits from introducing short extensions.

The payoffs to adding a short extension vary greatly from fund to fund, and different funds will gain maximum benefit from different levels of leverage. Figure 6 shows what happens to the active weight of the different groups of stocks as leverage is gradually increased from zero to 50% (assuming the manager sticks to a 3% tracking error).

At 135% gross exposure, the manager is able to employ the highest amount of active weight while still maintaining his 3% tracking error target.  As you can see from Figure 7 below, the maximum exposure to long positions occurs at 119% gross exposure.  From that point on, the manager starts reducing his active weight in the buy rated stocks and replaces them with neutral stocks, marked dead overweight in the chart.  Beyond 135% leverage, increases in active short positions would be more than fully canceled-out by corresponding requirements to decrease active long exposure in order to maintain the tracking error.  The point of optimal leverage is reached when the exposure or active weight in neutral stocks is minimized.

So what are the endogenous and exogenous variables that determine the optimal amount leverage (i.e. that level which yields the highest useful active weight)?

Continued tomorrow

(Ed: The full version of this paper is available on a pay per view basis via Reuters here or here if you do not have a Reuters account.)

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  1. wanderer
    August 2, 2007 at 9:24 pm

    A very key issue that has a bearing on level of X in 1X0/X0 is how good or bad is the stock picking model/ability/alpha. Two alternate ways to look at this issue are:

    (a) The level of optimal X in 1X0/X0 depends highly upon the Information Coefficient (or the Information Ratio) of the active strategy. More specifically, in law man’s terms the level of correlation of the active weights with the future returns. If the manager has very good alpha stock picking models, then a higher X is preferred.

    (b) Another alternate way to look at this is using the beta (which is different from the tracking error point of view). Most serious alpha stock picking models end up having negative beta with the general market. If we imagine the 1X0/X0 as made up of 100 & X0/X0, then the negative correlation can help the 1X0/X0 achieve a higher Sharpe, since negative correlation will reduce the combined volatility. The level of beta of the stock picking alpha process is an alternate way of deciding the X in 1X0/X0. Higher the negative correlation, the higher level of X we can take.

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