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# Let COMBO optimize your quantitative strategies !

Updated: Jun 28

Performance is the lifeblood of quantitative asset management and the one factor that always deteriorates this performance are the transaction costs incurred by the execution of the investment strategies.

What if you could reduce them by 10, 20 or even 30%?

First, let’s take a look at QIS …

## What is a quantitative investment strategy (QIS)?

Unlike strategies that are managed by a trader, quantitative investment strategies are derived from mathematical algorithms exploiting some market properties. A quant’s work is to identify the factors that explain the outperformance of some assets and to translate them into investment strategies to improve returns or better control portfolio risk. Depending on their profiles, strategies can be used for active or passive management, to track an index or to have a dynamic exposure on a part of the market…

In all cases, the composition of the investment portfolio is given and regularly updated by a quantitative algorithm. At each portfolio rebalancing, orders are sent to the market and this incurs trading costs which affect the portfolio’s global return.

Is there a way to reduce trading costs without losing performance? Yes, there is: COMBO!

## Principle

COMBO is based on an algorithm that acts as an overlay of the strategy. The algorithm slightly distorts the portfolio composition to reduce all trading costs while controlling the deviation from the original quantitative strategy.

Example: Below is an example of the portfolio allocation of a strategy composed of 40 assets (in orange) and the allocation following COMBO’s advice (in blue).

This distortion, and thus the resulting cost reduction, depends on the maximum deviation that the trader accepts.

COMBO is both data-driven and plug-and-play, and can be applied to any quantitative strategy. It is even possible to apply COMBO on a strategy that already admits cost minimization constraints!

## Track records

### Track record : outperform CAC 40

• Objective : track CAC 40 with a portfolio turnover penalty constraint·

• Portfolio made of 27 stocks (CAC 40 components)

• Data : 2009 – 2020

• Reference investment strategy :

• Minimization of

under the constraint

where K is the vector of compositions and

alpha is a hyperparameter to control variance against trading costs.

• Monthly update of compositions

The value of the index CAC 40 and the different portfolios

For approximately the same final portfolio value (the difference is less than 0.45%), COMBO was able to reduce transaction fees by 22%.

The trading costs (unit value) of both portfolios

And there is no significant change in the distribution of returns. The objective of the original strategy is preserved.

Warning :

The behavior of COMBO cannot be mimicked by simply adjusting alpha.

The first graph depicts the influence of alpha on the reduction of trading costs for both strategies, and the second graph depicts its influence on the increase of the tracking error of both strategies.

For example, the amount of trading costs when alpha = alpha_0 = 0 is divided by 3 when applying COMBO (1050 vs 320). The value of alpha that reduces the transaction costs by the same quantity in the reference strategy is alpha_1 = 2e-5. The corresponding tracking error is 6.53e-3, it is greater than the tracking error of the strategy using COMBO with alpha_0 (6.51e-3).

Note that applying COMBO on the strategy with alpha_1 entails another reduction of transaction costs.

To conclude, COMBO can be adapted to any quantitative strategy to reduce trading costs while controlling the tracking error.

COMBO is delivered to the user as an API. It can be invoked from a thick client (a front-office application developed in C++, Java etc.), from a Python script, or even from VBA.

The inputs required by COMBO are:

• Market data.

• The composition of the investment portfolio.

• Trader parameters (target risk ratio).

COMBO outputs the adjusted composition of the portfolio, computed to minimize trading costs while targeting the given risk constraint.

Kesitys_COMBO_DeltaOne
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