Selecting Strategy Assets by Exposure Characteristics

# Marginal effect of asset in a strategy


# Marginal effect of asset in a strategy












Im trying to develop a stastical arbitrage strategy that depends on a universe of assets and in a brief way, they replicate some factor(s), index(s), etf(s), etc, and then trade residuals. So, after having some interesting results, I was wondering how the universe selection affects the performance.

My approach until now consists of using an initial cutoff by liquidity (spread, turnover, etc) and model the strategy with this constant (K) of symbols. I think this method has a good economic reason and its relatively simple, but obviously depends on the cutoff.

The question arises when tunning parameters of the strategy, because upon this K symbols, some contribute more to the the performance than others, so its marginal contribution will be different. Naturally, using the set K - {symbol A} performs different from using K - {symbol B} or K - {symbol A,symbol C}. And perhaps including symbol A damage the strategy in most situations.

Some thoughts about this:

- Ranking by performance will sure lead to overfitting and also is computationally expensive (Trying all sets of sizes between [K - min(#symbols), and K])

- Since I use this K symbols to replicate some factor, index, etf, etc,...Maybe compute marginal effect of the inclusion of a symbol, by using the variance explained of a 1D PCA (Market Portfolio), and use it to select this K symbols, without looking performance. I say 1D for simplicity but it could be more dimensions.

- Just use the liquidity approach that I mentioned before. Keep it simple and parsimonious. I like this and its tempting, but also think that this is suboptimal and maybe there are better ways, idk. Sure inside this K symbols, some just are not fitted for the strategy or depend on external factors that the other symbols dont, so they have a life on their own.

Consider that I have a SOOS data that I havent touched and have been careful with survivorship bias.

I will appreaciate is you give me some guidance on how to handle this. Thanks

## Answer by lehalle (score 1)

https://quant.stackexchange.com/a/79441

Before answering, let me be sure that the way you select your tradable pool of instruments does not embeds a look-ahead bias: the thresholds you apply at day $d$ should only involve data available before the same day $d$.

That being said, I am not sure you should be concerned by the exact names of the companies that are affecting the most your portfolio performances. You should better focus on their characteristics, i.e. if you are exposed to BofA, it is better to know you are exposed to a large US bank, and moreover, it is worthwhile to check if you are (even more marginally) exposed to other US banks (insurances? the whole banking sector globally?).

Not only it protects you better vs overfitting (being exposed to one company is an anecdote, but knowing a portfolio logic exhibits weaknesses with respect to sector is a feature), but it replaces a combinatorial problem (a list of company names), by a continuous ones (the beta towards sectors, countries, factors, etc).