# Combining trading signals (equity long/short strategy)

Currently, I have developed three separate trading strategies on equity securities.

All involve taking long and short positions in the top and bottom decile with respect to some measure (say, a measure of each of Value/Growth/Momentum for simplicity).

So for an individual strategy, I am long the top 10% and short the bottom 10%. I've set gross exposure to 200% and net exposure to 0% (i.e. long and short exposures both effectively 100%). Then I am equally weighting all the securities without any consideration for covariance.

For the combined strategy, I am effectively summing up the signals from the three trading strategies. So if a security has a "Buy" (coded as a 1) signal coming from all three strategies, it is going to have a Signal=3. Conversely if a security has a "Sell" signal coming from all three strategies, it will have a Signal=-3. I then set the same gross and net exposure limits, however now it is not equally weighted, instead the weights are proportional to the summed signal (e.g. a security with Signal=3 will have 3x the weight of a security with Signal=1).

Backtest wise, this appears to be working quite well however it does not really take into account either:

a) The covariance structure (could be estimated with Barra approach) of the securities themselves

b) The covariance structure of the strategies themselves

c) The expected returns (in particular for the combined strategy which is implicitly assuming returns are directly proportional to the combined signal).

I'm aware of different portfolio constructions e.g. Sharpe optimisation etc, but I'm concerned that this won't be very robust at all (e.g. at time T, covariance estimate based on 1-2 years prior could vary significantly from covariance estimate at time T+1) and could be very costly due to these changing point estimates.

As a result, I'm wondering if there's a "more ideal" portfolio construction technique (vs equal weighting) based on my construction of the individual signals and combined signal? Also if there were any comments on the methodology I'm using?

Potentially of note, this is for my personal trading account which I'm looking to automate a small portion of towards such a strategy (or alternatively use the signals as filters to select stocks fundamentally)

• If you want some academic support for what you are doing already, see the deMiguel paper Optimal Versus Naive Diversification Feb 5 at 21:25
• Looks like naive isn't so naive. Thank you! Feb 6 at 0:29