In Short
There are two weighting schemes that dispersion investors focus on, namely theta and vega neutral.
Theta neutral schemes deliver an exposure to the correlation risk premium and involve selling 1 unit of index vega but only the buying back of a fraction of a unit of single stock vega. The fraction is determined by the ratio of the index implied volatility and the weighted average single stock volatility. Over the long run, this strategy delivers robust returns, but is subject to sharp drawdowns in market crises when implied correlation spikes. The most widely adopted weighting scheme is vega neutral and involves buying and selling equal units of vega. It therefore equates to a correlation strategy alongside a long single stock volatility exposure. Given implied volatility and correlation are correlated, a sharp spike in implied correlation should lead to a spike in single stock volatility thereby, mitigating the left tail of the return distribution.