I assume you can't hand Electra one of their shares and get back its constituents. And I assume because it's private equity, you can't do the obverse either, or do a long/short type trade.
Investment trusts themselves are publicly traded, they're closed-ended funds with capital raised once on launch - sort of like pooling private equity, but you can then sell your stake.
The public listing is of the company, whose business happens to be investing, so though I've never looked I don't see why CFDs & derivatives wouldn't be available.
Venture Capital Trusts (VCTs) are similar (perhaps a subset?) but focus on earlier stage companies (clearly) in exchange for a tax advantage for the initial investors - but not for those who subsequently purchase shares in the VCT itself from them.
You buy when the trust is at a larger discount than normal in a bear market or look for trusts where there is corporate action going on and the shares will be rerated or trust will be wound up.
You presumably could short a quoted trust or us CFDs or buy warrants but that's a bit rich for me.
That is not what is traditionally referred to as arbitrage. You are betting on an unknown variable (correct discount), not noticing pricing for the same asset being different in the same moment. Arbitrage is “sugar being sold at $2 at shop A, and bought at $3 at shop B, and the shops are next to one another”
And quite often you can look at the discount and do arbitrage on that I certainly did very well with Electra Private Equity (ELTA)