Higher fees and difficulty in agreeing on side letters with secondaries funds were among the reasons given.
The vehicle will be the firm's second flagship after becoming an independent entity in 2017.
Trustees of the £250bn Nationwide Building Society's pension turned down the chance to invest in a secondaries fund because they saw it as an unnecessary 'intermediary'.
Details of Abbott Secondary Opportunities II's hurdle rate and carried interest were revealed in US pension documents.
The move comes as a wave of activist pressure sweeps up against major LPs.
Jörg Goschin of KfW Capital said the firm is working with the government to make it easier for VC LPs to access liquidity.
Jase Auby says the $158bn pension will focus on co-underwriting as a way of adjusting its private markets portfolio.
The system's staff is formulating whether to take action on secondaries sale and/or co-investment initiative.