The pension fund was reportedly planning a partnership bid with private equity firm Affinity Equity Partners for the stake, but has decided to go it alone according to local newspaper the Chosun Ilbo.
It said the bid price was $190 a share, putting the total stake at about $398m.
Singapore government investor GIC was also understood to have teamed up with Affinity to bid for a 24 per cent stake in Kyobo in a deal that is expected to fetch around $1bn.
The pair would be required to join together for the bid to comply with a rule stating foreign companies cannot solely control more than 10 per cent of South Korean insurers without the approval of the regulator.
The larger stake is currently held by Daewoo International, while the smaller belongs to Korea Asset Management Corp and is expected to sell for about $425m.
Both assets combined were valued at $1.8bn late last month.
The auction presents a rare opportunity for buyout firms to access a market that has historically been dominated by cash-rich corporates prepared to pay higher valuations.
Global buyout house Carlyle has also bid for the larger stake according to local media reports.
In March it emerged rival Korea Life Insurance is looking to place a final bid for a controlling stake in insurer Tong Yang Life, the company that South Korean buy-out firm Vogo Fund bought in 2010 for KRW900bn ($798m).
Vogo Fund was looking to sell up to 60.7 per cent of the business, a stake that said to be valued at around 871m.
The firm bought it from three member companies of construction and finance conglomerate Tong Yang in November 2010.
Buyout firm Affinity primarily comprises the former investment professionals of UBS Capital Asia Pacific, the private equity arm of UBS.
It was spun out of UBS Capital Asia Pacific in March 2004.
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