The state Board of Investments shall invest in linked deposits as identified by the board through an approved application, provided that at the time of placement of the linked deposit, exclusive of the linked deposit program provided for in article one-a, chapter twelve of this code, not more than two percent of the state's total investment portfolio is so invested. The total amount initially deposited in any one year shall not exceed $2 million, and the total amount so deposited at any one time shall not exceed, in the aggregate, $20 million.