A Game Theory Approach to Stock Lending Transactions in the Brazilian Stock Market

Abstract

In Brazil's market, the institution of interest on equity transactions provides a precedent for gains resulting from the difference between the tax rates of individuals and those of investment funds through structured transactions. This difference creates incentives to lend stock; on the eve of an interest payment on equity, individual investors lend their stock to investment funds, which receive the interest in full and return only 85% of its value to the investors. Our goal is to understand how the surplus generated in this tax arbitration is split among the agents involved in the stock-lending transaction and to determine whether there are conditions under which the agents would have no incentive to conduct such a transaction. Using a non-cooperative games approach, we have structured this transaction and analyzed possible subgame perfect Nash equilibriums in three situations: (1) a direct relationship between the investor and the investment fund and an absence of transaction costs; (2) a direct relationship between the investor and the investment fund and the presence of transaction costs; (3) a relationship between the investor and the investment fund through a broker and the presence of (lower) transaction costs. In the cases in which the broker does not mediate the relationship, more contracts tend to be signed, but the fund's gain will only cover the record-keeping costs of the transaction. This situation is reversed in the presence of high transaction costs: in extreme cases, the investor loses bargaining power and his/her gain compensates only for his/her risk aversion. When a broker is introduced in to stock lending, only those investors who have a minimum amount of stock will receive offers from the fund through the broker. The fund's gain tends to decrease due to the broker's presence and in some situations, the investor loses bargaining power and accepts any contract that compensates for his/her risk aversion.