Portfolio selection with small transaction costs and binding portfolio constraints (Q2873124)

The authors consider a market with one risky asset following a geometric Brownian motion and one risk-free asset with constant interest rate. An investor with constant relative risk aversion and infinite planning horizon wishes to maximize the long-term growth rate of the utility function. In the presence of an upper bound on the risky weight and proportional transaction costs, the authors derive the optimal trading strategy as well as the associated welfare and trading volume. All formulas are explicit in terms of the market and preference parameters as well as an additional transaction cost gap.NEWLINENEWLINETwo applications are given here. The first one is the choice of a prime broker to buy a leveraged risky position on margin, among alternatives with different lending rates and margin requirements. It is found that among those brokers that are equally attractive in the absence of transaction costs, the investor typically prefers the broker with higher margin requirements and lower lending rates, as the transaction costs make highly leveraged portfolios less attractive than they appear to be in frictionless markets.NEWLINENEWLINEIn the second application, one considers a bank that can borrow from its depositors at the risk-free rate to provide long-term loans, whose book values are assumed to follow a geometric Brownian motion with constant drift and volatility. It is investigated here how the deposit rates offered by the bank react to harder regulatory constraints, as the bank will try to achieve the same performance with the new constraints.