Leverage management in a bull-bear switching market

Should an investor unwind his portfolio in the face of changing economic conditions? We study an investor's optimal trading strategy with finite horizon and transaction costs in an economy that switches stochastically between two market conditions. We fully characterize the investor's time dependent investment strategy in a “bull” market and a “bear” market. We show that when the market switches from the “bull” market to the “bear” market, complete deleveraging, reducing the degree of leverage, or keeping leverage unchanged may all be optimal strategies, subject to underlying market conditions. We further show that the investor may optimally keep leverage unchanged in the “bear” market, particularly so for illiquid asset. On the other hand, a lower borrowing cost in the “bear” market would prevent sell offs.