Leverage Management in a Bull-Bear Switching Market

Abstract

The large amount of leverage used by institutional investors and retail investors, corporations and households, is frequently cited as a major contributor of the current financial crisis. Recent events highlight the importance of leverage management, and the painful decision to de-leverage, especially when the market conditions may change drastically. Many institutional investors and university endowments managers debated heavily whether they should reduce leverage, or decrease their positions in risky asset holdings in a market downturn.Should an investor unwind his portfolio in the face of changing economic conditions?We completely characterize an investor's optimal trading strategy in the presence of transaction costs in an economy that switches stochastically between two market conditions. We show that absent transactions cost, the investor acts myopically in each market, as if the other market did not exist, and invests a constant fraction of wealth in stock and bond. With transaction cost, we find that de-leveraging, reducing the degree of leverage, or keeping leverage unchanged can all be optimal outcomes as the market switches from a bull regime with high expected return and low volatility to a bear regime with low expected return and high volatility. The investor's strategy depends crucially on the switch intensities between the two markets.If the switch intensity is high from the bear market to the bull market, leverage may be optimal even in the bear market. On the other hand, if this switch intensity is low, the investor may choose not to leverage at all in both markets. Furthermore, we find that it may be optimal for the investor not to sell off his illiquid asset in the bear market to reduce leverage. In addition, the investor may optimally increase leverage in the bear market for illiquid asset to avoid frequent re-balancing as the market switches conditions. This is in sharp contrast to the one market case where a higher transaction cost always implies a lower optimal leverage. We also show that a lower borrowing cost may also encourage the investor to keep his stock position and avoid sell offs.