Leverage Management in a Bull-Bear Switching Market

27 Pages Posted: 17 Mar 2010

See all articles by Min Dai

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Zhou Yang

South China Normal University - Department of Math

Hefei Wang

University of Illinois at Chicago - Department of Finance

Date Written: February 10, 2010

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.

Suggested Citation

Dai, Min and Yang, Zhou and Wang, Hefei, Leverage Management in a Bull-Bear Switching Market (February 10, 2010). UIC College of Business Administration Research Paper No. 10-08. Available at SSRN: https://ssrn.com/abstract=1571613 or http://dx.doi.org/10.2139/ssrn.1571613

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

Zhou Yang

South China Normal University - Department of Math ( email )

Guangzhou, 510631
China

Hefei Wang (Contact Author)

University of Illinois at Chicago - Department of Finance ( email )

2431 University Hall (UH)
601 S. Morgan Street
Chicago, IL 60607-7124
United States
312-413-8374 (Phone)

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