Academic journal article Financial Services Review

Wealth and Risk from Leveraged Stock Portfolios

Academic journal article Financial Services Review

Wealth and Risk from Leveraged Stock Portfolios

Article excerpt

Abstract

A modest amount of leverage enhances the performance of stock portfolios in the long run. However, higher amounts of leverage produce dramatic declines in long-run wealth. Using probability distributions constructed from value-weighted stock index returns and a borrowing rate two percentage points higher than Treasury bills, the maximum median ending wealth is achieved with an asset allocation of 170% stock. We use Value at Risk (VaR) to measure downside risk over a range of asset allocations and holding periods.

© 2002 Academy of Financial Services. All rights reserved.

JEL classification: G10; G11

Keywords: Asset allocation; Leverage; Value at Risk

1. Introduction

An investor is said to buy stock "on margin" when a portion of the purchase price is financed by a loan from his or her brokerage firm. This leveraged strategy magnifies investment profits when stock prices rise, but also deepens losses when the market declines. As a recent example, many companies in the technology sector experienced spectacular increases in their share prices during late 1999 and early 2000. Some investors attempted to exploit these gains with margin purchases. But when the market suddenly turned downward in April 2000, these same investors were facing huge losses. Further losses were experienced in technology downturns during 2001.

These recent declines draw attention to the potential risk in leveraged portfolios. But are the losses so large that they wipe out the bull market gains? We examine this question from a long-run perspective, by constructing probability distributions of returns on leveraged portfolios over various holding periods. Our findings show that a modest amount of leverage enhances the growth of wealth in the long run.

An interesting result from our research is that high amounts of leverage produce dramatic declines in long-run wealth. This result is consistent with an investment rule developed in the 1950s. According to the maximum expected log (MEL) rule, maximum growth of wealth over the indefinitely long run is achieved by investing each period so as to maximize the expected value of the logarithm of (1 + single-period return). In our empirical results the highest median ending wealth is achieved at an amount of leverage equal to the MEL optimum.

Section 2 reviews previous research on leveraged portfolios, long-run returns, and the MEL rule. Section 3 describes the data used in the current study. Section 4 outlines two empirical techniques that can be applied to this research area. Our findings are presented in Section 5. Section 6 describes some implications for investors, and Section 7 concludes the paper.

2. Literature review

Little attention has been given in the academic literature to investment strategies using leveraged portfolios. Among the few published studies, Grauer and Hakansson (1985, 1986) apply multi-period portfolio theory to the construction and rebalancing of portfolios. The Ibbotson SBBI monthly return series for common stocks, long-term corporate bonds, long-term government bonds, and Treasury bills are used in the 1985 study, with small stocks also included in the 1986 study. Investors are allowed to borrow at the call money rate plus one percent. However, Grauer and Hakansson do not explore the impact of using leverage every period.

Ferguson (1994) demonstrates that long-run returns decline as leverage increases. A key factor is that although the underlying securities have limited liability, leverage magnifies their volatility and leads to a positive probability of bankruptcy. He also shows that long-term returns can be disappointing even when bankruptcy is not possible. Ferguson's diagrams are based on binomial examples with only two equally likely stock returns. It is, therefore, difficult to apply his results to real-world investment portfolios.

One method of introducing realistic portfolio characteristics is to use observed capital market history. …

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