International Journal of

Financial Studies

Article

The Impact of Financial Leverage on the Variance of Stock Returns

David Yechiam Aharon 1,* and Yossi Yagil 2,3

1. Department of Business Administration, Ono Academic College, Haifa 55000, Israel
2. Department of Business Administration, University of Haifa, Haifa 3498838, Israel; yyagil@univ.haifa.ac.il
3. Department of Business Administration, Western Galilee College, Akko 2412101, Israel

* Correspondence: dudi.ah@ono.ac.il

Received: 10 January 2019; Accepted: 28 February 2019; Published: 6 March 2019

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Abstract: This paper investigates the direct theoretical relationship between the variance of stock returns (sigma;2E) and financial leverage (L) considering both corporate and personal taxes. Using a dataset of U.S. industrial firms, we examine the variance of stock returns as a function of the firmrsquo;s financial leverage. We demonstrate that (1) the variance of stock returns is positively related to the firmrsquo;s financial leverage, (2) the relationship between the variance of stock returns and financial leverage is positive when corporate and personal taxes are also considered, and (3) with regard to the relationship between the variance of stock returns and financial leverage, using market measures of the latter tends to generate a higher coefficient of determination and a more accurate approximation of the theoretical relationship between financial leverage and the variance of stock returns.

Keywords: volatility; financial leverage; market imperfections; corporate taxes; personal taxes

JEL Classification: G30; G32

Introduction

Volatility, which is commonly measured by the standard deviation of stock returns, has received a great deal of attention in the literature, as it is the key factor in portfolio theory, option valuation, and asset pricing models. Volatility is important to academics, policy makers, and financial market participants. For policy makers, a volatile stock market can be a source for concern, because the instability of the stock market creates uncertainty, which may have an adverse effect on growth prospects. In fact, volatility can be helpful for the formulation of the economic policies, rules, and regulations related to the stock market. Investors use the variance of stock returns as a measure of risk to assess the performance of their past and future investments. Also, volatility has a central role in the pricing theories of derivatives. The Black-Scholes option pricing model treats volatility as the only parameter, among the strike price, time to expiration, interest rate, and stock price that must be forecasted. Finally, academics try to identify the factors that affect the volatility of stock returns and its role in determining capital structure valuation.

While the literature is replete with studies devoted to the characteristics of the variance of stock returns (henceforth: sigma;2E or sigma;E), there are very few studies to the best of our knowledge on the direct relationship between financial leverage (henceforth: L) and sigma;E, a fortiori when both corporate and personal taxes exist. The closest type of studies that does refer to the impact of L on sigma;E is what is commonly named in the literature as “leverage effect” studies in which the impact of L on sigma;E is evident only indirectly. In such studies, financial leverage is provided as a potential explanation for the asymmetric sigma;E found under various market conditions. This possible explanation can be easily

Int. J. Financial Stud. 2019, 7, 14; doi:10.3390/ijfs7010014 www.mdpi.com/journal/ijfs

demonstrated based on the pioneering “leverage effect” works of Black (1976) and Christie (1982) described by Equation (1) below:

sigma;E = ∆E/E = ∆V/E = (∆V/V) times; (V/E) = (∆V/V) times; [(E D)/E)] = (∆V/V) times; L = sigma;V times; (1 L) (1)

where V is the value of the firm, E is the value of outstanding equity, and D is the value of debt, so that V = E D. According to this formulation, if debt is risk-free, a change in the value of the firmrsquo;s assets (∆V) is passed entirely through to the equity: ∆E = ∆V. Thus, Equation (1) expresses the change in the value of a firmrsquo;s stock caused by a given ∆V. Meaning, sigma;E = sigma;V(1 L), where sigma;V is the standard deviation of asset returns, and sigma;E is the standard deviation of equity returns. An important and well documented empirical feature in many financial markets is the financial leverage effect (Black 1976; Christie 1982). According to the latter, a higher return reduces L (because a positive return increases the value of the equity, while the risk free debt is unchanged) and is therefore expected to lower the volatility of equity returns. In contrast, a lower return should have the opposite effect on sigma;E. That is, an increase in L also increases sigma;E.

To summarize, to the best of our knowledge, the existing studies in the literature have not tested

the direct theoretical relationship between sigma;E and L when both corporate and

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