The impact of financial leverage on risk of equity measured by loss-oriented risk measures: An option pricing approach

We investigate how financial leverage influences the risk of equity in companies with limited liability. In our study, the risk is measured by loss-oriented risk measures (VaR, downside deviation, etc.). Also, the dependence of the risk premium on risk is under consideration. VaR-based and downside risk measures are considered in similar frameworks, and risk premium is introduced which is symmetrical to these risk measures. The value of equity is modeled by the price of a call option. In most cases there is a positive relationship between the level of leverage measured by the debt ratio and the risk measured by the loss-oriented risk measures. However, there exist exceptions. The risk premium is not a linear function of the risk. Still, for a reasonable range of leverage, the dependence of the risk premium on risk is approximately linear in most cases.