The effect of leverage on the magnitude of risk : can financial market Black Swan events, 10 Sigma events and Fat Tails be explained by leverage?

The effect of leverage on risk was examined. A method of measuring and accounting for the effect of leverage on the magnitude of risk was developed. By dividing the standard deviation (sigma) by the equity to valuation ratio (EVR) the magnitude of the risk can be measured which includes both asset risk and leverage. A 2 sigma event was shown to produce the same effect as a 10 sigma event if the EVR is 0.2. The effect of leverage on risk was examined for the S&P500. During the period 1926-2001 on the NYSE for the S&P500 there have been no 10 sigma events when measured on a yearly basis. There has not been even a 3 sigma year hich is a one in hundred year event. The number of 2 sigma years which is a 1 in 20 year event was 7. It was shown that a 2 sigma year can cause the same effect as a 10 sigma year with enough leverage. If there is a 2 sigma year and the EVR is 0.2 i.e. 20% Equity and 80% Debt, then the effect is the same as a 10 sigma year. for stocks, Black Swan Events, 10 Sigma Events and Fat Tails are Myths. The explanation is more likely Leverage. As the leverage is increased the magnitude of risk increases and approaches infinty as leverage approaches 100% debt. Many financial assets such as derivatives have high levels leverage. The level of risk for financial assets will be under estimated if the effect of leverage on the magnitude of risk is not taken into account.