By using the binomial option pricing model, this paper proves that with no arbitrage and no transaction costs, (i) under riskless debt, increasing the debt-equity ratio increases the variance of the rate of return on equity; and (ii) under risky debt, increasing the debt-equity ratio increases the variance of the rate of return on debt but does not affect the probability density function of the rate of return on equity. This finding refutes the Modigliani-Miller second proposition that the expected rate of return on the equity of the levered firm increases in proportion to the debt-equity ratio.