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In George and Hwang's 2010 JFE paper, they are trying to resolve the so called distress risk and leverage puzzles. This is their explanation:

This is a puzzle because high distress intensity or nearness to default means the firm has exhausted its capacity to issue low-risk debt.Since leverage amplifies the exposure of equity to priced systematic risks,firms with high distress measures should be those for which equity exposures are most amplified.

How does leverage amplify the exposure of equity to priced systematic risks? Can someone please elaborate this?

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Yes leverage amplifies the exposure of equity to systematic risks.

Just consider the standard textbook formula (Modigliani-Miller):

$\beta_e = \beta_a \times (1+\frac{D(1-\tau)}{V})$ where $\beta_e$ is the sensitivity of the stock to systematic risk, $\tau$ is the tax-rate and $D/V$ is the leverage ratio.

So beta (i.e. the exposure to systematic risk) increases with leverage. If we use Harris-Pringle or Milles-Ezzel formulas we get a similar result.

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