# Gearing and volatility

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why does gearing increase volatility of the portfolio?

Suppose a portfolio is worth $$R100$$ and has a gearing of $$10\%$$ - so R10 of the portfolio is funded through debt.
If the value of the assets decreases by $$20\%$$, the new value is $$R80$$, but there is still the loan of $$R10$$ that needs to be repaid. So the investor's new gearing is $$\frac{10}{80} = 12.5\%$$ and if the investor withdraws, they take home $$R70$$ making a loss of $$\frac{70-90}{90} = -22.22\%$$ - which is a bigger loss than the $$20\%$$ decrease in the asset value.