why does gearing increase volatility of the portfolio?

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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.

The higher the level of gearing, the more amplified profits and losses are to changes in the portfolio value.