DarienHacker

if equity beta increases, then risk on left side of balance sheet increases
in order to “offset” this increase in risk, you must lower risk somewhere on the right side of the balance sheet
in order to reduce risk on right side, you must lower your D/E ratio, and you do this by reducing the ratio, which is by increasing equity (the denominator goes up, so the D/E ratio goes down), and/or by decreasing debt (which makes numerator decrease, so D/E goes down) which results in less risk on right side of balance sheet
so, you have more risk on left side, less risk on right side  = no change in total risk