In vol 6, RD 33 page 78 - the formula they have used - 3 and 4 - is very confusing to me.
They call it leverage = assets/equity here? I do not get it.
A = L + E
\Delta A = \Delta L + \Delta E
\frac{\Delta A}{E} = \frac{\Delta L}{E} + \frac{\Delta E}{E}
\frac{\Delta A}{E}\left(\frac{A}{A}\right) = \frac{\Delta L}{E}\left(\frac{L}{L}\right) + \frac{\Delta E}{E}
\frac{\Delta A}{A}\left(\frac{A}{E}\right) = \frac{\Delta L}{L}\left(\frac{L}{E}\right) + \frac{\Delta E}{E}
Rearranging,
\frac{\Delta E}{E} = \frac{\Delta A}{A}\left(\frac{A}{E}\right) - \frac{\Delta L}{L}\left(\frac{L}{E}\right)
Hi Magician, that much is clear to me. My confusion starts after that and why is the a/e is called leverage?
where is debt going?
Suppose that:
- A = 100
- L = 80
- E = 20
Note that
\dfrac{A}{E} = \dfrac{100}{20} = 5
If assets increase by 1% (and liabilities are unchanged), then,
- A = 101
- L = 80
- E = 21
Equity has changed by:
\dfrac{21 - 20}{20} = \dfrac{1}{20} = 0.05 = 5\% = \%\Delta A \times 5 = \%\Delta A \times \dfrac{A}{E}
Leverage.
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ok. so we assume here that liabilities are not changing?
Yup.
Note that \dfrac{L}{E} is also a form of leverage. In my example, if liabilities decrease by 1% and assets don’t change, equity increases by 4%.
OK. Got it. What is the point of this exercise then? We know how much equity changes if assets value changes.
They’re setting up the formula for calculating the duration of the bank’s equity.