Leverage#
Week 5
Every other week, you go and do the thing#
This week you may not#
The policy#
Real-money positions are long-only and fully paid.
You own the thing. The most you can lose is what you paid.
That rule exists because of one number.
Start with last week’s position#
610 units of B at $18.00 = $10,980Your own money.
Now borrow the same again#
1,220 units at $18.00 = $21,960
your money = $10,980
borrowed = $10,980Your equity#
What is left after repaying the loan:
equity = 1,220P − $10,980At $18.00 that is $10,980. As it should be.
The lender is watching one number#
Maintenance margin. Keep equity above some
fraction of the position’s value, or it is closed for you.
Take 25%.
Solve for the price#
(1,220P − 10,980) / 1,220P = 0.25
1,220P − 10,980 = 305P
915P = 10,980P = $12.00#
Not a price you chose#
Not a price you were warned about.
Not a price at which you have any say.
Three inputs, one of them a fraction in a document you did not read.
Now suppose B does this#
$18.00 → $11.50 → $14.00Unleveraged#
You hold 610 units the whole way.
610 × $14.00 = $8,540Down. And still holding.
Leveraged#
Closed out at $12.00 on the way down.
1,220 × $12.00 − $10,980 = $3,660The move from $12 to $14 happened to somebody else.
But you would have guessed#
B fell 22.2%. Twice the exposure, twice the loss:
$10,980 × (1 − 2 × 0.222) = $6,101You have $3,660.
The missing $2,441#
is not the size of the fall.
It is the shape of it.
It happens without borrowing too#
0.50 × 1.50 = 0.75Down 25% after two moves that sound like they cancel.
To get back from 0.50 to 1.00 the price needs +100%, not +50%.
And if B keeps falling#
1,220P = $10,980 → P = $9.00At $9.00 your equity is zero.
Below $9.00 you owe money#
you never deposited.
At $8.00#
position 1,220 × $8.00 = $9,760
loan = $10,980
─────────
you owe $1,220On top of having lost everything you put in.
Unleveraged, at $9.00#
610 × $9.00 = $5,490A bad week. And yours.
A $20 cap is not a cap#
if the instrument can send you a bill#
So we derive the $12.00, and forbid you from paying to experience it.