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  =  $10,980

Your own money.

Now borrow the same again

1,220 units at $18.00  =  $21,960

   your money          =  $10,980
   borrowed            =  $10,980

Your equity

What is left after repaying the loan:

equity  =  1,220P − $10,980

At $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   =  10,980

P = $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  →  $14.00

Unleveraged

You hold 610 units the whole way.

610 × $14.00  =  $8,540

Down. And still holding.

Leveraged

Closed out at $12.00 on the way down.

1,220 × $12.00 − $10,980  =  $3,660

The 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)  =  $6,101

You 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  =  0.75

Down 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 = $9.00

At $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                        $1,220

On top of having lost everything you put in.

Unleveraged, at $9.00

610 × $9.00  =  $5,490

A 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.