In order to clarify the mechanics of the margin operation, please look at the following:

Buying on margin $-$ Let's assume we are buying N shares of a certain stock at a price PO $.$

We will start with a loan from the broker at Reg T levels $-50\%,$ Loan $={0\mathrm{.}5}^{**}{N}^{**}$ PO$.$ The margin

will be

$\frac{N*P-\text{L}\text{o}\text{a}\text{n}}{N*P}=M$

At the start $P=P0$ and thus $M=\frac{1}{2}.$ As the market moves the value of the Margin will change

but what we want to examine is when do we get a Margin Call. Remember, the value of the

Loan does not change, no matter what we owe that to the B$/$D$.$ Margin Call comes when our

Margin is less than Maintenance Margin, which is set by the B$/$D$.$

$\frac{N*P-\text{L}\text{o}\text{a}\text{n}}{N*P}MM$

Solving this for the price $P,$ we get:

$P^{**}\frac{\text{L}\text{o}\text{a}\text{n}}{N*(1-MM)}$

Once the price falls below $P^{**},$ we will get a Margin Call, which would require us to raise the

Margin to the initial level.

Short Sales $-$ in this case we borrow securities from the B$/$D and sell them on the market,

hoping that the price will fall. The proceeds of the sale are kept as a collateral with the B$/$D

and additional cash$/$marketable securities needs to be posted. The Reg T still applies,

therefore we need to post additional at least $50\%$ of the initial value of the sale: Collateralo

$={0\mathrm{.}5}^{**}$NPO. The margin will be given by:

$\frac{\text{E}\text{q}\text{u}\text{i}\text{t}\text{y}}{N*P}=M$

Expanded:

$\frac{N*P0+\text{C}\text{o}\text{l}\text{l}\text{a}\text{t}\text{e}\text{r}\text{a}\text{l}0-N*P}{N*P}=M$

It's important to understand here that the proceeds of the initial sale NPO are fixed and stay

in the account as cash. The value of Collateral$0$ might fluctuate if we posted securities$,$

although that will likely be very small since the requirement for high quality collatera

In order to clarify the mechanics of the margin operation, please look at the following:

Buying on margin $-$ Let's assume we are buying N shares of a certain stock at a price PO $.$

We will start with a loan from the broker at Reg T levels $-50\%,$ Loan $=0\mathrm{.}5**N**P0.$ The margin

will be

$\frac{N*P-\text{L}\text{o}\text{a}\text{n}}{N*P}=M$

At the start $P=P0$ and thus $M=\frac{1}{2}.$ As the market moves the value of the Margin will change

but what we want to examine is when do we get a Margin Call. Remember, the value of the

Loan does not change, no matter what we owe that to the B$/$D$.$ Margin Call comes when our

Margin is less than Maintenance Margin, which is set by the B$/$D$.$

$\frac{N*P-\text{L}\text{o}\text{a}\text{n}}{N*P}MM$

Solving this for the price $P,$ we get:

$P^{**}\frac{\text{L}\text{o}\text{a}\text{n}}{N*(1-MM)}$

Once the price falls below $P^{**},$ we will get a Margin Call, which would require us to raise the

Margin to the initial level.

Short Sales $-$ in this case we borrow securities from the B$/$D and sell them on the market,

hoping that the price will fall. The proceeds of the sale are kept as a collateral with the B$/$D

and additional cash$/$marketable securities needs to be posted. The Reg T still applies,

therefore we need to post additional at least $50\%$ of the initial value of the sale: Collateralo

$={0\mathrm{.}5}^{**}$NPO. The margin will be given by:

$\frac{\text{E}\text{q}\text{u}\text{i}\text{t}\text{y}}{N*P}=M$

Expanded:

$\frac{N*P0+\text{C}\text{o}\text{l}\text{l}\text{a}\text{t}\text{e}\text{r}\text{a}\text{l}0-N*P}{N*P}=M$

It's important to understand here that the proceeds of the initial sale NPO are fixed and stay

in the account as cash. The value of Collateral$0$ might fluctuate if we posted securities$,$

Rickety Transport Company has been trying to reinvent ride share in urban areas. The

stock has been volatile, but it currently sells for $$42.$ Your research shows that RTC$\text{'}$s

cost structure cannot compete with Uber and you recommend shorting the stock.

a$)$ You sell short $500$ shares. How much margin do you have to post initially?

b$)$ After you sold the stock, a rumor spreads that Lyft is interested in RTC$\text{'}$s

operation and the stock moves up$.$ At what point would you get a margin call if

the Maintenance Margin is $30\%?$

c$)$ The talks with Lyft break down and RTC stock resumes its precipitous fall. You

decide to close out your position when the stock hits $$30.$ What is your return on

this trade, ignoring any dividends?