# Margin Account Calculations for Short & Long Positions

Instructor: Yusuf Abdullah

Yusuf has taught Science and Mathematics at school level and Finance and Economics at University level. He has recently earned his Ph.D in Financial Econometrics.

The lesson deals with long and short positions in margin trading. Learn how to calculate profit and loss on long and short positions and assess the price at which margin call is made.

## Long & Short Positions

Ada is a medical researcher and is new to investing. She has been following two companies who are researching medicine to treat hypertension in adults. With publicly available knowledge and her research skills, she determines that medicine developed by one of these companies, ABC Inc, is likely to succeed in human trials whereas the medication from XYZ Corp is likely to fail in human trials. She has approached John, her financial advisor to make the best use of the knowledge.

As there is risk involved and she could face massive losses if she is wrong, John reaffirms with her that she is confident enough in her beliefs to move forward. Ada is very confident and John trusts her expertise. Therefore, John advises her to go long on ABC stock and go short on the XYZ stock. Ada does not quite understand the long and short positions. John describes short position as borrowing a stock and selling it at present (at a high price) and then buying it back at a lower price to return it back to the borrower at a later date. Naturally, there is a profit if the stock price falls. A long position is buying the stock. Long position benefits when the stock price rises.

Ada asks if there is a way that she can invest a larger amount than the \$10,000 she has saved to invest. John informs her than she can take a loan from the brokerage or a bank equal to the value of her investment. This is known as margin trading. There are limits to margin trading enforced by the regulators and the stock exchange. These limits enforce the value of the debt in the margin account to 50% initially. The trading may result in a loss or gain. The regulations dictate that the value of the equity shall never fall below 25%, and, if it does, the investor is required to deposit additional funds.

### Long Position

Ada invests \$20,000 in ABC stocks by borrowing \$10,000 on margin. She wants to know about her gains and losses with various changes in the price. The ABC stock is worth \$10 at the moment.

#### The number of stocks that can be bought is:

\$20,000 / \$10 = 2000

Loan Value = \$10,000

Equity = \$10,000 ( Ada's own money)

Total investment = \$20,000

#### If the stock price rises to \$12:

Total value = \$12 * 2000 = \$24,000

Profit = \$4,000

Now the composition of debt and equity would be:

Debt = \$10,000 , Equity = \$14,000

#### If the stock price falls to \$8:

Total value = \$8 * 2000 = \$16,000

Loss = \$4,000

Now the composition of debt and equity would be:

Debt = \$10,000 , Equity = \$6,000

### Margin Call

To receive the margin call, the value of the equity goes down to 25% from the current 50%.

#### Margin call is received at 25%:

x / (x + \$10,000) = 0.25

x = 0.25x + \$2,500

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