Equity | Margin accounts | Brokerage accounts

Equity

One of the most important margin formulas is the one that calculates an account’s equity. Equity is the customer’s net ownership value in the account.

When you invest using borrowed funds, part of the account value belongs to the broker-dealer until the loan is repaid. For example, a $50,000 margin account with a $20,000 loan has $30,000 of equity ($50,000 − $20,000).

We’ll use two equity formulas in this section:

Long account equity formula
Short account equity formula

Long account equity

First, here’s the formula for equity in a long margin account:

$LMV - Debit = Equity$

LMV means long market value: the total market value of all long (owned) securities in the account.
The debit is the outstanding loan balance: the amount borrowed from (and still owed to) the broker-dealer.

So, equity is what’s left after subtracting the loan (debit) from the value of the securities (LMV).

Let’s work through an example:

An investor purchases 100 shares of ABC stock at $50 in their newly-opened margin account and deposits their Regulation T requirement.

Can you determine the equity?

(spoiler)

$5,000 (LMV) - $2,500 (debit) = $2,500 (equity)

The investor buys $5,000 of stock (100 shares x $50). Under Regulation T, the investor must deposit the greater of:

50% of the purchase price, or
$2,000

Here, 50% of $5,000 is $2,500, so the investor deposits $2,500. The remaining $2,500 is borrowed from the broker-dealer, which becomes the debit.

Let’s try another example:

An investor purchases 200 shares of ABC stock at $70 in their newly opened margin account and deposits their Regulation T requirement. The market then rises to $80. What is the equity?

Can you figure it out?

(spoiler)

Answer = $9,000

First, here’s how the account starts:

$14,000 (LMV) - $7,000 (debit) = $7,000 (equity)

The investor buys $14,000 of stock (200 shares x $70). The Regulation T deposit is the greater of 50% or $2,000. Since 50% of $14,000 is $7,000, the investor deposits $7,000 and borrows the other $7,000 (the debit).

Next, the market price rises to $80:

$16,000 (LMV) - $7,000 (debit) = $9,000 (equity)

Now the LMV is $16,000 (200 shares x $80). The debit stays at $7,000 because the investor didn’t borrow more or repay any of the loan. Equity increases to $9,000.

In addition to calculating equity for an initial purchase, you also need to know when the variables change. Consider this example:

A client of yours goes long 400 shares of ZZZ stock at $20 per share. The stock rises to $30, and the investor sells 100 shares. What is the resulting equity formula?

Here’s the key rule: unless otherwise stated, sale proceeds in a long margin account are used to repay the loan, which reduces the debit balance.

(spoiler)

First, here’s how the account starts:

$8,000 (LMV) - $4,000 (debit) = $4,000 (equity)

The investor buys $8,000 of stock (400 shares x $20). The Regulation T deposit is the greater of 50% or $2,000. Since 50% of $8,000 is $4,000, the investor deposits $4,000 and borrows $4,000 (the debit).

Next, the stock rises to $30:

$12,000 (LMV) - $4,000 (debit) = $8,000 (equity)

The LMV increases to $12,000 (400 shares x $30). The debit stays at $4,000 because nothing has been repaid yet.

Last, the investor sells 100 shares at $30:

$9,000 (LMV) - $1,000 (debit) = $8,000 (equity)

Two values drop when stock is sold in a long margin account (assuming proceeds repay the loan):

LMV decreases because the account holds $3,000 less stock (100 shares x $30).
Debit decreases by the same $3,000 because the sale proceeds are used to repay the loan.

Notice that equity does not change here: it’s $8,000 before and after the sale. Selling shares shifts value from stock to cash (and then to loan repayment), but it doesn’t change the account’s net worth by itself.

Short account equity

Equity in a short margin account follows the same idea (net value), but the formula is different:

$Credit - SMV = Equity$

The credit is the cash held in the margin account from two sources:
- the proceeds from selling borrowed shares short, and
- the investor’s required margin deposit (usually 50%).
SMV means short market value: the current market value of the securities sold short.

Because the short equity formula can feel less intuitive, let’s walk through an example step by step:

An investor sells short 100 shares of XYZ stock at $80 and deposits the required margin.

First, find the credit:

Short sale proceeds: 100 shares x $80 = $8,000
Regulation T deposit: the greater of 50% or $2,000
- 50% of $8,000 is $4,000, so the investor deposits $4,000

So the credit balance is $8,000 + $4,000 = $12,000*.

*The credit balance is cash held in the account to support the future repurchase. Since the investor must buy back the shares later, the broker-dealer requires cash to be available for that repurchase. In this example, $12,000 is held in the account for that purpose.

Next, find the SMV:

SMV = 100 shares x $80 = $8,000

Now apply the formula:

$12,000 (credit) - $8,000 (SMV) = $4,000 (equity)

Now try one on your own:

An investor sells short 300 shares of BCD stock at $60 and deposits the required margin. The stock then falls to $50. What is the equity?

(spoiler)

Answer = $12,000*

First, here’s how the account starts:

$27,000 (credit) - $18,000 (SMV) = $9,000 (equity)

The credit equals:

Short sale proceeds: 300 shares x $60 = $18,000
Regulation T deposit: the greater of 50% or $2,000
- 50% of $18,000 is $9,000, so the investor deposits $9,000

So the credit balance is $18,000 + $9,000 = $27,000.

Next, the stock falls to $50:

$27,000 (credit) - $15,000 (SMV) = $12,000 (equity)

Now the SMV is $15,000 (300 shares x $50). The credit doesn’t change because the investor didn’t short more shares or buy back shares. Equity increases to $12,000.

You also need to know when the variables change in a short account. Consider this example:

A client of yours goes short 100 shares of CDE stock at $200 per share. The stock falls to $150, and the investor buys back 50 shares to close part of the position. What is the resulting equity formula?

Here’s the key rule: unless otherwise stated, repurchases to close a short position are paid for using the credit balance.

(spoiler)

$30,000 (credit) - $20,000 (SMV) = $10,000 (equity)

The credit equals:

Short sale proceeds: 100 shares x $200 = $20,000
Regulation T deposit: the greater of 50% or $2,000
- 50% of $20,000 is $10,000, so the investor deposits $10,000

So the credit balance is $20,000 + $10,000 = $30,000.

Next, the stock falls to $150:

$30,000 (credit) - $15,000 (SMV) = $15,000 (equity)

Now the SMV is $15,000 (100 shares x $150). The credit doesn’t change because the investor hasn’t bought back any shares yet.

Last, the investor buys back 50 shares at $150:

$22,500 (credit) - $7,500 (SMV) = $15,000 (equity)

Two values drop when part of a short position is closed:

Credit decreases because $7,500 of cash is used to repurchase shares (50 shares x $150).
SMV decreases by $7,500 because half of the short position is closed.

Notice that equity does not change: it’s $15,000 before and after the repurchase. The account is essentially exchanging $7,500 of cash (credit) to eliminate $7,500 of short market value.

Sidenote

Combined equity formula

At this point, we’ve covered two equity formulas:

LMV - debit = equity
Credit - SMV = equity

You may see a question asking for the combined equity formula. To build it, combine both formulas into one expression. Keep the signs straight:

LMV and credit are positive
debit and SMV are negative

For example:

LMV + credit - SMV - debit = equity

This could work as well:

-SMV - debit + credit + LMV = equity

There are several correct ways to write the combined formula. The key is placing the plus and minus signs correctly.

This video summarizes the important concepts related to margin equity:

Key points

Long equity formula

LMV - debit = equity
LMV is the long market value
Debit is the amount borrowed
Equity is the account’s net worth

Short equity formula

Credit - SMV = equity
Credit is the amount sold short plus the amount deposited
SMV is the short market value
Equity is the account’s net worth

Equity

One of the most important margin formulas is the one that calculates an account’s equity. Equity is the customer’s net ownership value in the account.

We’ll use two equity formulas in this section:

Long account equity formula
Short account equity formula

Long account equity

First, here’s the formula for equity in a long margin account:

$LMV - Debit = Equity$

LMV means long market value: the total market value of all long (owned) securities in the account.
The debit is the outstanding loan balance: the amount borrowed from (and still owed to) the broker-dealer.

So, equity is what’s left after subtracting the loan (debit) from the value of the securities (LMV).

Let’s work through an example:

An investor purchases 100 shares of ABC stock at $50 in their newly-opened margin account and deposits their Regulation T requirement.

Can you determine the equity?

(spoiler)

$5,000 (LMV) - $2,500 (debit) = $2,500 (equity)

The investor buys $5,000 of stock (100 shares x $50). Under Regulation T, the investor must deposit the greater of:

50% of the purchase price, or
$2,000

Here, 50% of $5,000 is $2,500, so the investor deposits $2,500. The remaining $2,500 is borrowed from the broker-dealer, which becomes the debit.

Let’s try another example:

An investor purchases 200 shares of ABC stock at $70 in their newly opened margin account and deposits their Regulation T requirement. The market then rises to $80. What is the equity?

Can you figure it out?

(spoiler)

Answer = $9,000

First, here’s how the account starts:

$14,000 (LMV) - $7,000 (debit) = $7,000 (equity)

Next, the market price rises to $80:

$16,000 (LMV) - $7,000 (debit) = $9,000 (equity)

Now the LMV is $16,000 (200 shares x $80). The debit stays at $7,000 because the investor didn’t borrow more or repay any of the loan. Equity increases to $9,000.

In addition to calculating equity for an initial purchase, you also need to know when the variables change. Consider this example:

A client of yours goes long 400 shares of ZZZ stock at $20 per share. The stock rises to $30, and the investor sells 100 shares. What is the resulting equity formula?

Here’s the key rule: unless otherwise stated, sale proceeds in a long margin account are used to repay the loan, which reduces the debit balance.

(spoiler)

First, here’s how the account starts:

$8,000 (LMV) - $4,000 (debit) = $4,000 (equity)

Next, the stock rises to $30:

$12,000 (LMV) - $4,000 (debit) = $8,000 (equity)

The LMV increases to $12,000 (400 shares x $30). The debit stays at $4,000 because nothing has been repaid yet.

Last, the investor sells 100 shares at $30:

$9,000 (LMV) - $1,000 (debit) = $8,000 (equity)

Two values drop when stock is sold in a long margin account (assuming proceeds repay the loan):

LMV decreases because the account holds $3,000 less stock (100 shares x $30).
Debit decreases by the same $3,000 because the sale proceeds are used to repay the loan.

Short account equity

Equity in a short margin account follows the same idea (net value), but the formula is different:

$Credit - SMV = Equity$

The credit is the cash held in the margin account from two sources:
- the proceeds from selling borrowed shares short, and
- the investor’s required margin deposit (usually 50%).
SMV means short market value: the current market value of the securities sold short.

Because the short equity formula can feel less intuitive, let’s walk through an example step by step:

An investor sells short 100 shares of XYZ stock at $80 and deposits the required margin.

First, find the credit:

Short sale proceeds: 100 shares x $80 = $8,000
Regulation T deposit: the greater of 50% or $2,000
- 50% of $8,000 is $4,000, so the investor deposits $4,000

So the credit balance is $8,000 + $4,000 = $12,000*.

Next, find the SMV:

SMV = 100 shares x $80 = $8,000

Now apply the formula:

$12,000 (credit) - $8,000 (SMV) = $4,000 (equity)

Now try one on your own:

An investor sells short 300 shares of BCD stock at $60 and deposits the required margin. The stock then falls to $50. What is the equity?

(spoiler)

Answer = $12,000*

First, here’s how the account starts:

$27,000 (credit) - $18,000 (SMV) = $9,000 (equity)

The credit equals:

Short sale proceeds: 300 shares x $60 = $18,000
Regulation T deposit: the greater of 50% or $2,000
- 50% of $18,000 is $9,000, so the investor deposits $9,000

So the credit balance is $18,000 + $9,000 = $27,000.

Next, the stock falls to $50:

$27,000 (credit) - $15,000 (SMV) = $12,000 (equity)

Now the SMV is $15,000 (300 shares x $50). The credit doesn’t change because the investor didn’t short more shares or buy back shares. Equity increases to $12,000.

You also need to know when the variables change in a short account. Consider this example:

A client of yours goes short 100 shares of CDE stock at $200 per share. The stock falls to $150, and the investor buys back 50 shares to close part of the position. What is the resulting equity formula?

Here’s the key rule: unless otherwise stated, repurchases to close a short position are paid for using the credit balance.

(spoiler)

$30,000 (credit) - $20,000 (SMV) = $10,000 (equity)

The credit equals:

Short sale proceeds: 100 shares x $200 = $20,000
Regulation T deposit: the greater of 50% or $2,000
- 50% of $20,000 is $10,000, so the investor deposits $10,000

So the credit balance is $20,000 + $10,000 = $30,000.

Next, the stock falls to $150:

$30,000 (credit) - $15,000 (SMV) = $15,000 (equity)

Now the SMV is $15,000 (100 shares x $150). The credit doesn’t change because the investor hasn’t bought back any shares yet.

Last, the investor buys back 50 shares at $150:

$22,500 (credit) - $7,500 (SMV) = $15,000 (equity)

Two values drop when part of a short position is closed:

Credit decreases because $7,500 of cash is used to repurchase shares (50 shares x $150).
SMV decreases by $7,500 because half of the short position is closed.

Notice that equity does not change: it’s $15,000 before and after the repurchase. The account is essentially exchanging $7,500 of cash (credit) to eliminate $7,500 of short market value.

Sidenote

Combined equity formula

At this point, we’ve covered two equity formulas:

LMV - debit = equity
Credit - SMV = equity

You may see a question asking for the combined equity formula. To build it, combine both formulas into one expression. Keep the signs straight:

LMV and credit are positive
debit and SMV are negative

For example:

LMV + credit - SMV - debit = equity

This could work as well:

-SMV - debit + credit + LMV = equity

There are several correct ways to write the combined formula. The key is placing the plus and minus signs correctly.

This video summarizes the important concepts related to margin equity:

Key points

Long equity formula

LMV - debit = equity
LMV is the long market value
Debit is the amount borrowed
Equity is the account’s net worth

Short equity formula

Credit - SMV = equity
Credit is the amount sold short plus the amount deposited
SMV is the short market value
Equity is the account’s net worth