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 (the loan must be repaid). Equity accounts for that. For example, a $50,000 margin account with a $20,000 loan has $30,000 of equity.
We’ll use two equity formulas in this section:
First, here’s the formula for equity in a long margin account:
To find equity, subtract the debit from the 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?
$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:
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?
Answer = $9,000
First, set up the account at the time of purchase:
$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, update the LMV after the price rises to $80:
$16,000 (LMV) - $7,000 (debit) = $9,000 (equity)
The investor now holds 200 shares at $80, so LMV is $16,000. The debit stays at $7,000 because the investor didn’t borrow more or repay any of the loan. Equity increases to $9,000.
You’ll also want to know when the variables in the long equity formula 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 for these problems: unless otherwise stated, sales proceeds in a long margin account are used to repay the debit balance, which reduces the loan.
First, set up the account at the time of purchase:
$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 50% (since it’s greater than $2,000), so the investor deposits $4,000 and borrows $4,000 (the debit).
Next, update the LMV after the price rises to $30:
$12,000 (LMV) - $4,000 (debit) = $8,000 (equity)
The investor still holds 400 shares, now worth $12,000. The debit hasn’t changed, so equity rises to $8,000.
Last, the investor sells 100 shares at $30. The account now has 300 shares, and the $3,000 in sale proceeds is used to repay the loan:
$9,000 (LMV) - $1,000 (debit) = $8,000 (equity)
Two values drop when the investor sells stock in a long margin account (assuming proceeds repay the loan):
Notice that equity doesn’t change here: it’s $8,000 before and after the sale. Selling simply converts $3,000 of stock value into $3,000 of loan repayment, leaving net worth unchanged.
Equity in a short margin account follows the same idea (net ownership value), but the formula is different:
Because this formula can feel less intuitive at first, 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:
So the credit balance is:
*The credit balance represents cash “on the sideline.” Since the investor must eventually repurchase the shares sold short, the broker-dealer requires cash in the account to support that future repurchase. In this example, $12,000 is available in the account for that purpose.
Next, find the SMV:
Now apply the equity 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?
Answer = $12,000*
First, set up the account at the time of the short sale:
$27,000 (credit) - $18,000 (SMV) = $9,000 (equity)
Next, update the SMV after the stock falls to $50:
$27,000 (credit) - $15,000 (SMV) = $12,000 (equity)
The investor is still short 300 shares, now valued at $15,000 (300 x $50). The credit doesn’t change because the investor didn’t short more shares or buy shares back. Equity increases to $12,000.
You should also know when the variables in the short equity formula change. 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 for these problems: unless otherwise stated, repurchases to close a short position are paid for using the credit balance.
First, set up the account at the time of the short sale:
$30,000 (credit) - $20,000 (SMV) = $10,000 (equity)
Next, update the SMV after the stock falls to $150:
$30,000 (credit) - $15,000 (SMV) = $15,000 (equity)
The investor is still short 100 shares, now valued at $15,000 (100 x $150). The credit hasn’t changed, so equity rises to $15,000.
Last, the investor buys back 50 shares at $150. The repurchase costs $7,500 (50 x $150) and is funded from the credit balance:
$22,500 (credit) - $7,500 (SMV) = $15,000 (equity)
Two values drop when part of a short position is closed:
Notice that equity doesn’t change here: it’s $15,000 before and after the repurchase. The transaction uses $7,500 of cash to eliminate $7,500 of short market value, leaving net worth unchanged.
This video summarizes the important concepts related to margin equity:
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