One of the most essential margin formulas to be aware of calculates an account’s equity, which represents the customer’s net ownership value. When investing with borrowed funds, investors must factor in the future repayment of those funds to determine what they own in the account. For example, a $50,000 margin account involving a $20,000 loan to the investor results in $30,000 of equity (the account’s net worth).
We’ll discuss two separate equity formulas in this section:
First, let’s establish the formula to calculate equity in a long account:
LMV stands for long market value, which represents the overall value of all (long/owned) securities held in the account. The debit represents the outstanding loan amount (the amount borrowed and owed back to the broker-dealer). The account equity is found when the debit is subtracted 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 purchases $5,000 of stock (100 shares x $50) in their margin account. The investor must deposit 50% of the overall purchase or $2,000, whichever is greater. 50% of the initial investment is the greater of the two, so the investor deposits $2,500. The other $2,500 is borrowed from the broker-dealer, which is reflected in 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, let’s establish how the account starts:
$14,000 (LMV) - $7,000 (debit) = $7,000 (equity)
The investor purchases $14,000 of stock (200 shares x $70) in their margin account. The investor must deposit 50% of the overall purchase or $2,000, whichever is greater. 50% of the overall purchase is the greater of the two, so the investor deposits $7,000. The other $7,000 is borrowed from the broker-dealer, which is reflected in the debit.
Next, let’s factor in the increase in market price to $80 per share:
$16,000 (LMV) - $7,000 (debit) = $9,000 (equity)
Now, the investor holds 200 shares at $80 per share, resulting in an overall LMV of $16,000. The debit does not change because the investor did not borrow more or pay any borrowed funds back, leading to a new equity of $9,000.
In addition to understanding the equity formula for initial purchases in a long margin account, you should also know when formula variables change. Let’s look at 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 a clue to answer this question: unless otherwise stated, any sales proceeds in a long account are used to pay back borrowed funds, effectively reducing the debit balance. Can you take it from here?
First, let’s establish how the account starts:
$8,000 (LMV) - $4,000 (debit) = $4,000 (equity)
The investor purchases $8,000 of stock (400 shares x $20) in their margin account. The investor must deposit 50% of the overall purchase or $2,000, whichever is greater. 50% of the overall purchase is the greater of the two, so the investor deposits $4,000. The other $4,000 is borrowed from the broker-dealer, which is reflected in the debit.
Next, let’s factor in the increase in market price to $30 per share:
$12,000 (LMV) - $4,000 (debit) = $8,000 (equity)
Now, the investor holds 400 shares at $30 per share, resulting in an overall LMV of $12,000. The debit does not change because the investor did not borrow more or pay any borrowed funds back, leading to a new equity of $8,000.
Last, the investor sells 100 shares at $30. When this occurs, this is the resulting equity formula:
$9,000 (LMV) - $1,000 (debit) = $8,000 (equity)
Two figures decline when a security is sold in a long margin account. First, the LMV falls because the account has $3,000 (100 shares x $30) less stock. Those proceeds are used to repay borrowed funds (unless otherwise stated). When this occurs, the debit balance falls by the dollar amount of stock sold. Remember, the debit balance represents the customer’s outstanding loan from the broker-dealer. If they repay $3,000, the debit balance will fall by that amount.
The equity amount is worth noting, which did not change when the investor sold shares. The sale of shares did not increase or decrease the equity ($8,000 before and after the sale). The investor transfers $3,000 of stock to $3,000 of cash, which doesn’t influence the equity. The mere act of buying or selling securities does not affect the account’s net value.
The same idea of equity applies to a short account, but the formula is a bit different:
The credit represents cash held in a margin account, which comes from two different places. First, a short sale involves selling borrowed securities, which puts cash in the account. Second, the investor deposits a certain amount of money (usually 50%) when creating the short position. The combination of those two cash inflows equals the credit. SMV stands for short market value, which is the overall value of the short securities in the account.
Given the difficulty with the short equity formula, let’s walk through an example together:
An investor sells short 100 shares of XYZ stock at $80 and deposits the required margin.
First, let’s find the credit. The credit equals the amount being sold short (100 shares x $80 = $8,000) plus the amount deposited by the investor. Similar to a long account, the investor must deposit the greater of 50% or $2,000. 50% of $8,000 is $4,000, so that’s what the investor deposits. The combination of the amount sold short ($8,000) and the customer’s deposit ($4,000) leads to the credit balance, which is $12,000*.
*The credit balance represents cash “sitting on the sideline.” Investors must repurchase the stock they sell short, so broker-dealers require their investors to have cash in the account to make the required repurchase in the future. In this scenario, the investor has $12,000 in cash waiting to repurchase the 100 shares.
Next is the SMV. The SMV represents the overall short position of $8,000 (100 shares x $80). Now we can do the formula:
$12,000 (credit) - $8,000 (SMV) = $4,000 (equity)
Let’s see if you can do 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, let’s establish how the account starts:
$27,000 (credit) - $18,000 (SMV) = $9,000 (equity)
The credit equals the amount being sold short (300 shares x $60 = $18,000) plus the amount deposited by the investor. The investor must deposit the greater of 50% or $2,000. 50% of $18,000 is $9,000, so that’s what the investor deposits. The combination of the amount sold short ($18,000) and the customer’s deposit ($9,000) leads to the credit balance, which is $27,000.
Next, let’s factor in the market price decrease:
$27,000 (credit) - $15,000 (SMV) = $12,000 (equity)
Now, the investor is short 300 shares at $50 per share, resulting in an overall SMV of $15,000. The credit does not change because the investor did not sell short more stock or repurchase shares to close the short position, leading to a new equity of $12,000.
In addition to understanding the equity formula for initial sales in a short margin account, you should also know when formula variables change. Let’s look at 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 a clue to answer this question: unless otherwise stated, any repurchase of shares to close a short position is funded with the credit balance. Remember, the credit balance represents cash waiting to be used to buy back shares. Can you take it from here?
$30,000 (credit) - $20,000 (SMV) = $10,000 (equity)
The credit equals the amount being sold short (100 shares x $200 = $20,000) plus the amount deposited by the investor. The investor must deposit the greater of 50% or $2,000. 50% of $20,000 is $10,000, so that’s what the investor deposits. The combination of the amount sold short ($20,000) and the customer’s deposit ($10,000) leads to the credit balance, which is $30,000.
Next, let’s factor in the market price decrease:
$30,000 (credit) - $15,000 (SMV) = $15,000 (equity)
Now, the investor is short 100 shares at $150 per share, resulting in an overall SMV of $15,000. The credit does not change because the investor did not sell short more stock or repurchase shares to close the short position, leading to a new equity of $15,000.
Last, the investor buys back 50 shares at $150. When this occurs, this is the resulting equity formula:
$22,500 (credit) - $7,500 (SMV) = $15,000 (equity)
Two figures decline in the equity formula when a short position is closed. The credit balance decreases because that’s where the $7,500 cash comes from to repurchase the shares (50 shares x $150). The SMV also fell by $7,500 because half of the position was closed.
The equity amount is worth noting, which did not change when the investor bought back shares. Buying back shares did not increase or decrease the equity ($15,000 before and after the sale). The investor transfers $7,500 of cash (credit balance) to close $7,500 of the short position, which doesn’t influence the equity. The mere act of buying or selling securities does not affect the overall value of an account.
This video summarizes the important concepts related to margin equity:
Sign up for free to take 8 quiz questions on this topic