Basic margin math

The mathematics involving margin accounts

There are 3 types of accounts in test world, and therefore 3 math processes depending on the account. To be fair, one of them is simply combining both the others. There are long margin accounts, there are short margin accounts, and combined margin accounts, that simply contain both long and short positions. For the combined account, the math is simply separating the long and short positions, doing the long math on the long positions, the short math on the short positions, and then adding them together.

Long margin positions

The first of the 2 important margin equations is $LMV-DR=EQ$, where $LMV$ is the long market value, $DR$ is the debit register, and $EQ$ is the investor’s equity. The long market value is simply the market value of all of the long positions in the account. Take the number of shares long, multiply by the market price, and that is the long market value for that position. Then, add up all the positions to find the $LMV$ for the account. The debit register is basically how much the investor borrowed from the broker-dealer when they set up the account. The long market value fluctuates with the market value, but the debit register doesn’t change, unless it is specifically paid off, so the $LMV$ fluctuates in the account, and the $DR$ doesn’t, meaning the $EQ$ also fluctuates. The investor’s equity, to a degree, is what “they own” in the account.

Example: Long margin account

An investor goes long 500 shares when they are $\$40$ a share. That is a total market value of $\$20,000$, which, if you recall Reg-T, means the investor needs to deposit a margin call of $\$10,000$. That can be accomplished by either $\$10,000$ in cash, or $\$20,000$ in marginable securities. Let’s assume the investor deposits $\$10,000$ in cash, therefore borrowing the other $10,000, making the debit register $DR=\$10,000$. Let’s check the equation. $LMV-DR=EQ=\$20,000-\$10,000=EQ=\$10,000$. Which sort of makes sense if we think of the $EQ$ as how much of the account the “investor owns”. Now if the account falls, things change. If the shares fall to $\$35$ a share, what does the equation say now; $LMV-DR=EQ$. 500 shares at $\$35$ is $\$17,500$, so the $LMV$ is now $\$17,500$, while the $DR$ stays the same at $\$10,000$. So the equation advances to $\$17,500-\$10,000=EQ=\$7,500$. Which again makes sense, if there is a loss, the broker dealer lending us the money doesn’t lose, we do. In cases like this, you should do a quick check of what percentage the equity is of the whole account, $\frac{EQ}{LMV}$. In this case, that becomes $\frac{\$7,500}{\$17,500}=42.9\%$. Not a problem until it hits a minimum required equity. As this is a long account, that minimum is 25%, so at least for now, we’re safe.

Remember (long accounts): 25% is the maintenance requirement for equity. If equity falls below 25%, the broker-dealer must issue a maintenance call under FINRA rules. Always remember, house maintenance could be higher, and can also be changed at any time, with no advanced notice. It isn’t something that occurs often, but it can be done. To figure out the equity percentage in the account, simply divide the equity the customer has, by the $LMV$ of the account. When equity exceeds the Reg T requirement, the excess is credited to the special memorandum account (SMA) - a line of credit the customer can draw on to withdraw cash or buy more securities, as long as the account stays above its maintenance requirement. It is not cash sitting in the account.

An additional equation that can be useful is the one for the lowest the LMV can go in a long account before a maintenance call. You should try to memorize the fewest number of equations needed, as the more you memorize, the easier it is to confuse them. There is no need to memorize duplicate equations or equations that can be modified from one to another. Adding, subtracting, multiplying, and dividing both sides moves things around and can turn one equation into another. $LMV-DR=EQ$ if we add $DR$ to both sides we get $LMV=EQ+DR$, no need to memorize both. You may want to trial and error, try each of the answer choices in the other equations, and see which is correct, but the equation for the lowest the LMV can fall before a maintenance call would be $\frac{DR}{1-M_{req}}$, where $M_{req}$ is the long maintenance margin requirement. Usually this is 25%, so the formula would typically be $\frac{DR}{.75}$. Then divide that by the number of shares to find the price per share before a maintenance call.

Short margin positions

The other margin equation involves the short position and is $CR-SMV=EQ$, the short market value, or $SMV$, is the current market value of the securities that have been sold short. This formula can be rewritten as $EQ+SMV=CR$, and this is useful to remember for initial setting up of the math. The $CR$ is the credit register, or credit balance: the proceeds of the short sale plus the investor’s margin deposit. Unlike the $DR$, it isn’t money the investor has borrowed (a short seller borrows shares, not cash), which makes it a little harder to internalize. The $EQ$ still represents the equity the investor has in the account.

Similarly with long positions, the $CR$ never changes, but the $SMV$ goes up and down with the market, therefore the $EQ$ will change as well with the market value of the securities in the portfolio.

Example: Short margin account

An investor decides they want to short 1000 shares when they are $50 a share. The total market value is $50,000, meaning the investor would need to deposit 50% of that, or $25,000, as the initial margin call, in either cash or $50,000 in marginable securities. They would then have a $CR$ of $EQ+SMV$, or $25,000 + $50,000 = $75,000, from the second equation. So we have a starting position of $SMV$ of $50,000, and a $CR$ of $75,000. If things change now, and the price rises to $\$55$, what happens in the account? Well the $SMV$, 1000 shares, $\$55$ each, $\$55,000$ in $SMV$. Just like in long, the $CR$ never changes, but the $SMV$ certainly does, and therefore so does the equity. Using the initial equity equation, $CR-SMV=EQ$, we have the $CR$ of $\$75,000$ still, and the current $SMV$ of $\$55,000$, so $\$75,000-\$55,000=\$20,000$ in equity. We started with $25,000, we now have $20,000, which makes sense - we lost equity, as the price went up, which in a short account is what we do not want to happen. Again, we always need to check the equity percentage, and remember with short, that is 30% limit, not 25% like long. $20,000 in equity, $55,000 in total value, $\frac{\$20,000}{\$55,000}=36.36\%$, above 30%, no maintenance call.

Remember (short accounts): 30% is the maintenance requirement for equity (for a short stock priced at $\$5$ or more, it is actually the greater of 30% or $\$5$ per share). If you have less than 30%, a maintenance call will absolutely be done by FINRA rules. As previously stated, house maintenance can be higher, and can be changed at anytime with no advanced notice. To figure out the equity percentage in the account, simply divide the equity the customer has, by the $SMV$ of the account. $\frac{EQ}{SMV}$

We have the same situation as with long accounts and the maximum the SMV can rise before a maintenance call. The formula is $\frac{CR}{1+M_{Sreq}}$, where $M_{Sreq}$ is the short maintenance margin requirement. Usually this is 30%, so the formula would typically be $\frac{CR}{1.3}$