# Mathematically precise explanation of buying power

Can someone please provide a mathematically precise description of how buying power works in a brokerage account? Everything I can find online is too dumbed down to be precise enough that you could take a portfolio and actually calculate buying power based on the explanations available.

So the way I will ask this question is to give a precise, although apparently incorrect, definition, hoping that any inaccuracies can be corrected. In other words, my question is where exactly the following goes wrong.

The maintenance margin requirement is only relevant to determining the issuance of margin calls (and disallowing a purchase that would cause a margin call), and the purchase margin requirement is only relevant to lending on new purchases.

For purchases, each security can act as collateral securing up to a certain percentage of the purchase price, not current price, so if stock A has a 75% initial margin requirement and it was purchased for \$100/share, it can secure lending up to \$25/share regardless of how it fluctuates in value.

Since lending is based on purchase price rather than current value, buying power does not change as security values fluctuate, except that the maintenance requirement is an independent and separate limitation on buying power in that no security can be purchased if after the purchase the maintenance requirement will not be met.

For maintenance, each security indicates a certain amount of equity that must be held in the account. So a security that has a 75% maintenance margin and is currently valued at \$100/share, indicates an equity requirement of \$25/share that is added to the account's overall minimum equity requirement. The amount of equity required by a security is based on the security's current value, not purchase price.

Options fit under these rules with 100% initial and maintenance requirements. This is equivalent to completely ignoring options: an account with the options removed has the same buying power as it had before the options were removed.

The above does not match the buying power reported to me in my Webull account, nor is it consistent with the fact that my Webull purchasing power fluctuates with security values in a setting where the maintenance requirement is definitely not an issue. So the above description, while unlike what I can find online is exact enough you could use it to actually calculate buying power in a real portfolio, it is also inaccurate in some way I can't find any information on.

EDIT: What I am asking for is a specific correction to my explanation given above. Every explanation of margin I can find is consistent with what I describe above, yet what I describe above doesn't match real world buying power. So what I describe above must be wrong somewhere, and I am hoping someone can point out the exact problem. Thanks!

Regulators set the minimum but individual brokerages are free to calculate their own option margin requirement/buying power reduction in excess of the minimums if they choose.

Here's a snippet from the CBOE Margin Manual:

I don't know what WeBull uses, but TastyWorks lists their formulas, here's what they use for naked short calls:

The margin requirement for an uncovered call is the greatest of the following calculations times the number of contracts times the multiplier (usually 100):

• 20% of the underlying price minus the out-of-the-money amount plus the option premium
• 10% of the underlying price plus the option premium
• \$2.50

The premium received from the sale of the short call may be applied to meet the initial margin requirement.

They provide an example and some exceptions and have similar info for short puts and strangles/straddles. If you can't find what your brokerage uses contact their support.

Also know that the terms and conditions you agree to when opening an account indicate that they are free to make changes to these requirements as they see fit to control their risk exposure, for example during the GME short-squeeze of early 2021 brokerages increased option margin requirements on GME to reduce their risk.

• Thank you for your response. My explanation is missing the fact that options are marginable in some accounts. My account tho claims they are not. As far as I can tell, other than the fact that options are marginable in some accounts, it looks like your response does not point out any misunderstanding in my proposed explanation? Or am I missing an inconstancy with my explanation and what you are saying? The issue is that I see the concept that is typically described, as you discuss above, which I restate in my question, but it just doesn't match my actual buying power.
– Kyle
Nov 19, 2022 at 22:06
• Ah, I see. I thought the deviation of option margin from what you described was likely the cause of discrepancy you observed. Do you have an example of a position where more/less buying power is used than you expect? Nov 19, 2022 at 22:41
• Ya, its really weird. I have an account with \$224,341.93 cash in it, of which \$106,749 is needed to secure some short vertical spreads (this is calculated by difference in strike prices and confirmed to be how they do those positions in another account with them that only has vertical spreads and long options where I can exactly calculate BP). Long options and the shares I have in that account are not marginable they say, so I should have \$117,592.93 BP. I actually have \$116,792.93, just a difference of \$800 which is closer than I was able to calculate it before my post, but still off.
– Kyle
Nov 20, 2022 at 1:12
• The weird thing tho is after hours, those non marginable shares dropped \$.06 which corresponded exactly with an after hours drop in BP of \$822 (there were 13.7k shares). So on one hand, calculating according to my above understanding got me off by exactly \$800, indicating I am probably just missing something minor, but on the other hand BP is apparently moving in step with the MV of these nonmarginable shares. So I have no idea what is going on.
– Kyle
Nov 20, 2022 at 1:13
• Per Reg T, long term options are marginable but that doesn't mean that your broker must offer that to you. Broker valuation during after hours is problematic. B/A spreads widen dramatically so that can throw off valuation. And then there's the issue of the broker's valuation method: Short positions at the ask, long at the bid or do they average the bid/ask for valuation? Nov 21, 2022 at 1:19

Fully paid marginable securities can be used to buy additional securities on margin. The formula for this is:

[ (Securities Value) x Margin % ] / [ (100% - Margin %) ]

In the US, Reg T initial margin is 50% (brokers can require more) so if you put up \$10,000 of securities then you could buy another \$10k of securities:

(\$10k x .50) / (100% -50%)

The Reg T maintenance margin for long equity is 25% (brokers can require more). This means that there must be a minimum amount of equity value of 25% or more of the total value of the margin account. At 25% maintenance, a margin call will be triggered at:

Account Value = (Margin Loan) / (1 – Maintenance Margin %)

Account Value = \$10,000/(1 - .25) = \$13,333

The shortcut formula for 25% maintenance is 4/3 x the Debit Balance. In your example, 4/3 of \$10,000 would be \$13,333. This level would be reached after you lost 1/3 of your position's value (1/3 x \$20,000).

This can be displayed as:

Mkt Val ... Loan ...... Equity .... Margin %

20,000 ....10,000 .... 10,000 .... 50% (initial position)

13,333 .... 10,000 ..... 3,333 .... 25% (after 1/3 drop)

• Thank you for taking the time to respond. As far as I can tell your explanation is consistent with my explanation I proposed in the question, or is my explanation missing something here? The issue is that this sort of explanation is often given, but it just doesn't match the buying power granted in the actual account. It seems there must be something incorrect in the explanation I proposed, and I just don't see what that is.
– Kyle
Nov 19, 2022 at 22:02
• There are some errors in your explanation. I'm not going to try to tackle the math of it because your description in words is subject to interpretation. Actual numbers, less so. Here's a web site that may assist you in understanding margin and getting to the root of your problem. Nov 21, 2022 at 1:13