Mathematically precise explanation of buying power

Question

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!

Answer 1

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:

Much more info in the 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.

Answer 2

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)