Margin Calcuation Example

Discussion in 'Risk Management' started by HappyTrader, Jun 28, 2016.

  1. Hello,

    I was digging around here (and the internet) for some good examples on margin calculations. All of the examples I see talk about being fully leveraged on your account (i.e.: have 10k cash, buy 20k securities). I would like to see some examples where you are NOT fully leveraged.

    So I thought I'd try this. I would appreciate it if someone would check my maths.

    I'm taking the expectation that we are dealing with a Reg T Margin Account, with 50% maintenance margin. For simplicity sake I'm looking at LONG positions kept overnight. I'm using SPY (S&P 500 ETF) as the asset to avoid specifics with regards to Futures/Indexes. Additionally, to make things interesting, I'm not dealing with an account holding cash, only with one that is fully invested.

    Start off with:
    Margin Account with $1,000,000 in SPY
    Equity = $1,000,000

    Day 1:
    Purchase $100,000 in SPY
    Loan Value = $100,000 (Broker lends you this amount to make the purchase)

    Total Asset Value = $1,000,000 (original positions) + $100,000 (new purchase) = $1,100,000
    Equity = Total Assets - Loan = ($1,000,000 + $100,000) - $100,000 = $1,000,000
    Maintenance Margin = 50% * Loan = $50,000

    (At this point we have no problems and do not worry at all about a margin call. We enjoy having the position in our portfolio as if we bought it with pure cash).

    Day 2:
    SPY drops 50%
    Total Asset Value = 50% * $1,100,000 = $550,000
    Equity = Total Assets - Loan = $550,000 - $100,000 = $450,000
    Equity ($450,000) > Maintenance Margin ($50,000)

    (At this point, even after a 50% drop, we are still safe and do not have to worry about a margin call).


    So the question is: How bad would the drop have to be before we do worry about the margin call?

    We will get a margin call if:
    Equity < Maintenance Margin
    Equity = Total Assets - Loan
    Maintenance Margin = $50,000

    Therefore simple algebra:
    Total Assets - Loan < Maintenance Margin
    Total Assets < Maintenance Margin + Loan
    Total Assets < $50,000 + $100,000
    Total Assets < $150,000

    Which means that total assets drops to 13.63% (or an 86.36% drop)
    150,000 / 1,100,000 = 13.63%
    1 - 13.63% = 86.36%

    If SPY drops more than 86.36% there will be a margin call.
    If SPY drops more than 86.36% we will have more to worry about than a margin call :p

    But this is a safe way to use margin on your account because the amount being borrowed is very small ($100,000).

    Anyone see any mistakes in my maths?

    Thank you.
     
  2. 1245

    1245

    That was a lot and you made it very complicated.

    With AUM of $1mm, you can buy up to $2mm of SPY. If you account value drops to 25% of the of the total market value of the securities in the margin account you will get a regulatory call. Most brokers will have a higher value for this. At $500K, you will have to bring the account back over $1mm or liquidate. I'm more familiar with PM, but I think this is correct.

    1245
     
    RobSwe likes this.
  3. JackRab

    JackRab

    This doesn't make sense at all... your maths might be alright... but you're using all kinds of fictional numbers.

    In the end, you really need to worry if you have no cash left to post margin...
    In your case, if the 1 mln is fully invested, the maintenance margin of 50.000 is too high. Would be more like 5k, maybe 10, because margin on the loan of 100k. If the total portfolio value drops to close to 100k, your broker will likely liquidate to safeguard the loan.

    At porfolio value of 1.100k, leverage is 1:10 (hardly any)... 200k, you are leveraged 2:1. At 110k 10:1....

    What you say in the end is correct, margin is all about the leverage... and when you borrow a small amount compared to the account/net liq. it's not a problem.

    If you would invest 1 mln in ES (+/- 10 futures), with 1 mln in cash in your account... the initial margin would be about 50k. But there's no worry at all ever... Effectively, you are not leveraged.... ES can go down 100% and you have no problems, because you can post margin all the way down (except for some nausea in the stomach).
     
  4. The purpose of this post was to illustrate trading on a small amount of margin (relative to account size) rather than maximizing margin availability. Also it was using stocks (specifically avoiding futures) and using Reg T Margin (50% margin rather than 10:1 or 20:1 leverage that some brokers would give).

    Keeping in mind: Stocks only (not futures), 50% Reg T Margin, and only using a small amount of the equity as the collateral towards the margin what do people think.

    ( I understand a lot of people on this forum are aiming towards full leverage on futures, which is the opposite intent of this post).

    Thank you.
     
  5. Fonz

    Fonz

    In portfolio margin account: $100,000. of SPY, initial margin = max $10,000. and maintenance margin = around $9,000.
    So, if you have the required capital depending on your broker (and low margin borrowing costs), that could open doors for sophisticated hedged strategies and minimize risks. Leverage by itself is not a problem. I don't think it is safe to build only one type of position or to have just one strategy, whatever the margin is or not used.
     
  6. drcha

    drcha

    You might want to check this out, which offers plenty of examples:

     
  7. marsman

    marsman

    I think it could be interessing for many people, also for me, if you gave a real example.
    You speak of "small amount of margin" with a $1M account. Something doesn't fit, or maybe the $1M is to be seen relatively very small... :D
    And at your start-point in your example you already make use of 2:1 margin, isn't it?

    What about giving a more realistic scenario using a really small acct of say $10k to $50k?
     
    Last edited: Jul 2, 2016
  8. Sorry :( For me the 1M account was the realistic example :( I understand there are many people out there who are dealing with 10k-50k but (please forgive me) I've never really dealt with an account with that much in it so I don't have much experience there.

    Also, I wanted to emphasize the small Reg T margin of 2:1 (rather than higher margins on Prop Trading firms or what you get with Futures --- there are already lots of examples of this on the internet so I did not want to repeat this). For me, I found very few examples on a well capitalized (1M+) account dealing with a Reg T Margin (50%) and only using a small portion (5%) of that margin. The purpose is to demonstrate how one can eek out additional gains by using margin and doing so in a safe manner (i.e. never even consider the possibility of a margin call due to its extreme unlikeliness -- therefore a safe option for risk averse investors).

    But I suppose with 10k you could divide my example by 100 :)

    (I guess this also helps illustrate that if you do have 1M you can make a *lot* more money with margin buying power than if you had only 10k -- which is why I guess a lot of people look towards Futures. I have one friend who only trades Commodities because he needs the leverage of Futures buying).
     
  9. marsman

    marsman

    It's all relative: seen percentagewise it's IMO the same relation... simple maths...
     
  10. Mostly true, the caveat being that certain trades you can not do without enough capital (i.e. you can't trade 1 option on AMZN with only 10k, therefore you are locked out of any option strategies that are unique to owning a lot of AMZN)
     
    #10     Jul 5, 2016