# Margin: Is my math correct?

I was recently introduced to the concept of margin and have been reading about it on and off for the last 2 months. I want to use margin funds for my house remodeling, and would appreciate if someone could ascertain my math below.

Problem: I own 300K worth of VTI stock in interactive brokers. I am planning to borrow 100K cash on margin and deposit it into my savings account. How much would my VTI investment have to drop before I am hit with a margin call?

Answer: Lets call this value x. When my VTI investment hits x, my total fund value is (x+100K). Since the overnight maintenance margin is 50%, the margin amount would be (x+100K)/2. I would be hit with a margin call if funds I own equal this margin, or in other words, x = (x+100K)/2. This implies that x=100K.

Since I don't believe VTI will drop to 1/3rd its value in the near future, I feel safe borrowing 100K.

Is this calculation correct? Anything else I should be aware of?

The above calculation is wrong. Let the amount VTI reduces to be x. Then my equity in the account is (x-100). Assuming margin to be 50%, we want (x-100)/x = .5 or x=200. So I will be hit with a margin call if VTI drops by 33%.
• Be aware that that kind of account size makes you eligible to apply for portfolio margin, which has the potential to reduce your margin requirement far below Reg T levels given that VTI is an inherently diversified instrument. Of course portfolio margin comes with its own potentially significant caveats and risks, so DYOR. Jan 5, 2022 at 8:23

If you take out \$100k, your position in VTI cannot drop below \$133k (cannot drop more than 55%).

Maintenance margin is usually 25%. This means that you cannot owe more than 75% your account's worth. If you borrow \$100k and your VTI position is worth \$300k, you owe 33% of your account's worth. If your position in VTI goes down in value to \$133k, you owe 75% of your account's worth (\$100k of \$133k), and margin calls will start to occur if it drops any further.

• The VTI position is completely mine, without any margin. So if I borrow another \$100K (cash for remodeling), and my VTI position is \$300K, I owe 25% of my account's worth right? Not 33%. Jan 4, 2022 at 0:48
• @elexhobby initially, yes, since your account balance will be \$300K VTI + \$100K cash = \$400K. However, once you start spending that cash on remodeling, it is no longer in your account; you still owe \$100K, but your account balance is now \$400K minus the cost of remodeling (+/- VTI performance) Jan 4, 2022 at 2:33
• @elexhobby I'm not sure I understand your comment. What do you mean by "borrow another \$100k"? A total of \$200k all else being equal? In that case, you owe 66% of your account's worth (\$200k of \$300k). That is over the 50% initial margin requirement, so you won't actually be able to borrow that much. The most you can borrow is \$150k (50% of \$300k).
– user19035
Jan 4, 2022 at 5:14
• I was wrong. @yoozer8 pointed out the error in my understanding. I agree with your answer. Jan 4, 2022 at 5:30

This answer is the same as what Axiomatic Nexus explained but just in a somewhat different fashion.

Reg T margin is 50% so if your broker's rate was the same, you could buy \$300k of stocks with cash or fully paid marginable securities.

In your case, you are taking a margin loan of \$100k and your equity reduces to \$200k. If the margin maintenance requirement is 25% then the short cut formula is 4/3 the debit balance which is 4/3 times \$100k or \$133,333. At that level you would have \$33,333 of equity which is 1/4 of the market value (.25%) margin. That level would represent a 55.6% drop in value of your holdings.

• Thanks. But I read that at the end of the day (also called overnight in some places), the margin is 50%. "IBKR enforces Regulation T initial margin requirements (typically 50% for stocks or 100% for nonmarginable securities) at the end of the trading day." (source interactivebrokers.com/en/software/glossary/content/glossary/…) Jan 4, 2022 at 5:05
• Reg T initial margin is 50% and 25% maintenance. Before the election in 2020, IBKR raised it to 67.5% for a new position and 33.75% for maintenance. I don't know whether it has been lowered. I suspect that your link has to do with PDTraders being allowed up to 4:1 leverage intraday which must drop to 2:1 by the end of the day. Jan 4, 2022 at 5:27