Calculating Portfolio Drawdown to a Margin Call
Summary
This note derives the market decline that would reduce a leveraged stock portfolio to its maintenance margin threshold. It defines cash or borrowing, the market value of long positions, and the maintenance margin fraction, then sets portfolio equity equal to the required fraction of the securities’ current value after a hypothetical decline. Solving that equality gives a drawdown formula based on the loan balance, portfolio value, and margin requirement.
For the example with a 400,000 loan against securities initially worth 1,000,000 and a 30% maintenance requirement, the answers give a threshold decline of about 42.86%, or roughly 43%. This calculation assumes the stated margin rule applies uniformly and that the positions move together with no deposits, withdrawals, fees, or broker-specific changes to requirements. Actual margin calls may occur earlier if a broker changes its rules or applies different requirements to particular holdings.
Key ideas
- The margin threshold is reached when account equity equals the maintenance requirement on the securities’ reduced market value.
- The formula uses the cash or loan balance, current long market value, and maintenance margin fraction.
- In the example, a 400,000 loan against 1,000,000 of securities with a 30% requirement implies a drawdown threshold near 42.86%.
- The calculation assumes fixed margin terms and does not account for broker discretion or other account changes.
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Full text
# % Drawdown on Stock Portfolio to hit Margin Call
# % Drawdown on Stock Portfolio to hit Margin Call
Margin requirement is industry standard at 30% of total portfolio (cash + margin loan)
e.g. You have 600k in equities purchased with cash and 400k in equities purchased on margin loan. The total portfolio is $1mil. The maintenance requirement is 600k + 400k = 1mil(30%) = 300k.
However, if your portfolio draws down 20% to 800k, the maintenance requirement also goes down to 800k(30%) = $240k
I'm looking for a formula where I can know what % drawdown my portfolio can handle until it hits a margin call.
I hope I explained that correctly, and thank you!
## Answer by Alex C (score 4)
https://quant.stackexchange.com/a/39296
Define
CoL = cash or loan (cash if positive, loan if negative)
MVL = market value of long positions
MRP = Maintenance Margin Requirement fraction (=0.3)
NetLiq = liquidation value (aka total equity) = CoL + MVL
DD = downward return due to market movement
The maintenance margin condition is: "the equity must be at least 30% of the value of the securities"
NetLiq >= MRP*MVL or CoL+MVL >= MRP*MVL
Suppose MVL drops by DD i.e. MVL is replaced by MVL*(1-DD) such that the margin condition holds exactly
Col+(1-DD)*MVL = MRP*MVL*(1-DD)
Solving for DD we get the desired result:
$$DD=1+\frac{CoL}{MVL*(1-MRP)}$$
Using CoL = -400,000 MVL = 1,000,000 MRP = 0.30 we get DD = 0.428571429 as amdopt also found through a more roundabout method.
## Answer by amdopt (score 2)
https://quant.stackexchange.com/a/39258
At a 43% draw your excess liquidity hits zero and you get a margin call.
Cash = -400,000 (400k margin loan)
Securities = 571,428.60 @ ~43% drawdown
Net Liquidation Value = 174,428.57 (Cash + Securities)
Margin Req @30% = 174,428.57
Excess Liquidity = 0 (Net Liq - Margin Req)
Solve for DD in the formula below or use something like the Goal Seek function in Excel. Below is an example of how you might set up a spreadsheet to use Goal Seek. 42.8571428571429% is the exact number Excel returns.
0 = Cash+Securities*(1-DD)-Securities*(1-DD)*Margin Req
```
Cash Securities Drawdown Margin Req
$(400,000.00) $1,000,000.00 43% 30%
Excess Liquidity
$(0.00)
```Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.