The conventional opinion said margin buying is dangerous. You may get a margin call or be forced to liquidate your stocks. It might be true or false. But to analyze the risk involved, we need to first understand what is margin buying.

Margin buying is to use other people’s money to buy stocks (Very simple). Your assets are the total amount of stocks you bought using both your own money and borrowed money. Your equity, however, is the difference of assets and borrowed amount.

## Margin requirements

To understand the calculations of margin requirements, it is helpful to understand the following sentence: “Debt is real. Equity frustrates.”

Stocks rise and fall every day. Therefore the value of the assets changes. But, the borrowed amount is fixed which is independent to the value of the assets. If you borrowed 100k to buy a stock and the stock goes up 100%, you only need to repay that 100k (plus interest). of course, the vice versa is also true. Even the stocks drop to zero, you still need to repay that 100k.

To protect the lender (usually the broker), there are two margin requirements, namely initial margin requirement and maintenance margin requirement. Initial margin requirement requires a certain amount of equity-to-asset ratio when you initiate the position (buying the stock). The maintenance margin requirement requires a certain amount of equity-to-asset ratio in the whole portfolio.

Assume that the initial margin is 50% and your equity is 100k. The maximum amount of stocks you can buy is 200k since equity-to-asset ratio is now 50% (100k/200k). However, you will not want to do that. If your portfolio drops, you may not meet the maintenance margin requirements.

Assume that the maintenance margin is 40% and you borrowed 100k (assets: 200k, equity: 100K). If your portfolio drops 20%, your assets will become 160k and equity becomes 60k (160k-100k). Your margin is now 37% which is below the maintenance margin requirement. What will happen? some of your positions will be liquidated to repaid the borrowed amount.

## Managing risks

It depends on your expectation of how much your portfolio will drop and the expected maintenance margin requirement (noted that it can be changed by the broker if market situation is bad).

The largest daily percentage loss of S&P 500 is -20.47% (the year 1987). The largest peak-to-trough drop of S&P500 is -83% (the year 1932). Of course, those are statistically rare events. It happens when it happens.

### Calculation formula for maximum amount to be borrowed

Given:
1. expectation of maximum percentage drop (say, 50% intraday assume that you can deposit the money within a day)
2. expectation of maintenance margin requirement (say, 40%)

Let:
Equity be “e” and amount to be borrowed is “b”

Solving \$b\$ for the following equation:

I have included the following calculator for your reference:

## Conclusion

If margin will not be called and positions will not be liquidated unwillingly, using margin can improve your return given the low interest rate environment. But the worst case scenario and expected maintenance margin requirements are something that investors need to make their own judgement.

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