Buying stocks on margin means using some borrowed funds to partially pay for the stocks. The portion of the price that you pay with your own money is your "equity." Your margin is the value of your equity divided by the total value of the asset.
For example, suppose you buy 10 shares of stock at $100 per share for a total of $1,000 worth of stock. If you bought all of it using your own money, then you'd pay $1,000 and you'd own the shares outright. Your equity is equal to the value of the asset (i.e. $1,000 in stocks) minus the value of your debt (i.e. $0 because you did not borrow any money), for a total equity of $1,000, and your margin is the equity divided by the value of the asset, or 100%.
Now suppose you buy the same stocks, but you borrow half the price from your broker. In other words, you use $500 of your own money and $500 of borrowed money. Now your equity or margin is only half what it was above--50%.
The impact of margin on returns
If the stock goes up to $110/share (meaning the total value of the shares goes up to $1100 from an initial value of $1000), then return on your investment is quite attractive in percent terms:
This higher return on investment is due to leverage. Borrowing money to buy an investment allows you to buy more than you could have purchased had you not used any debt at all. Therefore you can earn more or "lever" up your profit.
Just as the upside is pronounced using margin, so is the downside. Consider what happens if the stock price drops to $90 a share. The new value of the investment is 10 shares x $90/share or a $900. That's a $100 loss.
This is again the impact of leverage--more pronounced upside AND more pronounced downside.
This video explains the concept of buying on margin and the effect of leverage:
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