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Buying <a rel="nofollow" target="_blank" title="stock" href="http://stock.remmont.com/">stock</a> on margin-Buying <a rel="nofollow" target="_blank" title="stock" href="http://stock.remmont.com/">stock</a> on margin
Buying stock on margin-How to use and calculate margin for buying and shorting securities; margin agreement, intial margin requirement, maintenance margin requirement, and margin calls.

 Margin Percentage = 100 Leverage Ratio

### Example — Calculating the Margin Percentage from the Leverage Ratio

A 100 :1 leverage ratio yields a margin percentage of 100/ 100 = 1%. A 200 :1 ratio yields 100/ 200 = 0.5%. You’ll often see these leverage ratios advertised by forex brokers. A 100:1 ratio allows you to buy \$100,000 worth of currency while posting only a mere \$1,000! Forex brokers can offer these low margin requirements because currency doesn’t move with the same magnitude as stocks, especially in a short time, but the large leverage ratio does make currency trading very risky if all the margin is used. Leverage Ratio = 1/Margin Percentage = 100/Margin Percentage

### Example — Calculating the Leverage Ratio from the Margin Percentage

Most stock brokers require at least a 50% initial margin , therefore: Leverage Ratio = 1 / 0.5 = 2 In other words, you can buy twice as many stocks using maximum margin than you can without using margin. Your investment is leveraged for greater profits or greater losses. Margin ratios are usually much smaller in futures than for stocks, where leverage ratios are typically 10:1, which is equal to a 10% initial margin requirement, but this varies depending on the underlying asset, and whether the trader is a hedger or a speculator—speculators have a slightly higher margin requirement. Forex accounts have an even lower margin requirement, which may vary, depending on the broker. Regular forex accounts typically allow 100:1 ratios, which corresponds to a 1% margin requirement, and the typical ratio for a forex mini-account is 200:1. The rest of this article will discuss using margin for buying or shorting stocks. More information about using margin in futures and for forex can be found here:

## Margin Agreement, Initial Margin, Maintenance Margin, Margin Calls, and Restricted Accounts

The most general definition of margin, one that covers both buying and shorting securities, is the ratio of the equity of the account divided by the value of the securities. The equity of the account is simply what is left when the debit balance is paid in full or the shorted stocks have been bought back and returned to the lender. If money is borrowed, then it must be paid back, so the amount borrowed plus the accrued margin interest is a debit to the account; if stocks are sold short, then the shorted stocks must be bought back, so the value of the shorted stocks are a debit to the account.
 Margin = Equity Value of Securities

## Calculating Margin

 Long Margin = Equity Value of Securities
When margin is used as a performance bond to short securities, then equity equals the amount on deposit minus the value of the shorted securities. So if you sold short \$10,000 worth of stock instead of buying stock with your deposit, then your equity will equal the \$15,000 on deposit (\$5,000 deposit + \$10,000 from short sale) minus the value of the shorted security, which is initially the \$10,000 that you sold it for. If the value of the stock rises to \$12,000, then your equity is reduced by \$2,000, because you’re obligated to buy the stock back, so if you closed your position right now, you would pay \$12,000 to buy the stock back and have \$3,000 left in your account (minus transaction costs and dividend payouts). Since shorted securities have to be bought back, the debit balance is equal to the current market value of the shorted securities. Equity = Account ValueValue of Shorted Securities Note that the account value will be decreased by transaction costs and by any dividends that have to be paid out while the stock is borrowed.

### Example — Calculating the Equity of a Short Account

If you deposit \$5,000 and sell 1,000 shares of XYZ stock short for \$10 per share , then there is \$15,000 on deposit in your account, but your equity is still \$15,000 – \$10,000 = \$5,000 , which is, of course, what you initially deposited. If XYZ price rises to \$12 per share , then your equity = \$15,000 – \$12,000 = \$3,000 . If XYZ price drops to \$8 per share , then your equity = \$15,000 – \$8,000 = \$7,000 .
 Short Margin = Equity Value of Shorted Securities
So the only difference in calculating the margin for a purchase and for a short sale is that the equity for a purchase is the account value minus the debit balance whereas for a short sale, the equity is the account value minus the value of the shorted securities. Both the debit balance and the value of the shorted securities are obligations that you eventually have to pay.

### Example—Calculating the Current Margin and Current Equity of a Short Sale.

You open a margin account and deposit \$5,000 . You sell short 1,000 shares XYZ stock for \$10 per share . The proceeds of the sale, \$10,000 , is deposited in your account for a total account value of \$15,000 . Scenario 1 — The stock price declines to \$6 per share , so the 1,000 shares that you sold short is currently worth \$6,000 . Thus:
• your equity = \$15,000 – \$6,000 = \$9,000
• your margin = \$9,000 / \$6,000 = 1.5 = 150%
Thus, this short sale would be profitable if you bought back the shares now to cover your short, for a net profit of \$4,000 minus brokerage commissions and any dividends that had to be paid while the stock was borrowed. Scenario 2 — The stock price rises to \$12.00 per share , which means it will cost you \$12,000 to buy back the shares now.
• your equity = \$15,000 – \$12,000 = \$3,000
• your margin = \$3,000 / \$12,000 = .25 = 25%
Because your current margin is now less than 30%, you will be subjected to a margin call. If you dec >net loss will be \$2,000 plus brokerage commissions and any dividends that had to be paid while the stock was borrowed. Remember that the above formulas and calculations have been simplified by excluding transaction costs, margin interest, and any dividends that have to be paid for shorted stock. These excluded factors reduce the equity in your account.

## Calculating Margin Call Account Values

The margin maintenance requirement requires that the margin ratio always be greater than the margin maintenance requirement. If the margin ratio drops below this, then a margin call will be issued. At what account value will a margin call be issued? First, we consider the use of margin for buying securities. We can derive this formula from the formula for calculating the margin.
1. Margin = (Account Value – Debit) / Account Value
2. Let m = margin ratio; a = account value; d = debit
3. m = (a – d) / a
4. m × a = a – d Multiply both sides by a.
5. m × a – a = -d Subtract a from both sides.
6. a – a × m = d Multiply both sides by -1.
7. a (1 – m) = d Factor out a from the left side.
8. a = d / (1 – m) Divide both sides by (1 – m).
9. Account Value = Debit / (1 – Margin)

### Example – Finding the Account Value That Will Elicit a Margin Call

You deposit \$5,000 and borrow \$5,000 to buy \$10,000 worth of securities . If the maintenance margin requirement is 30% , what is the value of the securities that will cause a margin call to be issued?
1. Account Value = Debit / (1 – Margin)
2. Account Value = \$5,000 / (1 – .30 ) = \$5,000 / .7 = \$7,142.86
Hence, a margin call will be issued if the value of the securities drops below \$7,142.86 . To verify the answer, we’ll plug this account value into the margin formula to see if it comes out to the maintenance margin percentage: Margin = ( \$7,142.86 – \$5,000 ) / \$7,142.86 = \$2,142.86 / \$7,142.86 = 0.30 = 30% Now we determine the formula for calculating the value of securities that will elicit a margin call for shorted stock, which is a slightly different equation:
1. Margin = (Account ValueValue of Shorted Securities) / Value of Shorted Securities
2. Let m = margin ratio; a = account value; and v = value of shorted securities.
3. m = (a – v) / v
4. m * v = a – v Multiply both sides by v.
5. v + m * v = a Add v to both sides.
6. v (1 + m) = a Factor out v from the left side.
7. v = a / (1 + m) Divide both sides by 1 + m.
8. Value of Shorted Securities = Account Value / (1 + Margin)

### Example — Calculating the Margin Call Price of a Shorted Security

You open a margin account and deposit \$5,000. You sell short 1,000 shares XYZ stock for \$10 per share . The proceeds of the sale, \$10,000 , is deposited in your account for a total account value of \$15,000 . The margin maintenance requirement is 30% . Therefore, the margin call value = 15,000 /(1 + .3 ) = 15,000 / 1.3 = \$11,538.46 . This is equal to a price per share of \$11,538 / 1,000 = \$11.54 (rounded) per share. So a margin call will be triggered when the price of the shorted security rises to \$11.54 . To verify, we substitute \$11,538.46 into the margin formula for shorted stock, and find that ( 15,000 – 11,538.46 )/ 11,538.46 = 0.30 = 30% , the margin maintenance requirement. Note that if any dividends were paid out, this would have to be subtracted from the account value.

## Return on Investment

Margin increases the rate of return on investment, if the investment is profitable, but increases losses, if not. Furthermore, transaction costs, margin interest, and any dividend payments for shorted stock subtract from profits but add to losses. Any dividends received from purchased stock will increase profits and reduce losses. For a purchase, the rate of return is determined by the following equation: Rate of Return for a Long Position Formula
 Long Rate of Return = Stock Sale Price+ Dividends Received – Stock Purchase Price– Margin Interest Stock Purchase Price
For instance, if you purchased \$10,000 worth of stock with cash and the stock rises to \$12,000 , then your return on investment is: Rate of Return = ( \$12,000 + 0 – \$10,000 – 0 ) / \$10,000 = \$2,000 / \$10,000 = 20% If instead of paying cash for the stock, you pay \$5,000 cash and use \$5,000 of margin , then your rate of return, ignoring margin interest to simplify things: Rate of Return = \$2,000 / \$5,000 = 40% As you can see, using the maximum amount of margin almost doubles your rate of return if the holding period is short enough to keep margin interest negligible. From this example, you can also clearly see that if the value of the stock decreased by \$2,000 instead of rising, then there would be minus signs in front of the rates of return. Furthermore, margin interest increases potential losses and subtracts from potential profits. To illustrate, if your broker charges 6% annual margin interest and you hold the stock for 1 year, then your broker will charge \$300 of interest for the \$5,000 you borrowed for 1 year. Thus, the rate of return if stock is sold for \$12,000 is: Rate of Return = ( \$12,000 – \$10,000 – \$300 ) / \$5,000 = \$1,700 / \$5,000 = 34% If the stock is sold at a loss for \$8,000 : Rate of Return = ( \$8,000 – \$10,000 – \$300 ) / \$5,000 = -\$2,300 / \$5,000 = -46%. The longer the margin is borrowed, the more margin interest will decrease any potential profits and increase potential losses. Note that the equation for shorted stock would be slightly different, since, as a short seller, you must pay any dividends to the lender of the stock that the lender would have otherwise received, but you do not have to pay margin interest. However, you do have to post an initial margin requirement, which is typically equal to ½ of the value of the shorted stock. Thus, the equation for the rate of return for the short seller is: Rate of Return for a Short Sale Formula
 Short Rate of Return = Stock Sale Price – Dividends Paid– Stock Purchase Price Initial Margin Requirement

## Margin Risks

Using margin is risky. Sometimes stock prices drop so fast, there is no time for margin calls, so the broker is forced to sell margined stock at low prices, potentially devaluing an account to zero or even less! A good example is provided by the credit crisis of 2008. During the week ending October 13, 2008, the average stock price plunged 18%, forcing many investors who bought stock on margin to sell, which was probably a major factor contributing to the steep decline. Consider these examples reported in this New York Times article, Margin Calls Prompt Sales, and Drive Shares Even Lower:
• Aubrey K. McClendon, chief executive of Chesapeake Energy, was forced to sell his entire stake of 33.5 million shares in his company at a price range of \$15 – \$22 per share. In July, the stock price was above \$60 per share.
• Sumner M. Redstone, the chairman of Viacom and CBS, was forced to sell \$400 million worth of shares in his companies to pay down debt.
• One senior wealth management executive reported that people with \$30,000,000 in their brokerage accounts were wiped out in days.
This illustrates the risks of using margin: you may be forced to sell at the very time when stock prices hit bottom! And since other investors will also be forced to sell in the declining market, the market declines even further. When the stock market starts declining, it is best to sell some stock to lock in gains and to pay off margin; otherwise you will be forced to sell low after you bought high.

### Stocks in Margin Accounts Can Lead to Empty Voting and Payment in Lieu of Dividends

There are 2 disadvantages to holding stocks in a margin account, which are often lent out to short sellers: stock borrowers, but not stockholders, can vote shares when the shares are lent out, which leads to what is being called empty voting; and if the stocks pay a dividend, the stockholders actually get — instead of a dividend that may qualify for the favorable tax rate of 0%, 15%, or 20% — a payment in lieu of dividends, which is taxed as ordinary income that may be as high as 37%. See Taxation of Dividends for more information. Worse, the borrowers of the stock, often short-sellers, can vote against the corporation’s interest to put downward pressure on the stock price, so as to increase short-selling profits — thus, voting against the interests of the true stock owners. A possible scenario is for a hedge fund, which frequently profits from short selling, to borrow the shares right before the record date—usually 30 days before the vote, and vote in its own interests. Delaware law, which governs most large companies because they are incorporated in that state, gives voting rights to whomever happens to have the stock on the record date. Often, the beneficial owners of the stock are unaware of the lending, and that their right to vote has been transferred to someone else. Sometimes, because of inadequate accounting, both actual stockholders and the borrowers vote, leading to overvoting, which the New York Stock Exchange had found to be a frequent occurrence in some instances.

### Margin Calls May Force a Stock Sale at the Market Bottom

During the week ending October 13, 2008, the average stock price plunged 18%, forcing many investors who bought stock on margin to sell, which was probably a major factor contributing to the steep decline. For instance, according to the above article, Aubrey K. McClendon, chief executive of Chesapeake Energy, was forced to sell his entire stake of 33.5 million shares in his company at a price range of \$15 – \$22 per share. In July, the stock price was above \$60 per share. Sumner M. Redstone, the chairman of Viacom and CBS, was forced to sell \$400 million of shares in his companies to pay down debt. One senior wealth management executive reported that people with \$30,000,000 in their brokerage accounts were wiped out in days.

This illustrates the risks of using margin: you may be forced to sell at the very time when stock prices hit bottom! And since other investors will also be forced to sell in the declining market, the market declines even further. When the stock market starts declining, it is best to sell some stock to lock in gains and to pay off margin; otherwise you will be forced to sell low after you bought high.

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