Margin

Margin is the use of borrowed funds in brokerage accounts to buy securities using the securities as collateral. Like any loan, the borrower must pay interest while the loan is outstanding, and must eventually pay the loan back.

In the early years of stock exchanges, there were no legal minimum margin requirements. Indeed, during the 1920s, margin requirements were 10% or even less, leading to a highly inflated stock market that eventually crashed in 1929. Many people and businesses were wiped out because they were unable to pay for their stock, causing the bankruptcies of many others. This contagion spread throughout the economy, precipitating the Great Depression. Although many new financial regulations were passed in the 1930s, it was not until 1945 that the United States Federal Reserve instituted minimum margin requirements. Later, stock exchanges and even brokerages also set their own minimum requirements, although their requirements cannot be lower than the Federal Reserve requirement, since the Federal Reserve has national authority over the regulation of margin requirements.

The interest on the borrowed funds—margin interest—is slightly higher than the prime rate that banks charge to their best customers. To use margin, the customer must open a margin account with a broker, and the money is borrowed from the broker. The interest rate charged by the broker will depend on how much the broker pays its bank for the money—called the brokers rate—plus whatever amount the broker decides to add. Typically, brokers have a sliding scale of margin interest that depends on the size of the individual trading account, with larger accounts paying a lower interest rate than smaller accounts.

Margin can also refer to the minimum amount of equity required to insure the performance of an obligation. A common example is the margin needed to short stocks. To sell a stock short, you borrow the shares from a broker, then sell them in the market, with the hope of being able to buy the shares back at a lower price. The proceeds of the stock sale are placed in your brokerage account. Although you are not buying the stocks initially, you will still be required to have a minimum amount of equity in your account before you can short the stock to guarantee that you will be able to buy them back later, even if the price of the stock is higher than the shorted price. You do not have to pay interest nor do you earn any interest on the sale proceeds, because the money is not yours, but is held as security to buy the stock back later.

Similar to the margin requirement to short stocks, the term margin is also used in futures and forex accounts that specify the amount of cash or cash equivalents, such as U.S. Treasuries, that are required to guarantee the performance of the futures or currency contract. In futures, the margin requirement is frequently referred to as a performance bond, because it is not borrowed money, but is a deposit that guarantees the performance of the contract at the time of settlement. A trader pays no interest on the margin in a futures or forex account—in fact, traders can earn interest by depositing U.S. Treasuries in a futures account to cover the margin requirement.

In futures and forex, the margin requirement is often expressed as a leverage ratio, which is inversely related to the margin percentage:

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 of 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

To use margin for trading, you have to open a margin account by signing a margin agreement. The agreement stipulates, among other things, the initial margin requirement as a percentage, and the margin maintenance percentage. Any securities bought in a margin account are held in the broker's street name, and the margin agreement usually gives the broker the right to lend the securities out for a short sale.

Margin trading is governed by the Federal Reserve, and other self-regulatory organizations (SROs), such as the New York Stock Exchange and the FINRA. Regulation T, promulgated by the Federal Reserve, requires that the minimum deposit be $2,000, and that the initial margin percentage be at least 50%.

There is also a minimum maintenance margin requirement of 25%. The exchanges or the brokerages can set stricter requirements than those required by the Federal Reserve if they choose. At most brokerages, the maintenance margin requirement is set higher, usually at 30%.

The margin ratio cannot be less than the maintenance margin rate. If the margin ratio falls below 50%, but remains above the maintenance margin requirement, then the account will be restricted. No additional securities can be bought or sold short in a restricted account, unless the trader deposits additional cash or securities to increase the margin level to at least 50%.

The amount of margin available will depend on the price of the securities. If margin is used to buy securities, then the amount of margin increases with the market value of the securities, but if the margin is used to short securities, then the amount of margin is inversely related to the price of the shorted securities, and vice versa.

If the equity does drop below the maintenance margin requirement, then the broker will issue a margin call, requesting that additional cash or securities be deposited so that the margin ratio of the account is equal to at least 50%. If you do not respond to the margin call, then your broker will sell enough of your securities that were purchased on margin and/or buy back your shorted securities at the market to bring your margin ratio back to the initial margin requirement of 50%.

Margin Trading

The main reason to borrow money to buy securities is for financial leverage. Financial leverage can increase the rate of return for an investment, if it is profitable, but it also increases potential losses. Because of the potential for greater losses, traders become more emotional in their trading decisions, which may cause excessive trading, which increases transaction costs, and it may cause bad trades when emotion overrules reason. Furthermore, the longer the money is borrowed, the greater the amount of margin interest that must be paid, so using margin for buy-and-hold strategies is generally not a good idea.

Another major disadvantage to using margin is that the trader potentially loses some control over the account. If purchased stock drops too much, the broker has the right to sell the stock before notifying the customer. For a short sale, the broker may be forced to buy back the securities in an illiquid market, if the lender wants the securities back.

If the margin ratio increases because purchased securities have increased in value or because shorted securities have decreased in value, then the trader gains excess margin that can be used to purchase or short additional securities. Continually using excess margin to increase investments is called pyramiding. While pyramiding may work for a while, at some point, the equity of the account is going to decline, because stocks don't continually increase in value nor do shorted stocks continually decline in value. Therefore, eventually there will be a margin call. Hence, the use of margin should be restricted to short-term trades.

Calculating Margin

In a long transaction, you borrow money to buy securities, which you are obligated to pay back. Similarly, in a short sale, you sell securities short by borrowing the securities from a broker, then selling them, with the proceeds deposited in your account. But eventually you'll have to buy the securities back to return them to the lending broker, which is why the market value of the shorted securities is considered a debit to your account.

Equity is equal to the total value of cash and securities if all open positions are closed and all financial obligations are satisfied. So if you deposit $5,000 in an account, and borrow $5,000 to buy $10,000 worth of stock, then your equity is initially $5,000 minus transaction costs. Accruing margin interest will also decrease your equity. If the value of the stock declines to $8,000, then your equity is reduced to $3,000 minus costs, because now the stock is worth $8,000, but you are still obligated to pay your broker $5,000 plus interest for the loan, which is your debit balance. Hence, when using margin to borrow money to enter into a long position by buying stocks:

Equity = Account Value – Debit Balance

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 Value – Value 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:

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.

Because your current margin is now less than 30%, you will be subjected to a margin call. If you decide to buy back the shares now to cover your short, your 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 Value - Value 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:

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.

New

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

These articles underscore 2 important disadvantages to holding stocks in a margin account, which are often lent out to short sellers, and if they are:

  1. You cannot vote with your shares, but the borrowers of the stock can, in what is being called empty voting;

  2. and if the stocks pay a dividend, what you actually get instead of a dividend that may qualify for the favorable tax rate of 5% or 15%, is a payment in lieu of dividends, which is taxed as ordinary income that may be as high as 35%.

What's worse, the borrowers of the stock, often short-sellers, can vote in the worse interest of the corporation to try to deflate the stock price, and thereby profit from short selling—thus, voting against the interests of the true owners of the stock.

A possible scenario is for a hedge fund, which frequently profits from short selling, is 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 the state, give voting rights to whomever happens to have the stock on the record date. Often, owners of the stock are unaware of the lending, that their right to vote has been transferred to someone else.

Sometimes, because of inadequate accounting, both actual stockholders, and the borrowers, both vote, leading to overvoting, which the New York Stock Exchange has found to be a frequent occurrence in some instances.

NYSE Warns on Margin Loans - WSJ.com

How Borrowed Shares Swing Company Votes - WSJ.com

Margin Calls May Force a Stock Sale at the Market Bottom

Margin Calls Prompt Sales, and Drive Shares Even Lower

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.