Determining the Value of Shorted Securities That Will Elicit a Margin Call

The formula for calculating the value of securities that will elicit a margin call for shorted stock can be derived from the formula for calculating margin:

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)

Thus, the short account value that will trigger a margin call can be calculated with the following formula:

Calculating the Margin Call Account Value of a Shorted Security

Margin Call Account Value =	Account Value ───────────  1 + MMR	MMR = Margin Maintenance Requirement (usually 30%). Price per Share = Margin Call Account Value/Number of Shares

Example — Calculating the Margin Call Price of a Shorted Security

Using the above example, what market price of the shorted security will trigger a margin call?

The total amount on deposit in the account is $15,000 and 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 above, 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 amount on deposit.

Margin Effects on Return On Investment - ROI

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:

Long Rate of Return = (Stock Sale Price + Dividends Received - Stock Purchase Price - Margin Interest) / Amount Invested

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. Thus, the equation for the rate of return for the short seller is:

Short Rate of Return =

Stock Sale Price - Dividends Paid - Stock Purchase Price ───────────────────────────────────────                                Amount Invested

Margin Agreement, Initial and 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 NASD. 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%.