Showing posts with label margin-call-example. Show all posts
Showing posts with label margin-call-example. Show all posts

## Margin- Introduction

Margin

Introduction

Writers of naked puts and uncovered calls are considered to be short the stock because of the obligation of the option writer to purchase the underlying equity should the option holder exercise his or her rights. As a result, writers of naked puts and uncovered calls must maintain margin accounts in much the same way that any short seller does. Because of the potential need to purchase stock or close out positions, investors must have sufficient collateral in their accounts (in the form of capital and/or equities) to ensure that such obligations can be met. For writers of naked puts and uncovered calls, the collateral required is the greater of:

or

The OTM amount in the first formula is the amount by which the option is out of the money. For puts this is defined as the amount by which the stock price exceeds the strike price. For calls this is defined as the amount by which the strike price exceeds the stock price. By regulation, this collateral must be maintained in a margin account, and for that reason it is often referred to as the margin required.

Examples

In late May 1999, XYZ Corporation is at \$53.375, and you write a January 2001 LEAP put with strike price \$55. The stock pays no dividend and has a volatility of 0.35. The risk-free interest rate is 6 percent. Based on this, the initial margin requirement for this slightly in-the-money option is calculated as 0.20 × \$53.375 × 100 + \$8.28 × 100, or \$1,895.50. (Note that 10 percent of the stock price plus the premium would only be \$533.75 + \$828, or \$1,361.75.)

Suppose, six months later, that XYZ's stock has moved up to \$58.50 a share. With 14 months to expiration, the premium for that option will have fallen to \$5.46. The current margin requirement for this option is 0.20 × \$58.50 × 100 - (\$58.50 - \$55) × 100 + \$5.46 × 100, or \$1,366 (10 percent of the stock price plus premium would only be \$585 + \$546, or \$1,131).

Further suppose, six months later, that XYZ's stock has moved up to \$62.75 a share. With just eight months to expiration, the premium for that option will now have fallen to just \$2.87. The margin requirement for this option is now 0.10 × \$62.75 × 100 + \$2.87 × 100, or \$914.50 (the regular formula gives 0.20 × \$62.75 × 100 - (\$62.75 -\$55) × 100 + \$2.87 × 100, or \$767).

Now suppose that, some time after, XYZ's stock zooms to \$150 a share (perhaps due to a buyout offer) and that the premium for that option falls essentially to zero. The margin requirement for this option is now 0.10 × \$150 × 100, or \$1,500. This amount is greater than the \$914.50 margin required when the stock was at \$62.75 and even more than the \$1,320 margin required when the stock was only at \$58.50 a share. The put is getting safer and safer, yet the margin requirement is getting larger and larger!

The reason this paradox occurs is simply that the margin formulas used here were originally developed for uncovered (naked) call options: as the stock price increases, the greater the exposure to the call writer and the greater the margin has to be to ensure the writer's ability to meet his or her obligation (either to purchase the stock or buy back the call). Rather than develop alternative formulas for put options, the regulators simply adopted the same rules for use with puts. If the margin requirement becomes too high because of this quirk, the solution for investors is rather easy: simply buy back the option and close the position.

A full-service brokerage firm that wants your business will often charge just a nominal amount to close out an essentially worthless option under such circumstances. It is in its best interest to do so, for this permits investors to write additional puts and generate further commissions on an immediate basis rather than waiting for the original option to expire. If your broker does not wish to discount the commission under these circumstances, you should consider finding one who does.

Collateral Requirements

The amount of collateral that must be maintained in your account is determined not only by the naked puts and uncovered calls you have written but by the extent to which you have purchased stocks, bonds, and other securities on margin using funds borrowed from the broker to finance some portion of their acquisition. Collateral (margin) requirements for these other types of securities can range from 50 percent for stocks and mutual funds all the way down to just 10 percent for U.S. Treasury obligations. Because the combined value of these assets may decrease, the net equity (market value less borrowings) must meet certain minimum maintenance requirements established by the Federal Reserve Board, the New York Stock Exchange, and the brokerage house itself.

The minimum required maintenance equity on marginable securities is 25 percent of asset value under Rule 431 of the New York Stock Exchange but is usually set at a higher level, such as 30 percent, by most brokerage firms. The net equity in your account must be greater than the sum of the minimum maintenance equity on the marginable securities and the required margin on the naked puts, uncovered calls, and any other margined transactions (such as short sales, with their margin of 150 percent of the short sale value—a figure set high enough to guarantee replacement of the borrowed securities and payment of interim dividends). For example, suppose your account has \$100,000 in marginable stocks and mutual funds and that the required margin for the puts you wrote is \$25,000. How much can you borrow against your equity if the house rules require a minimum maintenance of 30 percent?

If B is the amount borrowed, the remaining equity will be \$100,000 - B. This figure must not fall below the sum of the \$25,000 option margin plus 30 percent of the \$100,000 market value; that is:

This shows that the maximum value that can be borrowed is \$45,000. It would be dangerous to borrow that much (or anywhere near that amount), because any decrease in equity value or increase in required option margin would instantly invoke a margin call, requiring the investor either to sell securities or to deposit enough cash or securities into his or her account to bring the account into balance. This is unfortunately exactly what happened to Victor Niederhoffer, who had bet the wrong way on an unbelievable number of currency and index options on the fateful day in October 1987 when the Dow Jones Industrial Average fell 554 points in a single session and he received an additional collateral call of \$45 million or so (which he did not have).

His autobiography, Education of a Speculator, published in early 1996 by John Wiley & Sons, is worthwhile reading. All brokers produce a daily margin report for each client maintaining a margin account, showing security by security and option by option the margin requirement for each item and how the combined amounts stand in relation to overall limits independently imposed by the brokerage house and Rule 431 of the New York Stock Exchange. Most reports will also show when the net equity falls below the internal warning level of 50 percent specified by Regulation T of the Federal Reserve Board.

Who Can Deal in Options?

There is much confusion as to which investors can utilize options as part of their investment programs. Fiduciaries (those administrating funds on behalf of others) are bound by the prudent-man rule of common law as well as by that of ERISA (Employees Retirement Income Security Act) for retirement accounts. Selling puts seems to meet the standard of the prudent-man rule in that the use of such a mechanism does not in and of itself violate the prudent-man rule. There are no legal restrictions on the use of options by persons investing for themselves in nonretirement accounts; in this situation, limitations placed on options activity are matters between the investor and the broker(s) involved.

The prudent-man restrictions of ERISA do not apply to self-administered pension, retirement, and profit-sharing plans covering a single employee (or the employee and his or her spouse). The reasoning behind this exemption is that as long as the individual is making his or her own investment decisions, it is not the government's place to restrict the level of risk or the investment activities involved, however speculative they may be. The reason there is confusion about this is because such a laissez-faire philosophy was not always the case. Prior to the enactment of ERISA in 1974, the Internal Revenue Service took the position that no security in a pension plan could be purchased at a price that exceeded the market price at the time of purchase. That would certainly seem to inhibit the writing of naked puts, because any assignment that took place would by definition involve the purchase of stock at (strike) prices greater than the market value whenever exercised.

The word inhibit rather than prohibit is used here because, in theory, if the investor was nimble enough, an in-the-money put could be bought back and the position closed prior to the option being exercised, thereby circumventing such an occurrence. In addition, Section 4975 of the Internal Revenue Code prohibits certain account holders from borrowing funds or using their funds as security for loans. This has been interpreted by some to mean that pension, retirement, and profit-sharing accounts cannot be margined or have the contingent liability of a stock purchase imposed by a naked put or uncovered call. This is not the case, however. What it comes down to is the fact that it is the brokerage houses, which serve as custodians for IRAs, SEPs, Keoghs, 401(k)s, and the like, that determine the extent to which options may be utilized as part of an individual's investment strategy.

Some firms are so conservative that they discourage purchasing calls, protective puts, or even the sale of covered calls—even though a margin account is not needed to conduct any of these option activities. Some brokerage houses will not permit retirement accounts to purchase calls or protective puts, limiting option transactions to the selling of covered calls alone. Even if option activities are permitted by the house rules, bear in mind that individual brokers may discourage such activities simply because of their unfamiliarity with, and lack of experience in, doing options. Many brokerage firms do, however, extend margin privileges to pension, retirement, and profit-sharing plans so they can participate in a wider range of option activities, including the sale of naked puts.

In such instances, the range and scope of option activities that brokerage houses permit depend on the experience, account balance, and investment objectives of the account holden Establish Your Comfort Zone To allow for day-to-day fluctuations in the market, and even modest corrections in stock prices along the way, you will want to maintain enough collateral in your brokerage account to avoid virtually any threat of a margin call. How much more collateral to have on hand in relation to the maintenance requirements depends on the premium yield rate desired and the corresponding comfort zone.

By the premium yield rate, I mean the dollars received in premiums from the sale of LEAP puts each year as a fraction of your overall portfolio account. Premium yield is maximized when collateral is equal to the minimum margin requirement.To get some idea of what this might be, let's determine the margin requirements associated with the receipt of each \$10,000 worth of LEAP put premiums. We see that for a stock price of \$100 a share, premiums for a European-style at-the-money LEAP put for a stock with a midlevel volatility of 0.30 range from \$8.892 to \$11.322 per share (\$889 to \$1,132 per contract) for times to expiration ranging from 12 to 30 months, respectively.

For American-style at-the money LEAP puts, Shows the premiums ranging from \$9.547 to \$13.276 (\$955 to \$1,328 per contract). On this basis, we can adopt a conservative figure of \$1,000 in premiums per contract for every \$100 in stock price. Thus \$10,000 in premiums would be the amount received if we sold at-the-money LEAP puts on 10 contracts of a \$100 stock. The aggregate stock price on these ten 100-share lots is 10 × 100 × \$100, or \$100,000. Because the margin requirement on at-the-money options is 20 percent of the stock price (plus option premium), you would need \$20,000 in cash and equities in your account to generate the \$10,000 in premiums. The premiums so received would have to be retained in your account as additional margin (but of course could be used to acquire more stock).

If the average time to expiration was 18 months, the annualized premium yield would be \$10,000 ÷ (\$20,000 × 1.5), or 33.3 percent per year. It would be foolish, of course, to sell anywhere near the number of options permitted by the margin requirements. As a practical matter, I would want to have at least three or four times the equity called for under the margin requirements in my account, or perhaps \$60,000 to \$80,000 in the situation described. Under these circumstances, the annualized premium yield would thus be \$10,000 ÷ (\$70,000 × 1.5), or roughly 10 percent per year. I have found that generating premiums equal to 10 percent of one's portfolio value is a readily achievable, conservative policy. When combined with dividends and capital appreciation, it can mean a substantial difference in the overall growth of an investor's portfolio.

Earthquakes Happen

Historically, there have been days when the bottom seemed to drop out of the market. Whether triggered by a sudden collapse of a foreign stock market, an unexpected increase in interest rates, or other causes, these crashes can result in domestic stock markets falling 10 or 15 percent during the course of a day or week. On October 19, 1987, the market fell a record 22.6 percent in a single trading session, and a substantial number of investors who were short puts with expiration dates not far away were impacted significantly. Because the market recovered within 18 months, had the same investors been short LEAP puts with expiration dates up to 30 months away, the financial impact would have been significantly lessened.

Events such as these, when they do occur, have a threefold impact on your portfolio. To start with, the value of your equity portfolio will likely decrease in the same proportion as the overall market. In addition to this, a great many of your short put positions may move from being out of the money to being in the money. And because of the manner in which margin is computed, the collateral requirements to maintain those short put positions may increase significantly (as they did for trader Niederhoffer). In a worst-case scenario, your required margin could move from the minimum level of 10 percent to the maximum level of 20 percent of the value of the underlying equities. Such an occurrence could in principle trigger a margin call for additional collateral for very aggressive investors overpositioned with far too many short puts.

When this happens, I have always used the opportunity to make additional money while reducing the risk of eventual assignment. In most instances, market drops reflect oversold situations which are temporary in nature. When this happens, I immediately take advantage of the situation not only by rolling the puts that have gone into the money out and down, but also by increasing the number of contracts. Let's go back to our previous example in which, in May of 1999, XYZ Corporation is at \$53.375 and you write a January 2001 LEAP put with strike price \$55 and receive a premium of \$8.28.  The reason you confidently entered this transaction was because the company earned \$2.50 a share and earnings were projected to increase to between \$2.90 and \$3 in one year.

As calculated earlier, the initial margin requirement for this option(based on 20 percent of the stock price plus the premium) is \$1,895.50. One year later, earnings are \$2.94 and XYZ moves up to \$62.75 a share. The premium for that option has fallen to \$2.87, for which the margin requirement for this option (based on 10 percent plus premium) falls to just \$914.50. Earnings are projected to go to \$3.40 to\$3.50 one year after that. Now suppose that shortly after that, the market falls a whopping 15 percent, with the stock price dropping to \$53.375, thus wiping out an entire year's gain overnight. With eight months to expiration, the premium jumps to \$6.03, with a corresponding margin requirement of 0.20 × \$53.375 × 100 + \$603, or \$1,670.50, more than 1.8 times what it was the day before.

Although you have taken a conservative approach to put writing, the aggregate impact on your overall margin requirements (because the market break has affected all your put positions in the same way) can be disconcerting. To compound matters, this option, like many of your other options, is now in the money, and early exercise at \$55 a share is a potential threat. In situations such as this, the idea is to take advantage of the temporary slump and not only roll out the option, but also consider increasing the number of contracts involved. You therefore buy back the option for \$603 a contract and sell one or more LEAP puts on XYZ with expiration dates 20 months away (because the current LEAP put expires in eight months, there will be one that expires in 20 months; two months must pass before LEAPS with 30-month expiration dates will open).

You can be aggressive and write a LEAP put with the same strike price of \$55, write a slightly out-of-the-money LEAP put with strike \$50, or be conservative and write a LEAP put with strike \$45. For a strike price of \$55, the premium will be \$8.28, for which the margin requirement will be \$1,895.50. For a strike price of \$50, the premium will be \$5.83, for which the margin requirement will be 0.20 × \$53.375 × 100 - (\$53.375 - \$50) × 100 + \$583, or \$1,313. For a strike price of \$45, the premium will be \$3.84, for which the margin requirement will be 0.10 × \$53.375 × 100 + \$384, or \$917.75. The appropriate decision here depends very much on how critical it is to maintain your margin requirements.

If you are still well within your margin limit, you could keep the \$55 strike price, thus pocketing a net premium of \$828 less \$603, or \$225 per contract, with overall margin increasing from \$1,670 to \$1,895. If margin maintenance is of some concern, you could sell five contracts with a strike price of \$50 for every four you buy back, thus essentially breaking even on the transaction after paying commissions while slightly decreasing margin requirements (\$1,670 margin on each of four contracts is \$6,680, and \$1,313 margin on each of five contracts is \$6,565). If margin requirements are of great concern, you might sell three contracts with a strike price of \$45 for every two you buy back, thus incurring a very small premium shortfall while significantly decreasing margin requirements (\$1,670 margin on each of two contracts is \$3,340, and \$918 margin on each of three contracts is \$2,754 ).

Another thing you should consider doing, if reducing margin becomes important, is to close out positions whose premiums have become relatively small. Even in a general market pullback or serious contraction, there will likely be issues still so far out of the money that the associated premiums are negligible. Consider the example of the XYZ Corporation stock that went from \$53.375 to \$150 in a little over a year and that has now perhaps backed off to \$100. With a strike price of \$55, the premium is essentially zero, yet the margin required to maintain this position is \$1,000 per contract (i.e., 10 percent of \$10,000). As previously indicated, many brokers will gladly work with their customers in such circumstances and charge a minimum commission to close out such positions.

Covered Put Writing

As stated before, margin is required for writing naked puts and uncovered calls. Investors seeking to increase portfolio income routinely use covered calls to do so. A covered call means the investor writes a call while also owning the stock. This is sometimes referred to as a buy-write if the investor writes the call while simultaneously purchasing the stock. In practice, there is no difference between a buy-write and selling a covered call. In either instance, there is no margin requirement, and the potential for unlimited exposure should there be a sharp rise in the price of the underlying equity is thereby eliminated. Does the same sort of thing happen if an investor resorts to covered put writing?

First of all, exactly what does it mean to write a covered put? Incredibly enough, there is no universal agreement as to what is meant by this expression. The latest edition of Understanding Stock Options (April 1996), published by the Options Industry Council (a trade organization composed of the various options exchanges and the Options Clearing Corporation), states that a ''put writer is considered to be uncovered if he does not have a corresponding short stock position or has not deposited cash equal to the exercise value of the put.'' The latest edition of Characteristics and Risks of Standardized Options (February 1994), published by the Options Clearing Corporation, does not use the term covered put as such but refers only to writers of cash-secured puts.

In the latest (ninth edition) and earlier editions of the Pass Trak® Series 7, General Securities Representative, published by Dearborn Financial Publishing, Inc., a naked (or uncovered) option is defined as "the position of an options investor who writes a call or a put on a security he does not own." An insert in the ninth edition expanded this definition, stating that "in a cash account, a put is covered and the writer is not required to meet option margin requirements if she deposits into the account or presents: cash equal to the aggregate exercise price of the put; an escrow agreement in which a bank certifies that it holds on deposit for the writer funds equal to the aggregate exercise price of the put; or money market securities with a current market value equal to or greater than the aggregate exercise price of the put."

As a result, there are people who believe a covered put writer is one who: (a) is long (owns) the stock; (b) is short the stock; or (c) has cash or cash-equivalent funds in an amount equal to the aggregate exercise price of the put. The correct answer, however, is (b) or (c) in a margin account and (c) in a cash account. Because we are going to be selling puts in a margin account, let's compare the relative risks and rewards of writing uncovered puts versus covered ones, wherein the investor is short the stock. Interestingly, writing a put while simultaneously short the stock can be more risky than writing a naked put.

To understand why, remember that when you write a naked put, the theoretical worst-case situation is where the stock plummets to zero for a net loss equal to the exercise price less the premium received. Should the price of the stock increase, the gain is the premium received. Now suppose you write a put and are simultaneously short the stock. In this situation, the investor is completely protected if the price collapses because any loss on the option as the price of the stock moves below the exercise price is matched dollar for dollar by the gain incurred on the shorted stock. On the other hand, should the price of the stock increase, the potential for loss increases without limit because the unlimited liability on the upside of the short position is mitigated only by the premium received from the sale of the put.

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