Understanding Margin Requirements

When implementing strategies for mutliple periods, it can be useful to consider leverage in margin accounts, where the leverage is accessed through a margin loan from the broker. With most brokers, a margin loan is available through Regulation T Margin for most investors or Portfolio Margin above a certain net worth. The potential benefits of using leverage are explored through lifecycle investing and, if used correctly, present the opportunity to decrease the overall risk during accumulation. As an alternative to margin loans, box spreads are mentioned which make it possible to borrow directly from the market instead of a broker. However, it is a perfectly acceptable and rational choice to avoid the possible disaster from leverage and simply perform regular contributions without further complications.

Brief Margin Overview

Buying on margin allows an investor to use their portfolio as collateral for a margin loan from their broker, where the margin loan then incurs interest paid by the investor on a daily basis. As regulated by the Federal Reserve through Regulation T, there are sets the rules for margin requirements. There is an initial margin requirement, which represents the requirements for margin at the time an order is placed, and there is a maintenance margin requirement, which represents the minimum amount of equity needed for the position to remain open (before a margin call is initiated). In most cases, the initial margin is at least 50%, while the maintenance margin is at least 25% (could be higher depending on the portfolio). Before considering the margin requirements, it is useful to consider the proportion of the margin loan relative to the portfolio value. This proportion is simply equal to the quotient of the margin loan and portfolio value. Subsequently, the difference between the portfolio value and margin loan can be considered relative to the portfolio value. This difference between the portfolio value and margin loan can be seen as the balance of the account. So, the percentage for the margin requirement is defined as the quotient of the balance of the account to the portfolio value. The initial margin is often quoted as being 50%, which can be either interpreted as the margin loan not exceeding 50% of the portfolio value or as the balance of the account not exceeding 50% of the portfolio value. The maintenance margin is often quoted as being 25%, which can be either interpreted as the margin loan not exceeding 75% of the portfolio value or as the balance of the account not exceeding 25% of the portfolio value. Starting at an initial margin of 50% with leverage of 2:1, a drawdown of 33.3% can be ...withstood... before a maintenance margin of 25% is realised and, at this point, the portfolio will be leveraged at 4:1 and will initiate a margin call if the drawdown continues. Contributed = 50 Loan = 50 Portfolio = Contributed + Loan = 100 Margin Proportion = Loan / Portfolio = 50% Balance Proportion = (Portfolio - Loan) / Portfolio = 50% 33.3% Drawdown > Portfolio = 66.7 Margin Proportion = Loan / Portfolio = 50 / 66.7 = 75% Balance Proportion = (Portfolio - Loan) / Portfolio = 25% Actual Value = Balance Proportion * Portfolio = Portfolio - Loan Leverage = 1 / Balance Proportion = Portfolio / (Portfolio - Loan) Balance Proportion = Maintenance Margin --> Margin Call Balance Proportion = (Initial Portfolio x (1 + Drawdown) - Loan) / (Initial Portfolio x (1 + Drawdown)) Graph: Y = (1 + Z * X) / (Z + Z * X) with X = Drawdown, Z = Initial Leverage, Y = Balance Proportion (X must be negative). This has X as positive: https://www.desmos.com/calculator/cdx17jzasi It should be noted that the portfolio value is defined to be equal to the sum of the value of the shares in the portfolio (excludes cash holdings). In some instances, the equity with loan value may refer to the difference between the portfolio value and margin loan (actual or net value of the portfolio), such that it must be greater than the product of the initial margin and portfolio value for an order to be placed or greater than the product of the maintenance margin and portfolio value for a position to remain open - in other words, the actual or net value of portfolio (including the margin loan) must not decrease below 50% or 25% of the portfolio value (excluding the margin loan). Accordingly, the available funds may refer to the difference between the equity with loan and product of the initial margin and portfolio value, while the excess liquidity may refer to the difference between the equity with loan and product of the maintenance margin and portfolio value - it should be emphasised that these values are dynamic and will change as the portfolio value changes, but the available funds must be positive for an order to be placed and excess liquidity must be positive for a position to remain open. The margin requirement limits usually restrict investors from reaching higher leveraged positions, so leveraged ETFs and options are typically used for investors who are seeking more leverage, although this is definitely not recommended for most investors.

Portfolio Margin Accounts

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Box Spreads With Options

In general, an option contract is an agreement between a buyer and seller which gives the purchaser of the option the right to buy or sell a particular asset at a specified future date at an agreed upon price - known as the strike price. In the case of a call option, the purchaser has the right (but not the obligation) to buy the asset, while the seller or writer has the obligation to sell the asset at the strike price if the contract is exercised. In the case of a put option, the purchaser has the right (but not the obligation) to sell the asset, while the seller or writer has the obligation to buy the asset at the strike price if the contract is exercised. The option will be bought or sold at a price (difference between this price and the strike price can be seen as the premium for the rights provided by the option) and usually with a multiplier for the number of shares in each unit of the transactions.

A box spread is the combination of a synthetic long position coupled with an offsetting synthetic short position through a combination of options on an equity security or equity index at the same expiration date. The synthetic long position conventionally consists of buying a call option and selling a put option on the same security or index, where the call option and put option share the same strike and expiration date. The synthetic short position conventionally consists of buying a put option and selling a call option on the same security or index, where the put option and call option share the same strike (different from the synthetic long position) and expiration date (same as the synthetic long position). When constructing a box spread (and assuming positive interest rates in a rational market), the synthetic long position will have a strike price which is less than the strike price for the synthetic short. The difference between the strike prices of the synthetic long position and synthetic short position will determine the expiration value or value at maturity of the box spread. An important feature of constructing a box spread is the elimination of risk associated with the underlying security or index. As a result, the return from the box spread remains constant no matter the movements in the price of the underlying security or index. When buying or holding a long position with a box spread, it is a mechanism to lend to the market through options instead of lending through a bond. When selling or holding a short position with a box spread, it is a mechanism to borrow from the market through options instead of borrowing from a broker (inverted order of buying and selling call options and put options).

...Plot... of the option contracts which make up a box spread (often referred to as legs):

Before continuing, it should be emphasized that a box spread cannot be easily reversed and special caution must always be taken when creating a box spread. In a way, a box spread can be seen as re-financing a margin loan, as it is usually possible to get a better effective interest rate than the interest rate offered by brokers through margin loans. This effective interest rate is typically equal to a benchmark interest rate plus 0.30% to 0.75% depending on the liquidity and amount being borrowed. From a margin perspective, the loan is still secured against the securities within the account, such that the same rules for leverage and maintenance apply as set out by the broker.

Effectively, when used for borrowing, a cash position will be received upfront once the box spread is filled and this will be repaid on the specified expiration date with a premium. It should be acknowledged that the effective interest rate is actually resulting from the difference between the strike prices of the synthetic long position and synthetic short position and, in this way, it is fixed for the duration of the options. In reality, this is not actually a transfer of cash, but the result is a cash position which needs to be repaid at the expiration date with a premium. Basically, the difference between the cash position received upfront and amount which needs to be repaid at the expiration date is the effective interest of the options when viewed as a loan.

So, to borrow from the market by selling or holding a short position with a box spread, the structure involves buying a put option and selling a call option at the lower strike price and buying a call option and selling a put option at the higher strike price (alternatively, it is also possible to buy a shorted box spread). A limit price is then set at which the order for the box spread and underlying options will be placed. The product between the limit price and multiplier for the contracts will form the cash position received upfront once the box spread is filled. The product between the difference between the strike prices and multiplier for the contracts will form the amount which needs to be repaid back at the expiration date. As the box spread is constructed as a single order, it can only be executed as a simultaneous trade with all of the options being accepted together. Most brokers will give an indication of net credit or debt, where credit is required to borrow money and debit is required to lend money. After execution, the cash position will be available with the options positions which have a net negative value equal to the total amount which needs to be repaid back at the expiration date.

This idea demonstrates that a box spread is akin to a zero-coupon bond (or loan only with a balloon payment) which does not pay periodic coupons but trades at a discount to its face value. The value at maturity of a zero-coupon bond is then comparable to the difference between the strike prices of the box spread, while the maturity date of a zero-coupon bond is then comparable to the expiration date of the box spread. As mentioned, when buying or selling a box spread, the buyer or seller generally expects the price of the box spread to be less than the difference between the strike prices, such that the buyer or seller will earn a profit or loss equal to the difference between the beginning price (as the cash paid if bought or cash received if sold) and ending price (expiration value as a profit received if bought or loss paid if sold).

Equations for calculating effective interest rate (APR).

As a simple example of buying or holding a long position with a box spread, the box spread would include the simultaneous purchase of a call option and sale of a put option with a strike of $1,000 on the S&P 500 Index (synthetic long position) with the simultaneous sale of a call option and purchase of a put option with a strike of $2,000 on the S&P 500 Index (synthetic short position), where all of these options share the same expiration date at 3 months and expiration value would equal the difference between the strike prices at $1,000. The expected profit realized would equal the sum of the price at which this box spread was bought at -$995 and expiration value of $1,000 to give $5 (minus transaction costs associated with the trades). Annualizing the profit over the price, the effective interest rate on each would be ...%. As a simple example of selling or holding a short position with a box spread, the box spread would include the simultaneous sale of a call option and purchase of a put option with a strike of $1,000 on the S&P 500 Index (inverted synthetic long position) with the simultaneous purchase of a call option and sale of a put option with a strike of $2,000 on the S&P 500 Index (inverted synthetic short position), where all of these options share the same expiration date at 3 months and expiration value would equal the difference between the strike prices at -$1,000. The expected loss realized would equal the sum of the price at which this box spread was sold at $995 and expiration value of -$1,000 to give -$5 (minus transaction costs associated with the trades). Annualizing the loss over the price, the effective interest rate on each would be ...%.

Example of the trades in orders placed to sell or hold a short position with a box spread: +------------+------------+--------------+---------------+-------------------+------------------+------------+----------+----------------+------------------+-----------------+--------+-----------------------+ | Trade Date | Expiry Date| Lower Strike | Higher Strike | Short Call Spread | Short Put Spread | Multiplier | Quantity | days to expiry | Short Box Spread | Value At Expiry | PV | Implied Interest Rate | +------------+------------+--------------+---------------+-------------------+------------------+------------+----------+----------------+------------------+-----------------+--------+-----------------------+ | 2021-08-30 | 2023-06-16 | 4,450 | 4,650 | $113.5 | 84.5 | 100 | 1 | 655 | $198 | $200 | $2.00 | 0.56% | | 2021-05-27 | 2022-12-16 | 4,100 | 4,300 | $115.0 | 83.0 | 100 | 1 | 568 | $198 | $200 | $2.03 | 0.66% | | 2021-04-16 | 2022-12-16 | 4,050 | 4,250 | $114.5 | 83.6 | 100 | 1 | 609 | $198 | $200 | $1.83 | 0.55% | | 2021-02-09 | 2022-12-16 | 3,700 | 3,900 | $118.5 | 79.5 | 100 | 1 | 675 | $198 | $200 | $2.03 | 0.55% | | 2020-12-17 | 2022-12-16 | 3,600 | 3,800 | $111.5 | 85.8 | 100 | 1 | 729 | $197 | $200 | $2.73 | 0.69% | | 2020-11-13 | 2022-06-17 | 3,450 | 3,650 | $112.7 | 83.7 | 100 | 1 | 581 | $196 | $200 | $3.53 | 1.13% | | 2020-07-29 | 2021-12-17 | 3,150 | 3,350 | $114.2 | 83.8 | 100 | 3 | 506 | $198 | $200 | $2.03 | 0.74% | | 2020-06-15 | 2021-12-17 | 2,900 | 3,100 | $113.8 | 83.9 | 100 | 3 | 550 | $198 | $200 | $2.28 | 0.76% | | 2020-03-11 | 2021-06-18 | 2,700 | 2,900 | $105.9 | 92.2 | 100 | 9 | 464 | $198 | $200 | $1.88 | 0.75% | +------------+------------+--------------+---------------+-------------------+------------------+------------+----------+----------------+------------------+-----------------+--------+-----------------------+

With additional emphasis, this should only ever be performed with cash-settled European-style options, as these cannot be exercised, terminated, or assigned before the expiration date. If American-style options are used, it is possible for the individuals options to be exercised, terminated, or assigned at any time before the expiration date which will unbalance the box spread. It is most common and reliable for the options to be implemented using an equity index (which are only ever cash-settled European options), with the most commonly used index being SPX for the S&P 500 in USD. For other currencies, the relevant indices to consider are the ESTX 50 (OESX) in EUR, FTSE 100 (OTUK) in GBP, SMI (OSMI) in CHF, and ... in JPY. It should be noted that the multiplier may be different depending on the index.

For reference, a benchmark interest rate can typically be taken to be the interest rate on the corresponding bonds of a comparable term issued by the government of the respective currency. For example, the benchmark interest rate for SPX can be assumed to be the yield for federal bonds issued by the United States relative to the duration of the options. Similarly, the benchmark interest rate for ESTX50 can be assumed to be the yield for stability bonds issued by Eurozone States relative to the durations of the options. It should also be kept in mind that a margin loan will typically be related to this benchmark interest rate plus an additional charge from the broker, but the interest rate will be variable for a margin loan but fixed for a box spread. BoxTrades is a useful tool for seeing the yield curve from previous transactions, setting up a box spread, and calculating the effective interest rate.

Example screenshot of the yield curve from historic transactions shown on BoxTrades:

An additional benefit of box spreads over other loans is that the interest may appear as a capital gains and losses on the options. Thus, depending on local regulations, it may qualify to be treated directly as capital gains with regard to tax. (Although, caution should be applied to the expiration date, as the gains and losses may be divided between the synthetic long position and synthetic short position, where it may be the case that the synthetic long position is taxed in the year it closes, while the synthetic short position is taxed in the year it settles (with settlement usually taking 2 business days), such that expiration near the last days of the tax year should be avoided).

However, there may be a concern around box spreads, where the margin requirements for the box spread may change depending on the current state of the market. This is related to the bid-ask spreads and options, where the value of the options will fluctuate with the market even though they will converge to the predictable value on the expiration date (especially wild when the market is closed). Although these values are not accurate, there is a chance that the algorithm used by the broker to evaluate margin calls is accidentally triggered. Likewise, during a market drawdown, the Options Clearing Corporation may increase margin requirements which may prompt brokers to increase the margin requirements for accounts. In practical terms, this will affect most portfolios which have high levels of leverage, although it is less of a concern for portfolios with low levels of leverage. Because of this, box spreads should only be used in an account with portfolio margin.

Summarized Conclusions

... . With box spreads, it should be emphasised that they cannot be easily reversed and special caution must be taken when creating them. It may be possible to enter an opposing box spread to balance a mistake, but there are no guarantees that an equivalent effective interest rate will be available (loss from a possible mistake can be many times more than the marginal potential gain from using a box spread). It is a perfectly acceptable and rational choice to avoid the possible disaster from a mistake and simply use a margin loan without further complications. Above all, this is only applicable if it is even decided to use leverage - it is also a perfectly acceptable and rational choice to avoid the possible disaster from leverage and simply perform regular contributions without further complications.