# Capital Efficiency & Portfolio Margin

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All the views expressed below are the personal views of the author, and are not financial or investment advice.

When trading with derivatives, the allocation of margin plays a key part in both risk management and improving returns. In this article we will discuss how margin requirements are calculated, and how portfolio margin can be used by advanced traders to reduce margin requirements, and improve capital efficiency.

In order to make the most of the below article, you will need to have a decent understanding of how positions, derivatives, as well as leverage and margining work. The linked articles will provide the background knowledge needed, and are therefore recommended reading.

## What is Capital Efficiency?

When it comes to trading or investing, using your capital (the funds you have) efficiently is very important. If you can make the same trade using less capital, then by definition you can make a higher rate of return. In the most basic sense, this is what leverage is, since it allows you to use less capital to control a larger position. Of course, with higher leverage comes a higher risk of liquidation, and the potential loss of your funds. Therefore, while using higher leverage is more efficient, it is also more risky, and therefore this risk has to be balanced with the capital savings.

The less capital that is required for same sized trade, the more capital efficient a trade is. Outside of leverage however, there are other things that affect how efficient a trade is. For instance, entering a position over multiple venues is often more efficient than slamming a large order into one exchange, resulting in huge slippage costs. In our earlier article about Smart Order Routers we demonstrated a technique for doing this. Reducing trading fees is also important, with many large market participants either actively avoiding aggressive orders if possible (to avoid taker fees), or negotiating with exchanges to reduce their fees.

However, the area of focus in this article will be the margining methods that are used by derivatives exchanges to margin positions. As we have discussed before, in order to open a derivative position you need to put up margin. This is a sum of money that is either the full cost of entering the position, or only part of it (in which case you have used leverage). For traders using derivatives, how their positions are margined plays a big part in how efficiently they can trade, since derivatives are often used not by themselves, but as part as of a strategy consisting of two or more products. As we will see, how a position is margined can greatly affect the amount of money a trader needs to put up.

## A Simple Example: Closing Orders

In the article on leverage, we noted that when placing an order, the exchange must lock up enough margin so that if the order fills, the position itself will have enough initial margin not to be liquidated. So for instance, if we wanted to buy a 1 BTC-USD perpetual swap at a price of \$40,000 with 1x leverage, we would need (ignoring fees etc) at least$\frac{\$40,000}{1} = \$40,000$of margin allocated to open that order. If our order were to fill, then the \$40,000 of margin we needed to support that order will be guaranteed to be available.

The above makes sense, but consider the following scenario. Say that our above order fills, and now we are holding a 1 BTC-USD position with an initial margin of \$40,000 because we are fully margined (1x leverage). Say we want to place another limit order, but this time to sell 1 BTC-USD, say at \$41,000. What margin will be required to place this order?

Reflexively, you might think that because we need to make sure we have sufficient capital to margin open orders, we would need to provide \$41,000 worth of margin. You may/may not be surprised to know that actually you do not need to provide any margin at all for this order! The reason for this is that this order is reducing/closing your current long position. Think about it, if your 1 BTC-USD sell order were to execute, what would your position be? In this case you were long 1 BTC-USD, and selling 1 BTC-USD will leave you with a position of 0 (aka flat). A flat position does not need any margin to cover it, and no matter what price you sold at your initial margin will always be able to cover your loss. Indeed, if it was not accounted for this way, a client may find themselves in the strange situation of being able to open a position, but then not able to ever close it! Because traders are not required to put up extra margin for the closing order, this is an example (though a simple one) of increased capital efficiency due to margining. ## Rules Based Margining One of the most common methods of margining positions is known as rules based margining. In such systems, the amount of margin required for a position is based of a set of rules, and each position is viewed in isolation. What this means is, if we have 3 futures positions for different instruments, the margin requirements of each position will be calculated based only on that individual position, and no other. In the US, this is famously known as Regulation T or Reg T for short. After the Great Market Crash of 1929, it was decided that the ability of investors to use margin to trade stocks needed to be curtailed, since it was believed that margin calls had contributed significantly to the event. The Federal Reserve Board established Regulation “T”, which set out a list of rules for the amount of margin (and therefore leverage) that could be provided to investors. Importantly, the amount of initial margin and maintenance margin required to maintain a position was specified. Since 1974, a traditional stock market margin account must provide at least 50% initial margin, and must maintain a maintenance margin level of at least 25%. This means that the highest leverage offered is 2x on such positions. As mentioned, each position must be evaluated separately. Rules based approaches such as this are popular on crypto exchanges because they are simple to understand and implement. Because of their simplicity, they are relatively straightforward to implement from a technology perspective, meaning they are also computationally performant. One issue with rules based methods however, is that they are known to overstate the risk of the position. One of the reasons this occurs is because they look at the risk at a position level, rather than at a portfolio level. Are there perhaps, more capital efficient methods that can be used? ## Risk Based (Portfolio) Margining Margining using rules is simple, but it is also inflexible. Typically, derivatives traders will not hold only one position but a combination of positions. There are a variety of strategies that call for this, such as the famous basis trade using futures, and a plethora of options combos such as spreads, collars and straddles. In finance terminology, a portfolio is a collection of financial instruments such as stocks, bonds, derivatives, crypto, and to be honest anything else valuable. As with the strategies mentioned above, when derivatives positions are combined, the value of the portfolio can behave differently to the individual positions. Because of this fact, exchanges came up with systems that took these interactions into account. Systems such as the Theoretical Intermarket Margining System (TIMS) used by the Options Clearing Corporation, or the Standard Portfolio Analysis of Risk (SPAN) used by the CME, are all examples of “risk based” margining systems. These systems look at the portfolio as a whole, instead of individual positions and are sometimes referred to as portfolio margin systems. Their method of action involves using a variety of market scenarios to estimate what the maximum losses of a portfolio might be. For instance, TIMS works by calculating the theoretical loss on the portfolio under a range of stock price moves between$\pm 15\%$, and choosing the worst outcome as the margin required for the portfolio. While the exact mechanisms used by these systems are extensive, we will cover some of the basics below. In our case, we are going to refer to whatever holdings we have on a crypto exchange to be our “portfolio”. For instance, consider the following portfolio: instrumenttypequantityleverageentry price (USD)mark price (USD) USDCSpot10,000--- BTCUSD-240422Future1.5541,00043,000 BTCUSD-240522Future-1.0542,00044,000 Our portfolio holds 3 instruments. One (spot) currency, and two derivatives positions. The first position is a long BTCUSD April future, while the second is a short BTCUSD May future (the negative on the quantity implies that it is short). Because of basis, the price of the longer dated future (May) is higher than the shorter dated future (April) as the market is currently in contango. Both futures also are using 5x leverage, and we assume the entire account (and therefore portfolio) is on cross margin. Under the rules based system described earlier, what are our margin requirements? We don’t need any margin for the spot currencies, as they are not borrowed and have no leverage. The two futures however, are on 5x leverage so will need initial margin. $$IM = \frac{\text{abs}(1.5) \times \41,000}{5} + \frac{\text{abs}(-1.0) \times \42,000}{5} = \20,700$$ Notice that we treat the long and the short position exactly the same when it comes to calculating margin. In a rules based system this means that we are paying the initial margin on both derivatives. ### Delta Hedging In derivatives, the concept of Delta ($\Delta$) is defined as follows: Delta (Δ) is a risk metric that estimates the change in price of a derivative, such as an options contract, given a$1 change in its underlying security.

In short, it is a metric that represents how the price of a finanical instrument behaves when the price of its underlying changes. For instance, in the case of the above April BTCUSD future, the underlying will be the Bitcoin spot price. In reality however, most exchanges will use an index in order to get a fair (and also less likely to be manipulated) price to mark their derivatives.

Futures (which we will be using as an example) fall into a class of products known as delta one. The name comes from the fact that their delta is always 1. Given the above defintion, it means that if the price of Bitcoin goes up one dollar, the price of the future should also go up be one dollar, and the same in any size and direction. Options however, are not delta one because their delta can vary over time as well as in response to other factors such as volatility, rates, etc.

In our case, we have two futures with two different maturity dates, but crucially, the same underlying (the Bitcoin spot index). We can get the profit of the futures we hold by valuing them at their mark price. Right now, the PnL (profit and loss) of our portfolio is:

$$V_{p} = \sum{Q_{x}(M_{x} - E_{x})}$$ $$V_{p} = 1.5 \times (\43,000 - \41,000) - 1.0 \times (\44,000 - \42,000) = \1,000$$

Where $Q_{x}$ is the quantity of contract $x$, and $M_{x}$ and $E_{x}$ are the mark and entry price of the positions respectively. So our portfolio is slightly profitable. Because these products are futures, we can model the mark price (approximately) as:

$$M_{x} = I_{BTC} + B_{x}$$

Where $x$ is the future in question, $I_{BTC}$ is the price of the bitcoin index, and $B_{x}$ is the basis for that specific future. The basis will differ between contracts, but typically less than a contract can vary in absolute price. For simplicity, we will assume that the basis doesn’t change (though in reality it can change, but more on this later).

Below is a chart showing what our futures portfolio profits and losses look like as the index price changes, as well as the individual futures. We assume that the Bitcoin index starts at \$40,000 at the current time and that the march/may contracts have a fixed basis of \$1,000 and \$2,000 respectively. Because one position is long, and one position is short, their PnL is opposite as the index (and therefore mark price) moves. The long position gains profits and the short position makes losses when the price goes up, and vice-versa. The blue line represents the profit and loss of the portfolio (the positions added together). Notice that the line is much shallower than the individual futures positions, and this is because the profits from one position offset the losses on the other position (to some degree). This offsetting is known as hedging, because you are using one instrument to protect against the losses of another. In our case, we are not fully hedged, because we have 1.5x more of the long position than of the short one. Therefore as the price goes down we will still make a loss, though much slower than if we didn’t have the short position at all. So, when viewed from the perspective of the portfolio as a whole, there is much less price risk compared to each position individually. ### Index Price Crash Scenario The purpose of initial margin is much like a deposit. It is there to provide a buffer to the counter party (the exchange) if the value of the asset drops. With the individual positions, we used 5x leverage, which means that we had to put up 20% of the cost of the position as initial margin. In e.g. the case of the long position, if the index (and therefore) mark price fell 20%, we would be bankrupt. The initial margin therefore protects us against a drop of 20% in the price of Bitcoin! Looking at our long/short future portfolio, what happens if the price falls 20%? How much money will we lose? Looking at the chart above, we can see that our loss would be$\approx\$4,000$. That means, that we could ask for that amount as the initial margin for our portfolio. Using the rules based margining, we calculated that it would require $\$20,700$to control the portfolio, and protect against a drop of 20%. Using the risk based method, we would only need$\$4,000$ to protect against the same drop.

Using portfolio margining was far more capital efficient (almost 5x), meaning less money could be used to hold a portfolio. For investors this is quite attractive, since higher capital efficiency means the saved capital can be used for other strategies, or to increase the size of the existing strategy.

## Other Risk Factors

We covered one of the simplest cases here, which was using instruments with the same underlying to offset delta. However, there are many other scenarios that risk based systems will analyse in order to determine what kind of margin is required. We describe some below:

### Basis Risk

In the above example we assumed that the basis of the futures from the underlying was fixed, however in real markets that is not usually the case (especially in crypto). Depending on market conditions the basis can both increase or decrease, or even flip to the other side. When holding a portfolio of two futures (one long one short) there exists basis risk.

In our case, despite sharing the same underlying, the March contract could decrease it’s basis (become more cheap), and the May contract could increase it’s basis (become more expensive). This would mean that our hedge might not protect our portfolio, since both positions would start losing money.

### Option Specific Risks

With futures the underlying and basis are important factors in the price. With options these factors and several others become important. For instance, changes in volatility can cause a change in the price of an option. As such, a risk based margining system needs to take into account these unique risks.

### Exit Cost & Liquidity

In order to close a position, a client will need to not only pay fees, but also make sure there is sufficient liquidity in order to absorb their closing order. Insufficient liquidity may result in significant slippage and market impact which might mean that exiting the position could be more costly than expected. In a risk based system, this risk needs to be taken into account. Therefore, larger positions may require more margin due to the fact that they will be harder and more costly to exit.

## Portfolio Margining In Crypto

In traditional finance, portfolio margin techniques have been around for some time. Indeed, the TIMS methodology described earlier has been around since at least the late 80’s. In crypto, the majority of exchanges have used rules based margining due to its simplicty. In recent years, exchanges have slowly started developing risk based systems themselves, and several are already operational.

Primarily, these systems are used with options, since this is where risk based systems are most useful due to the non-linear nature of these products. Exchanges that specialise in options such as OKX and Deribit have fairly mature portfolio margin systems, and details of how these systems calculate margin can be found here and here respectively.

## Glossary

Delta ($\Delta$)
A risk metric that measures how much a derivatives price changes with respect to its underlying.
Delta One
Products that have a delta of one.
Fully Hedged
When a portfolios value does not change when the price of the underlying changes.
Hedging
To fully or partially mitigate changes in value of a portfolio against some risk.
Portfolio
A collection of financial instruments that are treated as a unit.
Portfolio Margin
See Risk Based Margining.
Price Risk
The risk that the value of a portfolio will change vs. some underlying price.
Regulation T (Reg T)
A US regulation stipulating the minimum margin required for stock lending / derivatives margining.
Rules Based Margining
A simple form of margining that uses fixed rules for the allocation of margin.
Standard Portfolio Analysis Of Risk (SPAN)
A risk based margining method used by the CME.
Theoretical Intermarket Margining System (TIMS)
A risk based margining method used by the OCC.

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