What is Effective Exposure?

Effective exposure is a mechanical, mathematical way to represent a portfolio that provides insight into the factors that a portfolio is exposed to: its effective exposure. Sandwich utilizes two formulae which hold for every row in the Effective Exposures table:

• Wallet Balance + Unrealized Profit and Loss (UPnL) = Net Asset Value (NAV)
• Exposure from NAV + Exposure from Positions = Total Exposures

Effective Exposure is best understood through examples. Below there are three examples of how Effective Exposure analysis may be used. In these examples, we assume that the user has his base currency set as USD: he typically thinks of wealth in terms of USD. We also ignore transaction costs and slippage.

When we use the term Net Asset Value (NAV), we refer to the equity in a particular asset: for example, if a user has deposited 2 ETH, has unrealized PnL of 0.5 ETH, and 1 ETH is used for margin, his NAV will be 2.5 ETH. It is the number of coins he would expect to have if he closed out all his positions (i.e. realizing his PnL and freeing up margin).  

For the purpose of these examples, the following cryptocurrency price assumptions are made:

• Cryptocurrency = Price (USD) 
• BTC = 40000 
• ETH = 3000 
• BNB = 400 
• XRP = 0.8 
• ADA = 1.2 
• USDT = 1

Example 1: Hedging

Consider an investor who owns 1 BTC. His portfolio, through the lens of effective exposures can be seen in Table 1A below.

The table above shows effective exposure to a particular coin, denominated in the coin itself (left half of the table) and also denominated in user currency(right half of the table). Reading from the table, we see the user has a NAV / Equity / Balance of 1 BTC and has no positions that affect his BTC exposure or create any unrealized PnL, giving a total effective exposure (in coin) of 1BTC. The right half of the table is simply a currency conversion of the left side at prevailing market rates.

Our investor is however concerned that the price of BTC will decline and wishes to hedge his position. He could do so, for example, via a BTCUSD Coin-margined perpetual contract on Binance. After selling 1 BTC of notional value (exposure) in the instrument at a prevailing rate of $40 000, his exposure upon entering the position is shown in Table 1B.

Notice that his position -1 BTCUSD has caused his exposure to BTC to decrease and his exposure to USD to increase.

If the price of BTC were to decline to say $30 000, the investor would have 1BTC in his account (worth $30 000) and $10 000 worth of unrealized profits in his BTCUSD position; giving a total portfolio value of $40 000. The investor thus effectively hedged himself against an adverse price movement in BTC. This scenario is shown in Table 1C.

Similarly, price increases in BTC would be offset by losses in his position – maintaining a portfolio value of $40 000.

His position of -1 BTCUSD was thus a mechanism to transform his exposure from BTC to USD: and more generally, a mechanism to transform exposure in base currency to exposure in quote currency. Long positions will increase exposure to base currency and decrease exposure in quote currency. Short positions have the opposite effect.

Example 2: Target Exposure

Consider a portfolio manager who is given a portfolio of two assets on behalf of an investor: 1 BTC and USDT 10 000. The manager is tasked to diversify this portfolio exposure to one that gives equal weighting to 5 big cryptocurrencies: BTC, ETH, BNB, XRP and ADA. Furthermore, the investor asked that the BTC not be sold, as this would trigger long-term capital gains that the investor would like to defer if possible.

The exposure of the starting portfolio can be seen in Table 2A below.

The portfolio manager decides to implement the investor’s request using derivative instruments on Binance and engages in the five transactions below:

• Transaction 1: -0.75 BTCUSD @ $40 000
• Transaction 2: +$10 000 ETHUSDT @ $3 000
• Transaction 3: +$10 000 BNBUSDT @ $400
• Transaction 4: +$10 000 XRPUSDT @ $0.80
• Transaction 5: +$10 000 ADAUSDT @ $1.20

After these transactions, the portfolio exposure is shown in Table 2B below.

Looking at the table above, one sees that the manager did realize exposure to the five cryptocurrencies in equal proportions: $10,000 worth of exposure to each of BTC, ETH, BNB, XRP and ADA.

It is interesting to note that the manager’s choice led to long exposure in USD and short exposure to USDT. People who trust that USDT will remain at a rateof one-to-one to USD would feel more comfortable with the manager’s choice. The mathematically pure and six-sigma market watchers will take note of theinherent risks highlighted by this analysis due to the manager’s choice of instruments.

Example 3: Arbitrageur

Consider a scenario where an investor has USDT on two exchanges and is able to trade in the BTCUSDT contracts on both exchanges. If there is a discrepancy between the two BTCUSDT prices, the investor is able to exploit this mismatch. The investor’s intent is to have no directional exposure to BTC, and as such he goes long the contract on the exchange where prices are cheap and sells short the contract where prices are dear, in the same quantities.

Table 3A shows the investors desired exposure (assuming that the investor has 40 000 USDT on each exchange).

As a trading example, if the BTCUSDT price on Bybit is $39,500 and on Binance it is $40,500 the investor would go long on Bybit and short on Binance ine quivalent quantities, say 1 BTC, resulting in the following transactions:

• Transaction 1: -$40 000 BTCUSDT @ $40 500 on Binance.
• Transaction 2: +$40 000 BTCUSDT @ $39 500 on Bybit

In theory this should result in a ‘risk free’ profit of $1 000 when the prices converge, regardless of the price at convergence as any profit/loss in one direction is offset by the equivalent loss/profit in the other direction. Since the quantities invested on each exchange are equivalent, both the BTC and USDT exposures net off to zero.

It can however happen that his order does not fill on a particular exchange.

Consider a scenario where only 0.5 BTC was filled on Bybit and the order on Binance was fully filled. This would result in the following positions being held by the investor:

• Binance Position: -$40 000 BTCUSDT @ $40 500
• Bybit Position: +$20 000 BTCUSDT @ $39 500

Therefore the investor’s actual exposure would be as shown in table 3B below.

The effective exposure analysis highlights that the investor’s exposures have deviated from his intended exposure.