XBTとXBUチェーン比較

2 August 20182 August 2018 Sho Hirayama

注：本稿は古い情報に基づいている。2014～2016年、BitMEX ではクオントとインバースの両方を扱っていたが、その後、簡略化のため、インバースのみに移行している。

新しい情報については、XBT シリーズガイドをご覧いただきたい。

BitMEX では、総合的なビットコイン派生商品を取り扱うことを目標にしている。現在の主力商品はクオントとインバースの 2 種類に大別される。XBTUSD スワップ商品ではインバース方式を採用し、XBTU16 契約ではクオント方式を採用している。

XBTUSD はビットコイン価格 (任意) を 1 ドルで除した値に相当する。XBTU16 では、ビットコイン乗数が 1ドルあたり 0.00001 XBT に固定されている。いずれの契約も米ドル建てで提示され、Kaiko BitMEX インデックスビットコイン/米ドル (XBTUSD) 直物レートを参照する。下表は XBTUSD と XBTU16 の概要である。

シンボル	XBTUSD	XBTU16
種類	インバース	クオント
原資産	1 / XBTUSD または USDXBT	XBTUSD
乗数	-$1	0.00001 XBT
建値通貨	USD	USD
証拠金と損益通貨	XBT	XBT
満期	なし	2016 年 9 月 30 日
決済方式	未実現損益を毎日12:00 UTC に調整し直す	Kaiko BitMEX インデックスの10:00 UTC – 12:00 UTC の 1 分足時間平均加重価格 (TWAP)
1契約あたりXBT価値	1 / 価格 * $1	価格 * 0.00001 XBT
1契約あたり米ドル価値	$1	価格² * 0.00001 XBT
1契約の XBT 損益	(1 / 価格T – 1 / 価格0) * -$1	(価格T – 価格0) * 0.00001 XBT

XBTUSD は、XBTUSD と価格が提示されるためインバース (逆) 契約であるが、実際には、原資産は USDXBT または 1/XBTUSD である。インバースとしてクォートされる理由は、ビットコイン市場の大半のトレーダーがビットコインをベース通貨とするクォート方式に馴染んでいるためである。この商品は、ビットコインの米ドル建て価値を固定する必要のあるトレーダーに適している。3 か月以内に$100,000 のビットコインを受領する予定の場合、100,000 XBTUSD 契約を売却して、$100,000 の価値を確保する。

XBTU16 は、米ドル建てでクォートされるためクオント先物契約であるが、乗数は XBT 建てである。以下は Wikipedia の引用。

クオント とは、デリバティブの一種で、原資産は単一通貨建てであるが、商品自体は別の通貨建ての固定レートで決済される。

このチェーンはビットコイン保有者がビットコインの将来価格を適切に予測することでビットコイン収益をあげる場合に適している。

上のチャートには、1,000 XBTUSD 契約をロングした場合において、直物レートの推移に伴う米ドルと XBT のエクスポージャーを示している。米ドルのエクスポージャーは、$1,000 で一定であるが、XBT のエクスポージャーは非線形に変化している。この値が XBTUSD 価格 [XBT 価額 = 1/価格 * $1 * 契約数] に相当するためである。次のチャートでは、証拠金との関係が示されている。

1,000 XBTUSD 契約を$500 で購入したものと仮定する。この契約の XBT 価額は、1/$500 * $1 * 1,000 or 2 XBT の算式で計算される。慎重を期し、2 XBT を証拠金として預託する。この証拠金で価格下落時の損失が十分カバーできるという考えの下での預託であるが、上のチャートでその考えが間違っていることがわかる。青い線は 2 XBT の投資額を示している。赤い線は 1,000 XBTUSD 契約ロングポジションの損益を示している。緑の線は損益相殺後の純投資額を示している。価格が $300 を割り込むと、アカウントの投資額は実際にはマイナスつまり破産状態となる。XBTUSD はインバース契約であるため、1,000 契約を購入すると、実際には、USDXBT をショートしたことになる (XBTUSD のロングでなく)。その結果、XBTUSD 価格が下落すると、ポジションの想定価値相当の XBT を預託しても、追加証拠金が必要となり得る。

上のチャートには、XBTU16 契約を 1,000 枚ロングした場合において、XBTUSD 直物レートの変化に伴う米ドルと XBT のエクスポージャーが示されている。XBT のエクスポージャーは、非線形に変化している。価格変数が次の式のとおり、2乗されているためである：[USD 価額 = 価格² * 0.00001 XBT * 契約]。

XBTUSD 相場の見通しに応じて、どちらかのチェーンが他方より明らかに有利となる。上の 2 つのチャートには、XBT と米ドルの損益が示されており、1,000 XBTU16 の 1,000 契約のロングポジションとshort 2,500 XBTUSD の 2,500 契約のショートポジションで、いずれも価格 $500 と仮定されている。$500 では、この 2 つの商品の XBT と USD の価額は等しい。XBTUSD 相場に弱気な見方をしている場合、XBTUSD のショートが適した戦略である。XBTUSD 相場に強気な見方であれば、XBTU16 ロングが最適である。

Cash And Carry Arbitrage With BitMEX Futures

2 September 20152 September 2015 Arthur Hayes

One of the most common and profitable trading strategies when trading futures is cash and carry. Traders employing this strategy buy underlying asset and sell its corresponding futures contract. They hold the futures contract until expiry, and profit from the differential between the future and underlying asset.

There are two types of BitMEX futures one can use to execute this strategy. XBU futures have very low risk and low reward. XBT futures have more risk but more reward.

Futures premiums can vary widely depending on the optimism in the market. Executed correctly and at the right time, a cash and carry strategy can lock in guaranteed profit.

We’ll delve into the XBU (5x) futures first.

Using BitMEX 5x Leveraged Futures (XBU)

BitMEX offers a series of futures contracts that have 5x leverage. That means a trader who deposits 10 BTC can control a position worth 50 BTC. These contracts we classify as Hedging, and use the symbol prefix XBU. The contracts are worth $100 of Bitcoin. Put another way, no matter what the BTCUSD exchange rate is, the contract will equal enough Bitcoin such that its value is $100.

The below example will run through the mechanics and risks of a cash and carry strategy using these futures contracts.

Spot Bitcoin price = $200

March 2016 futures price = $250

Cash and carry profit = $50/Bitcoin

A trader will now buy spot Bitcoin and sell March 2016 futures contracts.

Assume the trader has $10,000. He buys 50 Bitcoin at a price of $200. He then must sell enough March futures contracts to hedge his long exposure.

March 2016 Futures Contracts = $10,000 / $100 = 100 Contracts

	Quantity	USD Value	Bitcoin Value
Spot	50 BTC	-$10,000	50 BTC
March 2016 Futures (XBU)	-100	$10,000	-50 BTC
Total Exposure		$0	0 BTC

The trader has locked in a risk free profit of $2,500 regardless of the subsequent BTCUSD exchange rate. The below example will illustrate why.

Assume that the spot price rises to $250. The below table shows the change in the USD and Bitcoin value of the spot and futures positions.

	Quantity	Price	USD Value	Bitcoin Value	PNL	Total USD Value	Total BTC Value
Spot	50 BTC	$250	-$12,500	50 BTC	$2,500	-$10,000	50 BTC
March 2016 Futures (XBU)	-100	$250	$10,000	-40 BTC	-10 BTC	$10,000	-50 BTC
Total Exposure						$0	0 BTC

The trader makes USD PNL on the long spot position, and BTC PNL on the short futures position. The net effect is the total portfolio exposure does not change. Because the trader bought spot at $200 but sold futures at $250, he has actually profited the difference and no price movement will change that.

Assume that the spot price falls to $150. The below table shows the change in the USD and Bitcoin value of the spot and futures positions.

	Quantity	Price	USD Value	Bitcoin Value	PNL	Total USD Value	Total BTC Value
Spot	50 BTC	$150	-$7,500	50 BTC	-$2,500	-$10,000	50 BTC
March 2016 Futures (XBU)	-100	$150	$10,000	-67 BTC	17 BTC	$10,000	-50 BTC
Total Exposure						$0	0 BTC

The trader makes USD PNL on the long spot position, and BTC PNL on the short futures position. The net effect is the total portfolio exposure does not change.

Once a trader has bought spot and sold futures contracts, there is nothing else to do but wait until expiry. This is a pure cash and carry strategy. For this reason, the XBU (5x leveraged futures) premium to spot will be much less than the XBT (25x leveraged futures) premium to spot.

Using BitMEX 25x Leveraged Futures (XBT)

BitMEX’s other Bitcoin futures have 25x leverage. That means a trader who deposits 10 BTC can control a position worth 250 BTC. These contracts we classify as Speculative, and use the symbol prefix XBT.

XBT contracts are differently structured. The contracts pay out 0.00001 BTC per $1 movement of the BTCUSD price. Put another way, if the BTCUSD prices rises by 1% the Bitcoin value of the futures contract rises by 1%. All profit and loss for the futures contract is paid out in Bitcoin.

The below example will run through the mechanics and risks of a cash and carry strategy using these futures contracts.

Spot Bitcoin price = $200

March 2016 futures price = $300

Cash and carry profit = $100/Bitcoin

A trader will now buy spot Bitcoin and sell March 2016 futures contracts.

Assume the trader has $10,000. He buys 50 Bitcoin at a price of $200. He then must sell enough March futures contracts to hedge his long exposure.

Given no volatility, the trader would profit 50 * ($300 – $200) or $5,000. But there will be volatility, so there are some considerations.

March 2016 Futures Contracts = 500 BTC / ( $200 * 0.00001 ) = 25,000 Contracts

We use the spot price of $200 to calculate the number of contracts to hedge instead of the futures price of $300. This is because you are holding the future until maturity, so it should be valued at the spot price.

	Quantity	USD	Bitcoin
Spot	50 BTC	-$10,000	500 BTC
March 2016 Futures (XBT)	-25,000	$10,000	-500 BTC
Total Exposure		$0	0 BTC

Because of the return profile of the futures contract, this trade is not risk free.

Assume that the spot price rises to $250. The below table shows the change in the USD and Bitcoin value of the spot and futures positions.

	Quantity	Price	USD Value	Bitcoin Value	PNL	Net USD PNL
Spot	50 BTC	$250	-$12,500	50 BTC	$2,500	$2,500
March 2016 Futures (XBT)	-25,000	$250	$15,625	-63 BTC	-13 BTC	-$3,125
Total Exposure			$3,125	-13 BTC		-$625

To flatten the exposure to 0, the trader would need to buy 13 BTC at a price of $250. In addition, he is locking in a loss of $625.

Assume that the spot price falls to $150. The below table shows the change in the USD and Bitcoin value of the spot and futures positions.

	Quantity	Price	Value	Bitcoin Value	PNL	Net USD PNL
Spot	50 BTC	$150	-$7,500	50 BTC	-$2,500	-$2,500
March 2016 Futures (XBT)	-25,000	$150	$5,625	-38 BTC	13 BTC	$1,875
Total Exposure			-$1,875	13 BTC		-$625

To flatten the exposure to 0, the trader would need to sell 13 BTC at a price of $150. In addition, he is locking in a loss of $625.

Due to a long spot vs. short futures position, as the price moves the trader must buy high and sell low to have no exposure to the Bitcoin price. Every time he hedges his portfolio he is losing money, meaning he is short volatility. If the price moves too much between now and March 2016, the cost of hedging his portfolio will outweigh the premium earned by selling the future above the spot price.

By employing this cash and carry strategy, the trader is selling volatility for a premium. To determine the trader’s break even volatility, we must solve for the upper and lower bound where the trade ceases to become profitable.

Solving the following quadratic equation will give the upper and lower bound

F = Future Price, in this example $300

S = Spot Price, in this example $200

Sqrt = Square Root

Upper Bound:

[ -2 * F – Sqrt( 4 * F^2 – 4 * S * F ) ] / -2

In this example, $473.21.

Lower Bound:

[ -2 * F + Sqrt( 4 * F^2 – 4 * S * F ) ] / -2

In this example, $126.79.

Assume there are 180 days until the March 2016 future expires. That means the trader sold volatility at this level:

( $473.21 / $126.79 -1 ) * Sqrt ( 365 / 180) = 386.40% Annualised Volatility

If the trader rebalanced his portfolio once daily, the price would have to move at greater than a 386.40% annualised volatility for the trader to lose money. For each day that the realised volatility is lower than 386.40% annualised, the trader makes money. This is the daily carry that he earns.

Summary

Cash and carry is a valuable strategy that can lock in great returns.

On BitMEX, cash and carry strategies using XBU have no price risk. For this reason, expect XBU contracts to have less premium over spot.

Doing cash and carry arbitrage on the XBT series carries more risk, but may have much more reward.

Synthetic Bitcoin Report – June 3

2 June 2015 Arthur Hayes

GBTC volume inched up slightly to 141 XBT. The premium declined 5% points to 30%.

XBT’s volume took a dive to 225 XBT. The premium declined and the ETN closed at fair value.

Synthetic Bitcoin Report – May 22

21 May 2015 Arthur Hayes

This report presents the daily trading premium to NAV and Bitcoin equivalent volume for any exchange listed investment securities that track Bitcoin. The report will analyse GBTC (the OTC Markets listing of the Bitcoin Investment Trust), and XBT ( an ETN listed on the Nasdaq OMX Nordic).

A lacklustre day for GBTC. Volume fell to 288 Bitcoin and the premium held constant at 35%.

Volume picked up to 681 Bitcoin. The premium has remained in a -0.20% to 0.20% band the entire week.

Synthetic Bitcoin Report – May 20

19 May 201519 May 2015 Arthur Hayes

The GBTC premium is off sharply from last week. Yesterday it rose 10% to 25%. Volume has levelled off around the 500 Bitcoin mark.

XBT’s second trading day had a respectable volume of 547 Bitcoin, which is down 50% from the listing date. The premium rose slightly to 0.20%.

XBT vs. XBU Chain

8 December 201423 July 2017 Arthur Hayes

Note: This information is outdated. From 2014 to 2016, BitMEX had both quanto and inverse offerings. To simplify our products, we moved to inverse-only.

For up-to-date information, see the XBT Series Guide.

BitMEX‘s goal is to provide the most complete Bitcoin derivatives product offering. There are currently two types of popular structures, quanto and inverse. The XBTUSD swap product uses the inverse structure, and the XBTU16 contract uses the quanto structure.

XBTUSD is worth $1 of Bitcoin at any price. XBTU16 has a fixed Bitcoin multiplier of 0.00001 XBT per $1. Both contracts are quoted in USD and referencing the Kaiko BitMEX Index Bitcoin / USD (XBTUSD) spot rate. The below table summarises XBTUSD and XBTU16:

Symbol	XBTUSD	XBTU16
Type	Inverse	Quanto
Underlying	1 / XBTUSD or USDXBT	XBTUSD
Multiplier	-$1	0.00001 XBT
Quote Currency	USD	USD
Margin & PNL Currency	XBT	XBT
Maturity	No Expiry	30 September 2016
Settlement Mechanism	Unrealised profits and losses are rebalanced daily at 12:00 UTC	10:00 UTC – 12:00 UTC 1 minute TWAP on Kaiko BitMEX Index
XBT Value of 1 Contract	1 / Price * $1	Price * 0.00001 XBT
USD Value of 1 Contract	$1	Price² * 0.00001 XBT
XBT PNL of 1 Contract	(1 / PriceT – 1 / Price0) * -$1	(PriceT – Price0) * 0.00001 XBT

The XBTUSD is an inverse contract because it is quoted as XBTUSD but in actuality the underlying is USDXBT or 1/XBTUSD. It is quoted as an inverse because most traders in the Bitcoin community are accustomed to seeing Bitcoin quoted as the home currency. This product is suitable for traders who need to lock in a USD value of Bitcoin. If you were to receive $100,000 of Bitcoin in three months, you would sell 100,000 XBTUSD contacts to lock in the $100,000 value.

The XBTU16 is a quanto futures contract because it is quoted in USD but the multiplier is in XBT. From Wikipedia:

A quanto is a type of derivative in which the underlying is denominated in one currency, but the instrument itself is settled in another currency at some fixed rate.

This chain is suitable for traders who have Bitcoin and want to earn Bitcoin by correctly predicting the future price of Bitcoin.

The chart above displays the USD and XBT exposure of being long 1,000 XBTUSD contracts as the XBTUSD spot rate changes. The USD exposure is constant at $1,000; however, the XBT exposure changes in non-linear way because you are taking the inverse of the XBTUSD price [XBT Value = 1/Price * $1 * Contracts]. The next chart shows the margin implications.

Assume you bought 1,000 XBTUSD contracts at a price of $500. The XBT value of those contracts is 1/$500 * $1 * 1,000 or 2 XBT. Being a cautious trader, you deposited 2 XBT as margin. You assume because you have fully margined the position that you cannot go bankrupt if the price drops. The chart above shows that you are incorrect. The blue line shows your 2 XBT of equity. The red line shows the PNL from the long 1,000 XBTUSD contracts. The green line shows your net equity after netting your PNL. Your account actually goes into negative equity a.k.a. bankruptcy as the price drops below $300. Because XBTUSD is an inverse contract, when you buy 1,000 contracts you are actually short USDXBT – not long XBTUSD – and as a result when the XBTUSD price drops, your account can be margin called even if you deposited the full XBT notional value of your position.

The chart above displays the USD and XBT exposure of being long 1,000 XBTU16 contracts as the XBTUSD spot rate changes. The XBT exposure changes linearly with respect to XBTUSD. The USD exposure changes in a non-linear fashion because the Price variable is squared [USD value = Price² * 0.00001 XBT * Contracts].

One chain is clearly better than the other depending on your view of future XBTUSD prices. The two charts above show the XBT and USD PNL assuming a portfolio of long 1,000 XBTU16 contracts and short 2,500 XBTUSD contracts both at a price of $500. At $500 the XBT and USD value of the two products is equal. If you have a bearish view on the XBTUSD price, going short XBTUSD is the optimal strategy. If you have a bullish view on the XBTUSD price, going long XBTU16 is the optimal strategy.