Bitcoin

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You work for a family office in Miami, investing a large fraction of the Da Silva’s family wealth. Brutus da Silva,  the family’s heir, is unhappy with the fact that the family office has no exposure to Bitcoin. “Bitcoin will

eventually reach $500,000 per bitcoin. I want a BIG bet in bitcoin now!” However, almost the entirety of the

family office’s portfolio is invested in relatively illiquid ventures that cannot be quickly sold out. There is,

however, $450,000 in cash available. The current price of bitcoin is $47,000. The price of the Bitcoin futures

contract maturing in two months is $47,120. Each futures contract involves 5 bitcoins. The initial margin is

$60,000 per contract and the maintenance margin is 50% of the initial margin.

a. How many Bitcoins can be purchased in the spot market using the cash available?  b. How many Bitcoin (not Bitcoin contracts!) can be arranged to be purchased in two months through the

futures market?  c. What is the annual, continuously compounded interest rate implied by the Bitcoin futures price

maturing in two months? Remember that Bitcoin provides no income.  d. Express the rate you found in c) as an annual rate with annual compounding.  e. What futures price of Bitcoin leads to a margin call?

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