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Tesla know tha it will need 500 bitcoin for it s exchanges in 6 months. Today bitcoin price in the direct market is 45000$ ,

Tesla know tha it will need 500 bitcoin for it s exchanges in 6 months. Today bitcoin price in the direct market is 45000$ , the standard deviation of the change of price per currency for the next 6 months is 0.069 . Tesla want to hedge the danger of bitcoin price increase by futures contracts. The stand deviation of a price change of a future contract for the 6 months is 0.075 when the correlation coefficient of the above changes is 0.75. Each future contract is 50 bitcoin and has the price of 44000$ per bitcoin. After six months the cash price in the market is 52000 $ and in future contracts is 51200$. What is the current position of the company, what position should take in future contracts and calculate the net cost of purchasing bitcoing following the hedge as well as the efficiency of hedge when the variance the changes of the base is 0.0035.

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