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# Hedging Guide

One of the main purposes of the derivatives markets is to provide protection and hedging for those who want to secure their holdings and future cash flows. Investors and traders alike can use either Short Futures positions or purchase Put Options in order to insulate themselves against the moves of the BTCUSD exchange rate. Both cases are presented in the examples below.

### Example - Hedging with Short Futures

Assume that investor bought on the market 10 BTC for \$110,000. In order to hedge these bitcoins investor needs to take short position in 110,000 futures contracts at the price of \$11,000 or higher. We have the following parameters of the contract:

• `Side = -1` (short position),
• `Notional Amount = 1` (\$1),
• `Quantity = 110,000`,
• `Entry Price = \$11,000`.

Investor also needs to deposit initial margin, which in this case equals to 0.4 BTC. We assume that investor never receives a margin call, so (computation of `Free balance` is presented in the previous example in the Arbitrage section)

``Unsettled P/L > - Balance + Initial Margin = - 9.6 BTC. ``

Hence, price must be smaller than \$275000(the value is so high, because for the investor `Free Balance = 9.6 BTC`, so this contract is almost fully collateralized).

Consider three scenarios of Exit Prices during the calculation of Realized P/L:

1. `Exit Price = \$6000` - then investor holds `(10 + (1/6000 - 1/11,000) * 110,000) * 6000 = \$110,000`.
2. `Exit Price = \$11000` - then investor holds `(10 + (1/11000 - 1/11,000) * 110,000) * 11000 = \$110,000`.
3. `Exit Price = \$20000` - then investor holds `(10 + (1/20000 - 1/11,000) * 110,000) * 20000 = \$110,000`.

From the above calculations we can see that investor’s bitcoins are successfully hedged. The dollar value of the investor’s portfolio vs. Exit Price is shown in the following graph. ## Hedging with Put Options

Assume that a miner estimates to mine about 4 BTC in the coming month, with variable costs of around \$6500 (mostly electricity power costs). We omit hardware costs as sunken costs here. Further, let's assume that miner predominantly want to maximize their BTC stash. Therefore at the end of the month, The miner's P/L would be

`P/L (BTC) = 4 - 6500/Price`,

where `Price` is the spot BTCUSD exchange rate.

As it can be seen, most of the time their revenues are secure but on the other hand it may happen that the losses grow arbitrarily big. This might be the case if BTCUSD exchange rate falls below \$16125.

Let us now say that the miner wants to protect themselves from the above scenario. He:

• is interested in protecting some tail risk (i.e. the risk of large losses),
• wants to minimize the cost of the insurance,
• can accept some moderate price risk,
• wants protection for the next month, as electricity is usually billed on a monthly basis.

That is why put options are his instrument of choice. He will achieve his goals by buying 10% out-of-the-money put with 1M expiration. He may choose to fully hedge his portfolio with put options (Strategy A), or apply partial hedge and protect only 60% of his holdings (Strategy B).

Assuming current `Futures Price = \$17000`, it obtains that

• `Hedging Cost(A) = 6500 * Single Option Price ~ 0.027 BTC`,
• `Hedging Cost(B) = 0.6*6500 * Single Option Price ~ 0.016 BTC`.

Consider two scenarios:

a) Option expires worthless b) Price falls significantly (by 30%)

In scenario a., both hedges turned out unnecessary and thus the A’s P/L is 0.027 less comparing to the situation without hedge. For B the profit is obviously 0.016 BTC smaller with hedge than without.

On the other side, in situation b., the option was executed and thus

• `P/L unhedged(A) = 4 - 6500 / (0.7 * 17000) ~ 3.453781513 = P/L unhedged(B)`,
• `P/L hedged(A) = 4 - 6500/(0.9*17000) - 0.027 = 3.548163399`,
• `P/L hedged(B) = 4 - 0.4 * 6500 / (0.7 * 17000) - 0.6 * 6500 / (0.9 * 17000) - 0.016 = 3.510610644`.

And thus Strategy A is almost 0.1 BTC better off if the miner has chosen to hedge and thanks to the full hedge Strategy A is around 0.05 BTC better than B.

What is more, in the case of full hedge, the investor can never go bankrupt. It can be easily seen that in case of A - her P/L cannot fall below 3.548163399 BTC no matter how severe the exchange rate fall would be. On the other hand, partial hedge is cheaper and thus if the investor perceives the risk of a breakdown as extremely small, it might be a better choice.