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I would like to calculate with R the inverse return of Bitcoin. My objective is to simulate the historical price and return of a short position opened in Bitcoin.

The first method is to cumulate the 1-dailyReturn of the Bitcoin price and the second option is to calculate the return of 1/(BTC/USD).

Both give slighty different result and I'm not sure which one I must use.

Here are the two options written in R and the results:

> dailyReturn(cumprod(1-dailyReturn(BTC_USD)))["2015-11-23::"]
           daily.returns
2015-11-23   0.007114063
2015-11-24   0.004140197
2015-11-25  -0.046087480
2015-11-26  -0.024507073

> dailyReturn(1/BTC_USD)["2015-11-23::"]
           daily.returns
2015-11-23   0.007165035
2015-11-24   0.004157409
2015-11-25  -0.044057004
2015-11-26  -0.023920843
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The first method gives the performance when rebalancing the position every day so you have a constant dollar exposure, the second is the result of shorting USD 1 and then keeping the position open, i.e. a short-and-hold return. They can be quite different in the long run and if there is high volatility. I recommend the short-and-hold with, possibly, rebalancing once a quarter or once a year only. Daily rebalancing is not very realistic unless you can trade very cheaply (I am not an expert in Bitcoin but I thought it was difficult to short). Inverse ETFs use daily rebalancing, but they are designed for short term holding only and oare not recommended for long term hold.

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  • $\begingroup$ Thank you Alex I'll choose the first option as it is designed to short term exposure. $\endgroup$ – Florent Nov 27 '15 at 21:26

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