# How to simulate historical performance of a short position of a security?

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