Short Position Returns: Daily Rebalancing Versus Buy and Hold
Summary
The document compares two ways to represent the historical return of a short position in Bitcoin. Applying the inverse of each day’s return and compounding it models a position whose dollar exposure is reset each day. Taking the reciprocal of the asset price instead represents shorting a fixed amount of currency and holding that position open, so exposure changes as the asset price moves.
The example reports slightly different daily returns from the two calculations, illustrating that the methods are not interchangeable. The answer characterizes the difference as potentially substantial over long periods or in volatile markets. It suggests that daily rebalancing can be costly or impractical and notes that inverse exchange-traded products, which typically rebalance daily, are intended for shorter holding periods. The discussion does not model borrow fees, financing, execution costs, or the mechanics and availability of shorting Bitcoin, so its return comparisons are simplified.
Key ideas
- Compounding inverse daily returns represents a short position rebalanced to maintain constant dollar exposure.
- Taking the reciprocal of the price series represents a fixed-currency short position held over time.
- The two approaches can diverge, especially over long horizons and in volatile markets.
- Frequent rebalancing has trading costs and may be impractical for a short position.
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Full text
# How to simulate historical performance of a short position of a security?
# 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
```
## Answer by Alex C (score 1, accepted)
https://quant.stackexchange.com/a/21963
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.