Statistical Evidence for Mean Reversion

Rather than using frequency distribution of prices itself, we have calculated frequency distribution of hourly returns. Lets look at some of the statistics that I obtained after analyzing hourly price returns for BTC/USDC pair trading on Coinbase from 13th November 2018 to 5th April 2019 and BTC/USD pair trading on Coinbase from July 2017 to April 2019.

Fig. 1.1 Distribution of Hourly % Returns BTC/USDC Coinbase

Table 1.1 Statistics for Fig. 1.1

Fig. 1.2 Distribution of Hourly % Returns BTC/USD Coinbase

Table 1.2 Statistics for Fig. 1.2

It can been seen that the graphs are not perfectly Bell Shaped. It is worth noting that the values are very tightly distributed and it resembles a double exponential distribution.With a little tolerance mean, median and mode are almost equal.

Quoting mathworld.wolfarm.com :

“Reversion to the mean, also called regression to the mean, is the statistical phenomenon stating that the greater the deviation of a random variate from its mean, the greater the probability that the next measured variate will deviate less far. In other words, an extreme event is likely to be followed by a less extreme event.”

It can be seen in the Fig. 1.1 & Fig. 1.2 that, the further we move away from the mean returns, the value of probability distribution function decreases, making the probability of having further higher deviation in returns less probable.

This might not be the best example to explain mean reversion but here we can see the tendency of periodic returns to return towards the mean which can explain the validity of mean reversion of freely traded instruments.

How does mean reversion compare with trend following strategies?

Table 1.3 Comparing Mean Reversion & Trend Following

An attempt at building my own Mean Reversion Strategy for Crypto Currencies

Disclaimer : This resource is for educational purpose only and does not constitute a recommendation to buy, sell or otherwise deal in investments or trading.

Entry Condition : SELL when RSI MA(14,close,triple,2,0) crosses below RSI MA(14,close,simple,10,0) and 14 RSI higher than 70.

Exit Condition : BUY at stop loss of 1.0% or target profit of 2.5%.

Cryptos have been in a bullish trend recently. Here we are trying to create a bearish strategy to demonstrate how corrections in prices can be traded within a broader general trend that is against our direction of trade by trying to catch the mean reverting moves. RSI higher than 70 condition is used to check for overbought levels. Since RSI itself is a very volatile indicator, we smoothen its value by applying averages.

Then we check for crossover of the smoothened RSI values when the RSI is already in the overbought region. Crossover of a smaller period MA with a larger period MA is checked for fading short term relative strength. And when the setup is complete, we go short.

Instead of defining mean and taking profits at the mean, to keep the strategy simple, profit taking is done on fixed %. The strategy was backtested to evaluate the performance. While it does not work for all the pairs, it performs well on some other pairs. Here are some of the successful backtest results :