A quick - and dirty - run through the argument that Bitcoin serves as a hedge or a safe haven for stocks. This argument has been popular in cryptocurrencies analytical circles of recent, and is extensively covered in the research literature, when it comes to 2014-2017 dynamics, but not so much for 2018 or even more recent period dynamics.
First, simple definitions:
A financial instrument X is a hedge for a financial instrument Y, if - on average, over time - significant declines in the value of Y are associated with lower declines (weak hedge) or increases (strong hedge) in the value of X.
A financial instrument X is a safe haven for a financial instrument Y, if at the times of significant short-term drop in the value of Y, instrument X posts increases (strong safe haven) or shallower decreases (weak safe haven) in its own value.
So here are two charts for Safe Haven argument:
The first chart shows that over the last 12 months, there were 3 episodes when - over time, on average, based on daily prices, stocks acted as a strong hedge for BTCUSD. There are zero periods when BTCUSD acted as a hedge for stocks. The second chart shows that within the last month, based on 30 minutes intervals data (higher frequency data, not exactly suitable for hedge testing), BTCUSD did manage to act as a hedge for stocks in two periods. However, taken across both periods, overall, BTCUSD only acted as a weak hedge.
The key to the above is, however, the time frame and the data frequency. A hedge is a longer-term, averages-defined relationship. Not an actively traded strategy. And this means that the first chart is more reflective of true hedging relationship than the later one. Still, even if we severely stretch the definition of a hedge, we are still left with two instances when the BTCUSD acts as a hedge for DJIA against two instances when DJIA acts as a hedge for BTCUSD.
People commonly confuse both hedging and safe haven as being defined by the negative symmetric correlation between assets X and Y, but in reality, both concepts are defined by the directional correlation: when X is falling, correlation myst be negative with Y, and when Y is falling, correlation must be negative with X. The downside episodes are what matters, not any volatility.
Now, to safe haven:
Again, it appears that stocks offer a safe haven against BTCUSD (6 occasions in the last 12 months) more often than BTCUSD offers a safe haven against stocks (2 occasions). Worse, the cost of holding BTCUSD long as a safe haven for stocks is staggeringly high: some 60-65 percentage points over 12 months, not counting the cost of trading.
In simple terms, BTCUSD is worse than useless as either a hedge or a safe haven against the adverse movements in stocks.