More Asymmetry

A couple of days ago I posted about the asymmetry of market returns capture by the target portfolio. The portfolio captured less than 100% of the upside in the markets but almost none of the downside. The chart below, inspired by a recent paper from AQR, shows the Bitcoin trading model's daily returns compared to the absolute percentage change in the price of Bitcoin futures for that day:

The rising diagonal line are all the days when the model was properly aligned with market direction. The descending diagonal line are all the days where it was incorrectly aligned with market direction. The remaining cloud of points is where the model changed direction. Some of those days were winners and some very bad losers when the model ended up incorrectly with the market in both directions that day. For example, it was stopped out of a long position and entered a short and then the market rose for the rest of the day...

The fitted quadratic curve shows that for low absolute price changes up or down in the price of Bitcoin, the model tends to lose money. This is because of "whipsaw". There is a strong asymmetry in the response for large moves and so the fitted curve shows that the model captures increasingly more of the return the larger the move.

The results do conform to AQR's argument that returns to trend-following have been poor recently because markets haven't been moving enough.

Varying Position Size Still Doesn't Make Sense

Last year, I posted that increasing trading position size when volatility is lower didn't make sense for my trading system. When the volatility was low trades tended to lose more and win less. So, trading bigger because risk was supposedly lower didn't pay off.

Now I am using a more traditional trading system that wins by letting winners run and cutting losses short, without pretending to predict the direction of the market. Here, I have found that there is no correlation between the profit from trades and the maximum loss possible given the initial stop loss:

The chart shows all the trades in Bitcoin futures my system would have made in the last year The x-axis shows the maximum loss on the trade of one contract (assuming we can exit at the stop loss, i.e. no Black Swans). The y-axis shows the profit for the trade. There is a slightly positive correlation, though it is not statistically significant. On the other hand, you can see that realized losses do increase with increased initial risk. The system won 46% of the time with the average win 4.1 times bigger than the average loss. The average trade lasted 5 days.

If you adjust position size so that the initial risk of each trade is the same, returns do increase, but so does the maximum drawdown. If you scale back the average size of trades so that the maximum drawdown in percentage terms is the same as for trading with the same number of contracts each time, then returns turn out to be very similar for both strategies.

Bottom line is that varying position size increases returns but also drawdowns by a similar amount. If you care about drawdowns it doesn't help. So, I think I will focus on controlling drawdowns when choosing position size rather than equalizing initial risk.

Target Portfolio vs. the MSCI World Index

The graph shows monthly returns for the target portfolio vs. the MSCI World Index in Australian Dollar terms. The linear fit shows a beta of about 0.3 – if the market rises 1% more , the portfolio tends to rise 0.3%. Alpha is at around 8% per year. The orange line is a quadratic fit. This suggests that beta increases, the more the market rises, while for large down moves beta is zero. This is the kind of asymmetric relationship you want to get.

Margin Requirements for Bitcoin Futures Trading

I just discovered that while going long a Bitcoin futures contract requires margin of about USD 16843.75 per contract, going short requires initial margin of USD 200k at Interactive Brokers. Do they really think that Bitcoin could rise by a factor of 7-8x when the market is closed?* This makes it much harder for people to go short and contributes to the inefficiency of this market. Importantly there are no options on these futures, so you can't hedge against large adverse movements. I can't see anything about this asymmetry in margin on the CME site, so I assume that it is set by the broker.

* Stops will only work when the market is open. The Globex futures market is open 23/5 - closed one hour each day and over the weekend.