This post is a follow-up to the previous one on a simple system for hedging long exposure during a market downturn. It was inspired by H. Krishnan’s book The Second Leg Down, in which he referred to an interesting research paper  on the power-law behaviour of the equity indices. The paper states,
We find that the distributions for ∆t ≤4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent α≈ 3, well outside the stable Levy regime 0 < α <2. .. For time scales longer than ∆t ≈4 days, our results are consistent with slow convergence to Gaussian behavior.
Basically, the paper says that the equity indices exhibit fatter tails in shorter time frames, from 1 to 4 days. We apply this idea to our breakout system. We’d like to see whether the 4-day rule manifests itself in this simple strategy. To do so, we use the same entry rule as before, but with a different exit rule. The entry and exit rules are as follows,
Short at the close when Close of today < lowest Close of the last 10 days
Cover at the close T days after entry (T=1,2,… 10)
The system was backtested on SPY from 1993 to the present. Graph below shows the average trade PnL as a function of number of days in the trade,
We observe that if we exit this trade within 4 days of entry, the average loss (i.e. the cost of hedging) is in the range of -0.2% to -0.4%, i.e. an average of -0.29% per trade. From day 5, the loss becomes much larger (more than double), in the range of -0.6% to -0.85%. The smaller average loss incurred during the first 4 days might be a result of the fat-tail behaviour.
This test shows that there is some evidence that the scaling behaviour demonstrated in Ref  still holds true today, and it manifested itself in this system. More rigorous research should be conducted to confirm this.
 Gopikrishnan P, Plerou V, Nunes Amaral LA, Meyer M, Stanley HE, Scaling of the distribution of fluctuations of financial market indices, Phys Rev E, 60, 5305 (1999).