By Sergei Belov, Ernest Chan, Nahid Jetha, and Akshay Nautiyal ABSTRACT We applied Corrective AI (Chan, 2022) to a trading model that takes advantage of the intraday seasonality of forex returns. Breedon and Ranaldo (2012) observed that foreign currencies depreciate vs. the US dollar during their local working hours and appreciate during the local working hours of the US dollar. We first backtested the results of Breedon and Ranaldo on recent EURUSD data from September 2021 to January 2023 and then applied Corrective AI to this trading strategy to achieve a significant increase in performance. Breedon and Ranaldo (2012) described a trading strategy that shorted EURUSD during European working hours (3 AM ET to 9 AM ET, where ET denotes the local time in New York, accounting for daylight savings) and bought EURUSD during US working hours (11 AM ET to 3 PM ET). The rationale is that large-scale institutional buying of the US dollar takes place during European working hours to pa
Triple leveraged ETFs marketed by Direxion have been all the rage lately. The fund management company says that they do not recommend buying and holding these ETFs. But is there any mathematical justification for this caution?
Before I answer this, it is interesting to note that these ETFs (e.g. BGU is 3x Russell 1000, TNA is 3x Russell 2000) are managed as constant rebalanced portfolios, a concept I discussed before. In other words, the fund manager has to sell stocks (or futures) when there is a loss, and buy stocks (or futures) when there is a gain in the market value of the portfolio, in order to maintain a constant leverage ratio of 3. This is also identical to what Kelly formula would prescribe, a methodology discussed extensively in my book, if the optimal leverage f were indeed 3.
However, the optimal f for such market indices are quite a bit lower than 3. Both Russell 1000 and 2000 have f at about 1.8. This means that since the funds are leveraged at 3, there is a real possibility that sustained losses could ruin the funds (i.e. NAV going to zero unless new capital is injected, which, er..., reminds me of a Ponzi scheme). So I would argue that not only should an investor not hold these funds for the long term, the funds themselves should not be leveraged at this level. Otherwise, it is a disaster waiting to happen.
Before I answer this, it is interesting to note that these ETFs (e.g. BGU is 3x Russell 1000, TNA is 3x Russell 2000) are managed as constant rebalanced portfolios, a concept I discussed before. In other words, the fund manager has to sell stocks (or futures) when there is a loss, and buy stocks (or futures) when there is a gain in the market value of the portfolio, in order to maintain a constant leverage ratio of 3. This is also identical to what Kelly formula would prescribe, a methodology discussed extensively in my book, if the optimal leverage f were indeed 3.
However, the optimal f for such market indices are quite a bit lower than 3. Both Russell 1000 and 2000 have f at about 1.8. This means that since the funds are leveraged at 3, there is a real possibility that sustained losses could ruin the funds (i.e. NAV going to zero unless new capital is injected, which, er..., reminds me of a Ponzi scheme). So I would argue that not only should an investor not hold these funds for the long term, the funds themselves should not be leveraged at this level. Otherwise, it is a disaster waiting to happen.
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