Pros and Cons of Leveraged and Inverse ETFs (2014-10-30 06:45:49)下一个 1 The rebalancing rules of leveraged and inverse etfs are in the same direction as the immediate past movement of the underlying. If underlying moved up, they buy more; if underlying moved down, they all sell more.
2 They do a decent job in replicating X times the DAILY returns of the underlying, X being the leverage factor (ie X=2, 3, -1, -2, -3);
3 Due to the rebalancing rule, leveraged etf will OUTPERFORM, ie return you more than X times the underlying returns over multiple days, if the underlying is trending, which is similar to compounding effects;
4 However if the underlying is consolidating, then leveraged etf will buy high and sell low, which leads to time decay. The faster the underlying moves (volatility), and the more directionless the underlying moves (negative correlation over time), the faster the time decay. The effect is similar to theta of option, and the term "time decay" comes from that literature.
5 The behavior of leveraged ETFs are also like that of option. As an option moves further and further into the money, the long position gains at an increasing speed due to positive gamma.
6 Time decay of leveraged per se is not a problem. Time decay is a cost you pay to gain convexity, ie compounding effect. The problem here is that market on average is more likely to be trading in range/directionless/mean reversting (80% of time) than trading in momentum/trending (20% of time). So if you plan to hold for multiple days, then leveraged ETF is not a good instrument.
7 If you do want a long-term position, but still need leverage what do you do? You can use futures to gain leveraged without suffering time decay. You can also use the underlying (ie X=1) with margin money. With a portfolio margin account, you can go up to 6-7X leverage with minimal margin interest payment at today's low FF rates. The key here is to keep notional exposure in check. On a return on capital basis, you will gain 5X, 10X, 20X leverage. However the multiplier will be a linear multiplier, ie you will not gain compounding. Do not use options, as options are non-linear contracts that are best reserved to trade the direction of volatility, not the direction of the underlying.
8 If you do not understand the points above, do not touch either leveraged etf or futures. Options certainly should also be out of your consideration.
“Given recent volatility levels for NDX, TQQQ will underperform QQQ if NDX is up less than 9.8% over the next year. TQQQ will outperform QQQ if NDX is up more than 12%.”
感谢SLOWQUICK提供这篇文章，分析了TQQQ和QQQ之间的关系。简化的说法是：TQQQ回报 = (QQQ回报)^3 exp(-3σ^2T)。这里，σ代表波动率，T代表持仓时间，exp则代表所谓的波动衰减。由于波动率σ不可能是常数，因此这可以理解为波动率（VOLATILITY）随时间的积分。
我研究TQQQ的目的是为了盈利，这个公式给了我重要的启发，并由此形成了一种交易思路。希望大家能批评指出其中的盲点，以减少损失。
首先，如果不考虑波动衰减，那么TQQQ的回报就是(QQQ回报)^3。这种回报远大于三倍杠杆。由于TQQQ每天都会重置，这相当于复利效应。更重要的是，TQQQ和QQQ是直接相关的。也就是说，如果大家认为QQQ会持续上涨，那么只要能承受更大的波动，就应该考虑投资TQQQ，因为其回报是QQQ的三次方。
然而，问题在于波动性。这一项是以指数级数衰减的。它告诉我们，在高波动性时期应该离开市场。这个公式启发我可以使用VIX作为一个指标。历史研究显示波动性往往是聚集在一起的。从VIX的图表可以看出，VIX急涨慢跌，这反映了市场对波动性的适应过程，并且这个指数是一个积分项。如果在VIX急涨之后能尽快卖出TQQQ，由于积分项很小，能够减少损失。因此，可以通过回测来设定一个阈值。当VIX超过这个阈值时，就卖出TQQQ。
但这里第1点和第2点存在矛盾。我还没有找到一个好的解决方案。有可能因为VIX和QQQ的回报高度相关，我们可以设定一个VIX的阈值。在这个阈值以下，QQQ的回报几乎总是正的，波动性也低。或者，我们可能还需要考虑其他指标，比如均线。
https://joim.com/wp-content/uploads/emember/downloads/p0283.pdf
宁外，概率分布不是高斯。散户可以博长尾。
decay = 1/2 * N * (N-1) * variance
the question is whether the underlying QQQ is trending or not.
if trending, then 3x will perform better than un-reblanced 3x with margin. if not trending then it is going to under-perform.
Long TQQQ is like long a Call option with Lambda of 3 (everyday sell old one and buy a new call with a constant lambda)
Pros and Cons of Leveraged and Inverse ETFs (2014-10-30 06:45:49)下一个 1 The rebalancing rules of leveraged and inverse etfs are in the same direction as the immediate past movement of the underlying. If underlying moved up, they buy more; if underlying moved down, they all sell more.
2 They do a decent job in replicating X times the DAILY returns of the underlying, X being the leverage factor (ie X=2, 3, -1, -2, -3);
3 Due to the rebalancing rule, leveraged etf will OUTPERFORM, ie return you more than X times the underlying returns over multiple days, if the underlying is trending, which is similar to compounding effects;
4 However if the underlying is consolidating, then leveraged etf will buy high and sell low, which leads to time decay. The faster the underlying moves (volatility), and the more directionless the underlying moves (negative correlation over time), the faster the time decay. The effect is similar to theta of option, and the term "time decay" comes from that literature.
5 The behavior of leveraged ETFs are also like that of option. As an option moves further and further into the money, the long position gains at an increasing speed due to positive gamma.
6 Time decay of leveraged per se is not a problem. Time decay is a cost you pay to gain convexity, ie compounding effect. The problem here is that market on average is more likely to be trading in range/directionless/mean reversting (80% of time) than trading in momentum/trending (20% of time). So if you plan to hold for multiple days, then leveraged ETF is not a good instrument.
7 If you do want a long-term position, but still need leverage what do you do? You can use futures to gain leveraged without suffering time decay. You can also use the underlying (ie X=1) with margin money. With a portfolio margin account, you can go up to 6-7X leverage with minimal margin interest payment at today's low FF rates. The key here is to keep notional exposure in check. On a return on capital basis, you will gain 5X, 10X, 20X leverage. However the multiplier will be a linear multiplier, ie you will not gain compounding. Do not use options, as options are non-linear contracts that are best reserved to trade the direction of volatility, not the direction of the underlying.
8 If you do not understand the points above, do not touch either leveraged etf or futures. Options certainly should also be out of your consideration.
Just my 2c.
顺便贴一篇类似的研究。
https://seekingalpha.com/article/4459750-a-deterministic-approach-to-tqqq
完全同意。 想TQQQ赚钱要判断对是range 还是trend market。VIX/VXN 可以帮助止损。如果VIX/VXN 还能分出RANGE/TREND market，那就找到印钞机了。margin 没法用上复利，而且有margin call。我去研究一下future。估计如果自己每天rebalance，交易spread，税会很不利。还不如在IRA里炒TQQQ。我在好好学学你的文章。
有研究说炒股如果避开10个大亏的交易日，回报会through the roof。 如果同时避开10个大亏的交易日和十个大涨的交易日会比BUY/HOLD 略好。我在学习是否类似的思路可以利用TQQQ不对称的高回报。
favorable tax treatment status
“Given recent volatility levels for NDX, TQQQ will underperform QQQ if NDX is up less than 9.8% over the next year. TQQQ will outperform QQQ if NDX is up more than 12%.”
QQQ 年化15%。
同理，如果VIX/VXN 降，就可以考虑上TQQQ。
所以先模拟一下再上真钱啊。
TQQQ还是移步大千吧，投坛更关注长期投资
Overnight.
if you have seven or eight figure account, NQ futures are far better product