基于过去，两倍杠杆eft 的 回报比 1 倍，3 倍好，但并不代表未来

1885 to 2009

1950 to 2009

more etf comparison:

 

Daily volatility hurts the returns of leveraged ETFs (including those with leverage 1). This is due to the equality

(1 - x)(1 + x) = 1 - x²

Suppose the market goes down by x and then the next day it goes up by x. For example if x = 0.05 then the market goes up by 5% then down by 5%. Then the net result is that the market has gone to (1-0.05) times (1+0.05) = 0.9975 which is a drop of 0.0025 or 0.25%.

That’s not fair! The market has gone down by 5% then up by 5% but our ETF that has a leverage of 1 has gone down by 0.25%. Doggone it!

This drop always occurs because x² is always positive and the sign in front is negative. So whenever the market has volatility we lose money. We call this volatility drag.

The larger x is the larger x² is so the larger the volatility drag. For a leveraged ETF the leverage multiplies x and so multiplies the volatility drag. Even an ETF with a leverage of 1 has volatility drag.

The myth has resulted from the belief that volatility drag will drag any leveraged ETF down to zero given enough time. But we know that leverage of 1 (i.e. no leverage) is safe to hold forever even though leverage 1 still has volatility drag. If 1 times leverage is safe then is 1.01 times leverage safe? Is 1.1 times safe? What’s so special about 2 times? Where are you going to draw the line between safe and unsafe?

Maybe 2 times is safe. Why shouldn’t an ETF with leverage 2 still be suitable for holding forever?

It turns out that there may be a reason but it’s not volatility drag.

 

如果一倍 eft 可以buy and hold， 为啥不能 1.1 倍？ 为啥不能1.2 倍？ 为啥不能 2 倍？

 

Conclusion

Leveraged ETFs can be held long term provided the market has enough return to overcome volatility drag. It usually does. For most markets in recent times the optimal leverage is about 2. But some markets and time frames will reward a leverage of up to 3. No markets will reward a leverage of 4.

Myth busted!

如果你不是很快退休的话，应该长投 qld 而不是 qqq

Usual Warning

Despite the findings in this article the usual warning about leverage still applies to leveraged ETFs:

In a rising market leverage greater than one will boost returns. In a falling market that leverage will boost losses. In any market leverage greater than one increases volatility.

Leveraged ETFs can drop to zero if the market drops enough in one day. You can lose all your money.

This article has not proved that the optimal leverage is about 2.

It has just demonstrated that 2 has been good in the past. The future may be different.

 

References

Schwert, W. Indexes of United States stock prices from 1802 to 1987
(1990) Journal of Business, 63, pp. 399-426.