I'm trying to better understand leveraged etfs, and specifically how they have convexity and volatility decay similar to options.
An older post on this site asked a similar question and one of the respondents and the article they linked talked about how if you pair trade 2 leveraged etfs, where you either short 2 related leveraged etfs or go long two leveraged etfs. The idea being, that by doing so you're creating a position similar to a straddle, so if you go long say SPXL and long SPXS you're long a straddle and you're long gamma (convexity) and short theta. But where does that show up? I created a simple example in excel where I tried to simulate something like this, but all I see is 0 PnL and no gamma and no theta.
I created a simple simulation. I assume you have 2 triple leveraged etfs, one is a triple long, the other is a triple short. I assumed the underlying index moves randomly anywhere between -15 and 15%, and the triples obviously move 3x each day.
I assume that both indices start off at $100, and we purchase 1,000 units each, and then systematically re-balance a the end of each day to maintain a 50-50 exposure.
When I do this, my portfolio value, unsurprisingly remains flat at $200k.
As an example, the first day we come in with a position of +1000 units in the 3x Long etf, and +1000 in the 3x Short etf. The index moves down 7%, so the long etf declines to 79 dollars and the short etf declines to 121. Portfolio value remains flat at $200k
Then I rebalance, increasing long index exposure to 1.26k and decreasing short index exposure to 826. Same result. I only included 10 days of data, but I tested this multiple times and nothing changes, this isn't surprising after all.
If we assume r is the return of the underlying index our portfolio value is this for any given day:
On the first day we have:
100k *(1+3R) + 100k(1-3R) = 200k
. So it never changes.
I must be missing something, and I can't figure it out. Where is the convexity, where's the theta? Can someone please explain?