Here is an example of 'easy money'. I've simulated a random walk (upper chart in blue) that has 50/50% chance of going up or down every day. And it always moves exactly by 3% (log, so it should be flat over the long run ). From this reference I've created two leveraged trackers, with +2x and -2x leverage, I'll call them 'up' and 'down'.

Suppose we start a 100 day period with a pair consisting of equal amounts of capital in 'up' and 'down', both equal to 100$. So the pair value on day 1 is $200. Pair value is plotted in the lower chart. Without a trend in the reference, the pair value decays at a constant rate

*exp(0.5log(leverage*(1+daily_delta))+0.5log(*. If we short both 'up' and 'down' the lower chart will flip upside down, producing pretty good looking pnl.

*leverage*(1-daily_delta)*))But before you short sell every available leveraged etf out there, take a look at the next chart:

All the parameters here are the same, only the underlying has two brief periods of consecutive wins or losses. This results in two heavy spikes in the pair value. If we would have shorted both 'up' and 'down' the result would be a pretty heavy drawdown. No easy money here...

unless you short using options, which is what would be preferable given that spikes can occur (don't need a simulation for that?)

ReplyDelete@Anonymous: yes, this type of strategy is similar to selling options: you get a steady return from theta, but time to time you can get hit by a drawdown.

ReplyDeleteVery similar to running a lottery: steady returns from selling tickets, but once in a while you have to cash out a jack-pot. If you get to pay too many jack-pots in a row, you're out of business.

Jev, your posts are very interesting and informative. Please keep up the good work.

ReplyDeleteIf you look at the strategy PnL profile in relationship to its underlying, the strategy is actually similar to a long gamma position rather than a short gamma/long theta position, i.e. selling an option:

1. When the underlying is volatile, you make money; when it has low realized vol, you lose money.

2. When you long a straddle, you make money from dynamic hedging (assume implied vol does not change to make things simpler). Hopefully that PnL is more than the theta decay. With the double short ETF positions, you don't have to do dynamic hedging yourself because the ETF sponsor is doing that for you on daily basis. But someone is doing it nevertheless.

3. You also incur a theta decay: consider the funding cost (or opportunity cost if it's your own capital) on your margin collaterals and borrowing costs. ETFs like FAS, FAZ are expensive to borrow if you can locate them at all. In volatile periods, you may find the borrow rate either too expensive or impossible to find; of course, you can get recalled and forced out your position if you had borrowed before. These are the costs of owning this synthetic straddle position.

4. As the underlying drifts up or down, you rebalance the ETFs positions, similar to rolling the straddle position forward at new strikes periodically.

5. Similar to the straddle position, the PnL of the ETF portfolio is path dependent of the underlying, a typical behavior of an option portfolio with dynamic hedging.

I find it quite intellectually intriguing to construct a synthetic option position using cash products, especially in this case little need for dynamic hedging. However from a practical perspective, the leverage will be limited due to Reg T Margin requirement for most people when shorting the ETFs, whereas you could gain much higher leverage when trading options, therefore affecting your return on capital. Of course, it's a different story if you run a prop desk in an investment bank.

I agree with you that this is no free lunch. The return of the strategy is driven by difference between the realized vol and the "implied vol" ( the cost of putting on the position). Which is higher? Let me know if someone knows the answer :-)

Wei, thank you for a very insightful comment. My plan is indeed to implement a similar strategy using options one day. I am aware of the difficulties involving shorting FAS and FAZ and I will most probably not trade their decay.

ReplyDeleteHowever, leveraged etfs provide an excellent case for hedging algorithm development.

Interest post, sjev, but I think your analysis is incorrect. If your reference index has expected return of 0 ( up/down x % with 50% chance ) then leveraged or inverse product will also have 0 expected return no matter the multiplier. What changes with leverage is median return - which becomes lower as absolute value of leverage factor increases. You can verify this by doing bootstrap - run 1000 simulations and you will see that most of them decay, but few go up, and make up for the rest with the average 0 return. Or if you want a theoretical perspective construct a two-period binomial model. You will see that average return stays at 0 while median return decreases. Also your formula for decay (and that would be median decay) most certainly should not have logs. As regards to Max Dama trade - judging from his response it looks like it was a paper trade - for example my broker changes 6% and 1% to short FAZ and FAS - which would significantly impact the profits.

ReplyDelete@~ : I have a feeling there is something not quite right with my analysis, but I can't put a finger on it.

ReplyDeleteI still have to make the puzzle fit in terms of expected return per period for multiple periods, which is clearly < 0 and the mean & median returns.

My understanding of this matter is clearly <100%, but I'm working on it.

From reading some of the posts here it's claear that most of you have a lot more technical experience than myself, but my question is this... in simple terms wouldn't short selling both long and short 3x etfs cancel out each others risk regardless of volatility because their prices have an inverse relationship?

ReplyDelete