Weird option strategies

[Deuteronomy_24_7]

Lets take a leveraged etf L with a leverage ratio of beta and model it's [sic] relationship with the underlying index returns.

To start, assume that underlying index is following a brownian motion process:
dS/S = vol * dW + m*dt
where W is Wiener process and m is drift. You would then express it's [sic] return process as:
dL/L = beta * dS/S - [ (beta - 1)* rate + fees ] * dt
= (rate - fees) * dt + beta * vol * dW
so, expressing the expected returns of the LETF in terms of the underlying index and it's [sic] vol:
Lt/L = (St/S) ^beta * exp{ -[ rate*(beta-1) + fees] * time - variance * time * (beta^2-beta)/2 }

the second term in the exponent implies that return of the leveraged ETF is going to be negatively related to variance of the underlying index.

If the return of a levered ETF is "negatively related to variance of the underlying index," then is a levered ETF on a more volatile underlying going to return less than one on a less volatile underlying? (Rhetorical question -- the answer is: of course not).

 

[tradelosses]

No it's what's called a subtle but crucial difference. Most of those things you listed, like fees, interest rates internal to the fund... are indeed decay. Decay, by the very meaning of the word, means to gradually go down, get worse... What you're not getting is that if you run a backtest where you rebalance the portfolio daily so that you're doing an apples to apples comparison, there is essentially no "decay" of this type. The entire difference in prices is accounted for by the fact that you're holding 2 different securities, on of which returns the daily percentage change of the index and one of which returns the index. It's pure math, you can do a spreadsheet simulation and see that in half the scenarios your bet goes up and in half it goes down. Something that is as likely to go up as down is not "decay" regardless of your lingo, that's like saying you're taking advantage of the "decay" of MSFT by buying the stock, and it likewise shows that you don't grasp the underlying idea. There are a large number of people who don't grasp this concept of leveraged and inverse ETFs. There are also a large number of people who don't grasp the sunk cost fallacy or the concept of Beta. I don't go with their incorrect view of an easily provable concept simply because there are "thousands" of them, but if you want to I'll always be happy to take the other side of your trades.

if done daily you're right but loner longer periods lag may occur depending on the path

 

[sle]

If the return of a levered ETF is "negatively related to variance of the underlying index," then is a levered ETF on a more volatile underlying going to return less than one on a less volatile underlying? (Rhetorical question -- the answer is: of course not).

Dude, did you work through the math? If you delta-hedge with the underlying, a levered ETF on a more volatile underlying will have a lower expected return. You don't need a model to grasp this concept, just sit down and do the math on a piece of paper.

PS. The borrow on these things will be consistent in most of the cases and if it does not, you can arb it against the options on the underlying.

 

[sle]

Only if you rebalance every day will you see the true inverse/2x/3x and if you do that you'll see there is virtually no tracking error. Backtest backtest backtest!

So what do YOU think will happen if you delta-hedge an LETF continuously (daily rebalancing is a good enough approximation)?

PS. any backtest of this will be probably missing an important component

 

[Sig]

So what do YOU think will happen if you delta-hedge an LETF continuously (daily rebalancing is a good enough approximation)?

PS. any backtest of this will be probably missing an important component

If you do what I think the OP was trying to propose, buying a put on UPRO and and selling a put on an equal notional value of ES taking into account the 3X of UPRO at roughly an equal percentage distance from the strike, and rebalanced daily at closing to get apples to apples, you would essentially be flat at the end of a given period. Actually you'd probably be down a good bit because of the transaction costs of rebalancing, so the opposite of what you wanted to accomplish. And the borrow rate on UPRO, which as you pointed out is reflected in the put price, is usually pretty high so you'd lose out based on that as well. I don't think, I've actually done the backtest, there's almost 0 tracking error in UPRO on 3X the daily change in the index, it does exactly what it says it's supposed to do absent the expense which is so small at .94% that you could never turn a profit off it with this kind of strategy. There is no "decay" in UPRO.

I spent a good day running down this rabbit hole and designing the backtest to show what I'm trying to describe. I'm trying to save others having to do it, although it is kind of fun so by all means replicate it if you enjoy that kind of thing like I do.

 

[tradelosses]

leveraged etfs are one of the small remaining goldmines in trading, as they are very complicated many don't understand them or appreciate their subtleties . For example, one could have made a literally risk free tidy sum during the flash crash of 2010 using 3x etfs...i'll let the reader figure out how . You need a good broker to trade them that charges very low commissions .

 

[tradelosses]

The ATM 71 UPRO put is $800/contract (going by the midpoint) that expires in 150 days. Buying 5x of these costs $4k and is almost the same as being short $52k SPY. The ATM SPY 214 put that expires in 150 days is $850/contract. Sell 5 of these = $4250 credit and is about the same as being long $52k SPY. Assuming the market ends unchanged after 150 days, UPRO will fall about $1 due to LEFT 'decay' factors, which means $500 profit. The total cost to run this is about 10k of collateral ,so the ROC is about 12% per year. more volatility means more profit

 

[sle]

leveraged etfs are one of the small remaining goldmines in trading, as they are very complicated many don't understand them or appreciate their subtleties.

Dude, you gotta take the borrow rate into account when trying to understand these things. This product is not a secret and it's been pretty efficient for a while now. You'd "get" even better results if you short inverse against regular leveraged, e.g. something like SSO vs SDO.

You can back out the fair borrow rate by taking the formula I posted above and taking logT-1 of the expected return using the underlying vol and the beta. Compare it to the forward implied by the options market and, surprise, there is no arb.

 

[Sig]

The ATM 71 UPRO put is $800/contract (going by the midpoint) that expires in 150 days. Buying 5x of these costs $4k and is almost the same as being short $52k SPY. The ATM SPY 214 put that expires in 150 days is $850/contract. Sell 5 of these = $4250 credit and is about the same as being long $52k SPY. Assuming the market ends unchanged after 150 days, UPRO will fall about $1 due to LEFT 'decay' factors, which means $500 profit. The total cost to run this is about 10k of collateral ,so the ROC is about 12% per year. more volatility means more profit

You need to iterate what "LEFT 'decay'" factors are. That "decay" could also turn out to be UPRO outperforming the SPY. By significantly more than 12% Just buy VIX futures if you want to make a volatility play.

 

[tradelosses]

lol buying vix futures is a cash incinerator . Because put options are used, losses are caped and it does not matter if UPRO outperforms