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replacement
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 2:28 am

Is it ever more profitable to short a long 2X product rather than just buy the -2X product?To test this, I wrote a program where each day's return is calculated as follows:return=mu/252 - (vol/sqrt(252))^2/2+randn(1,1)*vol/sqrt(252);Then, the 2X stock value was multiplied by exp(2*return) each day and the -2X was multiplied by exp(-2x) each day.Based on this process, it never makes sense to short the 2X long. But, what if I don't assume lognormal stock prices (i.e. the 2X product is multiplied by (1+2*return) each day)? When I run the program under these conditions (stock prices aren't lognormal) with the same methodology for calculating daily returns, sometimes it's profitable to short the 2X.Do I need to make an adjustment to the daily stock price calc when I don't assume lognormality or is it actually better to short the 2X product sometimes?
 
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bostonquant
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 3:35 am

Does your "model" tell you the market is heading up or down?
 
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 3:56 am

I ran it a few different ways (positive drift, negative drift, and zero drift). In all cases where lognormal stock prices are assumed (S(t)=S(t-1)exp(return), the mean ending stock price is just S(0)*exp(mu*t).This makes sense as the expected stock price is E(Y ) = exp(k+.5*sigma^2), where k is the cc rate of return (k has a mean of mu - .5*vol^2). This is shown here http://tinyurl.com/5uv7ao and in Hull.The way I interpret this: the "average" return per year (k) is lower than mu due to the difference between the arithmetic average and geometric average, while the +.5*sigma^2 in the expected stock price is due to the lognormal stock price distribution.Thoughts?
Last edited by replacement on November 18th, 2008, 11:00 pm, edited 1 time in total.
 
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bostonquant
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 11:00 am

QuoteThoughts?Over the long run corporate earnings and profits will keep increasing so unless earnings multipliers shrink the market will keep increasing.
 
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 12:30 pm

QuoteOriginally posted by: bostonquantQuoteThoughts?Over the long run corporate earnings and profits will keep increasing so unless earnings multipliers shrink the market will keep increasing.Any relevant thoughts?
 
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bostonquant
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 7:10 pm

QuoteOriginally posted by: rynoblasterQuoteOriginally posted by: bostonquantQuoteThoughts?Over the long run corporate earnings and profits will keep increasing so unless earnings multipliers shrink the market will keep increasing.Any relevant thoughts? I'm trying to tell you as nicely as possible that what you have is completely useless.
 
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Better to short 2X ETF or go long -2X ETF

November 19th, 2008, 8:48 pm

Oh... I think I get why you think the thread is "useless" and now I understand why you asked about the direction of the market: you thought I was basically asking whether it makes sense to go long or short the market. Ha!That's not what I was asking. There are 2X ETFs that target 2 times the daily return of the underlying index, and there are also -2X ETFs (inverse ETFs) that target 2 times the inverse daily return of the underlying index.So, if I wanted to short the market, I could either buy the inverse product, or short the long product.If you compare the returns over the past year from shorting the long 2X equity products (i.e. SSO) vs buying the inverse counterpart (i.e. SDS), you'll see you would have been better off shorting the 2X long (SSO) than buying the -2X product (SDS).The reason for this is mostly related to compounding and the oscillating daily returns. If the underlying had returns of 5% and -5%, buying the inverse (SDS) would have lost you $1, while shorting the 2X long (SSO) would have made you $1.But, using St=S0*exp(r1+r2) as in my orginal simulation, you'd be flat in both long SDS and short SSO, which is clearly wrong.So my main question is: if I want to simulate stock prices where St=S0*(1+daily_return) rather than St=S0*exp(daily_return), how do I adjust (if at all) the formula for generating daily returns?Apologies for the confusion and thanks for your help...
Last edited by replacement on November 19th, 2008, 11:00 pm, edited 1 time in total.
 
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glennchan
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Better to short 2X ETF or go long -2X ETF

January 10th, 2009, 2:28 am

Isn't there an easy way to solve this problem???1- The prospectus tells you what the risks are and what the management fees are. For the sake of simplicity, we'll ignore most of the risks like index tracking error.As far as management fees go, they will absolutely drag the price down. They may also increase in the future (for some proshares ETFs, they go up 3%). The excessive management fees may favour shorting the ETF.2- The dominating factor will be the constant leverage trap. If the market exhibits excess volatility + reversion to the mean, then the constant leverage will drag the price down. If however the market moves in the same direction for multiple days (or movement away from the mean), then the effect of increasing leverage can be explosive.Usually it is the case that markets will exhibit excess volatility + reversion to the mean (or act like Ben Graham's "mr. market") so shorting the ETF has higher expected return. Any backtesting will probably show this. (e.g. go to Google finance and plot SSO and SDS, or BGU and BGZ). However, you have to be careful that repeated movements in the same direction don't cause one ETF to explode (the other long/short ETF will move in the opposite direction, but not enough).I think it might be interesting to evaluate shorting SSO and SDS while hedging your position by buying far out of the money call options on both ETFs. You might have to roll your own model here if it doesn't take into account reversion to the mean (or away from it)?And then figure out if highly improbable events that we've never seen before (e.g. market goes +20%, 20% 20%) can hurt you.