tag:blogger.com,1999:blog-1346045313195961352.post1117561132747456200..comments2019-03-05T04:03:32.081-08:00Comments on MatlabTrading: Guess what, leveraged etfs don't decay!Unknownnoreply@blogger.comBlogger25125tag:blogger.com,1999:blog-1346045313195961352.post-13419445439725090672015-09-15T08:21:05.891-07:002015-09-15T08:21:05.891-07:00There is decay because leveraged ETFs double or tr...There is decay because leveraged ETFs double or triple the PERCENTAGE change of the non-leveraged ETF, not the monetary price. So if today the price of USO is $10 and it increases by $1 to $11, that is an increase of 10%. If UCO (the 2x leveraged ETF) was also $10, it would increase by 20%, meaning it would go to $12. However, if USO were to fall tomorrow by $1 from $11 back to $10, a decrease of 9.09%, UCO would decrease 18.18%, which is actually a $2.18 decrease, meaning that then the price of UCO would be $9.82 compared to USO still at $10.<br /><br />It's the same thing if the prices fall first then rise: USO falls $1 from $10 to $9, a loss of 10%, which would mean UCO would drop 20%, from $10 to $8. If USO then regained $1 the next day to $10, that is a gain of 11.11%, which means UCO would rise 22.22% from $8, which only gets it back to $9.77.<br /><br />So yes, if the price hovers around the exact same spot, you will slowly lose money, which completely depends on the volatility of the market. It also greatly increases your losses or gains if the price trends up or down over a period of time. If USO is $10 and rises $1, or 10% in one day, it's price would go to $11, whereas UCO would gain 20% to $12. However, if USO gained that same $1 over 2 days...observe:<br /><br />USO day 1: gains $0.50 to $10.50 (gain of 5%)<br />UCO day 1: gains $1.00 to $11.00 (gain of 10%)<br />USO day 2: gains $0.50 to $11.00 (gain of 4.762%)<br />UCO day 2: GAINS $1.04764 to $12.04764 (gain of 9.524%)<br /><br />USO gained the exact same monetary amount, but split over two days, it resulted in UCO gaining $2.04764 gain instead of a $2 gain.<br /><br />So, you can still make money in leveraged-ETFs (and it doesn't always have to be day trading), but you need a clear picture of timelines and the effects of the decay. You're doubling down but giving the house a 49-51 advantage. This is not a game you play a lot, it's only for when you are supremely confident your chosen investment is about to trend upward within a carefully thought out timeline. You cannot think "I'll just buy it and forget about it for 10 years, and hope it's doing good then". This is a "for very good reason I think that within x amount of time it will rise x amount, which supersedes the small, constant penalty I will pay". <br /><br />Another way to think about it is that you are buying your investments with a credit card that you are paying interest on. If you're paying 10% APR on your card but use the money to make 18% on real estate tax liens, great, but if put that money into a CD making 2%...not so much. Unknownhttps://www.blogger.com/profile/05363267673904975353noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-75506627301075529312015-03-11T15:21:29.604-07:002015-03-11T15:21:29.604-07:00John Jiang or someone else, can you explain that f...John Jiang or someone else, can you explain that further? It seems most people here don't understand the concept since everyone disagrees with another. Very interesting!Johan LindÃ©nhttps://www.blogger.com/profile/07530784419183726575noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-31570078949613941812014-04-02T10:24:17.773-07:002014-04-02T10:24:17.773-07:00Most leveraged ETF re-balance daily. Re-balance is...Most leveraged ETF re-balance daily. Re-balance is the cause of decay. John Jianghttps://www.blogger.com/profile/01619290341167212896noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-60687253458641577422014-01-14T10:25:25.645-08:002014-01-14T10:25:25.645-08:00The expected return is very misleading. From your ...The expected return is very misleading. From your binomial tree, at the 3rd timestep, there is a 75% chance that you've lost money. At the 4th timestep you're back to 50% > 100 and 50% < 100. At t=5, 68.75% of the returns are less than 100 (you've lost money). Here's the breakdown at t between 1 and 25. I'm not sure what happens as t becomes very large, but after t=20 it looks like there is consistently a greater than 50% probability that you lose money (despite the fact that the expected value is 100).<br /><br />t=1; avg=100.0; % < 100 = 0.0<br /> t=2; avg=100.0; % < 100 = 0.5<br /> t=3; avg=100.0; % < 100 = 0.75<br /> t=4; avg=100.0; % < 100 = 0.5<br /> t=5; avg=100.0; % < 100 = 0.6875<br /> t=6; avg=100.0; % < 100 = 0.5<br /> t=7; avg=100.0; % < 100 = 0.6563<br /> t=8; avg=100.0; % < 100 = 0.5<br /> t=9; avg=100.0; % < 100 = 0.6367<br /> t=10; avg=100.0; % < 100 = 0.5<br /> t=11; avg=100.0; % < 100 = 0.623<br /> t=12; avg=100.0; % < 100 = 0.5<br /> t=13; avg=100.0; % < 100 = 0.6128<br /> t=14; avg=100.0; % < 100 = 0.5<br /> t=15; avg=100.0; % < 100 = 0.6047<br /> t=16; avg=100.0; % < 100 = 0.5<br /> t=17; avg=100.0; % < 100 = 0.5982<br /> t=18; avg=100.0; % < 100 = 0.5<br /> t=19; avg=100.0; % < 100 = 0.5927<br /> t=20; avg=100.0; % < 100 = 0.5<br /> t=21; avg=100.0; % < 100 = 0.5881<br /> t=22; avg=100.0; % < 100 = 0.6682<br /> t=23; avg=100.0; % < 100 = 0.5841<br /> t=24; avg=100.0; % < 100 = 0.6612<br /> t=25; avg=100.0; % < 100 = 0.5806<br />David Ellishttps://www.blogger.com/profile/01767576976005462783noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-39418585412342851862013-05-22T18:50:33.776-07:002013-05-22T18:50:33.776-07:00Hi sjev,
Trevor is correct in that your example a...Hi sjev,<br /><br />Trevor is correct in that your example already will cause the ETF decay over time without any leverage.<br /><br />Let's take your example of an ETF priced at $100. If this stock goes up 10% one day, then drops 10% the next, the end price will be 99, as your example shows.<br /><br />The demonstration of leveraged ETF decay should be shown by the original unleveraged stock maintaining its value. For this, you should take an ETF that starts at 100, and either goes up 10% or -9.0909%. Assuming it continues this trend daily, the price will stay at 100. 100*1.1*0.90909 = 1.<br /><br />Now take my example and make it 2x leveraged. So instead of going up 10% and going down -9.0909%, it would go up 20% and go down 18.1818%.<br /><br />If you multiply 100*1.2*0.81818, you will get 98.18, showing that levered ETFs decay over time.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-25016020460615686062013-05-14T02:21:00.013-07:002013-05-14T02:21:00.013-07:00Hi Paul,
Making money from a random walk??? Wow, ...Hi Paul,<br /><br />Making money from a random walk??? Wow, how??? (provided that a random walk has no mean bias)sjevhttps://www.blogger.com/profile/17452562180989360928noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-46959385444786228402013-05-14T01:20:27.069-07:002013-05-14T01:20:27.069-07:00Hi
I am not sure if I understand E Chan's que...Hi<br /><br />I am not sure if I understand E Chan's question.<br />Geometric random walk means Geometric Brownian motion? If yes, then<br /><br />dS/S = mu dt + sigma dW<br /><br />E(S(T)) = S0 exp ( mu T)?<br /><br />it is all depending on whether the trader knows the "true" drift rate from a crystal ball when he enters to the position, and ideally the vol is constant etc. <br /><br />I think random walk doesnt mean we can't make money assuming that we are SOOO smart knowing all the true parameter values<br /><br />PaulAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-69824128096793673752012-10-04T10:54:51.084-07:002012-10-04T10:54:51.084-07:00Think in terms of half as much being invested in a...Think in terms of half as much being invested in a 2x ETF, half deposited in a cash deposit account, let's say $50 invested, $50 cash deposit, compared to $100 being invested in the 1x (non leveraged).<br /><br />The 2x ETF manager takes the $50 you invested with them, and borrows another $50 in order to invest $100 in the underlying asset.<br /><br />If the return on the cash deposit is the same as what the ETF pays to borrow, there's no drag. More typically it costs more to borrow than the interest that is paid on cash, but by investing cash for a slightly longer term (3 months perhaps), the daily cost of borrowing can compare to the return received on 'cash'.<br /><br />If there's no difference on a individual daily basis, there will be no difference over the longer term either. <br /><br />Where apparent drag becomes apparent is that comparisons are made of the 1x non leveraged with that of having twice as much (same amount invested in 1x and 2x), which are two totally different investments (one has twice the volatility as the other for a starter) and compound out differently over time.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-54218777520430330232012-08-07T12:12:49.049-07:002012-08-07T12:12:49.049-07:00Reexamine your binomial tree. When the price rises...Reexamine your binomial tree. When the price rises 10% and falls 10% you loose one percent. When the opposite happens you also loose one percent. Sure you gain 1% if there is 2 consecutive 10% gains or losses. The disconect between your simulation and reality lies here. You assume that there is an equal chance of two consecutive gains or losses, or alternating gains and losses. In reality regression towards the mean occurs and you experience the 1% loss more often than you recieve the one percent gain for this reason alone. Even if there was an equal likelihood of either results two consecutive moves in either direction only increases the descrepancy between "current" and "regular" pricing setting the stage for an adjustment which will eliminate what you earned times 2 (or 3 for 3x leveraged etfs). In all your math you loose the psychology of the buyers and sellers, which is where the irrationality inhearant in the market lies, and while well documented cases of reality time and time again contrast with your utopian equations.Trevor Schumannnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-49074328860384253362012-07-23T17:08:41.588-07:002012-07-23T17:08:41.588-07:00Please, Please, Please keep investing money into l...Please, Please, Please keep investing money into leveraged ETF's. <br /><br />I love articles like this - they take money from the suckers, and put it into the hands of those who can think for themselves, and actually do the math for themselves.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-37363088568749183982012-06-30T03:18:12.432-07:002012-06-30T03:18:12.432-07:00Shouldn't you have used risk-neutral probabili...Shouldn't you have used risk-neutral probabilities when constructing the binomial model above?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-7871517607822917082012-05-08T08:03:36.334-07:002012-05-08T08:03:36.334-07:00The analysis is correct based on the assumption th...The analysis is correct based on the assumption that daily price movements are either UP or DOWN by a fixed percentage (e.g. 0.5% per time step). Financial markets do not follow this rule. Some days the index remains unchanged.<br /><br />One option is to download daily price movements from Yahoo. Another is to just use a random number generator and scale the output distribution:<br /><br />N=200;<br />dY_percent = randn(N,1)./100; % one year of pct changes<br /><br />Now when you run the Monte Carlo simulution, use dY_percent for the price change:<br /><br /><br />values=nan*ones(N,1);<br />values(1)=1.00;<br />for i=2:N;<br /> values(i)=values(i-1).*(1+dY_percent(i));<br />end<br /><br />The numbers is 'values' will most always trend down in time, however sometimes they can go up. Put all the code in a second for loop and repeat a few hundred times. You can now calculate the expected probability that the leveraged ETF will be above 1.0 or below 1.0 after N trading days... or just plot the median for a quick idea if the trend is up or down. As number of trading days (N) increases, the probability of the ETF being DOWN is greater than the probability of it being UP.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-24406048615300844182012-03-13T08:10:43.971-07:002012-03-13T08:10:43.971-07:00question: if one was to short svxy or xiv as a hed...question: if one was to short svxy or xiv as a hedge on if the market crumbles, does con tango/ backwardation / decay help as a tailwind? I'm researching this topic of whether inverse etn/etf's have this advantage and I'm getting different directions from multiple websites. I would think there is some sort of decay. Case in point: chart 1year vxx vs xiv and 1 year chart xiv vs spy. Please help me understand thisJ.Douglas.wood@gmail.comnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-38269993532044273902012-03-07T08:08:36.415-08:002012-03-07T08:08:36.415-08:00There is decay relative to an underlying index. Y...There is decay relative to an underlying index. You are just showing the averages for each binomial tree and only using a two period case (a critical error of extrapolation is then made). Find the average value for a 2x vs an index for each simulation, not independently over many nodes. This average will be negative, ie.there is expected decay. This decay is based on the fact returns are both positive and negative over time. Even theoretically, you almost always get the middle modes of your binomial tree. If the returns are always up, or always down, like in the two cases of your two period binomial there is actually positive "decay." This is offsetting the negative decay you find in the middle node. With a bigger tree, your negative decay outcomes will far exceed your positive and the average will not be zero.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-91961988941446401932012-01-02T19:02:09.798-08:002012-01-02T19:02:09.798-08:00Ummm there IS decay, if you compare a leveraged ET...Ummm there IS decay, if you compare a leveraged ETF vs the underlying. Compare going through the SAME branches of the binary tree for a 10% vs a 5% return. The 10% does NOT yield 2x!!! It decays when there is any volatility!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-79694406060602325182011-12-17T23:49:34.924-08:002011-12-17T23:49:34.924-08:00Yes, you are right. Expected returns are indeed th...Yes, you are right. Expected returns are indeed the same under your assumptions. <br /><br />What others have said is true though. There is a clear decay in real market environments. Shorting a leveraged ETF does have an edge but it also requires more capital since the position can ago against you (plus the borrowing costs).iggyhttps://www.blogger.com/profile/03466293569222318388noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-41418698710416399242011-12-17T13:46:52.552-08:002011-12-17T13:46:52.552-08:00@iggy: I've got fooled by the geometric return...@iggy: I've got fooled by the geometric returns at one moment, but take a second look at the binomial tree. It is all about the expected return, which stays the same, no matter what kind of leverage is employed. Still not convinced? Just run a Monte-Carlo sim...sjevhttps://www.blogger.com/profile/17452562180989360928noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-60964401001406198022011-12-17T13:25:45.247-08:002011-12-17T13:25:45.247-08:00I might be wrong but I think you are looking at th...I might be wrong but I think you are looking at the wrong average. Shouldn't you be looking at the geometric average instead? Or alternatively, the mean of log returns. Notice that log(0.99) < -0.01 whereas log(1.01) < 0.01 so 1% gains and losses don't exactly match.<br />As a result, as sequence of 1% returns with an equal number of gains and losses will lose money: (1.01)^n * (0.99)^n < 1iggyhttps://www.blogger.com/profile/03466293569222318388noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-64737705736903131552011-07-30T19:31:22.085-07:002011-07-30T19:31:22.085-07:00Leveraged ETFs need not decay, in terms of expecta...Leveraged ETFs need not decay, in terms of expectation, in your idealized iid models, but the differences between the real world and your models for many of these products imply that they do decay under a more realistic expectation. <br /><br />For example, there are many leveraged ETFs where bonds are the underlying. Bond prices are mean reverting (interest rates are mean reverting), so are not realistically modeled by iid processes. This will imply a decay in expectation of these leveraged products over time.<br /><br />Even equities exhibit some mean reversion that would imply that these decay. For example, try computing the variance rate per unit time of SPY taken from yahoo daily, weekly, and monthly data. Any stochastic process with uncorrelated increments (e.g. GBM) has a variance rate that is independent of the sampling window. You will find, however, that for SPY that rate strongly shrinks as the sampling window increases. This is evidence of mean-reversion. To the extent that you believe the future prices will retain this feature, then any realistic expectation for a leveraged SPY shows it leaking value due to its mean-reversion.Winslownoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-29616030759712137172011-06-05T13:29:45.948-07:002011-06-05T13:29:45.948-07:00Absolutely! Leveraged etfs don't decay. At lea...Absolutely! Leveraged etfs don't decay. At least at theory (or in ideal world). This even can be shown analytically.<br /><br />Recently I performed Monte Carlo Simulation Model of some leveraged ETFs (based on GBM ... with Margin Call, with limitation on daily profit/loss, constant vs dinamic adjustment of leverage, etc). Results help me understand why this myth is so popular.<br /><br />Actually many people just are confused. There is a trick in puzzles like this. I'll try to publish my thoughts on this to my blog or seekingalpha soon.<br /><br />Anyway thanks for articles. I get a lot of pleasure from reading.<br /><br />Have a good time ...Nicholashttps://www.blogger.com/profile/09959976537957483849noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-15727935719854149132011-05-21T08:55:59.073-07:002011-05-21T08:55:59.073-07:00The expectation of a price process with 0 drift an...The expectation of a price process with 0 drift and even probabilities of up/down movements is 0, yes. So you are correct in terms of long run process under these assumptions.<br /><br />In fact in equities there is more often a significant bias towards positive return (i.e. higher prob of daily positive return). So with the compounded approach on an ultrashort, the capital / share base will bleed away on these days since at EOD these are closed out back into cash (in theory) and on the next day will be able to purchase fewer shares.<br /><br />Negative price movements tend to be much larger, but less frequent than positive. One could have k x as many positive movements as negative but because negative larger could net out in the end to a 0 return, say, over some period. Because of the price path over the period though, the short on $200 vs the ultrashort ETF on $100 loses less (or 0 in this case).<br /><br />So in practice this positive return bias (or bias of the price movement probabilities) plus the tracking error often make for the decay ...<br /><br />But I'm sure I'm not saying anything you don't already know. Just clarifying for my purposes.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-9986752673529975762011-05-21T02:16:28.791-07:002011-05-21T02:16:28.791-07:00@Tr8der: my point is that *expected* return over t...@Tr8der: my point is that *expected* return over the long run in case of leveraged etfs is zero. However, negative result is *most probable*.<br />The 'double-or-nothing' case presented in the comments illustrates this perfectly. <br />In other words, there is no 'edge' in shorting leveraged etfs without expressing a view on the <br />future volatility.sjevhttps://www.blogger.com/profile/17452562180989360928noreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-34964462071649065332011-05-20T17:02:21.086-07:002011-05-20T17:02:21.086-07:00Jev, hi. Your binomial tree is fine, but I am no...Jev, hi. Your binomial tree is fine, but I am not sure that it disproves ETF decay. Perhaps the question is decay relative to what? <br /><br />So for instance if one invests 100$ in a 2x ultrashort ETF and 200$ short on the underlying ETF for a period of a week, the end value of the two will surely be different because of:<br /><br />- the path up and down of the price at end-of-day decreases or increases the capital base for the next day's investment in the ETF (i.e. compounding)<br />- tracking error in the implementation of leverage either through options or borrowing costs, or both<br /><br />Perhaps I misunderstood what you are showing.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-86994183574746798532011-05-17T00:41:32.652-07:002011-05-17T00:41:32.652-07:00Great post, keep 'em coming!Great post, keep 'em coming!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-1346045313195961352.post-20318093385846344952011-05-16T22:07:53.090-07:002011-05-16T22:07:53.090-07:00This is easiest to see at the extreme: double or n...This is easiest to see at the extreme: double or nothing.<br /><br />The expectation E(X) = 2*X*(p=0.5)+0*X*(p=0.5) = X<br /><br />So the expectation is to be flat. However, after n rounds, you will have 2^n money with probability 2^-n, and zero otherwise. So, given enough time, you will almost surely have zero money, although the expectation is always to be flat.Anonymousnoreply@blogger.com