Simulating Returns of Leveraged ETFs

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Re: Simulating Returns of Leveraged ETFs
siamond: I would be happy to try to reproduce some of your results and play around with the data myself. Can you write a post or send me a PM with links to all of the raw and simulated data? It would be helpful to have all of that consolidated in one place.
Re: Simulating Returns of Leveraged ETFs
Yes, sorry, I didn't express myself clearly. I meant that we do not have any daily price or total return data series readily available until 1997. I did take note of the suggestions you expressed in an earlier post, this is exactly what I meant when I said that "This is an area where we can probably find a way to improve, if motivated enough". Do you want to give it a try generating such data for IT (7 to 10 years) and LT (20+ years) treasuries? What we really need is a solid proxy for daytoday volatility for each month, so I don't think we need the whole 'bond fund' model.Kevin M wrote: ↑Sat Mar 09, 2019 6:23 pmWe have daily 10year CMT from FRED starting in 1962. We have daily 30year CMT starting 1977, and daily 20year starting 1993, but of course with some gaps.
We have daily FRB 10year and 9year yields starting 1971, daily FRB 20year and 19year starting in 1981, and daily 30/29year starting in 1985.
All of these are par yields, so price return and income return can easily be calculated from the yields.
Re: Simulating Returns of Leveraged ETFs
This would be fantastic. Please check your PMs.interestediniras wrote: ↑Sat Mar 09, 2019 7:26 pmsiamond: I would be happy to try to reproduce some of your results and play around with the data myself. Can you write a post or send me a PM with links to all of the raw and simulated data? It would be helpful to have all of that consolidated in one place.
Re: Simulating Returns of Leveraged ETFs
Hm, silly me, I didn't apply the ER properly when I assembled the spreadsheet earlier yesterday. As a bonus for downloading an updated version, you'll get the midcap and smallcap leveraged numbers (extended back in the 50s).siamond wrote: ↑Sat Mar 09, 2019 2:35 pmHere is a Simba backtesting spreadsheet customized with annual LETF leveraged data (S&P 500, ITT, LTT; 2x and 3x; 1955+) coming from our modeling efforts. I assumed a 1% Expense Ratio for all leveraged funds, and used the various 'adjustment factors' we discussed in the past few posts. For more information about such backtesting spreadsheet, check the corresponding wiki page, check the README tab of the file, and if you have a point question, shoot me a private message.
https://drive.google.com/open?id=16ORud ... WfTP0FggA
Re: Simulating Returns of Leveraged ETFs
See PM!
Kevin
....... Suggested format for Asking Portfolio Questions (edit original post)
Re: Simulating Returns of Leveraged ETFs
I added Gold (price, not miners) leveraged data series, starting in 1969 (all daily), based on the LBMA Gold Price PM USD index.
And I ran my usual test against actuals. Not many leveraged funds tracking Gold besides ProShares (note that Direxion used to, then closed its 'BARS' fund, and now focuses on Gold Miners which is a completely different thing). I had to run a Total Return comparison instead of a Gross Return comparison, so that I could include DGP, a Velocity leveraged ETN, in addition to ProShares UGL. For whatever reason, I can't get Gross Returns data series for ETNs... Anyhoo, I used an ER averaging the ER of both funds, then had to add a 1% curvefitting 'adjustment' factor to make the telltale lines reasonably flat. I was surprised to find high friction costs in this case, as tracking the price of gold sounds much simpler than tracking entire segments of the stock/bond markets.
I updated all my spreadsheets (incl. the custom Simba), those of you I shared a link with only have to download again the file(s), same link. Enjoy.
And I ran my usual test against actuals. Not many leveraged funds tracking Gold besides ProShares (note that Direxion used to, then closed its 'BARS' fund, and now focuses on Gold Miners which is a completely different thing). I had to run a Total Return comparison instead of a Gross Return comparison, so that I could include DGP, a Velocity leveraged ETN, in addition to ProShares UGL. For whatever reason, I can't get Gross Returns data series for ETNs... Anyhoo, I used an ER averaging the ER of both funds, then had to add a 1% curvefitting 'adjustment' factor to make the telltale lines reasonably flat. I was surprised to find high friction costs in this case, as tracking the price of gold sounds much simpler than tracking entire segments of the stock/bond markets.
I updated all my spreadsheets (incl. the custom Simba), those of you I shared a link with only have to download again the file(s), same link. Enjoy.

 Posts: 369
 Joined: Fri Sep 21, 2012 1:55 pm
Re: Simulating Returns of Leveraged ETFs
It's noisy, but it doesn't look horrible. Can you tell what the average negative alpha is for DGP?siamond wrote: ↑Mon Mar 11, 2019 2:58 pmI added Gold (price, not miners) leveraged data series, starting in 1969 (all daily), based on the LBMA Gold Price PM USD index.
And I ran my usual test against actuals. Not many leveraged funds tracking Gold besides ProShares (note that Direxion used to, then closed its 'BARS' fund, and now focuses on Gold Miners which is a completely different thing). I had to run a Total Return comparison instead of a Gross Return comparison, so that I could include DGP, a Velocity leveraged ETN, in addition to ProShares UGL. For whatever reason, I can't get Gross Returns data series for ETNs... Anyhoo, I used an ER averaging the ER of both funds, then had to add a 1% curvefitting 'adjustment' factor to make the telltale lines reasonably flat. I was surprised to find high friction costs in this case, as tracking the price of gold sounds much simpler than tracking entire segments of the stock/bond markets.
I updated all my spreadsheets (incl. the custom Simba), those of you I shared a link with only have to download again the file(s), same link. Enjoy.
Re: Simulating Returns of Leveraged ETFs
DGP is noisy, but UGL is not. But then, this is ProShares and those folks seem to be the best around, from what I could observe in this modeling endeavor. On the other hand, an ETN isn't supposed to have much tracking error (that is, besides the ER)? Not that I know much about ETNs, to be honest.gtwhitegold wrote: ↑Mon Mar 11, 2019 4:46 pmIt's noisy, but it doesn't look horrible. Can you tell what the average negative alpha is for DGP?
Negative alpha? Well... around 1% as I already mentioned!
I did a more precise calculation, and the CAGR difference between the model (without an adjustment factor and using the DGP ER) and DGP was 1.5% (annualized). This actually triggered me to refine a bit the 'adjustment factor' in my model and now the chart looks like that, which is more satisfying. Shesh, that's a lot of friction costs...
Note that both funds have approximately $80M of assets as of today, which isn't too bad for this narrow market of leveraged funds. They were significantly bigger a few years ago though (in Jan12, ~$400M for UGL and ~$600M for DGP), the price of gold was higher by then, but still, they've been bleeding investment$ pretty bad.

 Posts: 369
 Joined: Fri Sep 21, 2012 1:55 pm
Re: Simulating Returns of Leveraged ETFs
I agree that it is ugly and I'm pretty sure that I don't want to take counterparty risk by investing in ETNs. I do appreciate the work you and others have put into this though.siamond wrote: ↑Mon Mar 11, 2019 5:13 pmDGP is noisy, but UGL is not. But then, this is ProShares and those folks seem to be the best around, from what I could observe in this modeling endeavor. On the other hand, an ETN isn't supposed to have much tracking error (that is, besides the ER)? Not that I know much about ETNs, to be honest.gtwhitegold wrote: ↑Mon Mar 11, 2019 4:46 pmIt's noisy, but it doesn't look horrible. Can you tell what the average negative alpha is for DGP?
Negative alpha? Well... around 1% as I already mentioned!
I did a more precise calculation, and the CAGR difference between the model (without an adjustment factor and using the DGP ER) and DGP was 1.5% (annualized). This actually triggered me to refine a bit the 'adjustment factor' in my model and now the chart looks like that, which is more satisfying. Shesh, that's a lot of friction costs...
Note that both funds have approximately $80M of assets as of today, which isn't too bad for this narrow market of leveraged funds. They were significantly bigger a few years ago though (in Jan12, ~$400M for UGL and ~$600M for DGP), the price of gold was higher by then, but still, they've been bleeding investment$ pretty bad.

 Posts: 369
 Joined: Fri Sep 21, 2012 1:55 pm
Re: Simulating Returns of Leveraged ETFs
Maybe the next thing to work towards is what level of leverage is the most efficient. I've seen mentions of 1.25x and 1.5x, but I don't see where the numbers came from. Any thoughts, or did I just miss it?
Re: Simulating Returns of Leveraged ETFs
There are multiple leveraged funds from Guggenheim, the Rydex family, which have been in existence for quite a while, and use this kind of odd multipliers, so I used some of them for my reality check testing. Check here:gtwhitegold wrote: ↑Mon Mar 11, 2019 7:59 pmMaybe the next thing to work towards is what level of leverage is the most efficient. I've seen mentions of 1.25x and 1.5x, but I don't see where the numbers came from. Any thoughts, or did I just miss it?
https://www.guggenheiminvestments.com/m ... leveraged
Re: Simulating Returns of Leveraged ETFs
Hi siamond  i was playing around with my own naive simulations using linear regression and feeling good till I stumbled upon this discussion. Amazing work by you and other on this thread to make simulations so close to the reality. Can you share daily/monthly simulated prices to play around with the real stuff?
Re: Simulating Returns of Leveraged ETFs
Tx. Please check your private messages.levitate wrote: ↑Tue Mar 12, 2019 6:03 pmHi siamond  i was playing around with my own naive simulations using linear regression and feeling good till I stumbled upon this discussion. Amazing work by you and other on this thread to make simulations so close to the reality. Can you share daily/monthly simulated prices to play around with the real stuff?
Re: Simulating Returns of Leveraged ETFs
I had two independent discussions today, which both reminded me that I had a lingering doubt about what I described here:
An alternate approach would be to simply use the intramonth volatility of the S&P 500 price series (until Dec87) and simply avoid to inject dividends. After all, price changes clearly drive volatility, while dividends flows tend to be much more stable. And since the 'magical formula' described here only requires monthly CAGR (of the index) and intramonth volatility, we could use a solid proxy for the latter and still have proper (and possibly better) results.
I gave it a quick try for the 1988+ time period (for which we have all daily data, hence no risk of distorted math). I used price volatility and the magical formula, computed leveraged returns and I can hardly notice the difference with the exact math.
Then I did the same for the 19551987 time period, and compared my previous approach to the new one. The differences are then noticeable, notably for the 3x leverage series. I mean, it's not huge, but it is visible (predictably making the leveraged returns a tad better). And the more I think about it, the more I convince myself that the approach using priceonly volatility is more straightforward AND should be more accurate than my previous approach with the spacedout dividends.
I will hold on making corresponding changes for now, as I'm having a parallel discussion with Kevin about bonds where I suspect we'll end up reaching a similar conclusion, relying on pricing data (derived from daily yields) as a more accurate volatility proxy for the old days.
What has been nagging me is that the 'derived' data series (needed until Dec87) displays a bit of a sudden 'hiccup' at the end of the month (or quarter) when dividends come in (because this is all we have with the corresponding historical data). And this 'hiccup' may have some unfortunate sideeffects on the intramonth (day to day) volatility math. While in reallife, dividends of the S&P 500 underlying components come in a much more distributed (over time) manner. I mean, this should be a fairly minor effect, but when the leveraging math applies its magnifying effect, I was wondering if this might create some non negligible distortion.siamond wrote: ↑Sat Mar 09, 2019 3:31 pmAbout S&P 500, I think we have a pretty solid data set going back to the mid50s. We don't have daily TR series for the index until the late 80s, but we do have monthly total returns and daily prices, and that's good enough to assemble a derived daily TR series and capture intramonth volatility. I provided more details in this post. Note that for some of the very early years, we only have quarterly dividends, which gave me some grief, but I made it work.
An alternate approach would be to simply use the intramonth volatility of the S&P 500 price series (until Dec87) and simply avoid to inject dividends. After all, price changes clearly drive volatility, while dividends flows tend to be much more stable. And since the 'magical formula' described here only requires monthly CAGR (of the index) and intramonth volatility, we could use a solid proxy for the latter and still have proper (and possibly better) results.
I gave it a quick try for the 1988+ time period (for which we have all daily data, hence no risk of distorted math). I used price volatility and the magical formula, computed leveraged returns and I can hardly notice the difference with the exact math.
Then I did the same for the 19551987 time period, and compared my previous approach to the new one. The differences are then noticeable, notably for the 3x leverage series. I mean, it's not huge, but it is visible (predictably making the leveraged returns a tad better). And the more I think about it, the more I convince myself that the approach using priceonly volatility is more straightforward AND should be more accurate than my previous approach with the spacedout dividends.
I will hold on making corresponding changes for now, as I'm having a parallel discussion with Kevin about bonds where I suspect we'll end up reaching a similar conclusion, relying on pricing data (derived from daily yields) as a more accurate volatility proxy for the old days.
Re: Simulating Returns of Leveraged ETFs
Kevin and I had a very productive exchange about this topic in the past couple of days. As a refresher, historical bond index data suffers from a severe lack of daily numbers, and all we have for index returns prior to mid97 are monthly total returns (for both IT treasuries and LT treasuries). In the current leveraged model, we made a very coarse assumption that average daily volatility of the known days (mid97 till now) is a halfdecent proxy for the older times (then we use the 'magic formula' described here). I was quite suspicious though that we didn't properly capture the dynamics of the late 70s and 80s (wild changes of interest rates) and of previous decades (mild changes of interest rates), possibly making the leveraged model overshoot or undershoot for corresponding decades.Kevin M wrote: ↑Sat Mar 09, 2019 6:23 pmWe have daily 10year CMT from FRED starting in 1962. We have daily 30year CMT starting 1977, and daily 20year starting 1993, but of course with some gaps.
We have daily FRB 10year and 9year yields starting 1971, daily FRB 20year and 19year starting in 1981, and daily 30/29year starting in 1985.
All of these are par yields, so price return and income return can easily be calculated from the yields.
What Kevin pointed out is that we can use daily yield data to fill that gap, at least partly. The idea is that we have daily 5yrs, 7yrs and 10yrs CMT yield data, helpful for IT Treasuries. And 10yrs, 20yrs and 30yrs yield data, helpful for LT treasuries. For each CMT series, we computed daily income (dividends) and capital (price) returns, based on a simple bond model. Let me quote Kevin:
The underlying assumption is that a bond is bought at par value (100 in standard bond pricing terms, which means 100% of face value), sold the next day at the calculated price, and then another par bond is bought at 100; rinse and repeat.
Such simple bond model maps to very simple spreadsheet formulas, the income return is the yield from the previous day, and the price return is easy to compute based on a Present Value formula (as typical for bond pricing) based on the yield of the day and the yield of the previous day. Once we have the daily outcome for each CMT series, it's a simple matter of combining the return series to mimic the average maturity of an IT treasury fund (~8.5yrs) and an LT treasury fund (~25yrs). The fact that there are some holes in the CMT series from FRED gave us a bit of grief, but we found simple ways around that.
I confess that I was a little skeptical, but when running such bond model and comparing against actuals for the 1998+ time period, the results are very impressive, notably when it comes to intramonth (day to day) volatility, which is what we were looking for. Computing the RMSE between monthly volatility actuals and Kevin's model for 19982018, we get 0.03% for IT treasuries and 0.05% for LT treasuries, which is remarkably low (average volatility is around 0.3% for ITTs and 0.6% for LTTs by then). Comparing individual values as well as overall averages showed that this is indeed a close match. Based on such validation, we can reasonably infer that this accuracy should extend to the past, and therefore get a solid volatility proxy for IT treasuries (1962+) and for LT treasuries (1977+).
Re: Simulating Returns of Leveraged ETFs
IT treasuries (1962+) and LT treasuries (1977+) improved volatility values are great, but what about the years before (goal is to start in Jan55)? For IT treasuries, we can observe that the trajectory of interest rates in the late 50s didn't seem overly eventful, and it seems ok to use a coarse volatility value equal to the average of the next 15 years (19621976), which, interestingly enough was really quite low (0.16% compared to the 0.33% for the last two decades).
For LT treasuries, there is just no good answer, we still have 20+ years missing. Given the observation about IT treasury volatility (lower by then than more recently), we really shouldn't use a recent measure of LT treasury volatility as proxy. Both Kevin and myself independently came up with the same answer: LTT volatility when known has been consistently roughly double the ITT volatility. So why not use the ITT results, simply multiply by 2, and fill the 19621976 LTT gap in such a way. This is less than ideal, of course, but at least we'd capture the ups and downs of this time period, while using mild volatility values which seemed to be prevalent at the time. And then fill the late 50s gap with the same approach as for IT bonds, use the average of the next 15 years.
I'm sure that some of you are cringing while reading those lines, and yes, it IS less than ideal. But this seems WAY better than we had before. Also, there is a point where further refinements may not move the needle very much, and after running a couple of sensitivity analysis experiments, I believe we're pretty close to that point.
I'll share the updated leveraged model tomorrow (to give myself a chance to sleep on it!). The big picture won't change, but the (rather dire) leveraged returns of the 50s to 70s will get a bit better, thanks to the milder volatility of the corresponding times. Feedback welcome.
PS. confusingly enough, treasury yields need to be divided by 365 to get to daily yields  while EFFR/LIBOR rates need to be divided by 360. We did exactly that, after doublechecking with multiple sources.
For LT treasuries, there is just no good answer, we still have 20+ years missing. Given the observation about IT treasury volatility (lower by then than more recently), we really shouldn't use a recent measure of LT treasury volatility as proxy. Both Kevin and myself independently came up with the same answer: LTT volatility when known has been consistently roughly double the ITT volatility. So why not use the ITT results, simply multiply by 2, and fill the 19621976 LTT gap in such a way. This is less than ideal, of course, but at least we'd capture the ups and downs of this time period, while using mild volatility values which seemed to be prevalent at the time. And then fill the late 50s gap with the same approach as for IT bonds, use the average of the next 15 years.
I'm sure that some of you are cringing while reading those lines, and yes, it IS less than ideal. But this seems WAY better than we had before. Also, there is a point where further refinements may not move the needle very much, and after running a couple of sensitivity analysis experiments, I believe we're pretty close to that point.
I'll share the updated leveraged model tomorrow (to give myself a chance to sleep on it!). The big picture won't change, but the (rather dire) leveraged returns of the 50s to 70s will get a bit better, thanks to the milder volatility of the corresponding times. Feedback welcome.
PS. confusingly enough, treasury yields need to be divided by 365 to get to daily yields  while EFFR/LIBOR rates need to be divided by 360. We did exactly that, after doublechecking with multiple sources.
Re: Simulating Returns of Leveraged ETFs
Hi. Using Libor for the assumed interest rate is not really correct, although it is close. Equity market funding is not libor + 0bp. There is a spread to this rate that is mostly based on specific supply and demand for equity leverage. For instance, if you price a futures contract on SPX (which is presumably the method through which SSO, UPRO, etc. achieve leverage), the implicit interest rate might be libor+10bp or so today. This value can trade in say a range of negative to positive 2%, and the average value is around 0.30%.
Anyway, borrowing at 3m libor flat for investing in equities sounds pretty good to me at 2.60%, plus a bit, and was a no brainer at 1% not too long ago
Anyway, borrowing at 3m libor flat for investing in equities sounds pretty good to me at 2.60%, plus a bit, and was a no brainer at 1% not too long ago
Re: Simulating Returns of Leveraged ETFs
Hi there. Thanks for the feedback, appreciated. We did discuss the spread issue a while ago, but couldn't find a way to properly quantify it. We ended up using 'adjustment' empirical factors to cover for friction costs at large (incl. spread), but this is of course not quite satisfying, and I'd be happy to make progress on the spread topic. Mind sharing where you got your numbers (e.g. range, average value, etc)?ohai wrote: ↑Thu Mar 14, 2019 4:37 pmHi. Using Libor for the assumed interest rate is not really correct, although it is close. Equity market funding is not libor + 0bp. There is a spread to this rate that is mostly based on specific supply and demand for equity leverage. For instance, if you price a futures contract on SPX (which is presumably the method through which SSO, UPRO, etc. achieve leverage), the implicit interest rate might be libor+10bp or so today. This value can trade in say a range of negative to positive 2%, and the average value is around 0.30%.
Re: Simulating Returns of Leveraged ETFs
It's not a bid/ask spread if that's what you mean (sorry, the thread is quite long), but this value for SPX can be assumed for simplification to be 0.125 points of the index (half the futures tick size). What I meant, in case was unclear, is the fair value of equity funding that is usually above libor: you can sell, as well as buy, at the same price.
Anyway, data on equity funding levels is not published anywhere. For the most part, only institutional trading desks (i.e. banks and specifically, delta one desks) really track this explicitly. I do have historical data for this, but unfortunately cannot share it due to proprietary reasons.
However, there is a really easy way to simulate leveraged ETFs returns, which is to track SPX front month futures prices, not SPX closing levels. When you buy a future on SPX, the price includes: 1) "risk free" interest rate, 2) equity funding spread, and 3) predicted or known cash dividends. 3) cancels out, since you are buying the future value of the index after dividends are paid. This leaves 1) and 2), which together show the total cost of leverage for the index. You don't need any further data for interest rates or equity funding if you have tradable futures prices.
Anyway, data on equity funding levels is not published anywhere. For the most part, only institutional trading desks (i.e. banks and specifically, delta one desks) really track this explicitly. I do have historical data for this, but unfortunately cannot share it due to proprietary reasons.
However, there is a really easy way to simulate leveraged ETFs returns, which is to track SPX front month futures prices, not SPX closing levels. When you buy a future on SPX, the price includes: 1) "risk free" interest rate, 2) equity funding spread, and 3) predicted or known cash dividends. 3) cancels out, since you are buying the future value of the index after dividends are paid. This leaves 1) and 2), which together show the total cost of leverage for the index. You don't need any further data for interest rates or equity funding if you have tradable futures prices.
Re: Simulating Returns of Leveraged ETFs
Yeah, I suspect I did get mixed up in some earlier posts, but your definition of spread as fair value of equity funding (above LIBOR) is well worded. Thank you for clarifying.ohai wrote: ↑Thu Mar 14, 2019 9:24 pmIt's not a bid/ask spread if that's what you mean (sorry, the thread is quite long), but this value for SPX can be assumed for simplification to be 0.125 points of the index (half the futures tick size). What I meant, in case was unclear, is the fair value of equity funding that is usually above libor: you can sell, as well as buy, at the same price.
Just out of curiosity, may I ask you a few indirect questions:ohai wrote: ↑Thu Mar 14, 2019 9:24 pmAnyway, data on equity funding levels is not published anywhere. For the most part, only institutional trading desks (i.e. banks and specifically, delta one desks) really track this explicitly. I do have historical data for this, but unfortunately cannot share it due to proprietary reasons.
a) how far back does this proprietary data history go? Probably not a lot, I would guess?
b) does it make sense to you that such spread would be near zero for bond/treasury funding (i.e. for a leveraged fund like UBT or TMF)?
c) does it make sense to you that such spread would be smaller for mid/smallcaps than for S&P 500? And higher for Int'l (e.g. EAFE)?
d) what are the fundamental drivers of a lower or higher spread?
That's clever. Unfortunately, such 'futures' data series are not publicly available, I am afraid. And even with your proprietary access, I suspect you can't go very far back in time, am I correct? We've been trying to develop a model that extends back in the 50s, so that we can fully capture the 3 major crises of the US stock market while backtesting.ohai wrote: ↑Thu Mar 14, 2019 9:24 pmHowever, there is a really easy way to simulate leveraged ETFs returns, which is to track SPX front month futures prices, not SPX closing levels. When you buy a future on SPX, the price includes: 1) "risk free" interest rate, 2) equity funding spread, and 3) predicted or known cash dividends. 3) cancels out, since you are buying the future value of the index after dividends are paid. This leaves 1) and 2), which together show the total cost of leverage for the index. You don't need any further data for interest rates or equity funding if you have tradable futures prices.
Re: Simulating Returns of Leveraged ETFs
I am still sitting on this. The whole topic of simulating bond funds (with daily and/or monthly inputs) sent me in a bit of a spin, Kevin's help is extremely valuable, but I didn't fully converge yet. The change will NOT be terribly impactful anyway, so I'd rather do it right and be done with it than providing incremental updates.siamond wrote: ↑Thu Mar 14, 2019 4:28 pmIT treasuries (1962+) and LT treasuries (1977+) improved volatility values are great, but what about the years before (goal is to start in Jan55)? [...]
I'll share the updated leveraged model tomorrow (to give myself a chance to sleep on it!). The big picture won't change, but the (rather dire) leveraged returns of the 50s to 70s will get a bit better, thanks to the milder volatility of the corresponding times. [...]
Shifting gears, I am hoping that ohai comes back to this thread and enlightens us a bit more about borrowing spreads... Something that crossed my mind is that US treasuries are the most liquid investment vehicle of all, if I am not mistaken. Maybe this explains why we didn't find much 'friction costs' when testing the model again leveraged bond funds actuals, while we found much more friction for leveraged stock funds.
Re: Simulating Returns of Leveraged ETFs
Back to volatility in the early days... I finalized an update of the leveraged model, generating numbers which seem more realistic for the first few decades than the coarse assumptions I made before.
For the S&P 500, the net effect is that the intramonth volatility numbers up to 1987 have been updated (see discussion here) and this made the 2x and 3x leverage numbers go up a bit in the model.
For IT and LT Treasuries, the net effect is that the intramonth volatility numbers up to 1997 have been updated (see discussion here and here), and this also made the 2x and 3x leveraged numbers go up (treasuries volatility in those older decades was significantly lower than in more recent decades). I ended up switching to FRB rates as input (instead of the CMT data series) for two reasons, first the CMT series have more 'holes' notably in the 60s, next the FRBbased model matches the actuals (the corresponding bonds index) better for 1998+. With Kevin's precious help, I also explored a more complicated model based on the ideas expressed here, using an M1 rung on a daily basis when available, but this wasn't convincing enough to be worth the change.
Overall, the exact 2x and 3x leverage numbers did change in a nonnegligible manner, but the big picture didn't change much, the 50s/60s/70s would still have been a really difficult time for an investor using a good dose of (leveraged) treasury funds.
The usual number crunchers (HedgeFundie, EfficientInvestor, Samsdad, etc) can use the same links I shared before to download the updated model. I also updated the corresponding customized Simba spreadsheet (check this post, same link).
For the S&P 500, the net effect is that the intramonth volatility numbers up to 1987 have been updated (see discussion here) and this made the 2x and 3x leverage numbers go up a bit in the model.
For IT and LT Treasuries, the net effect is that the intramonth volatility numbers up to 1997 have been updated (see discussion here and here), and this also made the 2x and 3x leveraged numbers go up (treasuries volatility in those older decades was significantly lower than in more recent decades). I ended up switching to FRB rates as input (instead of the CMT data series) for two reasons, first the CMT series have more 'holes' notably in the 60s, next the FRBbased model matches the actuals (the corresponding bonds index) better for 1998+. With Kevin's precious help, I also explored a more complicated model based on the ideas expressed here, using an M1 rung on a daily basis when available, but this wasn't convincing enough to be worth the change.
Overall, the exact 2x and 3x leverage numbers did change in a nonnegligible manner, but the big picture didn't change much, the 50s/60s/70s would still have been a really difficult time for an investor using a good dose of (leveraged) treasury funds.
The usual number crunchers (HedgeFundie, EfficientInvestor, Samsdad, etc) can use the same links I shared before to download the updated model. I also updated the corresponding customized Simba spreadsheet (check this post, same link).

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Re: Simulating Returns of Leveraged ETFs
Awesome. Thanks Siamond. The new data is indeed more optimistic.siamond wrote: ↑Thu Mar 21, 2019 2:19 pmBack to volatility in the early days... I finalized an update of the leveraged model, generating numbers which seem more realistic for the first few decades than the coarse assumptions I made before.
For the S&P 500, the net effect is that the intramonth volatility numbers up to 1987 have been updated (see discussion here) and this made the 2x and 3x leverage numbers go up a bit in the model.
For IT and LT Treasuries, the net effect is that the intramonth volatility numbers up to 1997 have been updated (see discussion here and here), and this also made the 2x and 3x leveraged numbers go up (treasuries volatility in those older decades was significantly lower than in more recent decades). I ended up switching to FRB rates as input (instead of the CMT data series) for two reasons, first the CMT series have more 'holes' notably in the 60s, next the FRBbased model matches the actuals (the corresponding bonds index) better for 1998+. With Kevin's precious help, I also explored a more complicated model based on the ideas expressed here, using an M1 rung on a daily basis when available, but this wasn't convincing enough to be worth the change.
Overall, the exact 2x and 3x leverage numbers did change in a nonnegligible manner, but the big picture didn't change much, the 50s/60s/70s would still have been a really difficult time for an investor using a good dose of (leveraged) treasury funds.
The usual number crunchers (HedgeFundie, EfficientInvestor, Samsdad, etc) can use the same links I shared before to download the updated model. I also updated the corresponding customized Simba spreadsheet (check this post, same link).
Re: Simulating Returns of Leveraged ETFs
Thank you very much, Siamond, it's great to have someone like you here to help the community. Thanks to all involved as well.siamond wrote: ↑Thu Mar 21, 2019 2:19 pmBack to volatility in the early days... I finalized an update of the leveraged model, generating numbers which seem more realistic for the first few decades than the coarse assumptions I made before.
For the S&P 500, the net effect is that the intramonth volatility numbers up to 1987 have been updated (see discussion here) and this made the 2x and 3x leverage numbers go up a bit in the model.
For IT and LT Treasuries, the net effect is that the intramonth volatility numbers up to 1997 have been updated (see discussion here and here), and this also made the 2x and 3x leveraged numbers go up (treasuries volatility in those older decades was significantly lower than in more recent decades). I ended up switching to FRB rates as input (instead of the CMT data series) for two reasons, first the CMT series have more 'holes' notably in the 60s, next the FRBbased model matches the actuals (the corresponding bonds index) better for 1998+. With Kevin's precious help, I also explored a more complicated model based on the ideas expressed here, using an M1 rung on a daily basis when available, but this wasn't convincing enough to be worth the change.
Overall, the exact 2x and 3x leverage numbers did change in a nonnegligible manner, but the big picture didn't change much, the 50s/60s/70s would still have been a really difficult time for an investor using a good dose of (leveraged) treasury funds.
The usual number crunchers (HedgeFundie, EfficientInvestor, Samsdad, etc) can use the same links I shared before to download the updated model. I also updated the corresponding customized Simba spreadsheet (check this post, same link).