## Simulating Returns of Leveraged ETFs

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

HEDGEFUNDIE wrote:
Wed Dec 11, 2019 3:31 pm
Uncorrelated wrote:
Wed Dec 11, 2019 12:30 pm

For Ultra S&P500, we find that (leverage - common_stock) * swap_spread is equal to (2 - .72) * .38% = 0.4864%. Siamond used a curve fitting method to arrive at the figure 0.5%.
For UltraPro S&P500, we find that (leverage - common stock) * swap_spread is equal to (2 - .58) * .42% = 1.0164%. Siamond used a curve fitting method to arrive at the figure 1%.

We still have to look into simulating LETF's with daily math and taking a closer look at the equations for inverse ETF's, but I think the friction cost mystery is solved.
Very nice work! So there are no more mystery costs to these LETFs. 1% ER + 1% Swap Spread + risk-free-rate is it.

Can I ask you to run a chart for TMF?
Well, this does seem like good progress (cool work, Uncorrelated!), but we need to dig a bit further:
- why did we need such a 0.5%/1% adjustment for S&P 500 2x/3x while we didn't need any adjustment for the ST/IT/LT Treasuries models?
- why did we need the same 0.5%/1% for S&P Midcap, but only a much smaller adjustment for Russell 2k (small-caps)?
- then there is the case of International and Gold, but here I suspect there are other considerations piling up, so... one thing at a time.
- and... how do we extend such logic in the past? Should we keep 0.5% and 1% as a constant adjustment as we did so far (not knowing any better!), or is the right number a function of other circumstances?

In any case, GREAT progress!

HEDGEFUNDIE
Posts: 3973
Joined: Sun Oct 22, 2017 2:06 pm

### Re: Simulating Returns of Leveraged ETFs

siamond wrote:
Wed Dec 11, 2019 6:34 pm
HEDGEFUNDIE wrote:
Wed Dec 11, 2019 3:31 pm
Uncorrelated wrote:
Wed Dec 11, 2019 12:30 pm

For Ultra S&P500, we find that (leverage - common_stock) * swap_spread is equal to (2 - .72) * .38% = 0.4864%. Siamond used a curve fitting method to arrive at the figure 0.5%.
For UltraPro S&P500, we find that (leverage - common stock) * swap_spread is equal to (2 - .58) * .42% = 1.0164%. Siamond used a curve fitting method to arrive at the figure 1%.

We still have to look into simulating LETF's with daily math and taking a closer look at the equations for inverse ETF's, but I think the friction cost mystery is solved.
Very nice work! So there are no more mystery costs to these LETFs. 1% ER + 1% Swap Spread + risk-free-rate is it.

Can I ask you to run a chart for TMF?
Well, this does seem like good progress (cool work, Uncorrelated!), but we need to dig a bit further:
- why did we need such a 0.5%/1% adjustment for S&P 500 2x/3x while we didn't need any adjustment for the ST/IT/LT Treasuries models?
- why did we need the same 0.5%/1% for S&P Midcap, but only a much smaller adjustment for Russell 2k (small-caps)?
- then there is the case of International and Gold, but here I suspect there are other considerations piling up, so... one thing at a time.
- and... how do we extend such logic in the past? Should we keep 0.5% and 1% as a constant adjustment as we did so far (not knowing any better!), or is the right number a function of other circumstances?

In any case, GREAT progress!
As Uncorrelated showed in his/her last post and as I described in my threads, treasury LETFs have no spread, in fact they get paid for taking the positive leg of the swap.

This is entirely due to the fact that the market has been expecting rates to rise for years now, a 3x long position on the LTT is quite unpopular.

siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

Uncorrelated wrote:
Wed Dec 11, 2019 4:41 pm
Additionally, we don't know what the swap rates were during the great recession or dot-com bubble. We should look into some of the longer running LETF's to observe how rates behave when the markets are more volatile.
ULPIX (2x S&P 500) has history since 1998... Would be a great candidate. Note that its Expense Ratio is higher than the usual culprits.

Any way you could put the raw numbers you collected in a simple sharable spreadsheet?

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

siamond wrote:
Wed Dec 11, 2019 6:34 pm
HEDGEFUNDIE wrote:
Wed Dec 11, 2019 3:31 pm
Uncorrelated wrote:
Wed Dec 11, 2019 12:30 pm

For Ultra S&P500, we find that (leverage - common_stock) * swap_spread is equal to (2 - .72) * .38% = 0.4864%. Siamond used a curve fitting method to arrive at the figure 0.5%.
For UltraPro S&P500, we find that (leverage - common stock) * swap_spread is equal to (2 - .58) * .42% = 1.0164%. Siamond used a curve fitting method to arrive at the figure 1%.

We still have to look into simulating LETF's with daily math and taking a closer look at the equations for inverse ETF's, but I think the friction cost mystery is solved.
Very nice work! So there are no more mystery costs to these LETFs. 1% ER + 1% Swap Spread + risk-free-rate is it.

Can I ask you to run a chart for TMF?
Well, this does seem like good progress (cool work, Uncorrelated!), but we need to dig a bit further:
- why did we need such a 0.5%/1% adjustment for S&P 500 2x/3x while we didn't need any adjustment for the ST/IT/LT Treasuries models?
- why did we need the same 0.5%/1% for S&P Midcap, but only a much smaller adjustment for Russell 2k (small-caps)?
- then there is the case of International and Gold, but here I suspect there are other considerations piling up, so... one thing at a time.
- and... how do we extend such logic in the past? Should we keep 0.5% and 1% as a constant adjustment as we did so far (not knowing any better!), or is the right number a function of other circumstances?

In any case, GREAT progress!
We can answer some of these questions:
It appears that the long swap spread on treasuries (2x) is sub-zero (around -0.10%) in the time period examined, so no adjustment is necessary.
For Ultra (2x) S&P, MidCap400 and Russell2000, the average swap spread on the long leg is 0.38%, 0.28% and -0.04% (!) respectively. That seems to indicate there is no adjustment necessary for Russel2000.
For UltraPro (3x), figures are 0.42%, 0.36%, -0.01%. This again seems to indicate no adjustment is necessary for Russel2000.

I don't have the data on gold currently but will get to it eventually. Here are a few data points:
as per December 31, 2017, the overnight LIBOR is 1.4% and the swap rate is 2.29%, spread = 0.9%.
as per December 31, 2018, the overnight LIBOR is 2.4% and the swap rate is 3%, spread = 0.4%.
ProShares Ultra Gold holds no common stock, all their exposure comes from the swaps and futures contracts. To arrive at the total friction costs we need to multiply these numbers by 200%, which results in 1.8% in 2017 and 0.8% in 2018. Your excel sheet appears to use friction costs of 1.4%, which is in the right ballpark. (more data is needed to confirm, but I'm not seeing anything that makes me doubt my methodology).

We should be careful drawing conclusions for international funds. VXUS (vanguard international ex-us) has around 0.07% unavoidable internal withholding tax leakage that can be completely avoided by funds (and banks) domiciled in the Netherlands. The tax leakage on individual countries can be far higher. This may or may not be reflected in the swap rate. All this information is included in the annual reports, but you have to know where to look... Looking at US funds that invest only in the US makes the situation far simpler because you can assume the taxes as the fund level are basically identical for swaps, futures and common stock.
siamond wrote:
Wed Dec 11, 2019 11:45 pm
Uncorrelated wrote:
Wed Dec 11, 2019 4:41 pm
Additionally, we don't know what the swap rates were during the great recession or dot-com bubble. We should look into some of the longer running LETF's to observe how rates behave when the markets are more volatile.
ULPIX (2x S&P 500) has history since 1998... Would be a great candidate. Note that its Expense Ratio is higher than the usual culprits.

Any way you could put the raw numbers you collected in a simple sharable spreadsheet?
The SEC website is currently broken, but I will look into ULPIX when it's back up again.

I will deliver data files for you to play with later today.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

A data file with the swap rates, swap spreads and % common stock holdings can be obtained here:
https://www.dropbox.com/s/o3tvl060v1g37 ... .xlsx?dl=1

The sheets contain:
The swap rate
The swap rate minus the overnight libor
The percentage of common stock holdings
The percentage of common stock holdings, linearly interpolated to match the date in sheet 1 and 2. If data is missing, it's safe to assume the correct figure is 0%.

Beware: the swap rates on long/short ETF's are probably calculated the wrong way, and first data point on every short ETF (Feb 2, 2014) appears to have the wrong sign.

I also have a json dataset that contains the individual swap contracts, which can be obtained here: https://www.dropbox.com/s/tgk1u1a3shvun ... .json?dl=1.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

It appears that we're out of luck.

I checked the SEC data for ULPIX, the annual reports appear to be made by the same company as ProShares (the table markup is extremely similar). Like ProShares, they only started reporting the swap rates in 2014.

I then went over to Guggenheim (Rydex). Their annual reports simply state "financing at a variable rate.", no actual swap figures are included. Useless.

Direxion is a bit more interesting. The swap contracts have a note that says:
2.7633% representing 1 month LIBOR rate + spread
Which confirms our suspicion that the swap contracts are based on some proxy for the risk free rate + spread.

Direxion reports the rate on the swap contracts since mid-2011 (SEC link), which would give us a bit more data to work with than ProShares which starts at mid-2014. I'm really looking for data back to at least 2008 to see how the rates behave under stress, but I'm running out of options here.

That brings us to another point that has been bothering me, which is the rates on these swaps. Empirical data shows that S&P500 total return swaps are is more expensive than Russell2000. Does that mean that the implied futures repro rate on S&P500 is higher than on Russell2000? S&P500 calls are more expensive than Russell2000? I suspect that the higher swap rates for large cap should be reflected in the implicit financing costs of options and futures. And how about leveraging futures vs stocks? Conventional bogleheads wisdom states that the implicit financing costs of options are the risk free rate plus a spread, but that wisdom seems to be incompatible with the total return spreads we have observed.

Does anyone have any idea how we can obtain historical implicit financing costs for options and futures? I suspect there is substantial overlap between the costs of these instruments and total return swaps.

siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

Uncorrelated wrote:
Thu Dec 12, 2019 9:16 am
A data file with the swap rates, swap spreads and % common stock holdings can be obtained here:
https://www.dropbox.com/s/o3tvl060v1g37 ... .xlsx?dl=1
Thank you! Terrific work. Two questions:
1. Did you use the LIBOR/overnight rate corresponding to the exact date of the reports where you found the swap rates?
2. Checking the Ultra/UltraPro S&P 500 funds, it appears that swap rate minus LIBOR (aka spread) has been hovering around 0.3 from mid-14 to mid-17, but went up to 0.5/0.6 since then. Any clue why that would be? This hardly seems in favor of viewing spreads as a constant of sorts...

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

siamond wrote:
Fri Dec 13, 2019 11:37 pm
Uncorrelated wrote:
Thu Dec 12, 2019 9:16 am
A data file with the swap rates, swap spreads and % common stock holdings can be obtained here:
https://www.dropbox.com/s/o3tvl060v1g37 ... .xlsx?dl=1
Thank you! Terrific work. Two questions:
1. Did you use the LIBOR/overnight rate corresponding to the exact date of the reports where you found the swap rates?
The rate on the day before was used, corresponding with your observations that the LIBOR data on FRED corresponds to the end-of-day rate. Now that I think about it, it might be better to use the rate on the exact day.
2. Checking the Ultra/UltraPro S&P 500 funds, it appears that swap rate minus LIBOR (aka spread) has been hovering around 0.3 from mid-14 to mid-17, but went up to 0.5/0.6 since then. Any clue why that would be? This hardly seems in favor of viewing spreads as a constant of sorts...
I don't know. I suspect this is related to my other question: why does the spread on the S&P500 differ from the spread on Russell2000?. I suspect that we need to learn more about the mechanics that the banks use to determine the spread before this starts to make any sense.

Stef
Posts: 340
Joined: Thu Oct 10, 2019 10:13 am

### Re: Simulating Returns of Leveraged ETFs

Is there a way in Portfolio Visualizer to upload data and backtest is further back than 1985?

siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

Sidetracking for one second from swaps and spreads... I've been asked multiple times why the model starts in 1955 and not in the 1928 as some articles appear to do. On another thread, I stated the following (referring to the rate used as the basis for borrowing costs):
I actually don't know how one can assemble a model starting in 1928, as the LIBOR interbank rate historical data started in 1986 and its proxy, the Effective Federal Funds Rate started mid 1954.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

Ken French has daily risk-free and total return market data available since July 1, 1926, which represents the 1-month t-bill obtained from Ibbotson Associates and the total (value weighted) return of the entire CRSP database. Yahoo has daily "S&P 500" data without dividends under the GSPC ticker back to 1927 but I don't know how accurate that is.

https://mba.tuck.dartmouth.edu/pages/fa ... brary.html (Fama/French 3 Factors)

siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

Uncorrelated wrote:
Thu Dec 12, 2019 6:11 pm
It appears that we're out of luck.

I checked the SEC data for ULPIX, the annual reports appear to be made by the same company as ProShares (the table markup is extremely similar). Like ProShares, they only started reporting the swap rates in 2014.

I then went over to Guggenheim (Rydex). Their annual reports simply state "financing at a variable rate.", no actual swap figures are included. Useless.

Direxion is a bit more interesting. The swap contracts have a note that says:
2.7633% representing 1 month LIBOR rate + spread
Which confirms our suspicion that the swap contracts are based on some proxy for the risk free rate + spread.

Direxion reports the rate on the swap contracts since mid-2011 (SEC link), which would give us a bit more data to work with than ProShares which starts at mid-2014. I'm really looking for data back to at least 2008 to see how the rates behave under stress, but I'm running out of options here.
Totally agreed with your goal to get something going through the financial crisis. Seems pretty hard though. Here are a few suggestions:
- getting the Direxion data from 2011 is better than 2014... This would bring 60% more data!
- I am also curious to compare Direxion with Proshares/Profunds as I never understood why Direxion is pretty poor at tracking daily moves of the index while the two others are way better
- maybe explore iPath ETNs? SFLA and ROLA go back to Q4-2010. The iPath Equity ETN page does explain that they use 3m LIBOR + 0.60% (as of today, I guess).

siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

Uncorrelated wrote:
Sat Dec 14, 2019 2:40 pm
Ken French has daily risk-free and total return market data available since July 1, 1926, which represents the 1-month t-bill obtained from Ibbotson Associates and the total (value weighted) return of the entire CRSP database. Yahoo has daily "S&P 500" data without dividends under the GSPC ticker back to 1927 but I don't know how accurate that is.

https://mba.tuck.dartmouth.edu/pages/fa ... brary.html (Fama/French 3 Factors)
That's a fair point. T-bills and EFFR/LIBOR are far from being perfectly aligned though (I just ran a quick test and there is a 0.5% CAGR difference between a spliced series EFFR+LIBOR and T-Bills as tracked in the Simba spreadsheet, starting from 1955). Still... that's a fair point.

Yes, we have S&P 500 daily price data going back a long way. But... S&P 500 dividends data is awfully sketchy in the first half of the century, e.g. Prof. Shiller only reports quarterly averages. Anyhoo, I have no intent to extend the model earlier than 1955, I just wanted to put in writing what drove us there.

Hydromod
Posts: 283
Joined: Tue Mar 26, 2019 10:21 pm

### Re: Simulating Returns of Leveraged ETFs

Just a random thought after reading TOTAL RETURN IS A TECHNOLOGY: would it be reasonable to assume that only a fraction of dividends were reinvested back in the dark ages, because of the necessary commissions at that time?

HEDGEFUNDIE
Posts: 3973
Joined: Sun Oct 22, 2017 2:06 pm

### Re: Simulating Returns of Leveraged ETFs

The Rydex funds go back quite a ways. Perhaps Uncorrelated can work his magic on these:

RYNVX (1.5x S&P 500): 07/1993
RYVYX (2x NASDAQ 100): 05/2000
RYTNX (2x S&P 500): 05/2000

siamond
Posts: 5127
Joined: Mon May 28, 2012 5:50 am

### Re: Simulating Returns of Leveraged ETFs

HEDGEFUNDIE wrote:
Sat Dec 14, 2019 9:36 pm
The Rydex funds go back quite a ways. Perhaps Uncorrelated can work his magic on these [...]
Was my first thought too, but...
Uncorrelated wrote:
Thu Dec 12, 2019 6:11 pm
I then went over to Guggenheim (Rydex). Their annual reports simply state "financing at a variable rate.", no actual swap figures are included. Useless.

HEDGEFUNDIE
Posts: 3973
Joined: Sun Oct 22, 2017 2:06 pm

### Re: Simulating Returns of Leveraged ETFs

siamond wrote:
Sat Dec 14, 2019 10:39 pm
HEDGEFUNDIE wrote:
Sat Dec 14, 2019 9:36 pm
The Rydex funds go back quite a ways. Perhaps Uncorrelated can work his magic on these [...]
Was my first thought too, but...
Uncorrelated wrote:
Thu Dec 12, 2019 6:11 pm
I then went over to Guggenheim (Rydex). Their annual reports simply state "financing at a variable rate.", no actual swap figures are included. Useless.
Not true at all. Look at the quarterly holdings reports.

https://www.guggenheiminvestments.com/m ... a/holdings

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

HEDGEFUNDIE wrote:
Sat Dec 14, 2019 9:36 pm
The Rydex funds go back quite a ways. Perhaps Uncorrelated can work his magic on these:

RYNVX (1.5x S&P 500): 07/1993
RYVYX (2x NASDAQ 100): 05/2000
RYTNX (2x S&P 500): 05/2000
I didn't search hard enough and some of the annual/quarterly reports do contain information about the swap rates... but the earliest data point is mid-2016.
siamond wrote:
Sat Dec 14, 2019 3:09 pm
- maybe explore iPath ETNs? SFLA and ROLA go back to Q4-2010. The iPath Equity ETN page does explain that they use 3m LIBOR + 0.60% (as of today, I guess).
The only reports I can find on these are the registrations, which were filed directly by Bayclays. I can't find any annual or quarterly reports. Perhaps there are no reporting requirements for ETN's? The swap rates also look terribly uncompetitive, I suspect they use Barclays as the only swap provider... This is what's stated in the prospectus (!):
Financing Rate: The financing rate will equal the sum of (a) 0.60% plus (b) the most recent 3-month London InterBank Offered Rate
(LIBOR) fixing for U.S. dollars effective on the immediately preceding business day, as published by the British Bankers’ Association. The
fixing is conducted each day at 11:00 a.m. (London time) and published on Bloomberg page “US0003M Index”.
I don't think this product is comparable to other leveraged ETF's.

If there are no other options I will work my magic on Direxion, but I really want to make sure it's our best option before I spend another day parsing SEC reports.

Uncorrelated
Posts: 249
Joined: Sun Oct 13, 2019 3:16 pm

### Re: Simulating Returns of Leveraged ETFs

I found this article with supports the idea that Russell2000 is cheaper to borrow than S&P500, and also claims that the higher borrowing costs are reflected in futures implied repo rates. I was unable to find any data for options, but there are various articles from CME (potentially biased?) that claim that S&P500 futures are slightly cheaper to trade than rolling options.