You should not be investing in this with “a lot of” any kind of funds.firebirdparts wrote: ↑Sat Aug 10, 2019 8:18 amI Guess that would eliminate a lot of people. I can’t buy ETFs in a 401k. I don’t have a lot of IRA funds. What sort of account do have this in?
HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

 Posts: 3559
 Joined: Sun Oct 22, 2017 2:06 pm
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
WisdomTree.MotoTrojan wrote: ↑Fri Aug 09, 2019 12:57 pmWhat ETFs are you looking at for your 2 leveraged options?
S&P 500 3x Leverage Daily ETP
3USL
US Treasuries 10Y 3x Leverage Daily ETP
3TYL
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
MotoTrojan wrote: ↑Fri Aug 09, 2019 11:27 pmWow, this is worth a further look. May be worth considering this fund in place of the S&P500 based ones.stipeman wrote: ↑Fri Aug 09, 2019 11:06 pmExplained in this link:rascott wrote: ↑Thu Aug 08, 2019 8:40 pmHEDGEFUNDIE wrote: ↑Thu Aug 08, 2019 8:36 pmIt's a shame PIMCO chose the obviously inferior small cap index, I guess they are a bond shop after all.rascott wrote: ↑Thu Aug 08, 2019 8:34 pm
I was comparing it to the Russell...since that's what it tracks.
https://www.portfoliovisualizer.com/bac ... total3=100
Agreed....but don't think they have an option.... believe you can only buy futures on the Russell. So blame CME for not giving us a better product
Just found it odd that the bonds bosted returns so much over the index of that fund....but not the original Stocks Plus fund. Would assume they used the same bond strategy with both, guess not.
https://www.pimco.com/enus/insights/in ... 02299831=1
In a nutshell the R2K is much more illiquid and it is more difficult to short individual stocks; this premium paid by those shorting results in futures (borrowing) costs that are usually below libor, boosting the potential outperformance of the bondpicking. Need to dig more into the bond strategy used itself but seems intriguing.
On second thought it looks like the S&P600 gets similar returns and is much more efficient... perhaps I am better off holding S&P600 value, as I already do.
Yeah those funds do a nice job of beating their index, issue is the index they have to use stinks. So might as well just stick with the SP600 value index.
The intl funds are maybe the most interesting....they have killed the index on that one. Haven't looked in detail as of yet, but assuming it had to due with the dollar hedging aspect.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
First, thanks for your contributions to this thread. I think critical and bearish perspectives are really important, as it's just as important to understand all the ways this strategy might not work.MoneyMarathon wrote: ↑Sat Aug 10, 2019 5:54 am...
And let me also back up a bit. Can the 40% UPRO / 60% TMF perform at 20% CAGR for the next 5 years? Yes, yes it can. That's definitely possible. Can the portion of return due to 60% TMF be positive over the next 32 years? Yes, that's also possible, maybe even likely. Should we look at performance starting from a start date like 1987 or 1982 and estimate that the performance of the portfolio "returns" 20% forward looking CAGR over the next 32 to 40 years? That's what my comment was about.
...
That said, I do find your time horizon (32 to 40 years) and CAGR (20%; OP's post indicated 16.7%) to be a bit overly optimistic. What about 10 or 15 years? CAGR of 15% or 16%? I'd be perfectly happy with either of these scenarios. If you change either of these parameters, things probably look a bit more doable.
I'm also not following you on dealing with each asset as a "constituent part", if you treat UPRO and TMF separately (no rebalancing) you get something like $520k from '87 to now (where my sim dataset begins... pick whatever starting point you like), with quarterly rebalancing you get over $3M. So you really can't just examine them in the vacuum, you need to consider the entire portfolio, complete with the chosen rebalancing strategy (i.e. static, momentum etc).
To be sure, I'm not suggesting there is a flaw in your analysis, I think to understanding what you are doing here is knowing what you mean by "Rebalancing with zeroreturn, zerocorrelation cash with the two components of the portfolio, separately, explains 99% of the returns." Can you elaborate on what you mean by this?

 Posts: 556
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I was going off various remarks actually made in this thread.
What is your goal with this strategy?
$10M. If past is prologue, I should be able to hit this number in 2530 years. If interest rates (and therefore borrowing costs) stay low, the CAGR should be in the mid20s, allowing me to reach $10M within 20 years.
The post you're replying to should be considered a hypothetical exercise in looking at a best case scenario. It is not what anyone should even expect to get out of it, more like the maximum one should think it could do in a scenario where yields continue to fall to zero and a little beyond. It certainly wasn't a bearish analysis, in a bearish analysis you just lose money, period.In the long run ('82'18) the strategy returns 20% CAGR at 28% annual volatility.
There are a lot of ways to look for a return in the midteens that are a lot less risky (especially when thinking about deeper risk than just a short term bear market for stocks... like inflation and other things of real horror):
https://www.portfoliovisualizer.com/bac ... total3=100
Anyone happy with a return in the midteens may be taking on too much risk with 60% TMF... unless their bet here is just play money, which of course it is for a lot of the people here (not sure about all of the people lurking, though, they may be way above 15% of their portfolio and much more likely to fold as soon as the going gets tough).
You need to download Simba's spreadsheet to replicate the analysis. Then you need to create a portfolio with 40% UPRO (3x S&P 500) and 60% noyield cash. And you need to create another portfolio with 60% TMF (3x long term treasuries) and 40% noyield cash. These are the two components driving the returns. Then create a third portfolio with 40% UPRO and 60% TMF. Using the first two portfolios, multiply the two total returns on cash together (for example, 20x return on 40% UPRO / rest noyield cash and 40x return on 60% TMF / rest noyield cash is an 800x return). Then look at the return for the combined portfolio. Over any time period you care to look at, at least 95% of the returns (and closer to 99% of the returns in the long run) are explained by the individual components, when they're rebalanced with noyield cash separately. This provides a simple and effective analytical framework for thinking about how the portfolio performed in the past and should perform in the future. Without worrying about a mystical rebalancing bonus from negatively correlated assets and worrying that the results cannot be analyzed based on the returns of the individual parts of the portfolio (historically, it was not significant, the vast majority of the "rebalancing bonus" came from minimizing volatility drag, which can be achieved just as well by rebalancing with a pile of cash that does absolutely nothing for return and has absolutely no correlation to anything). So we're not limited to being blinded and in the dark, groping around with backtests. You can just punch in your expected returns from 40% UPRO and your expected returns for 60% TMF, when each individually is in a portfolio with simple noyield cash. You will get back a good estimate for the performance of a 40% UPRO / 60% TMF portfolio. It is a better way to think about returns than using a (completely naive, if not disingenuous) "since 1982" backtest.mrspock wrote: ↑Sat Aug 10, 2019 1:17 pmTo be sure, I'm not suggesting there is a flaw in your analysis, I think to understanding what you are doing here is knowing what you mean by "Rebalancing with zeroreturn, zerocorrelation cash with the two components of the portfolio, separately, explains 99% of the returns." Can you elaborate on what you mean by this?
Given that this is Bogleheads and given the views of Jack Bogle, this comment in the OP is a little ironic (intentionally or not):
Jack Bogle quotes:$10M. If past is prologue, I should be able to hit this number in 2530 years.
“Every day I see numbers that, if not outright lies, are gross distortions of reality. Don’t count on it.”
“When we rely on the past to help us foretell the future, we are alltoolikely to reach invalid conclusions.”
“The world changes, in ways unimaginable and unpredictable.”
“Our best defenses against numerical illusions of certainty are the immeasurable, but nonetheless invaluable, qualities of perspective, experience, common sense, and judgment.”
“Today’s yield on a bond fund is an excellent proxy for its total return in the subsequent decade.”
“Rather than relying on hope, never a good idea in the stock market, rely on asset allocation that focuses on not only the probability of reward, but the consequences of risk.”
“While we look for corroboration of what we believe (confirmation bias), what we really ought to be looking for is the opposite—that observation that would prove us wrong.”
“RTM (Reversion to the Mean) – The pervasive law of gravity that prevails in the financial markets—never stops.”
“Whereas the duration of that pattern of reversion to the mean is not predictable, the pattern itself is as sure a phenomenon as can be witnessed in the stock market.”
“Alas, past performance is not only not predictive of the future, but, at least in speculative markets, predictive of quite the opposite.”
“Any strategy may have done very well in the past, but in this business, the past is not prologue.”
Good luck to everyone using a highconviction/highrisk investment idea, based on nothing more than the flawed premise that the recent past is prologue.“The past is not prologue. Indeed, it is usually antiprologue.”

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I am taking these critiques seriously, and will be issuing a revision to the strategy tomorrow.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
If you are not using M1, do you set limit or market orders when rebalancing? If one asset is performing very well, do you sell its counterpart and place a stop loss order for the appreciating asset and then rebalance? That was my intention. I plan to rebalance every 6190 days.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I appreciate the thoughtful discussion. These types of threads can sometimes be contentious because people don't want you to deviate so much from the Bogle prophet or contradict the Boglehead scripture (light jabbing here). This thread has been (for the most past) pretty reasonable because people are approaching it in a thoughtful and structured way.HEDGEFUNDIE wrote: ↑Sat Aug 10, 2019 3:12 pmI am taking these critiques seriously, and will be issuing a revision to the strategy tomorrow.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
great thread. Only controversy I can think of is rebalancing frequency.HEDGEFUNDIE wrote: ↑Sat Aug 10, 2019 3:12 pmI am taking these critiques seriously, and will be issuing a revision to the strategy tomorrow.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
A nice thing about investments that don't need a lot of rebalancing is that you can choose when to take capital gains. So, really, a lot of the reason for wanting to avoid rebalancing is just to be able to choose when to take capital gains.
For example, it's not farfetched at all to go from a 35% combined LTCG rate in California with NIIT (where I am) to a 15% LTCG rate somewhere else (when no longer working). That's what makes it less appealing to use strategies that require lots of rebalancing (or that throw off high yield). That, and not expecting the 20% CAGR thing.
Also: you don't get the same geometric return (e.g. 20% CAGR) if you have to pay taxes in the inbetween years on the growth. That's the math for taxdeferred. You have to reduce the CAGR along the way, because you have to pay the taxes every time you take capital gains. (That, or you have to come up with extra hidden money to pay for taxes, but then you could also throw that extra hidden money at tax efficient investments.) Delaying taxes is better than paying them as you go.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Has anyone just thrown in UPRO as a kicker to their "normal" portfolio of large cap? Say 90% VOO/10% UPRO? Which would be a theoretical 120% SP500 position?
Would one be better suited to use options instead?
Would one be better suited to use options instead?
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
First time I am seeing OP mentioning revision to the strategy after enduring 65+ pages of hardcore vetting/analysis (unless I missed other revisions in the first few days of discussions). May I request what warranted ‘revision’ to the strategy and what part needs revision?HEDGEFUNDIE wrote: ↑Sat Aug 10, 2019 3:12 pmI am taking these critiques seriously, and will be issuing a revision to the strategy tomorrow.
Jfyi, I am up ~30% since April on $50k compared to SPY ~0.5% negative during the same period.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I don't know about implications for this strategy, but the math is straightforward. Anyone can calculate the capital gain component of return for a given yield change using the spreadsheet PRICE or PV functions, and the income component of return is simply the coupon rate.HEDGEFUNDIE wrote: ↑Fri Aug 09, 2019 6:01 pmI dispute Kevin’s math, as well as his implications for this strategy.MoneyMarathon wrote: ↑Fri Aug 09, 2019 5:50 pm"Returned." If you substitute a 4x forwardlooking performance over that long run (optimistically, as a 60% portion of the portfolio  lower than the past return, for basic math reasons that Kevin has cited) from TMF instead of its 10x historical performance (which I previously calculated in this thread, from a 60% portion of the portfolio), the final result is about 60% less, and the strategy in taxable looks even less appealing.
<snip>
Kevin
....... Suggested format for Asking Portfolio Questions (edit original post)
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
My guess is a revision would be to what's realistically possible looking forward?
My biggest hesitation on this whole adventure is our starting point for LTTs. There isn't much landing pad available right now during a bear market in equities. Unless we are going sub zero!
My biggest hesitation on this whole adventure is our starting point for LTTs. There isn't much landing pad available right now during a bear market in equities. Unless we are going sub zero!
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Nov 16, 2012  20 year yield was 2.31
Jul 31, 2019  20 year yield was 2.31
from PV, 1 jan 2013 to 31jul 19, Upro/tmf annual rebalance 
40/60 =21.6 CAGR, 50/50=24.6 CAGR verse vgd 500 14.0 CAGR
Jul 31, 2019  20 year yield was 2.31
from PV, 1 jan 2013 to 31jul 19, Upro/tmf annual rebalance 
40/60 =21.6 CAGR, 50/50=24.6 CAGR verse vgd 500 14.0 CAGR

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
So in following the discussion over the course of so many pages (and not to derail the thread from its current focus on critiques and HEDGEFUNDIE's coming revision), is the consensus that replicating the strategy in a taxable account so that tax drag is reduced and one avoids unwieldy amounts at quarterly rebalances is best accomplished through just NTSX in taxable, provided one understands that returns will most likely be below 60/40 TMF/UPRO?
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
S&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Actually I found you just such a period. July 1993 to July 1996. Both interest rates and PE ended up approximately the same. Using VFINX, VUSTX and CASHX as a proxy would achieve 13.27% CAGR.305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
This is back when rates were at 6.6% and P/E ratio was at 22.50.
The PE is at 21 atm but rates are at 2%. So it would be unreasonable to expect the fundamental/expected returns of this strategy to be that 13%, let alone the OP's mid 20%. It can get there, but it is not the expected value. Unless you have an expectation for rates to drop or PE to soar that is.
I think most here agree that they can't predict rates or PE. So base your expected returns on the fundamentals of the strategy and periods where those stayed both constant and you'll get a lot closer to a more correct expected return.
Just my 2 cents.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
CHALLENGE ACCEPTED!305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
S&P 500 PE Jun 2003 = 28.60
S&P 500 PE Nov 2009 = 28.51
https://www.multpl.com/sp500peratio/table/bymonth
20 YR RATE Jun 2003 = 4.34
20 YR RATE Nov 2009 = 4.24 (by DEC it went up to 4.4)
https://fred.stlouisfed.org/series/GS20
40/60 UPRO/TMF JUN 2003  NOV 2009 = 5.94% CAGR; Vanguard 500 = 3.96% CAGR
That's what I could find quickly.
EDIT:
SP500 PE Dec 1959 = 17.42
SP500 PE Aug 1965 = 17.53
20 YR RATE Dec 59 = 4.33
20 YR RATE Aug 65 = 4.25
40/60 UPRO/TMF DEC 1959  AUG 1965 = 13.95% CAGR; Vanguard 500 = 10.66% CAGR
EDIT 2: whoops, forgot to make my original June 03Nov 09 numbers quarterly rebalanced. They're now revised.
Last edited by samsdad on Sat Aug 10, 2019 10:15 pm, edited 1 time in total.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
NTSX may be a nice fund, but I would not say that NTSX will likely replicate the OPs strategy. Concentrate on strategy, not returns. NTSX long bonds is 11 of 150 which is about 7 percent total fund long bonds, while OP is 60 percent. NTSX is a balanced fund , well vanguard balanced has a 99 percent correlation to total market. OP strategy has 31 percent correlation to total market. In my 3x portfolio, in 4 months i have made 32 percent on long bonds (even with half of the tmf holding being 2 months or less) and lost 3 percent on nasdaq. I doubt NTSX can ever replicate near that bond gain to stock ratio due to long bond differential.
Last edited by NMBob on Sat Aug 10, 2019 10:19 pm, edited 1 time in total.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
That's a good find. The rates were higher than today but so were the PEs so maybe we call that even. I'd say that ~8.510.5% is a pretty good estimate of what you could expect from this strategy if you don't have any inclination about rates or pricetoearnings appreciation. Which I imagine most don't.samsdad wrote: ↑Sat Aug 10, 2019 9:58 pmCHALLENGE ACCEPTED!305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
S&P 500 PE Jun 2003 = 28.60
S&P 500 PE Nov 2009 = 28.51
https://www.multpl.com/sp500peratio/table/bymonth
20 YR RATE Jun 2003 = 4.34
20 YR RATE Nov 2009 = 4.24 (by DEC it went up to 4.4)
https://fred.stlouisfed.org/series/GS20
40/60 UPRO/TMF JUN 2003  NOV 2009 = 9.42% CAGR; Vanguard 500 = 3.96% CAGR
That's what I could find quickly.
If you agree with the above logic (and some won't I imagine), then all you have left to ask is if you're willing to take the risk of x3 leverage for that return.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
See the revised, edited post. My original 0309 numbers were annual rebalancing, not quarterly.305pelusa wrote: ↑Sat Aug 10, 2019 10:12 pm
That's a good find. The rates were higher than today but so were the PEs so maybe we call that even. I'd say that ~8.510.5% is a pretty good estimate of what you could expect from this strategy if you don't have any inclination about rates or pricetoearnings appreciation. Which I imagine most don't.
If you agree with the above logic (and some won't I imagine), then all you have left to ask is if you're willing to take the risk of x3 leverage for that return.

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 Location: Colorado
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
How did you get those results from PV? I'm getting 5.77% CAGR for June 2003  Nov 2009.samsdad wrote: ↑Sat Aug 10, 2019 9:58 pmCHALLENGE ACCEPTED!305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
S&P 500 PE Jun 2003 = 28.60
S&P 500 PE Nov 2009 = 28.51
https://www.multpl.com/sp500peratio/table/bymonth
20 YR RATE Jun 2003 = 4.34
20 YR RATE Nov 2009 = 4.24 (by DEC it went up to 4.4)
https://fred.stlouisfed.org/series/GS20
40/60 UPRO/TMF JUN 2003  NOV 2009 = 5.94% CAGR; Vanguard 500 = 3.96% CAGR
That's what I could find quickly.
EDIT:
SP500 PE Dec 1959 = 17.42
SP500 PE Aug 1965 = 17.53
20 YR RATE Dec 59 = 4.33
20 YR RATE Aug 65 = 4.25
40/60 UPRO/TMF DEC 1959  AUG 1965 = 13.95% CAGR; Vanguard 500 = 10.66% CAGR
EDIT 2: whoops, forgot to make my original June 03Nov 09 numbers quarterly rebalanced. They're now revised.
https://www.portfoliovisualizer.com/bac ... 0&total3=0
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Whoah rebalancing frequency made a huge effect.samsdad wrote: ↑Sat Aug 10, 2019 10:16 pmSee the revised, edited post. My original 0309 numbers were annual rebalancing, not quarterly.305pelusa wrote: ↑Sat Aug 10, 2019 10:12 pm
That's a good find. The rates were higher than today but so were the PEs so maybe we call that even. I'd say that ~8.510.5% is a pretty good estimate of what you could expect from this strategy if you don't have any inclination about rates or pricetoearnings appreciation. Which I imagine most don't.
If you agree with the above logic (and some won't I imagine), then all you have left to ask is if you're willing to take the risk of x3 leverage for that return.
The ~9% still felt a little high but I figured "numbers don't lie I guess". It sounds like it's perhaps more like ~6%. That feels a little low but then again, this strategy doesn't have that much more market exposure (120 vs 100) and the current term premiums are low (or even negative). I expect the market to return (no prediction, just expectation based on fundamentals) of 56% so perhaps 67% expected for this one isn't far off.
The 19591965 period is another good find. There, rates are higher than today while the PE is lower than today. So fundamentally, it wouldn't be reasonable to expect that return today. I like the 20032009 find because while the rates are higher, the PE is lower so it's a bit closer to today's fundamentals.
Obviously the ideal is a period where the rates and PE started and ended the same AND they are similar to today's. Rates haven't generally been this low so they're hard to find. But the 20032009 I think is good enough for some crude estimates.
One could be more rigorous about the math and figure this out. Perhaps someone with actual skin in this game will desire to take the time to do so.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I was using the simulated dataset that goes back to 1955. When I switch to the OP dataset, I also get 5.77.HawkeyePierce wrote: ↑Sat Aug 10, 2019 10:20 pmHow did you get those results from PV? I'm getting 5.77% CAGR for June 2003  Nov 2009.
Whew! I thought I had screwed up the rebalancing period again!

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Interesting. The problem is more tractable when using the framework that I've suggested, where the returns of the components (the 40% UPRO component and the 60% TMF component) are each considered separately, as a holding rebalanced with nointerest cash.305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
The data series for UPROSIM in the OP goes to February 2019, when the P/E multiple was 20.6. The earliest year in the data series is 1986, and the first month that the P/E multiple pops over 20 P/E is in June 1987. So we could consider the data from June 1987 to February 2019. It's not a very good result  largely due to the flash crash in October, it returns only 5.48% CAGR compared to the S&P itself at 7.39% CAGR. Not to prejudice the estimate too much, suppose a flash crash like Oct 87 was a one time thing. Go forward to July 1991 to get a P/E of 20.14. This may be good enough.
From July 1991 to February 2019, the 40% UPRO / rest in cash portfolio returned 7.77% CAGR, compared to the S&P at 9.57% CAGR. Volatility, interest, and expenses are a drag. (This is in nominal terms. In a lowinflation environment... it could indeed be lower.)
November 2011 had the closest 30 year yield (3.09) to February 2019. The 60% TMF / rest in cash portfolio returned 3.55% CAGR.
Multiplying 1.077 x 1.0355, the combined portfolio would have an estimated 11.5% CAGR.
As you pointed out, things which are hard to predict, such as P/E multiple expansion and falling yields, could increase this figure (and the opposite could decrease it). Over the last few months, for example, a bit of both have increased it nicely.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Thank you!! Nicely done!MoneyMarathon wrote: ↑Sat Aug 10, 2019 2:58 pm
You need to download Simba's spreadsheet to replicate the analysis. Then you need to create a portfolio with 40% UPRO (3x S&P 500) and 60% noyield cash. And you need to create another portfolio with 60% TMF (3x long term treasuries) and 40% noyield cash. These are the two components driving the returns. Then create a third portfolio with 40% UPRO and 60% TMF. Using the first two portfolios, multiply the two total returns on cash together (for example, 20x return on 40% UPRO / rest noyield cash and 40x return on 60% TMF / rest noyield cash is an 800x return). Then look at the return for the combined portfolio. Over any time period you care to look at, at least 95% of the returns (and closer to 99% of the returns in the long run) are explained by the individual components, when they're rebalanced with noyield cash separately. This provides a simple and effective analytical framework for thinking about how the portfolio performed in the past and should perform in the future. Without worrying about a mystical rebalancing bonus from negatively correlated assets and worrying that the results cannot be analyzed based on the returns of the individual parts of the portfolio (historically, it was not significant, the vast majority of the "rebalancing bonus" came from minimizing volatility drag, which can be achieved just as well by rebalancing with a pile of cash that does absolutely nothing for return and has absolutely no correlation to anything). So we're not limited to being blinded and in the dark, groping around with backtests. You can just punch in your expected returns from 40% UPRO and your expected returns for 60% TMF, when each individually is in a portfolio with simple noyield cash. You will get back a good estimate for the performance of a 40% UPRO / 60% TMF portfolio. It is a better way to think about returns than using a (completely naive, if not disingenuous) "since 1982" backtest.
BoglesmindMoneyMarathon wrote: ↑Sat Aug 10, 2019 2:58 pmGiven that this is Bogleheads and given the views of Jack Bogle, this comment in the OP is a little ironic (intentionally or not):
$10M. If past is prologue, I should be able to hit this number in 2530 years.
Jack Bogle quotes:
“Our best defenses against numerical illusions of certainty are the immeasurable, but nonetheless invaluable, qualities of perspective, experience, common sense, and judgment.”“Today’s yield on a bond fund is an excellent proxy for its total return in the subsequent decade.”“Rather than relying on hope, never a good idea in the stock market, rely on asset allocation that focuses on not only the probability of reward, but the consequences of risk.”“While we look for corroboration of what we believe (confirmation bias), what we really ought to be looking for is the opposite—that observation that would prove us wrong.”“Any strategy may have done very well in the past, but in this business, the past is not prologue.”Good luck to everyone using a highconviction/highrisk investment idea, based on nothing more than the flawed premise that the recent past is prologue.“The past is not prologue. Indeed, it is usually antiprologue.”
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
One thing to bear in mind is that some approaches adjust the weights adaptively, like the risk parity schemes we've been discussing. In these approaches, the UPRO weight may vary from 0 to 100% (although I wouldn't recommend that upper limit), yet average near 40 percent.
With the backtesting UPROSIM/TMFSIM sequence, I've been able to push the average CAGR up from 17% for the nominal 40/60 weights to 20, 22 and even 24% percent using a variety of approaches that consider volatility and macroeconomic conditions, without particularly worsening maximum drawdown or much changing the average UPRO weight. I use every rolling 5year sequence for these calculations.
Of course, there's no guarantee that such behavior will continue in the future, but the point is that the straight weighting of UPRO/cash and TMF/cash may be pessimistic for those using adaptive schemes.
With that said, there have been and will be times when it is beneficial to drop the leverage back to reduce uncompensated expenses. Just keep the scheme ready to fire up again when conditions become favorable!
With the backtesting UPROSIM/TMFSIM sequence, I've been able to push the average CAGR up from 17% for the nominal 40/60 weights to 20, 22 and even 24% percent using a variety of approaches that consider volatility and macroeconomic conditions, without particularly worsening maximum drawdown or much changing the average UPRO weight. I use every rolling 5year sequence for these calculations.
Of course, there's no guarantee that such behavior will continue in the future, but the point is that the straight weighting of UPRO/cash and TMF/cash may be pessimistic for those using adaptive schemes.
With that said, there have been and will be times when it is beneficial to drop the leverage back to reduce uncompensated expenses. Just keep the scheme ready to fire up again when conditions become favorable!

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
You can also do this with Portfolio Visualizer. You can create your own monthly data series using 0% nointerest cash (just 0 out all monthly returns), or you can download this copy of my file that I posted here (I gave it the symbol "CASHZERO").MoneyMarathon wrote: ↑Sat Aug 10, 2019 2:58 pmYou need to download Simba's spreadsheet to replicate the analysis.
https://file.io/SrCdcC
You can then have fun replicating results. For example, 40% UPRO (or UPROSIM) / 60% CASHZERO to look at the return provided from the 40% UPRO portion, and 60% TMF (or TMFSIM) / 40% CASHZERO to look at the return provided from the 60% TMF portion.
You can also decide how much you believe the negativecorrelationrebalancingbonus to be, and add that on top. Historically, over the last 32 years (with a cumulative 12% bonus), that bonus added about 0.3% to 0.5% CAGR. The rest of the benefit of rebalancing (which minimizes volatility drag, which can be hugely detrimental to the returns of leveraged ETFs if allowed to run their course, as we all know) can be achieved with an asset that has zero correlation to everything and no return (cash, with no interest).
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
What is the sweet spot of leveraged stock exposure? Something like 70% to 30%, or in your testing do you allow it to be all or nothing? And I would imagine given the volatility it's optimal to have a few triggers which exist concurrently.Hydromod wrote: ↑Sun Aug 11, 2019 1:07 amOne thing to bear in mind is that some approaches adjust the weights adaptively, like the risk parity schemes we've been discussing. In these approaches, the UPRO weight may vary from 0 to 100% (although I wouldn't recommend that upper limit), yet average near 40 percent.
With the backtesting UPROSIM/TMFSIM sequence, I've been able to push the average CAGR up from 17% for the nominal 40/60 weights to 20, 22 and even 24% percent using a variety of approaches that consider volatility and macroeconomic conditions, without particularly worsening maximum drawdown or much changing the average UPRO weight. I use every rolling 5year sequence for these calculations.
Of course, there's no guarantee that such behavior will continue in the future, but the point is that the straight weighting of UPRO/cash and TMF/cash may be pessimistic for those using adaptive schemes.
With that said, there have been and will be times when it is beneficial to drop the leverage back to reduce uncompensated expenses. Just keep the scheme ready to fire up again when conditions become favorable!
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Agreed on all counts. I did some napkin math below, and I was probably underestimating the rebalancing costs, so this might be useful for anyone considering more than a trivial amount in taxable.MoneyMarathon wrote: ↑Sat Aug 10, 2019 4:30 pmA nice thing about investments that don't need a lot of rebalancing is that you can choose when to take capital gains. So, really, a lot of the reason for wanting to avoid rebalancing is just to be able to choose when to take capital gains.
For example, it's not farfetched at all to go from a 35% combined LTCG rate in California with NIIT (where I am) to a 15% LTCG rate somewhere else (when no longer working). That's what makes it less appealing to use strategies that require lots of rebalancing (or that throw off high yield). That, and not expecting the 20% CAGR thing.
Also: you don't get the same geometric return (e.g. 20% CAGR) if you have to pay taxes in the inbetween years on the growth. That's the math for taxdeferred. You have to reduce the CAGR along the way, because you have to pay the taxes every time you take capital gains. (That, or you have to come up with extra hidden money to pay for taxes, but then you could also throw that extra hidden money at tax efficient investments.) Delaying taxes is better than paying them as you go.
First, monthly and even quarterly rebalancing in taxable is a bad idea. High costs with minimal reward, based on past performance. So I decided to simulate annual rebalancing. The basic math was to pull the returns using a $10k starting amount in 1987, then modify each fund by its annual change, rebalance to 40/60 each year, and calculate the tax burden of that transaction assuming worst case scenario (highest LTCG and state rates, 33%). As you can see, the tax burden is fairly manageable, until it isn't. At some point, the investor will have to decide if it's worth the rebalancing cost, or if it's better to just sell the entire portfolio and enjoy the gains. That will likely be a hard decision at some point (looking at you, 20089).
I didn't factor in the annual $3k capital loss deduction. I also assumed LTCG only, and it's possible that assumption will not always hold.
Code: Select all
Year UPRO TMF Reb. Cost Reb. Tax Portfolio After Tax
 $4,000.00 $6,000.00   
1987 $2,506.00 $4,519.80 $304.32 $100.43 $8,007.29
1988 $3,452.20 $4,516.89 $264.56 $87.31 $8,639.29
1989 $5,588.24 $6,283.78 $839.43 $277.01 $11,254.26
1990 $3,322.27 $6,839.00 $742.24 $244.94 $10,108.05
1991 $7,374.64 $8,715.32 $938.66 $309.76 $14,080.27
1992 $7,282.96 $10,909.95 $5.79 $1.91 $15,489.25
1993 $8,604.52 $15,848.57 $1,176.72 $388.32 $19,683.57
1994 $8,904.84 $10,440.49 $1,166.71 $385.01 $16,261.37
1995 $17,300.92 $22,472.70 $1,391.47 $459.19 $29,948.32
1996 $24,890.33 $19,821.58 $7,005.57 $2,311.84 $33,256.98
1997 $33,914.87 $35,087.22 $6,314.04 $2,083.63 $49,531.40
1998 $45,938.84 $52,132.46 $6,710.32 $2,214.40 $69,007.77
1999 $56,606.75 $39,518.81 $18,156.53 $5,991.65 $67,704.13
2000 $21,547.51 $84,903.87 $21,033.04 $6,940.90 $74,622.42
2001 $23,074.40 $64,656.43 $12,017.93 $3,965.92 $62,079.66
2002 $12,977.14 $77,357.54 $23,156.73 $7,641.72 $63,824.24
2003 $67,859.42 $54,867.48 $18,768.66 $6,193.66 $85,527.02
2004 $62,011.45 $85,182.28 $3,133.95 $1,034.20 $101,919.80
2005 $60,949.98 $97,077.21 $2,260.90 $746.10 $109,178.22
2006 $84,544.55 $87,268.94 $15,819.15 $5,220.32 $118,415.03
2007 $66,017.61 $117,489.49 $7,385.23 $2,437.13 $126,249.76
2008 $10,210.34 $179,139.64 $65,529.65 $21,624.79 $130,164.48
2009 $121,699.01 $71,631.09 $44,366.97 $14,641.10 $132,831.17
2010 $104,723.05 $139,116.48 $7,187.24 $2,371.79 $166,672.49
2011 $86,406.98 $287,589.22 $63,191.50 $20,853.20 $253,877.45
2012 $218,443.70 $233,238.99 $37,770.62 $12,464.31 $305,927.40
2013 $399,161.03 $170,356.64 $171,353.96 $56,546.81 $384,876.84
2014 $315,717.82 $644,466.20 $68,355.79 $22,557.41 $646,623.29
2015 $364,293.82 $506,804.33 $15,854.56 $5,232.00 $586,935.76
2016 $456,211.52 $507,763.11 $70,621.67 $23,305.15 $649,163.00
2017 $667,378.91 $696,780.14 $121,715.29 $40,166.05 $917,286.57
2018 $408,756.62 $718,229.74 $42,037.93 $13,872.52 $758,380.86
2019 $558,759.84 $680,248.97 $63,156.32 $20,841.58 $833,435.90
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Just for the sake of completion, if we do assume that your $3k annual deduction applies AND you pay for rebalancing entirely through withdrawals, here's how the numbers would have looked:
CAGR of ~12.3% versus ~9.7% for the S&P500 over the same span.
For comparison, if you're able to rebalance without withdrawing from the portfolio, the CAGR in taxable is ~15% (after tax, assuming 33%) versus ~17% if this is done in a taxsheltered account.
CAGR of ~12.3% versus ~9.7% for the S&P500 over the same span.
For comparison, if you're able to rebalance without withdrawing from the portfolio, the CAGR in taxable is ~15% (after tax, assuming 33%) versus ~17% if this is done in a taxsheltered account.
Code: Select all
Year UPRO TMF Reb. Cost Reb. Tax Portfolio After Reb. Withdrawal
 $4,000.00 $6,000.00   
1987 $2,506.00 $4,519.80 $304.32 $100.43 $7,025.80
1988 $3,452.20 $4,516.89 $264.56 $87.31 $7,969.08
1989 $5,588.24 $6,283.78 $839.43 $277.01 $11,872.02
1990 $3,322.27 $6,839.00 $742.24 $244.94 $10,161.26
1991 $7,374.64 $8,715.32 $938.66 $309.76 $16,089.96
1992 $7,282.96 $10,909.95 $5.79 $1.91 $18,192.91
1993 $8,604.52 $15,848.57 $1,176.72 $388.32 $24,453.09
1994 $8,904.84 $10,440.49 $1,166.71 $385.01 $19,345.33
1995 $17,300.92 $22,472.70 $1,391.47 $459.19 $39,773.61
1996 $24,890.33 $19,821.58 $7,005.57 $2,311.84 $44,711.91
1997 $33,914.87 $35,087.22 $6,314.04 $2,083.63 $69,002.10
1998 $45,938.84 $52,132.46 $6,710.32 $2,214.40 $98,071.30
1999 $56,606.75 $39,518.81 $18,156.53 $5,991.65 $88,156.66
2000 $19,761.20 $77,865.26 $19,289.38 $6,365.50 $89,160.34
2001 $19,326.40 $54,154.21 $10,065.85 $3,321.73 $69,062.71
2002 $10,215.76 $60,896.73 $18,229.24 $6,015.65 $63,111.67
2003 $47,409.49 $38,332.77 $13,112.59 $4,327.15 $79,987.14
2004 $40,415.90 $55,517.48 $2,042.55 $674.04 $95,933.38
2005 $39,724.09 $63,269.98 $1,473.54 $486.27 $102,994.08
2006 $55,101.83 $56,877.45 $10,310.12 $3,402.34 $107,454.17
2007 $41,288.19 $73,479.31 $4,618.81 $1,524.21 $114,767.50
2008 $6,385.66 $112,036.03 $40,983.01 $13,524.39 $100,434.25
2009 $64,551.10 $37,994.28 $23,532.95 $7,765.87 $92,216.77
2010 $49,951.98 $66,357.34 $3,428.25 $1,131.32 $116,309.32
2011 $41,215.37 $137,177.54 $30,141.79 $9,946.79 $165,163.68
2012 $96,468.80 $103,002.67 $16,680.21 $5,504.47 $192,150.53
2013 $169,807.27 $72,471.49 $72,895.76 $24,055.60 $210,284.81
2014 $116,573.49 $237,958.29 $25,239.22 $8,328.94 $343,454.28
2015 $130,306.56 $181,282.04 $5,671.12 $1,871.47 $311,588.59
2016 $163,185.18 $181,624.99 $25,261.11 $8,336.17 $333,723.07
2017 $231,043.16 $241,221.71 $42,137.21 $13,905.28 $453,770.84
2018 $135,967.90 $238,910.35 $13,983.40 $4,614.52 $368,740.93
2019 $182,821.75 $222,572.02 $20,664.24 $6,819.20 $396,324.24
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I've been trying the range of exposures to get a good feel, up to and including all or nothing and the volatility limit idea.
The nice formulation for risk parity with a budget is (b_i/V_i)^m / (sum_j (b_j/V_j)^m), where V is variance, b is risk budget (0 <= b <= 1 and sum_i b_i = 1), and m is 0.5 for risk parity with volatility and 1 for risk parity with variance. The standard risk parity we've been using has b = 0.5 for both UPRO and TMF, and m = 0.5.
The variance can be symmetric or downwardonly, and the downwardonly can be calculated with upward returns set to zero or removed.
I'm personally starting to lean towards a scheme with m = 1 and downwardonly variance with upward returns removed, and adjusting b according to the unemployment rate index, using bands set to trigger at 10% or 15% drift from the current optimal and a minimum update frequency of two weeks (if a trigger goes off). I would set b = 0.75 or 0.8 at high confidence and b = 0 at low confidence from the signal, or at least b < 0.3. I would use 60day lookback for variance calculations to minimize noise chasing. The number of updates would have corresponded to an average update frequency somewhere in the one to two month range.
That's a scheme that pushes average 5yr CAGR up to 23 or 24% without having been hammered by Black Monday. Range of UPRO was 0 to 95%, typical maximum bounced around 60 to 80%, average was ~45%. Maximum drawdown was ~48%.
This will occasionally get UPRO up to >80%, but not to 100%.
The market timing approach, allowing UPRO to hit 100%, does a bit better in most periods but would have been hammered badly on Black Monday.
In general, I'm finding that setting an upper limit on b for UPRO around 0.75 or 0.8 is as far as I would go with any of the schemes; this limit allows UPRO to go higher than 80% occasionally when the volatility is favorable.
Hope that gives a good idea.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I think it's reasonable to expect PCFIX to beat SP600 value by about 1 or 1.5% long term due to 100/100 setup. RAE small looks as good as SP600 value to me.rascott wrote: ↑Sat Aug 10, 2019 1:01 pmMotoTrojan wrote: ↑Fri Aug 09, 2019 11:27 pmWow, this is worth a further look. May be worth considering this fund in place of the S&P500 based ones.stipeman wrote: ↑Fri Aug 09, 2019 11:06 pmExplained in this link:rascott wrote: ↑Thu Aug 08, 2019 8:40 pmHEDGEFUNDIE wrote: ↑Thu Aug 08, 2019 8:36 pm
It's a shame PIMCO chose the obviously inferior small cap index, I guess they are a bond shop after all.
Agreed....but don't think they have an option.... believe you can only buy futures on the Russell. So blame CME for not giving us a better product
Just found it odd that the bonds bosted returns so much over the index of that fund....but not the original Stocks Plus fund. Would assume they used the same bond strategy with both, guess not.
https://www.pimco.com/enus/insights/in ... 02299831=1
In a nutshell the R2K is much more illiquid and it is more difficult to short individual stocks; this premium paid by those shorting results in futures (borrowing) costs that are usually below libor, boosting the potential outperformance of the bondpicking. Need to dig more into the bond strategy used itself but seems intriguing.
On second thought it looks like the S&P600 gets similar returns and is much more efficient... perhaps I am better off holding S&P600 value, as I already do.
Yeah those funds do a nice job of beating their index, issue is the index they have to use stinks. So might as well just stick with the SP600 value index.
The intl funds are maybe the most interesting....they have killed the index on that one. Haven't looked in detail as of yet, but assuming it had to due with the dollar hedging aspect.
My domestic allocation has been split evenly between PSLDX and PCFIX for many years. Happy with the results even though small value has had a tough time lately. PSLDX has more than made up for it.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
3X ETF gets a tune out of the battered FTSE 100;
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I have no idea what math you just did on the bolded sentence. I would think the return would be a weighted average (1.077*0.4 + 1.0355*0.6 = 1.0521). So a 5.21% CAGR. And this would take rebalancing into account because the two CAGRs were derived from cashrebalanced portfolios.MoneyMarathon wrote: ↑Sat Aug 10, 2019 10:44 pmFrom July 1991 to February 2019, the 40% UPRO / rest in cash portfolio returned 7.77% CAGR, compared to the S&P at 9.57% CAGR. Volatility, interest, and expenses are a drag. (This is in nominal terms. In a lowinflation environment... it could indeed be lower.)
November 2011 had the closest 30 year yield (3.09) to February 2019. The 60% TMF / rest in cash portfolio returned 3.55% CAGR.
Multiplying 1.077 x 1.0355, the combined portfolio would have an estimated 11.5% CAGR.
What am I missing?
EDIT: Nvm I get it.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
The same could be said for focusing on expense ratios.firebirdparts wrote: ↑Fri Aug 09, 2019 4:24 pmYou do have to guard against that level of fanaticism where tax avoidance becomes earnings avoidance. It’s very common.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Since OP has disputed my bond math, but has not provided any alternate calculations, I thought it would be useful to walk through my bond return calculations. Then perhaps OP can point out which of the calculations is the problem. As mentioned earlier, anyone can do these calculations easily with a spreadsheet.
Since I'm just looking for ballpark numbers, I make some simplifying assumptions to make the calculations easier. For example, I assume a constant maturity Treasury bought at par (coupon rate = yield), an annual coupon, yield curve that is flat in the relevant maturity range, held for one year. These assumptions can be relaxed to fine tune the return estimates, but that won't change the ballpark.
There are two components to return: income return and capital return. My calculations are for annual return.
Annual income return is just the coupon rate. So annual income return for a bond with a 15% coupon is 15%, and for a bond with a 2% coupon it's 2%.
The annual capital return component is p1/p0  1, where p1 is the price at the end of the year and p0 is the price at the beginning of the year. For a bond purchased at par at the beginning of the year, p0 = 100 (in bond pricing terms), so we only need to calculate p1, price at the end of the year. As mentioned in earlier replies, price can be calculated using the PRICE or PV functions. I'll show examples of each.
Assume a constant maturity 25year bond for which yield drops from 15% at beginning of year, t0, to 14% at end of year, t1. So coupon rate is 15%, and yield at t1 is 14%. Here is the PRICE version for p1:
=PRICE("1/1/2000", "1/1/2025",15%,14%,100,1) = 106.9.
Plugging this into the capital return equation:
p2/p1 1 = 106.9/100  1 = 6.9%
For the PV version, I assume a future value of 1 (instead of 100) so I can use percentage directly as an argument for payment_amount as well as for rate. So the purchase price is 1 and the redemption value is 1. The time value of money cashflow conventions require reversing the sign of the PV result to get p1:
=PV(14%, 25, 15%, 1) = 1.069
and
p2/p1  1 = 1.069/1  1 = 6.9%.
Adding the income return and capital return gives the total oneyear return:
tr = ir + cr = 15% + 6.9% = 21.9%
Doing these calculations with same assumptions, except that yield drops from 3% at t0 to 2% at t1, we get:
ir = 3%
cr = 19.5%
tr = 22.5%
Most of the focus in this thread has been on the capital return component, but as the numbers above show, the income return component also is important. Even though the drop from 3% to 2% results in a much higher capital return than the drop from 15% to 14%, due to higher duration, the much higher coupon rate of 15%, compared to 3%, almost makes up for that difference in terms of total return.
The capital return component does increase more rapidly than the income return component decreases as yield approaches 0%, but you still only end up with tr = 26.0% for an annual drop from 1% to 0%. You just can't come close to the total return you get in going from 15% to 2% by going from 2% to 0% (or somewhat lower than 0%).
Kevin
Since I'm just looking for ballpark numbers, I make some simplifying assumptions to make the calculations easier. For example, I assume a constant maturity Treasury bought at par (coupon rate = yield), an annual coupon, yield curve that is flat in the relevant maturity range, held for one year. These assumptions can be relaxed to fine tune the return estimates, but that won't change the ballpark.
There are two components to return: income return and capital return. My calculations are for annual return.
Annual income return is just the coupon rate. So annual income return for a bond with a 15% coupon is 15%, and for a bond with a 2% coupon it's 2%.
The annual capital return component is p1/p0  1, where p1 is the price at the end of the year and p0 is the price at the beginning of the year. For a bond purchased at par at the beginning of the year, p0 = 100 (in bond pricing terms), so we only need to calculate p1, price at the end of the year. As mentioned in earlier replies, price can be calculated using the PRICE or PV functions. I'll show examples of each.
Assume a constant maturity 25year bond for which yield drops from 15% at beginning of year, t0, to 14% at end of year, t1. So coupon rate is 15%, and yield at t1 is 14%. Here is the PRICE version for p1:
=PRICE("1/1/2000", "1/1/2025",15%,14%,100,1) = 106.9.
Plugging this into the capital return equation:
p2/p1 1 = 106.9/100  1 = 6.9%
For the PV version, I assume a future value of 1 (instead of 100) so I can use percentage directly as an argument for payment_amount as well as for rate. So the purchase price is 1 and the redemption value is 1. The time value of money cashflow conventions require reversing the sign of the PV result to get p1:
=PV(14%, 25, 15%, 1) = 1.069
and
p2/p1  1 = 1.069/1  1 = 6.9%.
Adding the income return and capital return gives the total oneyear return:
tr = ir + cr = 15% + 6.9% = 21.9%
Doing these calculations with same assumptions, except that yield drops from 3% at t0 to 2% at t1, we get:
ir = 3%
cr = 19.5%
tr = 22.5%
Most of the focus in this thread has been on the capital return component, but as the numbers above show, the income return component also is important. Even though the drop from 3% to 2% results in a much higher capital return than the drop from 15% to 14%, due to higher duration, the much higher coupon rate of 15%, compared to 3%, almost makes up for that difference in terms of total return.
The capital return component does increase more rapidly than the income return component decreases as yield approaches 0%, but you still only end up with tr = 26.0% for an annual drop from 1% to 0%. You just can't come close to the total return you get in going from 15% to 2% by going from 2% to 0% (or somewhat lower than 0%).
Kevin
....... Suggested format for Asking Portfolio Questions (edit original post)

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 Location: Alabama
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
I recently started implementing the strategy with futures contracts and use the 2year treasuries for the bonds. I was looking back the other day to see when 2year rates were equal to what they are now. I ended up at January 2003. I then looked to see what the PE ratio was in Jan 2003 vs today. It was 31.4 then (per multpl.com) and is 21.7 now (using your number above). So the PE fell a good bit while the interest rate is now the same as it was then. The backtest below uses 120% stock (like in our standard 3X LETF 40/60 implementation) and uses 960% 2year treasuries. For the treasury allocation, I just picked a point that would have been similar volatility to stocks over the time period. The resulting CAGR was 18.7% and the max drawdown was 33%. Not bad considering how for the PE ratio dropped and that interest rates finished where they started.305pelusa wrote: ↑Sat Aug 10, 2019 9:46 pmActually I found you just such a period. July 1993 to July 1996. Both interest rates and PE ended up approximately the same. Using VFINX, VUSTX and CASHX as a proxy would achieve 13.27% CAGR.305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
This is back when rates were at 6.6% and P/E ratio was at 22.50.
The PE is at 21 atm but rates are at 2%. So it would be unreasonable to expect the fundamental/expected returns of this strategy to be that 13%, let alone the OP's mid 20%. It can get there, but it is not the expected value. Unless you have an expectation for rates to drop or PE to soar that is.
I think most here agree that they can't predict rates or PE. So base your expected returns on the fundamentals of the strategy and periods where those stayed both constant and you'll get a lot closer to a more correct expected return.
Just my 2 cents.
https://www.portfoliovisualizer.com/bac ... 0&total3=0

 Posts: 6569
 Joined: Wed Feb 01, 2017 8:39 pm
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Active on the bond side is something I can tolerate with the advantage of them managing the futures but I like the passive equity aspect of PSLDX and similar options. Given that I have limited IRA space for all of these I think I'd prefer PSLDX for some bond exposure and then passively hold my smallvalue elsewhere.stipeman wrote: ↑Sun Aug 11, 2019 11:18 amI think it's reasonable to expect PCFIX to beat SP600 value by about 1 or 1.5% long term due to 100/100 setup. RAE small looks as good as SP600 value to me.rascott wrote: ↑Sat Aug 10, 2019 1:01 pmMotoTrojan wrote: ↑Fri Aug 09, 2019 11:27 pmWow, this is worth a further look. May be worth considering this fund in place of the S&P500 based ones.stipeman wrote: ↑Fri Aug 09, 2019 11:06 pmExplained in this link:rascott wrote: ↑Thu Aug 08, 2019 8:40 pm
Agreed....but don't think they have an option.... believe you can only buy futures on the Russell. So blame CME for not giving us a better product
Just found it odd that the bonds bosted returns so much over the index of that fund....but not the original Stocks Plus fund. Would assume they used the same bond strategy with both, guess not.
https://www.pimco.com/enus/insights/in ... 02299831=1
In a nutshell the R2K is much more illiquid and it is more difficult to short individual stocks; this premium paid by those shorting results in futures (borrowing) costs that are usually below libor, boosting the potential outperformance of the bondpicking. Need to dig more into the bond strategy used itself but seems intriguing.
On second thought it looks like the S&P600 gets similar returns and is much more efficient... perhaps I am better off holding S&P600 value, as I already do.
Yeah those funds do a nice job of beating their index, issue is the index they have to use stinks. So might as well just stick with the SP600 value index.
The intl funds are maybe the most interesting....they have killed the index on that one. Haven't looked in detail as of yet, but assuming it had to due with the dollar hedging aspect.
My domestic allocation has been split evenly between PSLDX and PCFIX for many years. Happy with the results even though small value has had a tough time lately. PSLDX has more than made up for it.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
That makes a lot of sense. Mega backdoor Roth can help create a lot of IRA space if you/spouse have the right kind of 401k. But I guess that's another thread ...
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Interesting strategy......how did you go about coming up with 960% 2years?EfficientInvestor wrote: ↑Sun Aug 11, 2019 2:51 pmI recently started implementing the strategy with futures contracts and use the 2year treasuries for the bonds. I was looking back the other day to see when 2year rates were equal to what they are now. I ended up at January 2003. I then looked to see what the PE ratio was in Jan 2003 vs today. It was 31.4 then (per multpl.com) and is 21.7 now (using your number above). So the PE fell a good bit while the interest rate is now the same as it was then. The backtest below uses 120% stock (like in our standard 3X LETF 40/60 implementation) and uses 960% 2year treasuries. For the treasury allocation, I just picked a point that would have been similar volatility to stocks over the time period. The resulting CAGR was 18.7% and the max drawdown was 33%. Not bad considering how for the PE ratio dropped and that interest rates finished where they started.305pelusa wrote: ↑Sat Aug 10, 2019 9:46 pmActually I found you just such a period. July 1993 to July 1996. Both interest rates and PE ended up approximately the same. Using VFINX, VUSTX and CASHX as a proxy would achieve 13.27% CAGR.305pelusa wrote: ↑Sat Aug 10, 2019 9:24 pmS&P 500 PE Nov 2012 = 16.12
S&P 500 PE Aug 2019 = 21.72
Do you feel like you can predict interest rates? They could go up or down.
Do you feel like you can predict stock appreciation? They could go up or down.
So find yourself a time period where both treasury rates and the PE ratio ended somewhat the same each. That period should give you a representative return of the strategy's fundamental returns. You might get more if rates drop or the price per earnings soar. You might get less if rates increase or price per earnings drop. But on average, one can say your expected return will be close to whatever that time period shows.
It might be a hard period to find. There might not be one. But if you want a realistic expectation, this is what you need to look at IMO.
This is back when rates were at 6.6% and P/E ratio was at 22.50.
The PE is at 21 atm but rates are at 2%. So it would be unreasonable to expect the fundamental/expected returns of this strategy to be that 13%, let alone the OP's mid 20%. It can get there, but it is not the expected value. Unless you have an expectation for rates to drop or PE to soar that is.
I think most here agree that they can't predict rates or PE. So base your expected returns on the fundamentals of the strategy and periods where those stayed both constant and you'll get a lot closer to a more correct expected return.
Just my 2 cents.
https://www.portfoliovisualizer.com/bac ... 0&total3=0

 Posts: 556
 Joined: Sun Sep 30, 2012 3:38 am
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Nice. I do have something to say about this.EfficientInvestor wrote: ↑Sun Aug 11, 2019 2:51 pmI recently started implementing the strategy with futures contracts and use the 2year treasuries for the bonds. I was looking back the other day to see when 2year rates were equal to what they are now. I ended up at January 2003. I then looked to see what the PE ratio was in Jan 2003 vs today. It was 31.4 then (per multpl.com) and is 21.7 now (using your number above). So the PE fell a good bit while the interest rate is now the same as it was then. The backtest below uses 120% stock (like in our standard 3X LETF 40/60 implementation) and uses 960% 2year treasuries. For the treasury allocation, I just picked a point that would have been similar volatility to stocks over the time period. The resulting CAGR was 18.7% and the max drawdown was 33%. Not bad considering how for the PE ratio dropped and that interest rates finished where they started.
https://www.portfoliovisualizer.com/bac ... 0&total3=0
120% SPY with a negative cash position isn't an especially accurate representation of 40% UPRO. It doesn't have the expenses, and it doesn't have the same volatility decay. For example: https://www.portfoliovisualizer.com/bac ... 0&total3=0
If you have the UPROSIM data set, you can see 40% UPRO / 960% SHY (13 yr treasury) / 900% CASHX here: https://www.portfoliovisualizer.com/bac ... 0&total3=0
That came out to 16.42% CAGR, starting from Jan 2003. If you have both the UPROSIM and the CASHZERO data set, you can see the returns broken out for the S&P 500 and for the SHY position here: https://www.portfoliovisualizer.com/bac ... total3=100
The 40% UPRO portion contributed 8.42% CAGR, the 960% SHY and 900% cash portion contributed 6.41% CAGR. Combined, that's 1.0842 x 1.0641 = 15.37% CAGR. There was a substantial, additional 1.05% CAGR negativecorrelation rebalancing bonus when using the highlyleveraged shorterduration treasuries, given the total 16.42% CAGR.
Jan 2003 was catching the bottom of a bear market, with a P/E slightly higher than it was in Jan 2000 during the euphoria of the long 90s bull market. The P/E peaked even higher in 2002 around the 40s, just as it shot up over 100 in 2009, thanks more to a recession depressing earnings than prices bidding up the P/E to the same level it is today. I'm not sure the suggestion to find similar P/E implies that finding a higher P/E during the bottom of a bear market will get you a good estimate of the expected return from stocks. But, hey, 8.42% CAGR from a leveraged 1.2x S&P 500 position, even after costs, isn't crazy high either, so this could just be nitpicking.
I think you may have shown that leveraging the 2 year up that much can do better, assuming you can implement it that cheaply! And maybe you're also doing S&P 500 trading more effectively than using UPRO? I'm not clear on that.
Considering my estimate for 40% UPRO / 60% TMF to be only 12% when including the rebalancing bonus (or closer to 13% if the S&P has the higher returns that there were in the time period you considered), a 16%ish figure could convince some people that they want to learn your options trading ways.
Last edited by MoneyMarathon on Sun Aug 11, 2019 8:10 pm, edited 1 time in total.
 privatefarmer
 Posts: 598
 Joined: Mon Sep 08, 2014 2:45 pm
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Doesn’t this strategy rely more on the return of equities vs LTTs? LTTs are more there as a hedge, to reduce drawdowns, so that we can then lever the heck out of the equities. Even if LTTs had net zero return after borrowing costs but they reduced the max drawdown enough to allow us to leverage a 40/60 portfolio 3x, then you’d still be getting 120% the return of equities, no? From what I’ve seem in the backtests, the portfolio did really well during stock bull markets regardless of what the LTTs were doing. The glaring exception is during the 70s when inflation was out of control.Kevin M wrote: ↑Sun Aug 11, 2019 2:45 pmSince OP has disputed my bond math, but has not provided any alternate calculations, I thought it would be useful to walk through my bond return calculations. Then perhaps OP can point out which of the calculations is the problem. As mentioned earlier, anyone can do these calculations easily with a spreadsheet.
Since I'm just looking for ballpark numbers, I make some simplifying assumptions to make the calculations easier. For example, I assume a constant maturity Treasury bought at par (coupon rate = yield), an annual coupon, yield curve that is flat in the relevant maturity range, held for one year. These assumptions can be relaxed to fine tune the return estimates, but that won't change the ballpark.
There are two components to return: income return and capital return. My calculations are for annual return.
Annual income return is just the coupon rate. So annual income return for a bond with a 15% coupon is 15%, and for a bond with a 2% coupon it's 2%.
The annual capital return component is p1/p0  1, where p1 is the price at the end of the year and p0 is the price at the beginning of the year. For a bond purchased at par at the beginning of the year, p0 = 100 (in bond pricing terms), so we only need to calculate p1, price at the end of the year. As mentioned in earlier replies, price can be calculated using the PRICE or PV functions. I'll show examples of each.
Assume a constant maturity 25year bond for which yield drops from 15% at beginning of year, t0, to 14% at end of year, t1. So coupon rate is 15%, and yield at t1 is 14%. Here is the PRICE version for p1:
=PRICE("1/1/2000", "1/1/2025",15%,14%,100,1) = 106.9.
Plugging this into the capital return equation:
p2/p1 1 = 106.9/100  1 = 6.9%
For the PV version, I assume a future value of 1 (instead of 100) so I can use percentage directly as an argument for payment_amount as well as for rate. So the purchase price is 1 and the redemption value is 1. The time value of money cashflow conventions require reversing the sign of the PV result to get p1:
=PV(14%, 25, 15%, 1) = 1.069
and
p2/p1  1 = 1.069/1  1 = 6.9%.
Adding the income return and capital return gives the total oneyear return:
tr = ir + cr = 15% + 6.9% = 21.9%
Doing these calculations with same assumptions, except that yield drops from 3% at t0 to 2% at t1, we get:
ir = 3%
cr = 19.5%
tr = 22.5%
Most of the focus in this thread has been on the capital return component, but as the numbers above show, the income return component also is important. Even though the drop from 3% to 2% results in a much higher capital return than the drop from 15% to 14%, due to higher duration, the much higher coupon rate of 15%, compared to 3%, almost makes up for that difference in terms of total return.
The capital return component does increase more rapidly than the income return component decreases as yield approaches 0%, but you still only end up with tr = 26.0% for an annual drop from 1% to 0%. You just can't come close to the total return you get in going from 15% to 2% by going from 2% to 0% (or somewhat lower than 0%).
Kevin
I believe your math has to be accurate. However, there is a reason why the market has set LTT yields so low. Whatever the reason is, the market believes they are still worth investing in despite their volatility and low yields. I feel like this is akin to arguing whether or not stocks are over priced due to their PE. The reality is, the market generally is efficient and there may be reasons the market prices bond yields so low and stock valuations so high that we are not seeing.
Perhaps the market believes LTTs will have significant negative correlation with stocks going forward? Perhaps the market is predicting a major equity bear market and LTTs will be the only thing keeping ones portfolio afloat? Perhaps the market IS pricing in major cuts in the fed fund rate, going well into negative territory? I am far from an expert but I have been hearing Ng for years how rates can ONLY go up from here and yet something like 25% of global govt bonds are now yielding negative.

 Posts: 556
 Joined: Sun Sep 30, 2012 3:38 am
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
No, this is wrong. Given the expenses and the costs of leverage, in that case you would get a higher return from buying SPY (the S&P 500). You get more than 1% higher CAGR by using an unleveraged position in the S&P 500, if you are getting a net zero return from the other component of returns.privatefarmer wrote: ↑Sun Aug 11, 2019 8:10 pmEven if LTTs had net zero return after borrowing costs but they reduced the max drawdown enough to allow us to leverage a 40/60 portfolio 3x, then you’d still be getting 120% the return of equities, no?
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Did I miss the revision or has it not happened yet? Asking for a friend...HEDGEFUNDIE wrote: ↑Sat Aug 10, 2019 3:12 pmI am taking these critiques seriously, and will be issuing a revision to the strategy tomorrow.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
OP stated bluntly that OP disputes my math. I'm just laying out the math so we can try and figure out the nature of the dispute.privatefarmer wrote: ↑Sun Aug 11, 2019 8:10 pmDoesn’t this strategy rely more on the return of equities vs LTTs? LTTs are more there as a hedge, to reduce drawdowns, so that we can then lever the heck out of the equities.
That's all I'm trying to establish.
Kevin
....... Suggested format for Asking Portfolio Questions (edit original post)
 privatefarmer
 Posts: 598
 Joined: Mon Sep 08, 2014 2:45 pm
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
Denmark is now issuing mortgages with NEGATIVE interest rates. The bank will PAY you to borrow money from them and buy a house.
Germany and Japan issue govt bonds that pay negative yields. Britain pays 0.5% for their 10yr bond (far less than United States). All these countries have far smaller economies than US does and arguably, with brexit, have far more uncertainty.
I don’t know nothin’, but to assume that this strategy can’t keep working going forward just bc yields are “low” (even though they’re actually higher than much of the rest of the developed world) seems flawed.
Germany and Japan issue govt bonds that pay negative yields. Britain pays 0.5% for their 10yr bond (far less than United States). All these countries have far smaller economies than US does and arguably, with brexit, have far more uncertainty.
I don’t know nothin’, but to assume that this strategy can’t keep working going forward just bc yields are “low” (even though they’re actually higher than much of the rest of the developed world) seems flawed.

 Posts: 3559
 Joined: Sun Oct 22, 2017 2:06 pm
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
So much math, and yet missing the obvious, which is that we are using 3x leverage.
The 30 year yield was at 2.97% at the beginning of this year, and as of Friday it was 2.26%. The 0.7% drop has yielded a YTD return of 52%.
So we have at least another 168% in return to squeeze out of TMF, if we assume zero as a lower bound.
Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]
The issue becomes is this strategy supremely beneficial when LTT rates are this low? The 30 year treasury was roughly where it is now in Jan 2015 (and again in July 2016). In the 4.5 years since Jan 2015, this strategy has mainly trailed the SP500. After the runup this year it's back to about even with it....all while being much more volatile.privatefarmer wrote: ↑Sun Aug 11, 2019 8:10 pmDoesn’t this strategy rely more on the return of equities vs LTTs? LTTs are more there as a hedge, to reduce drawdowns, so that we can then lever the heck out of the equities. Even if LTTs had net zero return after borrowing costs but they reduced the max drawdown enough to allow us to leverage a 40/60 portfolio 3x, then you’d still be getting 120% the return of equities, no? From what I’ve seem in the backtests, the portfolio did really well during stock bull markets regardless of what the LTTs were doing. The glaring exception is during the 70s when inflation was out of control.Kevin M wrote: ↑Sun Aug 11, 2019 2:45 pmSince OP has disputed my bond math, but has not provided any alternate calculations, I thought it would be useful to walk through my bond return calculations. Then perhaps OP can point out which of the calculations is the problem. As mentioned earlier, anyone can do these calculations easily with a spreadsheet.
Since I'm just looking for ballpark numbers, I make some simplifying assumptions to make the calculations easier. For example, I assume a constant maturity Treasury bought at par (coupon rate = yield), an annual coupon, yield curve that is flat in the relevant maturity range, held for one year. These assumptions can be relaxed to fine tune the return estimates, but that won't change the ballpark.
There are two components to return: income return and capital return. My calculations are for annual return.
Annual income return is just the coupon rate. So annual income return for a bond with a 15% coupon is 15%, and for a bond with a 2% coupon it's 2%.
The annual capital return component is p1/p0  1, where p1 is the price at the end of the year and p0 is the price at the beginning of the year. For a bond purchased at par at the beginning of the year, p0 = 100 (in bond pricing terms), so we only need to calculate p1, price at the end of the year. As mentioned in earlier replies, price can be calculated using the PRICE or PV functions. I'll show examples of each.
Assume a constant maturity 25year bond for which yield drops from 15% at beginning of year, t0, to 14% at end of year, t1. So coupon rate is 15%, and yield at t1 is 14%. Here is the PRICE version for p1:
=PRICE("1/1/2000", "1/1/2025",15%,14%,100,1) = 106.9.
Plugging this into the capital return equation:
p2/p1 1 = 106.9/100  1 = 6.9%
For the PV version, I assume a future value of 1 (instead of 100) so I can use percentage directly as an argument for payment_amount as well as for rate. So the purchase price is 1 and the redemption value is 1. The time value of money cashflow conventions require reversing the sign of the PV result to get p1:
=PV(14%, 25, 15%, 1) = 1.069
and
p2/p1  1 = 1.069/1  1 = 6.9%.
Adding the income return and capital return gives the total oneyear return:
tr = ir + cr = 15% + 6.9% = 21.9%
Doing these calculations with same assumptions, except that yield drops from 3% at t0 to 2% at t1, we get:
ir = 3%
cr = 19.5%
tr = 22.5%
Most of the focus in this thread has been on the capital return component, but as the numbers above show, the income return component also is important. Even though the drop from 3% to 2% results in a much higher capital return than the drop from 15% to 14%, due to higher duration, the much higher coupon rate of 15%, compared to 3%, almost makes up for that difference in terms of total return.
The capital return component does increase more rapidly than the income return component decreases as yield approaches 0%, but you still only end up with tr = 26.0% for an annual drop from 1% to 0%. You just can't come close to the total return you get in going from 15% to 2% by going from 2% to 0% (or somewhat lower than 0%).
Kevin
I believe your math has to be accurate. However, there is a reason why the market has set LTT yields so low. Whatever the reason is, the market believes they are still worth investing in despite their volatility and low yields. I feel like this is akin to arguing whether or not stocks are over priced due to their PE. The reality is, the market generally is efficient and there may be reasons the market prices bond yields so low and stock valuations so high that we are not seeing.
Perhaps the market believes LTTs will have significant negative correlation with stocks going forward? Perhaps the market is predicting a major equity bear market and LTTs will be the only thing keeping ones portfolio afloat? Perhaps the market IS pricing in major cuts in the fed fund rate, going well into negative territory? I am far from an expert but I have been hearing Ng for years how rates can ONLY go up from here and yet something like 25% of global govt bonds are now yielding negative.