HEDGEFUNDIE's excellent adventure Part II: The next journey

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Lee_WSP
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Lee_WSP » Thu Aug 15, 2019 3:09 pm

MotoTrojan wrote:
Thu Aug 15, 2019 2:59 pm
Lee_WSP wrote:
Thu Aug 15, 2019 2:56 pm
MotoTrojan wrote:
Thu Aug 15, 2019 2:49 pm
Lee_WSP wrote:
Thu Aug 15, 2019 2:36 pm
MotoTrojan wrote:
Thu Aug 15, 2019 2:30 pm


So it sounds like the rebalancing bonus is quite a bit bigger than 0.5%.
Can someone explain to me how we know with something approaching certainty that rebalancing bonuses isn't anything more than random happenstance? Is there a way to model this without using historical information?
Isn't rebalancing bonus the whole premise of risk-parity? When one asset falls, the other has a high probability of rising, thus reducing overall volatility and improving overall returns.
I'm not well versed in risk parity, but why does risk parity require you to rebalance at all? If both assets revert to the mean eventually, they'll rebalance themselves. Only minimal tweaking would be necessary per year or every other year to maintain the parity.
Risk parity says nothing about the return of either asset, only the volatility. Rebalancing is necessary or you will drift away from parity.
Makes sense, but what about the frequency of rebalancing?

elderwise
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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by elderwise » Thu Aug 15, 2019 3:22 pm

I built a test pie, liquidated my old pie of 60/40 TMF/UPRO

As follows:

45% - UPRO/TMF 40/60

45% - UPRO/TMF 55/45

10% - 100% UPRO

To see which slice does best...

Invested 78K

Image

MoneyMarathon
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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MoneyMarathon » Thu Aug 15, 2019 3:26 pm

Hydromod wrote:
Thu Aug 15, 2019 3:05 pm
One of the fundamental underlying assumptions in risk parity is that return is proportional to risk.

Which isn't necessarily such a good assumption with something like gold.
For the last four years, gold and long term treasuries have been doing the tango.

Image

Which one is GLD? Which one is VGLT? :shock:

MotoTrojan
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MotoTrojan » Thu Aug 15, 2019 3:44 pm

Lee_WSP wrote:
Thu Aug 15, 2019 3:09 pm
MotoTrojan wrote:
Thu Aug 15, 2019 2:59 pm
Lee_WSP wrote:
Thu Aug 15, 2019 2:56 pm
MotoTrojan wrote:
Thu Aug 15, 2019 2:49 pm
Lee_WSP wrote:
Thu Aug 15, 2019 2:36 pm


Can someone explain to me how we know with something approaching certainty that rebalancing bonuses isn't anything more than random happenstance? Is there a way to model this without using historical information?
Isn't rebalancing bonus the whole premise of risk-parity? When one asset falls, the other has a high probability of rising, thus reducing overall volatility and improving overall returns.
I'm not well versed in risk parity, but why does risk parity require you to rebalance at all? If both assets revert to the mean eventually, they'll rebalance themselves. Only minimal tweaking would be necessary per year or every other year to maintain the parity.
Risk parity says nothing about the return of either asset, only the volatility. Rebalancing is necessary or you will drift away from parity.
Makes sense, but what about the frequency of rebalancing?
Impossible to say what is best.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Thu Aug 15, 2019 3:49 pm

elderwise wrote:
Thu Aug 15, 2019 3:22 pm
I built a test pie, liquidated my old pie of 60/40 TMF/UPRO

As follows:

45% - UPRO/TMF 40/60

45% - UPRO/TMF 55/45

10% - 100% UPRO

To see which slice does best...

Invested 78K

Image
Interesting experiment, especially with the pure UPRO play. I just made my final (hopefully... this has been the death of my smooth and steady investment plan) adjustment; I have a pie of ~$10K in the OPs 55/45 UPRO/TMF and the rest of my Roth is 43/57 UPRO/EDV, which is the equivalent equity to treasury volatility split. I plan to continue contributing to the 43/57 portfolio for the foreseeable future but will let the 55/45 ride alone. I will be considering the 43/57 slice as Total US/US Large Cap for the purpose of my AA, with the 55/45 off-radar.

Hydromod
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Hydromod » Thu Aug 15, 2019 4:24 pm

Lee_WSP wrote:
Thu Aug 15, 2019 3:09 pm
Makes sense, but what about the frequency of rebalancing?
Without trading costs, my backtests clearly show that daily rebalancing is best. The benefit drops off rapidly with increasing rebalancing frequency. I interpret this consistent daily effect as the rebalancing benefit. It seemed to increase CAGR by 10 to 20%.

Otherwise, there isn't much consistent benefit between 10 days rebalancing and perhaps quarterly to semiannual rebalancing.

I think that, longer than a few days between rebalancing, noise related to the luck of the starting date drowns out rebalancing benefits.

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Kevin M
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Kevin M » Thu Aug 15, 2019 6:34 pm

MotoTrojan wrote:
Thu Aug 15, 2019 2:30 pm
Kevin M wrote:
Thu Aug 15, 2019 1:39 pm
Which as shown above, gives a cumulative growth factor of 110.5.
So it sounds like the rebalancing bonus is quite a bit bigger than 0.5%.
I don't know, as I'm not sure what you're comparing to. If you agree with the general approach of using CASHX in the individual portfolios (which I think was to minimize the volatility decay for a cleaner estimate of the individual returns, as opposed to just using 100% UPRO and 100% TMF), then the CAGR to compare to is 15.84% (the no rebalancing bonus number).

Kevin
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MoneyMarathon
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Thu Aug 15, 2019 6:38 pm

Kevin M wrote:
Thu Aug 15, 2019 6:34 pm
the general approach of using CASHX in the individual portfolios (which I think was to minimize the volatility decay for a cleaner estimate of the individual returns, as opposed to just using 100% UPRO and 100% TMF)
Not "CASHX," because that implies that we could actually get to invest in 40% UPRO / 60% TMF (or something like that) while also having the return of 100% CASHX "for free" (without actually having to use our cash to buy t-bills or a short term treasury fund), basically double-dipping our portfolio into the leveraged ETFs and an all-cash position.

To avoid that issue, I used the "cash - no return" line of Simba's spreadsheet, or a data set with 0 returns in PV called "CASHZERO."

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Thu Aug 15, 2019 6:46 pm

MotoTrojan wrote:
Thu Aug 15, 2019 2:30 pm
So it sounds like the rebalancing bonus is quite a bit bigger than 0.5%.
I think it was bigger in the recent past when using quarterly rebalancing (instead of annual rebalancing).

I am still wondering if there is any reason why "annual" compounding is important, relevant, or more accurate. I don't think it is.
Kevin M wrote:
Thu Aug 15, 2019 1:39 pm
CAGR (compound annual growth rate) and CCGR (compound continuous growth rate)

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Kevin M » Thu Aug 15, 2019 6:51 pm

MoneyMarathon wrote:
Thu Aug 15, 2019 3:07 pm
Kevin M wrote:
Thu Aug 15, 2019 1:39 pm
CAGR (compound annual growth rate) and CCGR (compound continuous growth rate).
Kevin M wrote:
Thu Aug 15, 2019 1:39 pm
To resolve this discrepancy, let's calculate CCGR for growth factors 11.98 and 10.96 for 32 years:

CCGRu = LN(11.98)/32 = 7.48%

CCGRt = LN(10.96)/32 = 7.76%

These are of course slightly smaller than CAGR values, since continuous compounding results in larger cumulative growth for a given growth rate. Using the derived approach, we add these to get 15.24% as the weighted CCGR, and:

e^(rt) = e^(15.24% * 32) = 131.4

This verifies the derivation; i.e., e^(CCGR * t) is the product of the cumulative growth factors, 10.96 * 11.98 = 131.4.

But again, multiplying the individual growth factors does not give the correct growth factor for annual compounding.
Thanks for working this out.
Thank you for sharing your derivation.
MoneyMarathon wrote:
Thu Aug 15, 2019 3:07 pm
Are you saying that a "compound annual growth rate" is more relevant here than a "compound continuous growth rate"?
No. I'm just saying that we need to be consistent in using one or the other.

Starting with the individual cumulative return factors, you can calculate the individual CAGR or CCGR for each, then add them to get the combined CAGR or CCGR. Then if you want, you can calculate either the annual or continuous combined cumulative return factor from CAGR or CCGR using either the annual or continuous compounding formula respectively. This always works.

The shortcut of multiplying the individual cumulative return factors to get the combined cumulative return factor only works for continuous compounding.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Thu Aug 15, 2019 6:52 pm

Kevin M wrote:
Thu Aug 15, 2019 6:51 pm
MoneyMarathon wrote:
Thu Aug 15, 2019 3:07 pm
Kevin M wrote:
Thu Aug 15, 2019 1:39 pm
CAGR (compound annual growth rate) and CCGR (compound continuous growth rate).
Kevin M wrote:
Thu Aug 15, 2019 1:39 pm
To resolve this discrepancy, let's calculate CCGR for growth factors 11.98 and 10.96 for 32 years:

CCGRu = LN(11.98)/32 = 7.48%

CCGRt = LN(10.96)/32 = 7.76%

These are of course slightly smaller than CAGR values, since continuous compounding results in larger cumulative growth for a given growth rate. Using the derived approach, we add these to get 15.24% as the weighted CCGR, and:

e^(rt) = e^(15.24% * 32) = 131.4

This verifies the derivation; i.e., e^(CCGR * t) is the product of the cumulative growth factors, 10.96 * 11.98 = 131.4.

But again, multiplying the individual growth factors does not give the correct growth factor for annual compounding.
Thanks for working this out.
Thank you for sharing your derivation.
MoneyMarathon wrote:
Thu Aug 15, 2019 3:07 pm
Are you saying that a "compound annual growth rate" is more relevant here than a "compound continuous growth rate"?
No. I'm just saying that we need to be consistent in using one or the other.

Starting with the individual cumulative return factors, you can calculate the individual CAGR or CCGR for each, then add them to get the combined CAGR or CCGR. Then if you want, you can calculate either the annual or continuous combined cumulative return factor from CAGR or CCGR using either the annual or continuous compounding formula respectively. This always works.

The shortcut of multiplying the individual cumulative return factors to get the combined cumulative return factor only works for continuous compounding.
Okay, thanks Kevin. :beer

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Kevin M » Thu Aug 15, 2019 7:31 pm

MoneyMarathon wrote:
Thu Aug 15, 2019 6:38 pm
Kevin M wrote:
Thu Aug 15, 2019 6:34 pm
the general approach of using CASHX in the individual portfolios (which I think was to minimize the volatility decay for a cleaner estimate of the individual returns, as opposed to just using 100% UPRO and 100% TMF)
Not "CASHX," because that implies that we could actually get to invest in 40% UPRO / 60% TMF (or something like that) while also having the return of 100% CASHX "for free" (without actually having to use our cash to buy t-bills or a short term treasury fund), basically double-dipping our portfolio into the leveraged ETFs and an all-cash position.

To avoid that issue, I used the "cash - no return" line of Simba's spreadsheet, or a data set with 0 returns in PV called "CASHZERO."
Thanks for the clarification. Can you provide a link to the post in which you originally worked this out and explained the reasoning for using this approach as opposed to 100% each UPRO and TMF to get the individual returns?

Thanks,

Kevin
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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by Tyler Aspect » Thu Aug 15, 2019 8:40 pm

Does historical sharp ratio predict future risk?

We can calculate proposed portfolio's sharp ratio and risk adjusted return, but these are historical based figures. We know what the histories are; the future is what we are interested in. Is the future merely a continuation of the past where historical sharp ratio applies exactly, or is the future shrouded in uncertainty?

Anyway, we have two securities that seemed to have opposite directional correlations in UPRO and TMF. But there is nothing that says that stocks and long term Treasuries must move in opposite directions. There are possible scenarios where stock can go down at the same time as the price of long term Treasury bonds. I will not list these scenarios because they are speculative. My point is that UPRO + TMF can go to $0, while un-leveraged portfolio suffers a loss then bounce back in a few years. In examples such as the firm Long Term Capital Management and trades involving securities of opposite directional correlations, these trades were highly profitable until they stopped working; then the company went bankrupt.
Past result does not predict future performance. Mentioned investments may lose money. Contents are presented "AS IS" and any implied suitability for a particular purpose are disclaimed.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Thu Aug 15, 2019 8:42 pm

Kevin M wrote:
Thu Aug 15, 2019 7:31 pm
Thanks for the clarification. Can you provide a link to the post in which you originally worked this out and explained the reasoning for using this approach as opposed to 100% each UPRO and TMF to get the individual returns?
Note (I haven't posted this before): There is a perfect rebalancing strategy for eliminating volatility decay, if you're able to rebalance at the same cadence as the reset in leverage. It's explained in this thesis: https://www.math.nyu.edu/faculty/avella ... _Zhang.pdf

Image

So, for example, say that your LETF is a 3x LETF (like UPRO), then beta = 3 (b = 3) because it's 3x leveraged. And St and So refer to the value of the underlying (the S&P 500) right now and when you started. So, your money in UPRO, every day, to eliminate volatility decay, would be:

(1/3 the initial investment) * (current value of the underlying / original value of the underlying)

What's noteworthy here is that you will need to take some money out of UPRO when the underlying goes up (because your gains are magnified) and put some money into UPRO when the underlying goes down (because losses are magnified). For example, if the original investment is $6000 in 1/3 UPRO (3x S&P) and 2/3 SPY (1x S&P), but the S&P goes up 25% on the first day (and we say that it started at $1 for simple math), and thus UPRO is at $2000 * 1.75 = 3500 for an extra $1500, then the new amount to put into UPRO is:

(1/3 * 6000) * (1.25 / 1.0) = $2500

That is, you'd have to take 2/3 of the winnings, or $1000, out of the LETF, to be able to eliminate vol decay. Then if the S&P went down 20% on the second day, returning to the original $1 price (0.25 / 1.25 = 20%), then UPRO is at $2500 * 0.4 = $1000 for a loss of $1500. And the new amount to put into UPRO is:

(1/3 * 6000) * (1.0 / 1.0) = $2000

That is, you'd have to put in $1000 to get UPRO back to the correct amount to be able to eliminate volatility decay. Note that we're able to eliminate volatility decay completely, here, even while putting the rest of the money into something perfectly correlated with UPRO on a daily basis (an unleveraged S&P fund).

Even without this perfect rebalancing strategy, similar effects of reducing volatility decay can be observed if you take out money when the LETF is gaining and put in money when the LETF is losing.

In this post I recapped some things:
MoneyMarathon wrote:
Tue Aug 13, 2019 1:47 pm
MotoTrojan wrote:
Tue Aug 13, 2019 12:32 pm
Can you remind me how you calculated the rebalancing bonus?
Here:
MoneyMarathon wrote:
Sun Jul 14, 2019 4:11 am
privatefarmer wrote:
Sun Jul 14, 2019 12:08 am
a narrow yield curve is of concern however I am not one to try and "time the market" so I would look at this strategy for the long-term as a buy-and-hold strategy. This strategy has worked very well since 1983 even though borrowing costs were significantly higher back in the 80s.
privatefarmer wrote:
Sun Jul 14, 2019 12:08 am
But I think that we have to remember that the strategy is not relying on TMF or LTTs to generate returns. The strategy rather relies on LTTs/TMF to provide negative correlation to stocks when the market tanks, thus increasing our sharpe ratio. You have to remember that we are leveraging the heck out of stocks as well so even though stocks are "only" 40% of our portfolio because of the leverage we effectively have 120% exposure to stocks. So the LTTs are more to soften the downside risk vs provide actual return.
I would like to tease out an important point here. Consider these different goals and observations:
  • not "timing the market," long-term buy-and-hold strategy
  • this strategy has worked very well since 1983
  • the strategy is not relying on TMF or LTTs to generate returns
  • rather relies on LTTs/TMF to provide negative correlation to stocks when the market tanks
All of these points individually seem pretty intuitive:
  • it's a fixed allocation
  • since 1983 is a long time... and maybe a more relevant time period since it's more recent?
  • bonds are for safety
  • bonds have gone up when stocks go down
The apparently counter-intuitive thing here is that TMF has generated great returns... during 1987-2018. That's the most important part of what makes the backtest with a full TMF allocation so amazing. The "stock market tanks" anti-correlation-based rebalancing effects are also a factor, but a secondary one: if TMF was a drag or did little for the portfolio otherwise, but just had great anti-correlation, things would have been very different for a backtest on this range of dates.

Using Simba's spreadsheet:

40% UPRO rebalanced annually with plain cash (zero correlation, no interest) provided 7.77% CAGR and 10.97x return.
60% TMF rebalanced annually with plain cash (zero correlation, no interest) provided 8.07% CAGR and 11.96x return.
40% UPRO / 60% TMF rebalanced annually with each other provided 16.89% CAGR and 147.45x return.

Backing out the different factors, if there were no anti-correlation effect during annual rebalancing (just zero correlation), we might have expected to get a return of 10.97 x 11.96 = 131.2x. A return of 131.2x over 32 years is a CAGR of 16.46%. We actually got a CAGR of 16.89% which allowed us to get an extra 12.4% accumulated over a 32 year time period.

The added value of 60% TMF over the 32 years here was divided between 11.96x return, by itself with zero correlation to no-yield cash, and an extra 1.12x return thanks to the incremental benefit of being anti-correlated with UPRO. Understandably, then, I believe it should be plain that if TMF doesn't deliver strong positive yield all on its own, then you're not going to get it anything close to working like it did 1980s to present.

I think there is possibly an argument that TMF rebalancing with plain cash delivers its own premium, maybe by making good trades. But a starting 60% TMF (not even 100%) without rebalancing actually did even better. Without rebalancing into cash, a portfolio that drifted into a larger percentage allocation to TMF over time returned 15.6x or 8.96% CAGR. TMF just plain did well in this time period.

The main reason why TMF did very well (not middling, neutral, or negative) is simply linked to how the price of a bond is calculated.

That is, the yield on 30-year treasuries went down.

If the 30-year treasury yield had gone up during this time period, you'd get some very poor results like the ones that are hidden when choosing a time period like this that (yes) is long, (yes) is recent... but which, unfortunately, is also (pretty clearly, IMO, given that the entire long term, secular trend here was rates going down with only a bit of backtracking just to go more down) a biased / error-prone way to try to make an averaged estimate using historical data for the expected return for leveraged long-term treasuries. And, of course, accordingly, it's also not going to give an unbiased estimate for the risks and expected return of a two-fund portfolio with a 60% allocation to them.

It could still make a lot of money, of course. But to me, at least, it looks like (in part) a bet that interest rates and inflation won't go up significantly over the time period invested. If that's true, it pays off, at least a little. If that's not true, it could crash and burn. And if the 30-year yield actually keeps going down from here over the next 20-30 years, combined with strong economic growth, then sure, I guess someone might get similar results.
I consider mitigation of the volatility decay thanks to rebalancing with zero-correlation zero-interest cash, and then separately consider the 'rebalancing bonus due to negative correlation'. To get the returns of the individual components, I consider them inclusive of the mitigation of the volatility drag thanks to rebalancing with zero-correlation zero-interest cash. This provides a better representation of the amount of return from the individual components and the amount of return from assets having negative correlation.

Putting 100% of any portfolio into a 3x leveraged ETF can get crushed from volatility drag, but it doesn't take much of anything special to make a lot of that volatility drag go away. See also one of my first posts in this thread, trying to understand better the effect of rebalancing.
MoneyMarathon wrote:
Thu Jul 11, 2019 4:31 am
I've been working on getting a better understanding of the nature of "volatility decay." Rebalancing interacts a lot.

Here is 100% SDY (blue) and 50% SDYL, 50% CASHX (red) with no rebalancing. SDYL is a monthly resetting leveraged 2x ETF.

Image

Notice that the SDYL portfolio is shifting its allocation over time to have more SDYL than the original 50%. This increases its exposure to the underlying, over time, to be greater than 1x. Basically, beta is drifting up over time, and as the beta increases, the portfolio does what you'd expect: further gains are magnified, but so are subsequent losses.

That is, until you rebalance. At that point you can reset the portfolio to have 1x exposure by making the 2x part be 50% again. The only issue still remaining here is that you waited to reset the portfolio, so you've already drifted away from your underlying due to the already-deviated returns of the previous 11 months in which you had not yet rebalanced. With annual rebalancing, the two portfolios are much closer.

Image

Because the path dependency of returns can work for you or against you, the annual-rebalanced portfolio here gains and loses several times compared to its underlying. But once you rebalance monthly, with a monthly-resetting 2x ETF at 50% weight, the tracking error of the ETF itself is the only remaining issue.

Image

How does it track so well now? The basic idea in this case is that you take about half of the cash off the table when you win (and your next bet would naturally be bigger), but you put about half of what was lost back in when you lose (and your next bet would naturally be smaller). This is intended to keep a relatively-constant level of exposure in the next bet (it's not a prediction, no reversion is really expected).
Rebalancing with anything that isn't correlated is going to do a lot to offset the volatility decay and get you closer to the return of the underlying, because it will let you take some money off the table when the underlying is up and put some back in when the underlying is down.

However, if the underlying didn't have strong positive returns, you won't get strong positive returns by mitigating volatility decay. You need the strong positive returns from the underlying in order for the mitigation of the volatility decay to provide strong positive returns overall. If the underlying had weak returns, then you may still see some rebalancing bonus from negative correlation (as I've described it), but you won't get the humongous advantages from rebalancing (that someone would assume with a naive calculation), because that's counting a lot of the effect where you're just preserving the gains of leveraging the underlying from being drained away by volatility decay.
However, my original goal wasn't to pin down the precise extent of the "rebalancing bonus" (and, since most people aren't using annual rebalancing, their "rebalancing bonus" may be higher... in the recent past, quarterly rebalancing did better than annual... yet the original post here referred to Simba's spreadsheet and so used annual returns & annual rebalancing).

Originally, it was just to explain that looking at 100% TMF returns was extraordinarily misleading & understating the contribution to returns that have been achieved since the 1980s due to high starting yields and falling yields. It was to correct the misconception that the main thing TMF was doing for returns was saving UPRO in stock bear markets.

Secondarily, it's an interesting way to think about the 'negative correlation rebalancing bonus', beyond what can just be achieved by rebalancing with zero-correlation, zero-interest boring cash. Which is quite a lot, of course, because volatility decay is such a scourge to a 3x LETF (when a portfolio is set to have 100% in the LETF without any money ever taken off or put in again).

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by Lee_WSP » Thu Aug 15, 2019 8:56 pm

Tyler Aspect wrote:
Thu Aug 15, 2019 8:40 pm
Does historical sharp ratio predict future risk?

We can calculate proposed portfolio's sharp ratio and risk adjusted return, but these are historical based figures. We know what the histories are; the future is what we are interested in. Is the future merely a continuation of the past where historical sharp ratio applies exactly, or is the future shrouded in uncertainty?

Anyway, we have two securities that seemed to have opposite directional correlations in UPRO and TMF. But there is nothing that says that stocks and long term Treasuries must move in opposite directions. There are possible scenarios where stock can go down at the same time as the price of long term Treasury bonds. I will not list these scenarios because they are speculative. My point is that UPRO + TMF can go to $0, while un-leveraged portfolio suffers a loss then bounce back in a few years. In examples such as the firm Long Term Capital Management and trades involving securities of opposite directional correlations, these trades were highly profitable until they stopped working; then the company went bankrupt.
It would if the data set was large enough. But even 100 years is a tiny fraction of human history and non existent in world history not to mention cosmic history, but I digress. Point being, there's not enough data.

They are not negatively correlated, they are non-correlated. Not even slightly negatively correlated. They just have a slight historical tendency to rise when stocks are in free fall, but this is probably due to the central bank's lowering rates to boost growth.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Hydromod » Thu Aug 15, 2019 9:26 pm

MoneyMarathon wrote:
Thu Aug 15, 2019 8:42 pm
However, my original goal wasn't to pin down the precise extent of the "rebalancing bonus" (and, since most people aren't using annual rebalancing, their "rebalancing bonus" may be higher... in the recent past, quarterly rebalancing did better than annual... yet the original post here referred to Simba's spreadsheet and so used annual returns & annual rebalancing).

Originally, it was just to explain that looking at 100% TMF returns was extraordinarily misleading & understating the contribution to returns that have been achieved since the 1980s due to high starting yields and falling yields. It was to correct the misconception that the main thing TMF was doing for returns was saving UPRO in stock bear markets.

Secondarily, it's an interesting way to think about the 'negative correlation rebalancing bonus', beyond what can just be achieved by rebalancing with zero-correlation, zero-interest boring cash. Which is quite a lot, of course, because volatility decay is such a scourge to a 3x LETF (when a portfolio is set to have 100% in the LETF without any money ever taken off or put in again).
Your explanation suggests that daily rebalancing should see the biggest rebalancing bonus in theory, because that has the most events for the bonus to act on. That seems to be consistent with the paper derivation and your mention of volatility decay. Sub-daily might even do better, but costs quickly intervene.

That explanation would be consistent with my empirical observation that simply using daily rebalancing tends to consistently increase CAGR for the UPROSIM/TMFSIM data compared to biweekly and longer. For example, 17% at monthly might go to 20% CAGR at daily.

If the bonus is proportional to the number of events, it makes sense that ten-day rebalancing would have 1/10 of the daily bonus. This would be 17.3% for the same example.

The empirical study suggests that the rebalancing bonus dies off rapidly as the frequency decreases, and there is little benefit at rebalance frequency greater than 10 days.

Does that make sense? If so, I don't think seeking a rebalancing bonus is really actionable for this group.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Thu Aug 15, 2019 11:41 pm

MoneyMarathon wrote:
Thu Aug 15, 2019 8:42 pm
Kevin M wrote:
Thu Aug 15, 2019 7:31 pm
Thanks for the clarification. Can you provide a link to the post in which you originally worked this out and explained the reasoning for using this approach as opposed to 100% each UPRO and TMF to get the individual returns?
Note (I haven't posted this before): There is a perfect rebalancing strategy for eliminating volatility decay, if you're able to rebalance at the same cadence as the reset in leverage. It's explained in this thesis: https://www.math.nyu.edu/faculty/avella ... _Zhang.pdf

Image

So, for example, say that your LETF is a 3x LETF (like UPRO), then beta = 3 (b = 3) because it's 3x leveraged. And St and So refer to the value of the underlying (the S&P 500) right now and when you started. So, your money in UPRO, every day, to eliminate volatility decay, would be:

(1/3 the initial investment) * (current value of the underlying / original value of the underlying)

What's noteworthy here is that you will need to take some money out of UPRO when the underlying goes up (because your gains are magnified) and put some money into UPRO when the underlying goes down (because losses are magnified). For example, if the original investment is $6000 in 1/3 UPRO (3x S&P) and 2/3 SPY (1x S&P), but the S&P goes up 25% on the first day (and we say that it started at $1 for simple math), and thus UPRO is at $2000 * 1.75 = 3500 for an extra $1500, then the new amount to put into UPRO is:

(1/3 * 6000) * (1.25 / 1.0) = $2500

That is, you'd have to take 2/3 of the winnings, or $1000, out of the LETF, to be able to eliminate vol decay. Then if the S&P went down 20% on the second day, returning to the original $1 price (0.25 / 1.25 = 20%), then UPRO is at $2500 * 0.4 = $1000 for a loss of $1500. And the new amount to put into UPRO is:

(1/3 * 6000) * (1.0 / 1.0) = $2000

That is, you'd have to put in $1000 to get UPRO back to the correct amount to be able to eliminate volatility decay. Note that we're able to eliminate volatility decay completely, here, even while putting the rest of the money into something perfectly correlated with UPRO on a daily basis (an unleveraged S&P fund).

Even without this perfect rebalancing strategy, similar effects of reducing volatility decay can be observed if you take out money when the LETF is gaining and put in money when the LETF is losing.
One more comment here: using plain, zero-return cash along with a fixed allocation of 1/3 UPRO will do the same thing as above, and it would eliminate volatility decay as described in this paper. Suppose again you had $2000 in UPRO and $4000 sitting in no-interest cash, then you had the S&P go up 25%, so your UPRO went up to $3500. You now have $7500. You need to get back to 1/3 UPRO to maintain a fixed allocation, so you need to get back to $2500 in UPRO by holding onto 1/3 of the gains ($500) and putting the other 2/3 of gains ($1000) into the cash position.

Likewise, using the "wrong" fraction (a fixed allocation but not 1/3) will mitigate volatility, by taking off money and putting it in at the right times (but not to the right extent), compared to the perfect strategy for eliminating volatility decay completely.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Fri Aug 16, 2019 12:07 am

physixfan wrote:
Tue Aug 13, 2019 9:18 pm
I setup the Simba spreadsheet to quickly output the rebalancing bonus for a few allocations and I have to say I am pretty unsatisfied with the findings.

55/45 UPRO/TMF
1955-2018 - 0.11%
1955-1982 - 0.22%
1982-2018 - 0.53%

40/60 UPRO/TMF
1955-2018 - 0.12%
1955-1982 - (-0.01%)
1982-2018 - 0.69%

This really takes a hit on my feelings towards the strategy.
Can you do this calculation for 2000-present? As I mentioned in a previous thread viewtopic.php?f=10&t=272007&p=4688976#p4688976, the negative correlation actually is confirmed for 2000-present, but not for the several decades before that.
Sure, I can do this with quarterly rebalancing (which improved things, over annual), from 1987-2018 and from 2000-2018. To do quarterly rebalancing, to find the returns of the components when rebalanced with an uncorrelated asset, I am using Portfolio Visualizer. I've uploaded a 'CASHZERO' data set with just zero'd out returns (no returns, and, necessarily, no correlation).

55/45 UPRO/TMF
1987-2018 - 182.72x (actual), 122.95x (part-wise), (182.72)^(1/32) - (122.95)^(1/32) = 1.45% CAGR (bonus)
2000-2018 - 9.28x (actual), 6.1x (part-wise), (9.28)^(1/19) - (6.1)^(1/19) = 2.46% CAGR (bonus)

40/60 UPRO/TMF
1987-2018 - 154.42x (actual), 110.09x (part-wise), (154.42)^(1/32) - (110.09)^(1/32) = 1.23% CAGR (bonus)
2000-2018 - 11.65x (actual), 8.08x (part-wise), (11.65)^(1/19) - (8.08)^(1/19) = 2.17% CAGR (bonus)

So, if going by the 2000-2018 time period and using the 55% UPRO/45% TMF allocation with quarterly rebalancing, there was roughly a 2.5% CAGR 'negative correlation' bonus.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MoneyMarathon » Fri Aug 16, 2019 1:58 am

Here's an attempt to think about the amount of leverage that is optimal, for maximizing compounding growth rate by the Kelly criterion.

Suppose we take the time period 1978-2019 and consider three asset classes: US large caps, long term treasuries, and gold. Apparently the highest Sharpe portfolio is achieved with 47.6% large caps, 45.73% long term treasuries, and 6.66% gold. But I'd rather use a portfolio that doesn't deal with strange fractions, so consider this nearby allocation:

50% US Large Caps
45% Long Term Treasuries
5% Gold

The Kelly criterion is described here:

https://en.wikipedia.org/wiki/Kelly_criterion

The calculation we're supposed to make is (m - r) / s^2, where m is the mean of logarithmic returns, r is the risk-free rate, and s is the standard deviation of logarithmic returns. What's weird about this is that the risk-free rate, r, changes over time. So instead I'd like to look at m / s^2 where m is the mean of logarithmic excess returns (above/below the risk-free rate) and where s is the standard deviation of logarithmic excess returns.

The Portfolio Visualizer data can be exported into Excel to make the calculations easier:
https://www.portfoliovisualizer.com/bac ... 0&total3=0

Using log base 2, the mean of logarithmic excess returns is 0.079, and the standard deviation of logarithmic excess returns is 0.1385. The variance is s^2 = 0.01919. And m / s^2 = 4.11. Yes, that's suggesting that, if the future looks like this sample of the past, and if financial returns were log-normal, you could have leveraged up to about 4x without diminishing expected CAGR. Obviously, the future won't look just like this sample.

Historically, over this time period, long term treasuries returned 8.45% CAGR and the risk-free cash returned 4.46% CAGR. Let's suppose that long term treasuries are no less volatile than they've been in the past, but that the produce much lower returns in excess of the risk-free rate. Let's say that this cuts down on the mean of the logarithmic excess return considerably. Say, for example (just to pick a number), that the mean of the log excess return is now 0.05, instead of 0.079, a reduction in expected compounding returns of about 37%.

Now m / s^2 = 2.6 and the maximum amount of leverage to apply is 2.6x (i.e., to bet 160% more than you have in cash). This is with an efficient 50% US large cap / 45% long term treasury / 5% gold portfolio, and doesn't account for any expenses, beyond the idea of paying the risk-free rate for leverage. Because expenses reduce return and lower expected return reduces the optimal leverage, then the optimal leverage is lower yet.

So far, so good...

Now let's look at 55% UPRO / 45% TMF and consider it as a leveraged version of 55% US stocks / 45% long term treasuries. Let's add in 1% to the risk-free rate to represent the cost of expense ratios and the costs of leverage beyond just the risk-free rate of T-bills. And let's once again look at 1978-2018, starting from the first year we have data on long term treasuries.

https://www.portfoliovisualizer.com/bac ... 0&total3=0

Using log base 2, the mean of logarithmic excess returns is 0.06845, and the standard deviation of logarithmic excess returns is 0.1455. The variance is s^2 = 0.02117. And m / s^2 = 3.2334. So, if you believe you will get returns like those from 1978-2018 and that they will be log-normal, and if your total cost of leverage is 1% over the risk-free rate, you may want to go up to 3.2x leverage.

We can then create a table for how much leverage you may want, depending on how much you believe returns may be depressed going forward. In the same way that I added in a cost that reduced the excess return by 1%, I will consider depressed forward-looking returns in 0.5% increments (in addition to the 1% cost).

0.5% less per year = 0.0615 / 0.1462^2 = 2.88x Kelly criterion leverage.
1.0% less per year = 0.0546 / 0.1469^2 = 2.53x Kelly criterion leverage.
1.5% less per year = 0.0476 / 0.1476^2 = 2.18x Kelly criterion leverage.
2.0% less per year = 0.0405 / 0.1483^2 = 1.84x Kelly criterion leverage.

So, with as little as 1.5% to 2% less return expected per year (relative to 1978-2018), in addition to 1% costs above buying low-cost index funds, as well as considering the cost of borrowing as being just the risk-free rate, the Kelly criterion leverage for 55% US stock / 45% long term treasuries seems to be between 1.8x and 2.2x.

If the 45% portion in long-term treasuries no longer contributes about 4% CAGR above the risk-free rate, that could be a negative impact of about 2% less per year in excess return for the whole portfolio. On the other hand, if we accept the idea of an almost 2.5% rebalancing bonus with quarterly rebalancing, something that isn't included above, that could tip the scales, meaning you might continue to get similar returns in excess of the risk free rate, and 3x leverage might be, just barely, Kelly criterion optimal.

Edit: No, wait, it's not quite like that. :? You can't add in the 2.5% rebalancing bonus, just like that, because it can't be leveraged up: it is a result of using leverage. At best you could, say, plug in 0.8% as a rebalancing bonus and let the Kelly criterion expect 2.4% excess return when leveraged up 3x. If the excess return of the portfolio (because of long term treasuries) is lower by 1.8% and if the rebalancing bonus gives you 0.8% to work with, that's still a depressed return of 1%. At that point, 2.5x leverage is optimal. But I think we could also take issue with adding in the 1% costs, too, because you're not leveraging up costs. So forget the costs, and you're back at 3x leverage being optimal, albeit with a drag on portfolio performance due to costs.

Long story short, about 3x leverage could be optimal if the rebalancing bonus is quite as big as it has been recently, even if the returns of long term treasuries are lower than the past. So the 55% UPRO / 45% TMF does indeed depend on the assumption of a negative correlation between stocks and long term treasuries. It could make sense even in a world where long term treasuries didn't deliver excess return above the risk free rate. However, it is dangerously close to the maximum leverage that could be considered optimal.
Last edited by MoneyMarathon on Fri Aug 16, 2019 2:37 am, edited 1 time in total.

MoneyMarathon
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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by MoneyMarathon » Fri Aug 16, 2019 2:22 am

Hydromod wrote:
Thu Aug 15, 2019 9:26 pm
Your explanation suggests that daily rebalancing should see the biggest rebalancing bonus in theory, because that has the most events for the bonus to act on. That seems to be consistent with the paper derivation and your mention of volatility decay.
Rebalancing at the same cadence as the reset in leverage can be used to mitigate volatility decay, pretty much perfectly if a rote formula is followed. However, that's not connected to the number of rebalancing events. That's connected to matching the frequency of the reset in leverage. You could also mitigate volatility decay near-perfectly with a monthly-resetting ETN. Actually, I originally stumbled on the "take half off the table when up, put half back in when down" perfect strategy for eliminating volatility decay by looking at a 2x monthly resetting ETN. Finding the paper clarified what I was looking at.

Eliminating or mitigating volatility decay of the leveraged ETFs is good (should increase returns in the long run) but isn't the same thing as a "negative correlation rebalancing bonus," which is based on a modern portfolio theory idea that, by combining negatively correlated assets, you can reduce the volatility of the portfolio while keeping the combined arithmetic returns of the components, thus achieving a higher portfolio geometric return (CAGR). It's pretty confusing that you can achieve both objectives with just one simple button push (rebalancing at a fixed schedule to a fixed allocation), but you can.
Hydromod wrote:
Thu Aug 15, 2019 9:26 pm
The empirical study suggests that the rebalancing bonus dies off rapidly as the frequency decreases, and there is little benefit at rebalance frequency greater than 10 days. Does that make sense? If so, I don't think seeking a rebalancing bonus is really actionable for this group.
Empirically, you may see something like this with these leveraged ETFs: Daily or near-daily >> monthly or quarterly >> annually >> every 5 years or less often or never. Even if people couldn't achieve daily (and I'm not sure about that -- there are lots of APIs that would let someone do it more often, or people could just spend more time on M1 finance and less time on Facebook), they can definitely do it quarterly or annually.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 9:57 am

MoneyMarathon wrote:
Fri Aug 16, 2019 1:58 am
Here's an attempt to think about the amount of leverage that is optimal, for maximizing compounding growth rate by the Kelly criterion.

Suppose we take the time period 1978-2019 and consider three asset classes: US large caps, long term treasuries, and gold. Apparently the highest Sharpe portfolio is achieved with 47.6% large caps, 45.73% long term treasuries, and 6.66% gold. But I'd rather use a portfolio that doesn't deal with strange fractions, so consider this nearby allocation:

50% US Large Caps
45% Long Term Treasuries
5% Gold

The Kelly criterion is described here:

https://en.wikipedia.org/wiki/Kelly_criterion

The calculation we're supposed to make is (m - r) / s^2, where m is the mean of logarithmic returns, r is the risk-free rate, and s is the standard deviation of logarithmic returns. What's weird about this is that the risk-free rate, r, changes over time. So instead I'd like to look at m / s^2 where m is the mean of logarithmic excess returns (above/below the risk-free rate) and where s is the standard deviation of logarithmic excess returns.

The Portfolio Visualizer data can be exported into Excel to make the calculations easier:
https://www.portfoliovisualizer.com/bac ... 0&total3=0

Using log base 2, the mean of logarithmic excess returns is 0.079, and the standard deviation of logarithmic excess returns is 0.1385. The variance is s^2 = 0.01919. And m / s^2 = 4.11. Yes, that's suggesting that, if the future looks like this sample of the past, and if financial returns were log-normal, you could have leveraged up to about 4x without diminishing expected CAGR. Obviously, the future won't look just like this sample.

Historically, over this time period, long term treasuries returned 8.45% CAGR and the risk-free cash returned 4.46% CAGR. Let's suppose that long term treasuries are no less volatile than they've been in the past, but that the produce much lower returns in excess of the risk-free rate. Let's say that this cuts down on the mean of the logarithmic excess return considerably. Say, for example (just to pick a number), that the mean of the log excess return is now 0.05, instead of 0.079, a reduction in expected compounding returns of about 37%.

Now m / s^2 = 2.6 and the maximum amount of leverage to apply is 2.6x (i.e., to bet 160% more than you have in cash). This is with an efficient 50% US large cap / 45% long term treasury / 5% gold portfolio, and doesn't account for any expenses, beyond the idea of paying the risk-free rate for leverage. Because expenses reduce return and lower expected return reduces the optimal leverage, then the optimal leverage is lower yet.

So far, so good...

Now let's look at 55% UPRO / 45% TMF and consider it as a leveraged version of 55% US stocks / 45% long term treasuries. Let's add in 1% to the risk-free rate to represent the cost of expense ratios and the costs of leverage beyond just the risk-free rate of T-bills. And let's once again look at 1978-2018, starting from the first year we have data on long term treasuries.

https://www.portfoliovisualizer.com/bac ... 0&total3=0

Using log base 2, the mean of logarithmic excess returns is 0.06845, and the standard deviation of logarithmic excess returns is 0.1455. The variance is s^2 = 0.02117. And m / s^2 = 3.2334. So, if you believe you will get returns like those from 1978-2018 and that they will be log-normal, and if your total cost of leverage is 1% over the risk-free rate, you may want to go up to 3.2x leverage.

We can then create a table for how much leverage you may want, depending on how much you believe returns may be depressed going forward. In the same way that I added in a cost that reduced the excess return by 1%, I will consider depressed forward-looking returns in 0.5% increments (in addition to the 1% cost).

0.5% less per year = 0.0615 / 0.1462^2 = 2.88x Kelly criterion leverage.
1.0% less per year = 0.0546 / 0.1469^2 = 2.53x Kelly criterion leverage.
1.5% less per year = 0.0476 / 0.1476^2 = 2.18x Kelly criterion leverage.
2.0% less per year = 0.0405 / 0.1483^2 = 1.84x Kelly criterion leverage.

So, with as little as 1.5% to 2% less return expected per year (relative to 1978-2018), in addition to 1% costs above buying low-cost index funds, as well as considering the cost of borrowing as being just the risk-free rate, the Kelly criterion leverage for 55% US stock / 45% long term treasuries seems to be between 1.8x and 2.2x.

If the 45% portion in long-term treasuries no longer contributes about 4% CAGR above the risk-free rate, that could be a negative impact of about 2% less per year in excess return for the whole portfolio. On the other hand, if we accept the idea of an almost 2.5% rebalancing bonus with quarterly rebalancing, something that isn't included above, that could tip the scales, meaning you might continue to get similar returns in excess of the risk free rate, and 3x leverage might be, just barely, Kelly criterion optimal.

Edit: No, wait, it's not quite like that. :? You can't add in the 2.5% rebalancing bonus, just like that, because it can't be leveraged up: it is a result of using leverage. At best you could, say, plug in 0.8% as a rebalancing bonus and let the Kelly criterion expect 2.4% excess return when leveraged up 3x. If the excess return of the portfolio (because of long term treasuries) is lower by 1.8% and if the rebalancing bonus gives you 0.8% to work with, that's still a depressed return of 1%. At that point, 2.5x leverage is optimal. But I think we could also take issue with adding in the 1% costs, too, because you're not leveraging up costs. So forget the costs, and you're back at 3x leverage being optimal, albeit with a drag on portfolio performance due to costs.

Long story short, about 3x leverage could be optimal if the rebalancing bonus is quite as big as it has been recently, even if the returns of long term treasuries are lower than the past. So the 55% UPRO / 45% TMF does indeed depend on the assumption of a negative correlation between stocks and long term treasuries. It could make sense even in a world where long term treasuries didn't deliver excess return above the risk free rate. However, it is dangerously close to the maximum leverage that could be considered optimal.
Sounds like 43/57 UPRO/EDV could fall in the Kelly sweet spot :).

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by dspencer » Fri Aug 16, 2019 10:51 am

MotoTrojan wrote:
Fri Aug 16, 2019 9:57 am

Sounds like 43/57 UPRO/EDV could fall in the Kelly sweet spot :).
For lower levels of leverage, is there a particular rationale for leveraging the stock or bond side?

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 10:57 am

dspencer wrote:
Fri Aug 16, 2019 10:51 am
MotoTrojan wrote:
Fri Aug 16, 2019 9:57 am

Sounds like 43/57 UPRO/EDV could fall in the Kelly sweet spot :).
For lower levels of leverage, is there a particular rationale for leveraging the stock or bond side?
Well, 43 X 3 is > 100 so some degree of leverage would be required on the equity side for my particular example. I could have replaced some EDV with TMF & unleveraged S&P500 but EDV is a very efficient way to leverage duration exposure compared to regular 20 year treasuries, without actually leveraging any assets. I haven't analytically validated this but I also would prefer to have the leverage on the equity side assuming we are using daily-rebalancing ETFs as this thread is, since equities are more likely to go up over time and thus volatility decay should be less likely to drag down returns. As an example, I believe since inception that UPRO has returned closer to 5x the S&P500 while TMF is closer to 1.5x 20-year treasuries, showing the extent of the delta in decays.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by dspencer » Fri Aug 16, 2019 11:23 am

MotoTrojan wrote:
Fri Aug 16, 2019 10:57 am
dspencer wrote:
Fri Aug 16, 2019 10:51 am
MotoTrojan wrote:
Fri Aug 16, 2019 9:57 am

Sounds like 43/57 UPRO/EDV could fall in the Kelly sweet spot :).
For lower levels of leverage, is there a particular rationale for leveraging the stock or bond side?
Well, 43 X 3 is > 100 so some degree of leverage would be required on the equity side for my particular example. I could have replaced some EDV with TMF & unleveraged S&P500 but EDV is a very efficient way to leverage duration exposure compared to regular 20 year treasuries, without actually leveraging any assets. I haven't analytically validated this but I also would prefer to have the leverage on the equity side assuming we are using daily-rebalancing ETFs as this thread is, since equities are more likely to go up over time and thus volatility decay should be less likely to drag down returns. As an example, I believe since inception that UPRO has returned closer to 5x the S&P500 while TMF is closer to 1.5x 20-year treasuries, showing the extent of the delta in decays.
Interesting, thanks. I am considering lowering the leverage and risk of my portfolio. I think the concerns about how much gain can be expected out of TMF are valid given current interest rates. I'm hesitant about making a switch to 55/45 though as that seems to be taking on a lot of risk.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by frank11 » Fri Aug 16, 2019 1:10 pm

I've been reading through this thread. This question has probably been answered somewhere, but other articles about leveraged ETFs say to not hold these types of investments long term because they do daily rebalancing. But, here we are suggesting long term holding.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 1:13 pm

dspencer wrote:
Fri Aug 16, 2019 11:23 am
MotoTrojan wrote:
Fri Aug 16, 2019 10:57 am
dspencer wrote:
Fri Aug 16, 2019 10:51 am
MotoTrojan wrote:
Fri Aug 16, 2019 9:57 am

Sounds like 43/57 UPRO/EDV could fall in the Kelly sweet spot :).
For lower levels of leverage, is there a particular rationale for leveraging the stock or bond side?
Well, 43 X 3 is > 100 so some degree of leverage would be required on the equity side for my particular example. I could have replaced some EDV with TMF & unleveraged S&P500 but EDV is a very efficient way to leverage duration exposure compared to regular 20 year treasuries, without actually leveraging any assets. I haven't analytically validated this but I also would prefer to have the leverage on the equity side assuming we are using daily-rebalancing ETFs as this thread is, since equities are more likely to go up over time and thus volatility decay should be less likely to drag down returns. As an example, I believe since inception that UPRO has returned closer to 5x the S&P500 while TMF is closer to 1.5x 20-year treasuries, showing the extent of the delta in decays.
Interesting, thanks. I am considering lowering the leverage and risk of my portfolio. I think the concerns about how much gain can be expected out of TMF are valid given current interest rates. I'm hesitant about making a switch to 55/45 though as that seems to be taking on a lot of risk.
I personally think 55/45 UPRO/TMF is less risky than 40/60. I came up with 43/57 UPRO/EDV as it has the same ratio of equity/duration as 55/45 UPRO/TMF and back-tests quite well. If treasuries and equities continue to perform above average it will lose out, but it will be less sensitive to rising rates and also perform better in a more modest, volatile equity environment. Drawdown during 2008 was similar to 100% S&P500 too.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by HEDGEFUNDIE » Fri Aug 16, 2019 1:42 pm

frank11 wrote:
Fri Aug 16, 2019 1:10 pm
I've been reading through this thread. This question has probably been answered somewhere, but other articles about leveraged ETFs say to not hold these types of investments long term because they do daily rebalancing. But, here we are suggesting long term holding.
You should start with Part 1 of this Excellent Adventure:

viewtopic.php?t=272007

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 1:56 pm

HEDGEFUNDIE wrote:
Fri Aug 16, 2019 1:42 pm
frank11 wrote:
Fri Aug 16, 2019 1:10 pm
I've been reading through this thread. This question has probably been answered somewhere, but other articles about leveraged ETFs say to not hold these types of investments long term because they do daily rebalancing. But, here we are suggesting long term holding.
You should start with Part 1 of this Excellent Adventure:

viewtopic.php?t=272007
I’d also suggest MoneyMarathons recent post in this thread which illustrates how rebalancing with an uncorrelated asset reduces the volatility decay.

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Re: HEDGEFUNDIE's excellent adventure [risk parity strategy using 3x leveraged ETFs]

Post by Kevin M » Fri Aug 16, 2019 3:29 pm

MoneyMarathon wrote:
Thu Aug 15, 2019 11:41 pm
MoneyMarathon wrote:
Thu Aug 15, 2019 8:42 pm
Kevin M wrote:
Thu Aug 15, 2019 7:31 pm
Thanks for the clarification. Can you provide a link to the post in which you originally worked this out and explained the reasoning for using this approach as opposed to 100% each UPRO and TMF to get the individual returns?
Note (I haven't posted this before): There is a perfect rebalancing strategy for eliminating volatility decay, if you're able to rebalance at the same cadence as the reset in leverage. It's explained in this thesis: https://www.math.nyu.edu/faculty/avella ... _Zhang.pdf

<snip>

So, for example, say that your LETF is a 3x LETF (like UPRO), then beta = 3 (b = 3) because it's 3x leveraged. And St and So refer to the value of the underlying (the S&P 500) right now and when you started. So, your money in UPRO, every day, to eliminate volatility decay, would be:

(1/3 the initial investment) * (current value of the underlying / original value of the underlying)

<snip>

Even without this perfect rebalancing strategy, similar effects of reducing volatility decay can be observed if you take out money when the LETF is gaining and put in money when the LETF is losing.
One more comment here: using plain, zero-return cash along with a fixed allocation of 1/3 UPRO will do the same thing as above, and it would eliminate volatility decay as described in this paper. Suppose again you had $2000 in UPRO and $4000 sitting in no-interest cash, then you had the S&P go up 25%, so your UPRO went up to $3500. You now have $7500. You need to get back to 1/3 UPRO to maintain a fixed allocation, so you need to get back to $2500 in UPRO by holding onto 1/3 of the gains ($500) and putting the other 2/3 of gains ($1000) into the cash position.

Likewise, using the "wrong" fraction (a fixed allocation but not 1/3) will mitigate volatility, by taking off money and putting it in at the right times (but not to the right extent), compared to the perfect strategy for eliminating volatility decay completely.
I'd like to try and summarize this simply.

If you were using 50% each of two 2X LETFs, you could just double the returns of the 1X versions of the funds (perhaps after accounting for higher costs of the 2X funds) to get the individual 2X returns without volatility decay.

My next thought was: couldn't you just use the 1X versions and apply the appropriate multiplier (e.g, 3X for TMF and UPRO) regardless of the percentage in each fund? I think the problem with that is that for any percentage other than 1/m, where m is the leverage multiplier), you are only mitigating, not fully eliminating, the volatility decay.

So using the approach of combining 40% UPRO with 60% CASHZERO, for example, provides a better approximation of the volatility decay mitigation you get with 40/60 UPRO/TMF (without the rebalancing bonus from negative correlation) than simply using 40% of 3 * SPY return in calculating the portfolio return. If you were using 33.3% UPRO in the portfolio, you could use 33.3% of 3 * SPY in calculating portfolio return.

The reason we want to apply the appropriate volatility-decay mitigation to the return of each individual portfolio component is that we're going to get volatility-decay mitigation by periodically rebalancing with any asset with a correlation of less than 1, and to evaluate the rebalancing bonus of a negatively-correlated asset, we use a baseline of combining the asset of interest with another asset with a correlation of 0 and a return of 0%.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by LadyGeek » Fri Aug 16, 2019 3:54 pm

I'm researching concepts that are new to me.

Volatility decay is one new concept. Here's a tutorial: Volatility Decay In Levered ETFs - This Is No Free Lunch

Kelly criterion is another, with a good discussion here: The Kelly Criterion: You Don’t Know the Half of It - the comments section confirms the Wikipedia formula.
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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by mitaumi » Fri Aug 16, 2019 3:59 pm

hi
Which file used for backtesting? On Siamond`s file I only see data with yearly return. Where I can download data for backtesting with monthly return? Thanks

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 4:53 pm

LadyGeek wrote:
Fri Aug 16, 2019 3:54 pm
I'm researching concepts that are new to me.

Volatility decay is one new concept. Here's a tutorial: Volatility Decay In Levered ETFs - This Is No Free Lunch

Kelly criterion is another, with a good discussion here: The Kelly Criterion: You Don’t Know the Half of It - the comments section confirms the Wikipedia formula.
Certainly is interesting indeed.

One concept that really intrigued me was shorting an inverse 3x fund (a bear fund). There will be additional borrowing costs, and infinite downside assuming a market decline, but the volatility decay actually works for you, not against you. I have not done a backtest but interesting none-the-less :twisted:. I think I'll stick with direct holding of the bull funds...

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by samsdad » Fri Aug 16, 2019 6:41 pm

The Fed is considering 50- and 100-year treasuries.

https://www.bloomberg.com/news/articles ... nd=premium

I wonder if they’re issued if vineviz will feel that perhaps, just perhaps, the 100-year variety might be just a tad beyond the individual investor’s investing horizon... :wink:

Also wonder if the underlying ICE index will pick them up and be part of TLT (and thus TMF) or if they’ll be placed in another index.

Deep thoughts on a Friday night in bogleheadland...

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 7:17 pm

samsdad wrote:
Fri Aug 16, 2019 6:41 pm
The Fed is considering 50- and 100-year treasuries.

https://www.bloomberg.com/news/articles ... nd=premium

I wonder if they’re issued if vineviz will feel that perhaps, just perhaps, the 100-year variety might be just a tad beyond the individual investor’s investing horizon... :wink:

Also wonder if the underlying ICE index will pick them up and this be part of TLT (and thus TMF) or if they’ll be placed in another index.

Deep thoughts on a Friday night in bogleheadland...
I am waiting for hedgefundie's 3rd variation; 70% UPRO, 30% 100-year treasuries :) (no leverage needed).

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by LadyGeek » Fri Aug 16, 2019 7:20 pm

LadyGeek wrote:
Fri Aug 16, 2019 3:54 pm
I'm researching concepts that are new to me.

Volatility decay is one new concept. Here's a tutorial: Volatility Decay In Levered ETFs - This Is No Free Lunch

Kelly criterion is another, with a good discussion here: The Kelly Criterion: You Don’t Know the Half of It - the comments section confirms the Wikipedia formula.
I forgot to mention that nisiprius gave a very detailed and easy-to-understand explanation of the Kelly criterion in another thread: Re: Interest rates low: leverage up? - it's worth a read.
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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by caklim00 » Fri Aug 16, 2019 7:28 pm

For those of you doing the upro target volatility, are you using TMF as the out of market asset? Since TMF has no influence over the UPRO allocation, I'm just wondering if it really makes the most sense.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by HEDGEFUNDIE » Fri Aug 16, 2019 7:29 pm

MotoTrojan wrote:
Fri Aug 16, 2019 7:17 pm
samsdad wrote:
Fri Aug 16, 2019 6:41 pm
The Fed is considering 50- and 100-year treasuries.

https://www.bloomberg.com/news/articles ... nd=premium

I wonder if they’re issued if vineviz will feel that perhaps, just perhaps, the 100-year variety might be just a tad beyond the individual investor’s investing horizon... :wink:

Also wonder if the underlying ICE index will pick them up and this be part of TLT (and thus TMF) or if they’ll be placed in another index.

Deep thoughts on a Friday night in bogleheadland...
I am waiting for hedgefundie's 3rd variation; 70% UPRO, 30% 100-year treasuries :) (no leverage needed).
100 year treasuries would be a game changer. No need for swaps with borrowing costs and 1% ERs.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 7:32 pm

caklim00 wrote:
Fri Aug 16, 2019 7:28 pm
For those of you doing the upro target volatility, are you using TMF as the out of market asset? Since TMF has no influence over the UPRO allocation, I'm just wondering if it really makes the most sense.
I’m not but I do think it makes sense. I could see an argument for placing an upper bound on duration exposure and diluting it with EDV should you have a super low UPRO exposure; I wouldn’t be thrilled about having 80%+ TMF exposure for very long.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Fri Aug 16, 2019 7:35 pm

HEDGEFUNDIE wrote:
Fri Aug 16, 2019 7:29 pm
MotoTrojan wrote:
Fri Aug 16, 2019 7:17 pm
samsdad wrote:
Fri Aug 16, 2019 6:41 pm
The Fed is considering 50- and 100-year treasuries.

https://www.bloomberg.com/news/articles ... nd=premium

I wonder if they’re issued if vineviz will feel that perhaps, just perhaps, the 100-year variety might be just a tad beyond the individual investor’s investing horizon... :wink:

Also wonder if the underlying ICE index will pick them up and this be part of TLT (and thus TMF) or if they’ll be placed in another index.

Deep thoughts on a Friday night in bogleheadland...
I am waiting for hedgefundie's 3rd variation; 70% UPRO, 30% 100-year treasuries :) (no leverage needed).
100 year treasuries would be a game changer. No need for swaps with borrowing costs and 1% ERs.
And a presumably higher yield too. Realistically I think the 100 year would be too much exposure to only use UPRO so you could also reduce costs on that end via a regular S&P500 fund, or maybe even another factor such as small-value.

EDIT: I suppose the duration won’t be 100 so this may be incorrect.
Last edited by MotoTrojan on Fri Aug 16, 2019 8:09 pm, edited 1 time in total.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by HawkeyePierce » Fri Aug 16, 2019 7:56 pm

Someone want to model a portfolio with UPRO and Austria's century bonds? :P

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by Kevin M » Fri Aug 16, 2019 8:04 pm

samsdad wrote:
Fri Aug 16, 2019 6:41 pm
The Fed is considering 50- and 100-year treasuries.
TIPS of those maturities would help solve the problem of residual-retirement-expense liability matching for more than 30 years. But there would be an even bigger ladder-rung-gap problem than there is now.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by BogleBobby » Fri Aug 16, 2019 9:17 pm

I've been using Simba's backtesting spreadsheet graciously updated by siamond to test out different strategies for leveraged ETFs.

There are a few years that really worried me about holding UPRO:

1981
Unleveraged return: -4.92%
3x leveraged return: -42.13%

1990
Unleveraged return: -3.1%
3x leveraged return: -29.3%

The worry was that you could see such a large loss for years where the stock market was mostly flat due to volatility decay.

However, this is only half right. One thing I forgot to realize was about the size of borrowing costs in these years and the borrowing costs for a 3X ETF. I believe the borrowing costs for a 2X ETF are equal to 1-month libor and for a 3X ETF they are equal to 1-month libor multiplied by 2.

If you ignore borrowing costs, the 1981 3X return is equal to about -20% and the 1990 loss is equal to about -17%. They are still bad years, but not as bad as I thought. (Note: these numbers are only approximate and I don't have as good of daily data as siamond, but I was able to get close to the calculations in siamond's leverage workbook.)

If you re-run the leveraged ETF calculations with minimal borrowing costs (like today's environments), you get a ridiculous CAGR for UPRO since 1950. Although I don't recommend that we do this, it's still useful to understand why historical returns look the way that they do.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by caklim00 » Fri Aug 16, 2019 10:55 pm

MotoTrojan wrote:
Fri Aug 16, 2019 7:32 pm
caklim00 wrote:
Fri Aug 16, 2019 7:28 pm
For those of you doing the upro target volatility, are you using TMF as the out of market asset? Since TMF has no influence over the UPRO allocation, I'm just wondering if it really makes the most sense.
I’m not but I do think it makes sense. I could see an argument for placing an upper bound on duration exposure and diluting it with EDV should you have a super low UPRO exposure; I wouldn’t be thrilled about having 80%+ TMF exposure for very long.
Upro is probably going to be low on monthly rebalance at end of the month. Maybe something like max tmf amount of 70% and dilute with edv?

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MoneyMarathon » Sat Aug 17, 2019 2:59 am

MotoTrojan wrote:
Fri Aug 16, 2019 9:57 am
MoneyMarathon wrote:
Fri Aug 16, 2019 1:58 am
Long story short, about 3x leverage could be optimal if the rebalancing bonus is quite as big as it has been recently, even if the returns of long term treasuries are lower than the past. So the 55% UPRO / 45% TMF does indeed depend on the assumption of a negative correlation between stocks and long term treasuries. It could make sense even in a world where long term treasuries didn't deliver excess return above the risk free rate. However, it is dangerously close to the maximum leverage that could be considered optimal.
Sounds like 43/57 UPRO/EDV could fall in the Kelly sweet spot :).
Yes. One cute way to think of it is that the true Kelly fraction is the dividing line between heaven and purgatory. Somewhere off to the right side, beyond the true Kelly fraction, there is a dividing line between purgatory and hell, where you're leveraging up so much you're actually expecting to get a return lower than the risk-free rate, possibly even flirting with complete ruin. Just over to the far side of the Kelly fraction, if you haven't strayed much, you'll still land in purgatory, pay for your greed with higher volatility and also lower expected returns, but come out mostly okay.

Just on the near side of the Kelly fraction, you go to heaven and also enjoy getting close to the maximum returns. Everyone on the near side of the Kelly fraction enjoys a certain kind of nirvana, where they are getting the maximum return they can with that portfolio given a certain level of volatility. To the extent that lower volatility is its own reward, being on the safe side is divine.

The problem is that nobody knows what the true Kelly fraction is. We can make guesses, but all of those guesses would have to build in assumptions about what the expected return of the underlying investments are. And those answers are unknown and unknowable. So everyone has to make their best reckoning, and a somewhat lower more-on-the-safe-side estimate based on that, and then put in their money and take their chances. Any one of us may get closest to the true Kelly fraction (although some may be more likely than others based on an interpretation of the evidence for what to expect, and some may just have dumb luck).

Those who risk less, may gain more. Who gains the most is not known.

What is for certain, however, is that they who risk less, even if they've miscalculated, will be punished less for their greed and rewarded with pleasantly lower volatility, along with all the benefits of lower volatility for those of us with limited time who may need to make a withdrawal some day. So there should generally be some kind of a preference for trying to go under whatever the true Kelly fraction limit may be, unless someone actually enjoys volatility for its own sake.

(PS -- if anyone's bothered by the imagery above, please don't take this as expressing any non-financial opinions. I thought it was a helpful analogy only. Not trying to ruffle any feathers or kick off any tangents here.)

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by mikestorm » Sat Aug 17, 2019 7:00 am

Everyone seems to be focused on the optimal UPRO / TMF split, but I don't see as much discussion on the optimal % of one's portfolio to commit to this strategy, unless I missed it in MoneyMarathon's really good explanation of the Kelly Criterion.

I've seen two disclaimers. One pertaining to the onset: "don't commit too much" and one pertaining to the scenario where this portion of the portfolio becomes overbalanced: "let it ride". People seem to be viewing this portfolio in a bubble and refraining from mentally incorporating it into their larrger portfolio. That sounds like mental accounting to me.

ACADEMICALLY SPEAKING and assuming no adverse tax repercussions, if you view your portfolio as a whole and assuming the $$ not committed to this approach are in a sensible Boglehead-approved portfolio, what is the sweet spot in terms of committed dollars?

I'm asking because I have a relatively small % of my portfolio committed to this strategy, but I've come to firmly believe in this approach and have more tax advantaged space to work with if necessary. On the other side, I'd like to know when, from a risk/return standpoint, it makes the most sense to take some money off of the table down the road.

EDIT: I'm assuming figuring out the optimal TMF/UPRO split is the first step to answering the above (I'm still using the OG 40%/60% split and don't plan on changing unless I move to the monthly risk parity adjusting) but viewing your portfolio has a whole might cast an alternative viewpoint on the overall wisdom of committing too much or too little to the leveraged equity option.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by privatefarmer » Sat Aug 17, 2019 7:27 am

I’m a little slow on the uptake here. Is EDV essentially a better option than using a levered ETF? It seems it’s about 1.7x as volatile as VGLT but has less volatility drag than TMF?

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by jaj2276 » Sat Aug 17, 2019 8:32 am

Legitthe wrote:
Thu Aug 15, 2019 12:28 pm
jaj2276 wrote:
Thu Aug 15, 2019 7:57 am
privatefarmer wrote:
Thu Aug 15, 2019 7:19 am
jaj2276 wrote:
Thu Aug 15, 2019 6:45 am
First journey was supposed to last somewhere between 20 and 30 years. It lasted approximately 6 months. Let's see how long this next journey lasts (I'm in for 50% 40/60, 25% 16-vol, 25% Adaptive Allocation).
Thats a naive way to look at it. He hasn’t defaulted from the overall strategy (using LETFs on a balanced portfolio to get higher returns with market like risk). Making minor adjustments as more information comes in just being practical.
It might be practical but the logical foundation he used for the original portfolio has changed. He said there was no need for a bull market for treasuries but in fact there is a need for 40/60.
It is practical as OP is recognizing that TMF’s risk is understated. Still the same risk parity balance.
I literally said it was practical.

My point wasn't that it was wrong or impractical (heck I started 40/60 and moved to three slices [a 40/60 historical RP, a 21-day RP, and 16-vol]), but that the "journey" which was supposed to last a long time has already changed. I expect this one to change too so all those who are claiming "55/40 as the best" will probably be disappointed when it gets changed again when additional information arises (which it should).

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by Steve Reading » Sat Aug 17, 2019 8:39 am

Legitthe wrote:
Thu Aug 15, 2019 12:28 pm
jaj2276 wrote:
Thu Aug 15, 2019 7:57 am
privatefarmer wrote:
Thu Aug 15, 2019 7:19 am
jaj2276 wrote:
Thu Aug 15, 2019 6:45 am
First journey was supposed to last somewhere between 20 and 30 years. It lasted approximately 6 months. Let's see how long this next journey lasts (I'm in for 50% 40/60, 25% 16-vol, 25% Adaptive Allocation).
Thats a naive way to look at it. He hasn’t defaulted from the overall strategy (using LETFs on a balanced portfolio to get higher returns with market like risk). Making minor adjustments as more information comes in just being practical.
It might be practical but the logical foundation he used for the original portfolio has changed. He said there was no need for a bull market for treasuries but in fact there is a need for 40/60.
It is practical as OP is recognizing that TMF’s risk is understated. Still the same risk parity balance.
Could you explain how TMF's risk is understated? What do you mean by that?

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by MotoTrojan » Sat Aug 17, 2019 10:31 am

BogleBobby wrote:
Fri Aug 16, 2019 9:17 pm
I've been using Simba's backtesting spreadsheet graciously updated by siamond to test out different strategies for leveraged ETFs.

There are a few years that really worried me about holding UPRO:

1981
Unleveraged return: -4.92%
3x leveraged return: -42.13%

1990
Unleveraged return: -3.1%
3x leveraged return: -29.3%

The worry was that you could see such a large loss for years where the stock market was mostly flat due to volatility decay.

However, this is only half right. One thing I forgot to realize was about the size of borrowing costs in these years and the borrowing costs for a 3X ETF. I believe the borrowing costs for a 2X ETF are equal to 1-month libor and for a 3X ETF they are equal to 1-month libor multiplied by 2.

If you ignore borrowing costs, the 1981 3X return is equal to about -20% and the 1990 loss is equal to about -17%. They are still bad years, but not as bad as I thought. (Note: these numbers are only approximate and I don't have as good of daily data as siamond, but I was able to get close to the calculations in siamond's leverage workbook.)

If you re-run the leveraged ETF calculations with minimal borrowing costs (like today's environments), you get a ridiculous CAGR for UPRO since 1950. Although I don't recommend that we do this, it's still useful to understand why historical returns look the way that they do.
Borrowing costs are somewhat tied to inflation I would wager so I don’t think it’s likely to see an extended period with similar raw equity growth but super low rates.

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Re: HEDGEFUNDIE's excellent adventure Part II: The next journey

Post by stipeman » Sat Aug 17, 2019 10:37 am

mikestorm wrote:
Sat Aug 17, 2019 7:00 am
Everyone seems to be focused on the optimal UPRO / TMF split, but I don't see as much discussion on the optimal % of one's portfolio to commit to this strategy, unless I missed it in MoneyMarathon's really good explanation of the Kelly Criterion.

I've seen two disclaimers. One pertaining to the onset: "don't commit too much" and one pertaining to the scenario where this portion of the portfolio becomes overbalanced: "let it ride". People seem to be viewing this portfolio in a bubble and refraining from mentally incorporating it into their larrger portfolio. That sounds like mental accounting to me.

ACADEMICALLY SPEAKING and assuming no adverse tax repercussions, if you view your portfolio as a whole and assuming the $$ not committed to this approach are in a sensible Boglehead-approved portfolio, what is the sweet spot in terms of committed dollars?

I'm asking because I have a relatively small % of my portfolio committed to this strategy, but I've come to firmly believe in this approach and have more tax advantaged space to work with if necessary. On the other side, I'd like to know when, from a risk/return standpoint, it makes the most sense to take some money off of the table down the road.

EDIT: I'm assuming figuring out the optimal TMF/UPRO split is the first step to answering the above (I'm still using the OG 40%/60% split and don't plan on changing unless I move to the monthly risk parity adjusting) but viewing your portfolio has a whole might cast an alternative viewpoint on the overall wisdom of committing too much or too little to the leveraged equity option.
I mentioned mental accounting in this thread weeks ago to the sound of crickets and dogs barking in the distance.

If you have a lot of tax advantaged space you are much better off with PSLDX. Problem solved and you can spend your time on other things. Perhaps not as exciting though.

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