HEDGEFUNDIE's excellent adventure Part II: The next journey

[privatefarmer]

I am far from an expert on the bond market. FAR from it. However, why should we assume that bond funds would have a negative return if rates go negative? One thing I full heartedly believe is that the market is highly efficient. Why would there be a market for negative yielding bonds if they were not going to give a risk-appropriate return?? Why are there negative yielding bonds around the globe that people are buying if they were going to almost certainly give a negative return?

HEDGEFUNDIE mentioned that he believes there is a “floor” to how low yields can go. Again, no expert here, but if that were the case wouldn’t it ALREADY be priced into the market? Why would institutions be buying negative yield bonds if they knew that there was a cap on the capital appreciation, not to mention a negative yield?

All I’m saying is I believe the market to be very efficient. I believe holding long term treasuries is still riskier than holding short term treasuries, no? So why on earth would the market allow yields to go this low if the market did not still expect a higher return for taking on the risk? Perhaps that return comes from the rebalancing bonus you’d get during market crashes or the negative correlation LTT have with equities? Perhaps the market IS pricing in a certain likelihood of DEFLATION in which case up is down and down is up... or perhaps none of this is true and institutional investors are just throwing money away.

[privatefarmer]

Wild idea I just thought of and I am certainly no economist but hear me out:

What if we are entering a world where NOTHING pays a yield or dividend? What if yields do go negative, you have to PAY to own an investment, but the same becomes true for stocks? What if dividend paying stocks become a “thing of the past” and shareholders can only hope for capital appreciation?

In that world, yield no longer matters. Rather, the market will try to appropriately price in expected CAPITAL APPRECIATION relative to an investments risk and some investments, ie LTTs will even have an investor “pay to own” the investment in hopes of getting a certain amount of capital appreciation.

[MotoTrojan]

True, but the increase in bond fund price is also exponential as rates go lower, so even a single basis point change past zero could mean a 10 or 20% gain in LTT.

If rates rise, TMF is going to look like stocks in 1999.

Doesn't that phenomenon's derivative peak at 0% rates and then start to reduce symmetrically as the rates go to negative? Ie the change from 0.5% to 0% is the same as 0% to -0.5%.

In order for the rate to be negative for existing bonds, people need to pay for the right to own them. Ie, they're still going to pay more. Unless my math is wrong.

I am not arguing that the bond prices won't continue to go up, just stating that the maximum rate of capital price gain per interest rate change (due to convexity) occurs as the yield passes through 0%.

What math dictates that the exponential climb upwards stops at zero?

What math dictates it doesn’t? Why is it exponential as rates approach 0% to begin with?

[privatefarmer]

https://www.multpl.com/s-p-500-dividend-yield

the yield on the stock market has closely resembled the declining yield of treasuries... if bond yields were to go "significantly" negative, perhaps stocks would follow suit (have no yield, only capital appreciation). in other words, maybe all those high flying "growth" stocks aren't so irrational after all?

[MotoTrojan]

I am far from an expert on the bond market. FAR from it. However, why should we assume that bond funds would have a negative return if rates go negative? One thing I full heartedly believe is that the market is highly efficient. Why would there be a market for negative yielding bonds if they were not going to give a risk-appropriate return?? Why are there negative yielding bonds around the globe that people are buying if they were going to almost certainly give a negative return?

HEDGEFUNDIE mentioned that he believes there is a “floor” to how low yields can go. Again, no expert here, but if that were the case wouldn’t it ALREADY be priced into the market? Why would institutions be buying negative yield bonds if they knew that there was a cap on the capital appreciation, not to mention a negative yield?

All I’m saying is I believe the market to be very efficient. I believe holding long term treasuries is still riskier than holding short term treasuries, no? So why on earth would the market allow yields to go this low if the market did not still expect a higher return for taking on the risk? Perhaps that return comes from the rebalancing bonus you’d get during market crashes or the negative correlation LTT have with equities? Perhaps the market IS pricing in a certain likelihood of DEFLATION in which case up is down and down is up... or perhaps none of this is true and institutional investors are just throwing money away.

How efficient was it in the 60’s and 70’s?

[MotoTrojan]

https://www.multpl.com/s-p-500-dividend-yield

the yield on the stock market has closely resembled the declining yield of treasuries... if bond yields were to go "significantly" negative, perhaps stocks would follow suit (have no yield, only capital appreciation). in other words, maybe all those high flying "growth" stocks aren't so irrational after all?

If you include buybacks in the yields it hasn’t changed all that much.

[allwin]

I'm also on this strategy with < 1% of my net worth. The ride has been interesting so far with ~ 30% return in last 3.5 months. I'm still on the 40/60 allocation and wondering if I should move to 50/50 or 55/45.

If nothing else, this strategy is distracting me from needlessly fiddling with my main 3 fund portfolio, so there's that.

[inatangle]

...

All bull markets die a painful death via bear mauling. As such, we'll all be taking a bath even if only on paper.

Oh right, well that's a given.

The way I read the original strategy is that an investor takes $100k puts it into the proposed portfolio. The risk with that strategy is buying at ATH and then watching the markets drop. This could be further compounded by a need to withdraw funds from the portfolio, thereby crystallising the loss.

To mitigate this risk, I decided to invest an initial sum of $10k and regularly contribute to the fund with $1.5k-2k top ups. If the bull market continues I won't be as far ahead as what I would be if I dropped the whole $100k all at once, but I think with current world events, volatile times lay ahead. I took advantage of the little dip the other week to drop a further $2.5k into my portfolio thereby lowering my average cost of entry.

When I was swing trading, I developed a nice little strat that timed entries very nicely, but as OP outlined, trying to time exit points caps potential gains. So my approach with this portfolio is to let invested funds ride, rebalance as desired (probably on a mix of 5-7% bands and quarterly) and use my contributions where possible to balance the portfolio for as long as they can.

[privatefarmer]

I am far from an expert on the bond market. FAR from it. However, why should we assume that bond funds would have a negative return if rates go negative? One thing I full heartedly believe is that the market is highly efficient. Why would there be a market for negative yielding bonds if they were not going to give a risk-appropriate return?? Why are there negative yielding bonds around the globe that people are buying if they were going to almost certainly give a negative return?

HEDGEFUNDIE mentioned that he believes there is a “floor” to how low yields can go. Again, no expert here, but if that were the case wouldn’t it ALREADY be priced into the market? Why would institutions be buying negative yield bonds if they knew that there was a cap on the capital appreciation, not to mention a negative yield?

All I’m saying is I believe the market to be very efficient. I believe holding long term treasuries is still riskier than holding short term treasuries, no? So why on earth would the market allow yields to go this low if the market did not still expect a higher return for taking on the risk? Perhaps that return comes from the rebalancing bonus you’d get during market crashes or the negative correlation LTT have with equities? Perhaps the market IS pricing in a certain likelihood of DEFLATION in which case up is down and down is up... or perhaps none of this is true and institutional investors are just throwing money away.

How efficient was it in the 60’s and 70’s?

Well that’s the point. The market prices in RISK to the expected return. Hence, LTTs are expected to go through bear markets as they are risky. Doesn’t mean, however, that they don’t have a long term expected return greater than a less risky asset. The same can be argued against owning stocks - they lost ~90% in the Great Depression and 55% in the GFC. Why own them?

[privatefarmer]

https://www.multpl.com/s-p-500-dividend-yield

the yield on the stock market has closely resembled the declining yield of treasuries... if bond yields were to go "significantly" negative, perhaps stocks would follow suit (have no yield, only capital appreciation). in other words, maybe all those high flying "growth" stocks aren't so irrational after all?

If you include buybacks in the yields it hasn’t changed all that much.

Which has increased the capital appreciation right? So maybe we are entering an investment world where capital appreciation = 100% of the total return. And thus even negative yielding bonds with high expected capital appreciation would be in demand partly for their expected appreciation and partly because they are still “safer” than owning equities.

[Lee_WSP]

Doesn't that phenomenon's derivative peak at 0% rates and then start to reduce symmetrically as the rates go to negative? Ie the change from 0.5% to 0% is the same as 0% to -0.5%.

In order for the rate to be negative for existing bonds, people need to pay for the right to own them. Ie, they're still going to pay more. Unless my math is wrong.

I am not arguing that the bond prices won't continue to go up, just stating that the maximum rate of capital price gain per interest rate change (due to convexity) occurs as the yield passes through 0%.

What math dictates that the exponential climb upwards stops at zero?

What math dictates it doesn’t? Why is it exponential as rates approach 0% to begin with?

The first part of the answer is simple. If we take the easiest example, a zero coupon bond, and if rates are zero, that means you pay $1 to get $1 X years later. If rates are negative you pay $1.y dollars to get $1 back in X years. The vertical tangent is not at zero. (if I'm even using the correct terminology, I'm probably not).

Here's a decent article on convexity. My understanding is that it has to do with the time value of money as to why long bonds are more convex.
https://blogs.cfainstitute.org/investor ... ty-primer/

[Lee_WSP]

...

All bull markets die a painful death via bear mauling. As such, we'll all be taking a bath even if only on paper.

Oh right, well that's a given.

The way I read the original strategy is that an investor takes $100k puts it into the proposed portfolio. The risk with that strategy is buying at ATH and then watching the markets drop. This could be further compounded by a need to withdraw funds from the portfolio, thereby crystallising the loss.

To mitigate this risk, I decided to invest an initial sum of $10k and regularly contribute to the fund with $1.5k-2k top ups. If the bull market continues I won't be as far ahead as what I would be if I dropped the whole $100k all at once, but I think with current world events, volatile times lay ahead. I took advantage of the little dip the other week to drop a further $2.5k into my portfolio thereby lowering my average cost of entry.

When I was swing trading, I developed a nice little strat that timed entries very nicely, but as OP outlined, trying to time exit points caps potential gains. So my approach with this portfolio is to let invested funds ride, rebalance as desired (probably on a mix of 5-7% bands and quarterly) and use my contributions where possible to balance the portfolio for as long as they can.

We're only worse off if we stop contributing. If we keep on contributing 10% of the total portfolio value, the losses will never amount to much in the end. I think this statement holds true even if we scale back contributions to 1% of the portfolio value. But I could be wrong, I know it works up to about 5%. Contributions just overwhelm losses and then you make it all back in the next bull run or we all die horrible deaths or the world ends or something truly bad happens.

[Lee_WSP]

https://www.multpl.com/s-p-500-dividend-yield

the yield on the stock market has closely resembled the declining yield of treasuries... if bond yields were to go "significantly" negative, perhaps stocks would follow suit (have no yield, only capital appreciation). in other words, maybe all those high flying "growth" stocks aren't so irrational after all?

If you include buybacks in the yields it hasn’t changed all that much.

Which has increased the capital appreciation right? So maybe we are entering an investment world where capital appreciation = 100% of the total return. And thus even negative yielding bonds with high expected capital appreciation would be in demand partly for their expected appreciation and partly because they are still “safer” than owning equities.

If people weren't buying up negative yield bonds like they were the best thing since index funds, they wouldn't be netting negative rates. Central banks only have so many levers and those levers only do so much. The rest is dictated by demand.

[comeinvest]

Using your first example, are you saying that the difference between making an initial investment of 55/45 and not rebalancing it in anyway compared to rebalancing it on a periodic basis (like monthly) nets you around 0.5 CAGR in a best case scenario?

I think he's saying that doing the 55/45 UPRO/TMF investment with annual rebalancing can be compared to making two investments, 55/45 UPRO/CASH and 55/45 CASH/TMF, both with annual rebalancing.

The first case would have yielded a CAGR that was 0.5 larger than the second case. That's the benefit from negative correlation.

Correct me if I'm wrong.

Precisely, and the CASH isn't generating a return in that analysis. If TMF is flat and this 0.5% rebalancing bonus persists (it was often less) then you'd actually have been better off holding 55% UPRO and 45% in money market, as the 45% money market yield would likely exceed 0.5%.

The OPs premise stated that UPRO generates the returns and TMF just balances it out in downturns, but this proves that is not the case and TMF actually had a HUGE part in the returns since 1982. Given current yields there are limits to TMF's potential future returns, and thus the strategy as a whole. I always knew this to be the case, but did not realize how small the rebalancing bonus really was.

Isn't "55% UPRO and 45% in money market" the same as 165% SPY, and -110% +45% = -65% money market? The only difference will be the frequency of rebalancing, and the first version would have two levels of rebalancing, UPRO internally daily and then UPRO with cash less frequently?

[MoneyMarathon]

Using your first example, are you saying that the difference between making an initial investment of 55/45 and not rebalancing it in anyway compared to rebalancing it on a periodic basis (like monthly) nets you around 0.5 CAGR in a best case scenario?

I think he's saying that doing the 55/45 UPRO/TMF investment with annual rebalancing can be compared to making two investments, 55/45 UPRO/CASH and 55/45 CASH/TMF, both with annual rebalancing.

The first case would have yielded a CAGR that was 0.5 larger than the second case. That's the benefit from negative correlation.

Correct me if I'm wrong.

Precisely, and the CASH isn't generating a return in that analysis. If TMF is flat and this 0.5% rebalancing bonus persists (it was often less) then you'd actually have been better off holding 55% UPRO and 45% in money market, as the 45% money market yield would likely exceed 0.5%.

The OPs premise stated that UPRO generates the returns and TMF just balances it out in downturns, but this proves that is not the case and TMF actually had a HUGE part in the returns since 1982. Given current yields there are limits to TMF's potential future returns, and thus the strategy as a whole. I always knew this to be the case, but did not realize how small the rebalancing bonus really was.

Isn't "55% UPRO and 45% in money market" the same as 165% SPY, and -110% +45% = -65% money market? The only difference will be the frequency of rebalancing, and the first version would have two levels of rebalancing, UPRO internally daily and then UPRO with cash less frequently?

Yeah, and since 1988 the 55% UPRO / 45% CASHX performs much like just 30% UPRO / 70% VFINX (S&P).

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

In the flash crash of Oct 87, though, the 55% UPRO position takes a bigger hit.

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

Unless you rebalanced quarterly.

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

100% stocks isn't a very efficient (high Sharpe) portfolio, and applying leverage to all-stocks is pretty dicey: great if the timing's right, but not so great if you plow all your money in right before a bear market for stocks. Diversification in pursuit of higher risk-adjusted returns (prior to leverage) can make sense for a leveraged portfolio (which scales up both returns and volatility, so can have more return for a given level of volatility if starting from a high Sharpe portfolio). Lower amounts of leverage than 3x and more diversification than 2 assets could be an improvement, though.

BTW, apparently market timer has $600k short on LTT right now, so at least somebody will make money if yields go up.

[comeinvest]

I am far from an expert on the bond market. FAR from it. However, why should we assume that bond funds would have a negative return if rates go negative? One thing I full heartedly believe is that the market is highly efficient. Why would there be a market for negative yielding bonds if they were not going to give a risk-appropriate return?? Why are there negative yielding bonds around the globe that people are buying if they were going to almost certainly give a negative return?

HEDGEFUNDIE mentioned that he believes there is a “floor” to how low yields can go. Again, no expert here, but if that were the case wouldn’t it ALREADY be priced into the market? Why would institutions be buying negative yield bonds if they knew that there was a cap on the capital appreciation, not to mention a negative yield?

All I’m saying is I believe the market to be very efficient. I believe holding long term treasuries is still riskier than holding short term treasuries, no? So why on earth would the market allow yields to go this low if the market did not still expect a higher return for taking on the risk? Perhaps that return comes from the rebalancing bonus you’d get during market crashes or the negative correlation LTT have with equities? Perhaps the market IS pricing in a certain likelihood of DEFLATION in which case up is down and down is up... or perhaps none of this is true and institutional investors are just throwing money away.

Interesting and valid thoughts. I think markets are not expecting deflation, at least not yet, as inflation expectations can be measured using other derivatives. My understanding is that the real risk-free return, which has declined in the last decade or so, is a major driver of all the other valuation parameters. Equity risk premium has remained relatively stable. Also, don't forget that assumptions on profit margins in a low-growth world are another major driver of equity returns and valuations, but not bond returns. Lastly, German 30-year government bonds ("Bund") just dropped below zero nominal, while European inflation expectations are still around 1.5% last time I checked. 0.985 ^ 30 = 0.635. I don't know who would buy an investment with guaranteed 36.5% real loss, but I hear a lot of pension funds are forced to do so. It's like every Euro that you work hard for today on your daily job, you would get to spend 0.636 Euros worth of merchandise or services 30 years later, and that is not even considering the risk that you die between now and 30 years from now. If this seems like a dumb idea, then how about instead taking the counterparty position and borrowing at the 30-year Bund rate and investing the proceeds for 30 years in the global equity markets? If the 3-year Bund has negative yield, you get paid a small additional amount every year by the bondholder (for the "pain" of borrowing money for 30 years), which you can add to your global equity portfolio yearly - nice accumulation, right? I think that could be done by buying equity index futures and simultaneously selling long-term German Bund futures, so that the inherent cash positions cancel out (correct me if I'm wrong), to achieve, say, 130% long equities so you are unlikely to ever get a margin call. I am realizing this would be contrary to Hedgefundies's strategy which is long LTTs. Which of the two is smarter for the European investor (and maybe sooner or later for the U.S. investor)? It's an honest question and I don't know the answer.

[Lee_WSP]

There is no theoretical floor, but ther has to be a practical floor. Otherwise the stuff has hit the fan.

If you think of negative rates as a fee the government charges you to safeguard all your cash, its not irrational when there is no alternative.

Actually, that's probably how to think about them. It's the least bad choice. Paying the government will have the least bad outcome since everything else will lose even more money.

[celerity]

What ETFs are you looking at for your 2 leveraged options?

WisdomTree.

S&P 500 3x Leverage Daily ETP
3USL

US Treasuries 10Y 3x Leverage Daily ETP
3TYL

Fellow EU investor here. What’s the difference between ETP and ETF? Is the counterparty risk the same? Too bad 3TYL isn’t traded on Xetra though.

[comeinvest]

What ETFs are you looking at for your 2 leveraged options?

WisdomTree.

S&P 500 3x Leverage Daily ETP
3USL

US Treasuries 10Y 3x Leverage Daily ETP
3TYL

Fellow EU investor here. What’s the difference between ETP and ETF? Is the counterparty risk the same? Too bad 3TYL isn’t traded on Xetra though.

3USL says it is "physically secured" https://www.wisdomtree.eu/de-de/etps/eq ... -daily-etp .
Expense ratio is 0.75%, measurably cheaper than UPRO. Kind of surprising, as usually U.S. products are more efficient. I don't know what the internal cost of leverage is. Maybe U.S. investors following Hedgefundie's strategy can buy this at Interactive Brokers and gain an additional 0.17% CAGR?

3TYL says 0.3% ER https://www.wisdomtree.eu/en-gb/etps/fi ... -daily-etp vs 1.09% for TMF. Can somebody verify if this is based on equity or assets? Also have to verify the meaning of "Daily Swap Rate", and the effective internal cost of leverage. I can buy 3TYL in my U.S. IB account. Maybe I'm going to reconsider my futures based strategy.

[privatefarmer]

Looking at my account value before the market is open on IB... looks like today is going to be another big day for LTTs...

[JBeck]

With the new 55/45 allocation what does the drawdown in 2008 look like compared to the original 40/60?

[caklim00]

I've been in this for about a week or so now. 30K total split 3 ways between
1 - OP Strategy - changing it to 55/45 UPRO/TMF so I can stay with the base strategy; Quarterly rebalance
2 - 20 Day Risk Parity lookback; Monthly rebalance
3 - 20% Volatility lookback over 20 days (weighting recent days higher than less recent days) Monthly rebalance

Right now I'm up 1.2K. I'm going to have to resist the urge to add to this strategy as part of me thinks this is going to end badly.

Why do you think this will end badly?

All bull markets die a painful death via bear mauling. As such, we'll all be taking a bath even if only on paper.

The Yield curve inverted, typically bad for stocks.
Interest rates are already low, typically bad for Long Term Treasuries.

But... I'm still in on this. I would not be comfortable with more than 5% of my portfolio right now though. It is a nice distraction from my losses from tilt to SCV and Intl.

[MotoTrojan]

BTW, apparently market timer has $600k short on LTT right now, so at least somebody will make money if yields go up.

Glad someone else caught that, wild!

[HEDGEFUNDIE]

With the new 55/45 allocation what does the drawdown in 2008 look like compared to the original 40/60?

-65%

[robertmcd]

BTW, apparently market timer has $600k short on LTT right now, so at least somebody will make money if yields go up.

Glad someone else caught that, wild!

Never short treasury bonds should be the #1 rule of investing because they seem to defy logic. Shorting JGB's was the original widowmaker trade and should have taught people a lesson.

[samsdad]

I'm still trying to figure out how PV calculates the 2-month simple moving average. I'm not the only one who can't figure it out. See this thread: viewtopic.php?f=10&t=288143

It may have a bearing on this strategy, so if you like math riddles, head on over and perhaps win a prize...

[hdas]

2. I also acknowledge that at 2%, TMF’s upside from here is capped. Which is why I made my AA change to 55/45.

As expected, ppl can’t help themselves and despite planning and IPS’s, “switches” are bound to happen. And this is only 6 months into the adventure and tiny $$ balance....

This strategy has a very low ratio of total money invested/time spent writing about it. I predict not nobody can’t stick with this in the long run. That’s why money handlers and their fees will always have a place in the ecosystem.

Cheers

[ocrtech]

These are not two portfolios held separately then added together, they are means of simulating each assets contribution to the portfolio as a whole. If one of them goes up 10x and the other 3x, then the total growth was 30x, not 13x.

Let me try to explain the hand-wavy math I used (but... be warned it might only be more confusing than the original hand waving).

Weighted average rate of returns is a weighted sum of the rate of growth of each investment. Wikipedia page:

https://en.wikipedia.org/wiki/Rate_of_r ... _portfolio

When I set up my little experiment, I calculated a total return (over time) that had an associated CAGR that was tied to a larger amount of capital than what was relevant (e.g., the whole 100% instead of the 40% in UPRO). To get the weighted sum of the rate of growth of each investment, we'd first want to get the CAGR based on each individual smaller amount of capital allocated to the investment. But, if we use these weird, unadjusted whole-portfolio CAGR to get a weighted sum, then the weighted sum: 0.4 * (x / 0.4) + 0.6 * (y / 0.6) = x + y, where x and y are the respective CAGRs of the 40% UPRO/60% CASHZERO and 60% TMF/40% CASHZERO rebalanced portfolios. So the weighted sum for the rate of growth is just x + y of the weird (unadjusted to the actual amount of principal for the individual investment, and instead looking at contribution to the whole portfolio) CAGRs. So expected portfolio CAGR = x + y, with steady growth (and without including any bonus effects from rebalancing negatively correlated investments).

A = P * e ^ (rt) is one expression of the exponential growth formula. And if r = x + y, then:

A = P * e ^ ( (x + y) t) = P * e ^ (x t) * e ^ (y t)

Now if we compute B = P * e ^ (x t) / P = e ^ (x t) and compute C = P * e ^ (y t) / P = e ^ (y t), where B is the total return on cash over the whole time period for the 40% UPRO/60% CASHZERO portfolio and where C is the same thing for 60% TMF/40% CASHZERO, and where P is the original principal, then:

P * B * C = P * e ^ (x t) * e ^ (y t) = P * e ^ ( (x + y) t) = P * e ^ (rt) = A

And to the extent that the observed result is different from P * B * C, that looks like the effect of the 'rebalancing bonus' from negative correlation. Note again that it's larger for the quarterly rebalancing, so the 0.5% CAGR figure that was thrown around does not necessarily apply to quarterly rebalancing. The approximate 0.5% CAGR figure was based on looking at annual rebalancing over the last 32 years. So anyone using quarterly rebalancing may want to include an appropriately larger bonus from rebalancing based on that method.

In some of the work Bernstein did on the rebalancing bonus, he states:

"Since the rebalancing bonus is proportional to the variance of the asset, a doubling of SD results in a quadrupling of variance, and thus of rebalancing benefit."

The 10 year S&P500 (SPY) StdDv is 12.53 and UPro is 38.77. The 10 year LTT (TLT) StdDev is 12.15 and TMF is 38.35. That means the entire portfolio StdDev is roughly triple which should result in roughly 9 times increase in variance. Since it is proportional, wouldn't that mean we would expect the rebalancing bonus for the UPRO/TMF to be in the range of 4.5% CAGR?

[Walkure]

2. I also acknowledge that at 2%, TMF’s upside from here is capped. Which is why I made my AA change to 55/45.

As expected, ppl can’t help themselves and despite planning and IPS’s, “switches” are bound to happen. And this is only 6 months into the adventure and tiny $$ balance....

This strategy has a very low ratio of total money invested/time spent writing about it. I predict not nobody can’t stick with this in the long run. That’s why money handlers and their fees will always have a place in the ecosystem.

Cheers

I'm still at the original 40/60 with quarterly rebalance. I'm doing this mainly in taxable, so as this thing grows (using new contributions to top up the underperforming asset [UPRO!] to avoid ST gains), I will have the added "lock-in" factor to help me stay the course.

[MotoTrojan]

These are not two portfolios held separately then added together, they are means of simulating each assets contribution to the portfolio as a whole. If one of them goes up 10x and the other 3x, then the total growth was 30x, not 13x.

Let me try to explain the hand-wavy math I used (but... be warned it might only be more confusing than the original hand waving).

Weighted average rate of returns is a weighted sum of the rate of growth of each investment. Wikipedia page:

https://en.wikipedia.org/wiki/Rate_of_r ... _portfolio

When I set up my little experiment, I calculated a total return (over time) that had an associated CAGR that was tied to a larger amount of capital than what was relevant (e.g., the whole 100% instead of the 40% in UPRO). To get the weighted sum of the rate of growth of each investment, we'd first want to get the CAGR based on each individual smaller amount of capital allocated to the investment. But, if we use these weird, unadjusted whole-portfolio CAGR to get a weighted sum, then the weighted sum: 0.4 * (x / 0.4) + 0.6 * (y / 0.6) = x + y, where x and y are the respective CAGRs of the 40% UPRO/60% CASHZERO and 60% TMF/40% CASHZERO rebalanced portfolios. So the weighted sum for the rate of growth is just x + y of the weird (unadjusted to the actual amount of principal for the individual investment, and instead looking at contribution to the whole portfolio) CAGRs. So expected portfolio CAGR = x + y, with steady growth (and without including any bonus effects from rebalancing negatively correlated investments).

A = P * e ^ (rt) is one expression of the exponential growth formula. And if r = x + y, then:

A = P * e ^ ( (x + y) t) = P * e ^ (x t) * e ^ (y t)

Now if we compute B = P * e ^ (x t) / P = e ^ (x t) and compute C = P * e ^ (y t) / P = e ^ (y t), where B is the total return on cash over the whole time period for the 40% UPRO/60% CASHZERO portfolio and where C is the same thing for 60% TMF/40% CASHZERO, and where P is the original principal, then:

P * B * C = P * e ^ (x t) * e ^ (y t) = P * e ^ ( (x + y) t) = P * e ^ (rt) = A

And to the extent that the observed result is different from P * B * C, that looks like the effect of the 'rebalancing bonus' from negative correlation. Note again that it's larger for the quarterly rebalancing, so the 0.5% CAGR figure that was thrown around does not necessarily apply to quarterly rebalancing. The approximate 0.5% CAGR figure was based on looking at annual rebalancing over the last 32 years. So anyone using quarterly rebalancing may want to include an appropriately larger bonus from rebalancing based on that method.

In some of the work Bernstein did on the rebalancing bonus, he states:

"Since the rebalancing bonus is proportional to the variance of the asset, a doubling of SD results in a quadrupling of variance, and thus of rebalancing benefit."

The 10 year S&P500 (SPY) StdDv is 12.53 and UPro is 38.77. The 10 year LTT (TLT) StdDev is 12.15 and TMF is 38.35. That means the entire portfolio StdDev is roughly triple which should result in roughly 9 times increase in variance. Since it is proportional, wouldn't that mean we would expect the rebalancing bonus for the UPRO/TMF to be in the range of 4.5% CAGR?

Certainly curious to hear more thoughts here. I did a quick study last night looking at periods where TMF was flat (usually 3-5 year periods) and found that a 4-6% CAGR improvement existed for 55/45 UPRO/TMF over 55/45 UPRO/CASHX, so it certainly seems like the rebalancing bonus is larger. Quarterly rebalancing was best but the bonus persisted across other periods. Most of these periods were in the last 2 decades though when apparently the correlation has been most negative. Unfortunately TMF has been on such a tear that it is tough to compare.

From 1955-2002 TMF returned 0.4% CAGR. Using quarterly rebalance, 55/45 UPRO/TMF returned 9.6% with a 76% drawdown while 55/45 UPRO/CASHZERO returned 8.7% with a 68% drawdown, so there was about a 0.5% rebalancing bonus indeed during that period. It seems the bonus is much larger in the last 2 decades.

[butricksaid]

I'm still at the original 40/60 with quarterly rebalance. I'm doing this mainly in taxable, so as this thing grows (using new contributions to top up the underperforming asset [UPRO!] to avoid ST gains), I will have the added "lock-in" factor to help me stay the course.

Same.

All of these traders were celebrating a one day victory yesterday by moving over to 55/45 and today they got crushed more than 40/60. We're coming up on the end of a long economic cycle with volatility spikes every other day and now you want to tilt heavier into equity? Are you a pig? Because you're going to get slaughtered.

Maybe change your AA to more UPRO after/during a recession instead of leading up to one?

[MotoTrojan]

I'm still at the original 40/60 with quarterly rebalance. I'm doing this mainly in taxable, so as this thing grows (using new contributions to top up the underperforming asset [UPRO!] to avoid ST gains), I will have the added "lock-in" factor to help me stay the course.

Same.

All of these traders were celebrating a one day victory yesterday by moving over to 55/45 and today they got crushed more than 40/60. We're coming up on the end of a long economic cycle with volatility spikes every other day and now you want to tilt heavier into equity? Are you a pig? Because you're going to get slaughtered.

Maybe change your AA to more UPRO after/during a recession instead of leading up to one?

The only person making assumptions for trading and market timing is you. I am not celebrating one day moves, I am evaluating the best set-and-forget allocation. Frankly I am torn between 55/45 and this whole thing is a waste of time .

[HEDGEFUNDIE]

I'm still at the original 40/60 with quarterly rebalance. I'm doing this mainly in taxable, so as this thing grows (using new contributions to top up the underperforming asset [UPRO!] to avoid ST gains), I will have the added "lock-in" factor to help me stay the course.

Same.

All of these traders were celebrating a one day victory yesterday by moving over to 55/45 and today they got crushed more than 40/60. We're coming up on the end of a long economic cycle with volatility spikes every other day and now you want to tilt heavier into equity? Are you a pig? Because you're going to get slaughtered.

Maybe change your AA to more UPRO after/during a recession instead of leading up to one?

55/45 down 1.2% today. Hardly “crushed”.

If I knew we were going into a recession I wouldn’t have any UPRO.

[Freefun]

I'm still at the original 40/60 with quarterly rebalance. I'm doing this mainly in taxable, so as this thing grows (using new contributions to top up the underperforming asset [UPRO!] to avoid ST gains), I will have the added "lock-in" factor to help me stay the course.

Same.

All of these traders were celebrating a one day victory yesterday by moving over to 55/45 and today they got crushed more than 40/60. We're coming up on the end of a long economic cycle with volatility spikes every other day and now you want to tilt heavier into equity? Are you a pig? Because you're going to get slaughtered.

Maybe change your AA to more UPRO after/during a recession instead of leading up to one?

If I understood OP correctly this is a long term strategy.

[Steve Reading]

BTW, apparently market timer has $600k short on LTT right now, so at least somebody will make money if yields go up.

Glad someone else caught that, wild!

Never short treasury bonds should be the #1 rule of investing because they seem to defy logic. Shorting JGB's was the original widowmaker trade and should have taught people a lesson.

Why not short treasury bonds?

[Lee_WSP]

I'm still at the original 40/60 with quarterly rebalance. I'm doing this mainly in taxable, so as this thing grows (using new contributions to top up the underperforming asset [UPRO!] to avoid ST gains), I will have the added "lock-in" factor to help me stay the course.

Same.

All of these traders were celebrating a one day victory yesterday by moving over to 55/45 and today they got crushed more than 40/60. We're coming up on the end of a long economic cycle with volatility spikes every other day and now you want to tilt heavier into equity? Are you a pig? Because you're going to get slaughtered.

Maybe change your AA to more UPRO after/during a recession instead of leading up to one?

55/45 down 1.2% today. Hardly “crushed”.

If I knew we were going into a recession I wouldn’t have any UPRO.

If I knew we were headed into a recession, I'd be 100% UPRO right up to the first drop. But I know nothing, so I hedge my bets. And one of those hedges is that this strategy may be better than B&H non-leveraged.

[schismal]

55/45 down 1.2% today. Hardly “crushed”.

If I knew we were going into a recession I wouldn’t have any UPRO.

My Boglehead portfolio is getting hit harder today than this leveraged risk parity experiment.

VTI, VXUS, and VT are all down -2.4%. VIOV and IVOV are down even more. Talk about getting crushed.

[Lee_WSP]

55/45 down 1.2% today. Hardly “crushed”.

If I knew we were going into a recession I wouldn’t have any UPRO.

My Boglehead portfolio is getting hit harder today than this leveraged risk parity experiment.

VTI, VXUS, and VT are all down -2.4%. VIOV and IVOV are down even more. Talk about getting crushed.

This is very true.

[MotoTrojan]

55/45 down 1.2% today. Hardly “crushed”.

If I knew we were going into a recession I wouldn’t have any UPRO.

My Boglehead portfolio is getting hit harder today than this leveraged risk parity experiment.

VTI, VXUS, and VT are all down -2.4%. VIOV and IVOV are down even more. Talk about getting crushed.

+1. XIRR of this portfolio is still 89.85% compared to an S&P500 5.14% (dividend reinvestment is now factored into that too). Will take a good bit more pain before it is a poor decision.

I'll continue to play with you all...

[Hydromod]

Just for grins, I checked out the returns from an asset allocation strategy with downward-only variance parity weights (look-back 60 days) over the last 6 months, assuming daily rebalance.

This is the type of scheme I'm favoring (except for daily rebalance). Its weights averaged 22% for UPRO and it would have been up 81% over this period, compared to 68% and 51% for the 40/60 and 55/40 schemes.

Over the last month, it would have seen 16% gain, compared to 13% (40/60) and 5% (55/45).

With a risk budget of 60% to UPRO, the portfolio would have risen 71%. With 70% risk to UPRO, the gain would have been 52%.

The base case weighted UPRO between 28 and 40% over the last month, today it's at 35%.

I'd be cautious bumping UPRO weights too much nowadays. Just saying.

Note that I purposely have not been looking at the dataset beyond the UPROSIM dates when looking at strategies in order to avoid recency bias.

[MotoTrojan]

Just for grins, I checked out the returns from an asset allocation strategy with downward-only variance parity weights (look-back 60 days) over the last 6 months, assuming daily rebalance.

This is the type of scheme I'm favoring (except for daily rebalance). Its weights averaged 22% for UPRO and it would have been up 81% over this period, compared to 68% and 51% for the 40/60 and 55/40 schemes.

Over the last month, it would have seen 16% gain, compared to 13% (40/60) and 5% (55/45).

With a risk budget of 60% to UPRO, the portfolio would have risen 71%. With 70% risk to UPRO, the gain would have been 52%.

The base case weighted UPRO between 28 and 40% over the last month, today it's at 35%.

I'd be cautious bumping UPRO weights too much nowadays. Just saying.

Note that I purposely have not been looking at the dataset beyond the UPROSIM dates when looking at strategies in order to avoid recency bias.

I'm confused. You say you are avoiding recency bias, but then say to be cautious about bumping UPRO weights because TMF has outperformed in the last month....

Also I thought downward-only was worse in backtests? Or perhaps that is with StDev, not variance?

[Kevin M]

2. I also acknowledge that at 2%, TMF’s upside from here is capped. Which is why I made my AA change to 55/45.

I do not know of any reason bond funds cannot go up in value even if rates go negative. In fact, they should go up by a very large amount if rates indeed went negative.

I agree, but I do think there is a cap on how negative rates can go, it’s probably in the low single negative digits.

True, but the increase in bond fund price is also exponential as rates go lower, so even a single basis point change past zero could mean a 10 or 20% gain in LTT.

If rates rise, TMF is going to look like stocks in 1999.

Doesn't that phenomenon's derivative peak at 0% rates and then start to reduce symmetrically as the rates go to negative? Ie the change from 0.5% to 0% is the same as 0% to -0.5%.

We can just do some bond math to see what happens as rates drop through 0%.

If yields go negative, the lowest coupon rate would be 0%, since I don't think there's a way to implement a negative coupon rate. I recall someone posting that the minimum coupon rate for a US Treasury is 0.125%, and a negative yield would be implemented by selling the bond at a sufficient premium (price > 100). The results of the math aren't much different for 0% and 0.125% coupon rates, and with a zero-coupon bond, we don't have to factor in coupon return (it's all capital return), so I'll just use a 0% coupon rate.

As someone pointed out, price of a 0% coupon bond at 0% yield is 100--I'll normalize 100 to 1 for use in the PV function to calculate price (and hence return). Continuing to use a constant maturity 25-year bond:

p(0%) =-PV(0%,25,0%,1) = 1.00

To calculate the return for a change of yield from 1% to 0%, we first calculate the price at 1% yield:

p(1%) =-PV(1%,25,0%,1) = 0.78

Then we calculate the return as:

r(1%->0%) = p(0%) / p(1%) - 1 = 1.00 / 0.78 = 28.2%

Similarly, to calculate the return for 0% -> -1%, we first calculate the price at -1% yield:

p(-1%) =-PV(-1%,25,0%,1) = 1.286,

and the return for 0% to -1% is:

r(0%->-1%) = 1.286/1.000 - 1 = 28.6%

So 28.6% is a little higher than 28.2%, but not that much higher.

Doing similar calculations for all one-percentage-point changes from 10%->9% to -9%->-10%, and graphing the results, we get this:



So as yields drop, return increases with slight curvature, but pretty close to linear, and nothing special happens at 0% yield.

Kevin

[JBeck]

Removed

[Hydromod]

Just for grins, I checked out the returns from an asset allocation strategy with downward-only variance parity weights (look-back 60 days) over the last 6 months, assuming daily rebalance.

This is the type of scheme I'm favoring (except for daily rebalance). Its weights averaged 22% for UPRO and it would have been up 81% over this period, compared to 68% and 51% for the 40/60 and 55/40 schemes.

Over the last month, it would have seen 16% gain, compared to 13% (40/60) and 5% (55/45).

With a risk budget of 60% to UPRO, the portfolio would have risen 71%. With 70% risk to UPRO, the gain would have been 52%.

The base case weighted UPRO between 28 and 40% over the last month, today it's at 35%.

I'd be cautious bumping UPRO weights too much nowadays. Just saying.

Note that I purposely have not been looking at the dataset beyond the UPROSIM dates when looking at strategies in order to avoid recency bias.

I'm confused. You say you are avoiding recency bias, but then say to be cautious about bumping UPRO weights because TMF has outperformed in the last month....

I'm in the adaptive allocation camp. I've been looking at what adaptive strategies performed well without using 2019 data.

Now I'm looking at 2019 data (actually the last year, with the first 3 for calculating volatility and then 9-month returns) to see what the strategies would have done. Especially in light of the recent market volatility.

This is just a data point for folk's info.


Also I thought downward-only was worse in backtests? Or perhaps that is with StDev, not variance?

Downward-only has two flavors, either setting upwards returns to zero or removing them entirely. With variance, setting them to zero was worse, removing them entirely was better, relative to standard risk parity. Overall it seems that the best returns tended to be using variance parity with upward variations removed.

[MotoTrojan]

If you are embarking on this strategy, you are basically betting that the S&P 500 will continue to be a significant driver of returns going forward. This is why you are levering up the index by 3x, and why the benchmark of the strategy is the S&P 500.

The inclusion of long Treasuries has always primarily been for stock crash insurance. The biggest risk of that insurance is a long term rise in long rates, but I have explained here and elsewhere why I do not consider this risk to be material, in the US, at this juncture.

So all that remains to be decided is how much gas we should throw on the fire (UPRO), and how much insurance we should take out (TMF).

When long interest rates are at 2% as they are now, the insurance tends to be rather costly, not because rates are more likely to rise from here - they are not. But rather because while we wait for the insurance to eventually pay out, its inclusion crowds out UPRO that could be generating serious returns.

Hedgefundie, I would appreciate it if you could address what you think the expected outperformance is in a flat-rate environment, where TMF is providing say 2% return? Based on the analysis I have seen, through equity market cycles, it shouldn't be vastly outperforming unleveraged S&P500 by more than 1%-2%, with significantly more risk. Is your thesis that the bear markets of the past will not repeat themselves?

[LadyGeek]

Since HEDGEFUNDIE changed his strategy on August 12, 2019, the discussion has gotten somewhat off-track.

The thread was split to allow focusing on the revised strategy.

(Also note this was done for a prior discussion: Updated Modification of Harry Browne Permanent Portfolio).

[siamond]

Why is it that siamonds data says the max DD for s/p500 was only 38%? It lost like 50% in the GFC...

It's always the first trading day of January. It ignores intra-year peaks and intra-year valleys.

Yes, correct. The Simba backtested spreadsheet works on annual returns (Jan 1st to Jan 1st), ignoring intra-year events, while Portfolio Visualizer works on monthly returns, ignoring intra-month events.

[butricksaid]

Same.

All of these traders were celebrating a one day victory yesterday by moving over to 55/45 and today they got crushed more than 40/60. We're coming up on the end of a long economic cycle with volatility spikes every other day and now you want to tilt heavier into equity? Are you a pig? Because you're going to get slaughtered.

Maybe change your AA to more UPRO after/during a recession instead of leading up to one?

55/45 down 1.2% today. Hardly “crushed”.

If I knew we were going into a recession I wouldn’t have any UPRO.

My point was that the new 55/45 gang was celebrating after hours on Tuesday (only to lose out to 40/60 gang today) which is a short-sighted view of overall portfolio performance. Even if you say you're -1.2% today, 40/60 was up 1.2%. My mistake for saying "crushed" as it caused folks to focus on that word. I still stand by my perspective to remain 40/60 until an actual downturn, which does not require knowing when the recession is, because 40/60 was what was initially determined to be appropriate in most market conditions from thorough backtesting.

If I understood OP correctly this is a long term strategy.

No $#@% Sherlock, I'm saying the portfolio shift ("adaptive allocation") to 55/45 is a short-sighted knee-jerk reaction to recent trends, everyone following this thread knows it's buy-and-hold on steroids.

[MotoTrojan]

because 40/60 was what was initially determined to be appropriate in most market conditions from thorough backtesting.

40/60 was only determined to be appropriate through one market condition, which is all but impossible to persist in the future. 40/60 did not look so hot when you go through a full interest rate cycle (1955-present). 55/45 still had a rough ride but did indeed pay-off. I disagree with your assertion and I think you are the one focusing on too small of timeframes/conditions.

[Lee_WSP]

because 40/60 was what was initially determined to be appropriate in most market conditions from thorough backtesting.

40/60 was only determined to be appropriate through one market condition, which is all but impossible to persist in the future. 40/60 did not look so hot when you go through a full interest rate cycle (1955-present). 55/45 still had a rough ride but did indeed pay-off. I disagree with your assertion and I think you are the one focusing on too small of timeframes/conditions.

Agreed. The era of rising rates was my chief criticism of the strategy. If rates are rising there is no way TMF is making any money as the leveraged principal losses will devastate the nearly nonexistent dividends the fund pays.