## Uncle Fred’s Second Coin – The Case for Leveraged Bonds

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Topic Author
EfficientInvestor
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Joined: Thu Nov 01, 2018 7:02 pm

### Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Below is the text from a blog post I recently published regarding the use of leveraged bonds. There are a few active threads that I have been wanting to present this concept to (viewtopic.php?f=10&t=288192, viewtopic.php?f=10&t=273666), but it just made more sense to write out my full narrative and start a new thread. Here goes:

One of my favorite investing books is William Bernstein’s, The Intelligent Asset Allocator. If you haven’t read the book, I highly recommend you grab a copy. In the book, Bernstein introduces us to Uncle Fred and his coin that determines the annual return of an investment. He then shows how if you have two identical coins that have similar but uncorrelated return and risk profiles, you receive a diversification benefit that results in better risk-adjusted returns. The following analysis is a recreation of Bernstein’s concept, but I use different numbers to better align with the denomination of the various coins in Uncle Fred’s pocket. I also take it a step further to make a case for the asset (leveraged bonds) that should represent Uncle Fred’s second coin.

As in Bernstein’s book, let’s assume you have an Uncle Fred that has a coin (we will say it’s a quarter) that dictates the annual return of your investments. When it flips heads, you get a 25% return (because a quarter is \$0.25). When it flips tails, you get a -5% return. The average of these two outcomes is 10% while the standard deviation is 15%. It just so happens that these metrics are similar to the long term average and standard deviation of the S&P 500.

Now, let’s assume Uncle Fred has a second coin that produces the same +25%/-5% results and the outcome of this second coin is completely independent from the first. In order to spread your bets, you decide to split your investments between the outcome of both coins equally. The result is that you now have four potential outcomes instead of just two. If both coins flip heads, you get +25%. If the first is heads and the second is tails, you get 10%. Likewise, if the first is tails and the second is heads, you get 10%. Lastly, if both are tails, you get -5%. Overall, your average of the four outcomes is still 10%. However, the standard deviation is now reduced to only 10.6%.

For those that are a little rusty on statistics, standard deviation helps you determine how often occurrences fall within a certain range of the average. 68% of outcomes occur within one standard deviation of the average, 95% occur within two standard deviations, and 99.7% occur within three standard deviations. When it comes to investing, I like to look at three standard deviation events (to the downside) to determine the type of worst case scenario that could be expected. For stocks, a three standard deviation event would result in a return of -35%. It just so happens that this was near the return in 2008 when the stock market crashed. Alternatively, if you look at the returns of the two-coin asset allocation, the three standard deviation event is -21.6%. Therefore, you get the same long term average returns of being 100% stock but do so with much less downside risk.

So now you are probably thinking, “I really like this concept in theory, but what asset could represent the second coin.” If we do a quick overview of various asset types, we can see that there isn’t really anything else that provides the same kind of returns as the stock market while being completely uncorrelated. Real estate can have the same potential returns as the stock market, but it has shown to be highly correlated to the market in the past. Commodities (e.g. gold) lack correlation to stocks, but you can’t expect much real return from them over the long run because they are ultimately just keeping up with inflation. That mainly leaves us with bonds.

Bonds lack correlation with stocks, but they don’t generally have the same kind of return potential. In fact, if bonds were to be represented by one of Uncle Fred’s coins, it would need to be a dime. On heads, you get a 10% return. On tails, you get a 2% return. In other words, you could expect a long term average of 6% with a standard deviation of 4%. But, what would the return and risk profile look like if we added some leverage?

It just so happens that if you apply leverage to bonds (via the use of futures, options, leveraged ETFs, etc.), you can approximate the return and risk profile of stocks. Since 1955, had you leveraged 2-year treasury bonds by a factor of 6, you would have produced an annualized return of around 9% and a standard deviation of 14.4%. Portfolio 1 in the Portfolio Visualizer results at the bottom of the page shows these results. Over this same time period, the stock market had an annualized return of 10.3% and a standard deviation of 14.5%. Had you split your bets evenly between stocks and leveraged bonds over this time period, you would have had an annualized return of 10.3% , a standard deviation of 10.5%, and a worst year of only -10.5% in 1969 (see Portfolio 2). You would have had similar returns to being 100% stock, but with substantially less risk!

It is quite fascinating how similar these real world results are to the theoretical results represented by the coin flips. What is even more fascinating is that you can take it a step further. Through the use of leverage, you don’t have to just limit yourself to splitting your results between the two coin flips. You can add the results of both coin flips. Since 1955, had you invested 100% in stocks AND 600% in 2-year treasuries, you would have generated an annualized return of 15.1%, a standard deviation of 21.8%, and a worst year of -28.8% in 1974 (see Portfolio 3). In this instance, your volatility is much greater than being all stock, but your return is (in my opinion) well worth the added volatility.

In summary, I would like to reiterate that “leverage” does not need to be a bad word. Most (if not all) companies you invest in use leverage to produce better returns and increase their stock price. Therefore, most investors are already comfortable with the idea of investing with leverage, they just don’t know they are. By applying leverage to bonds, you are essentially just trying to keep pace with what is already happening on the equity side of your portfolio. By applying leverage to bonds, you are creating a second coin flip that helps you spread your bets as an investor and better balance risk across the assets in which you invest.

aristotelian
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

How do you get the numbers going back to 1955 on Portfoliovisualizer?

50% Large Cap US/50% Long Term Treasuries going back to 1972 gives you a higher CAGR with lower Standard Deviation and lower max drawdown than your portfolio #2. Did you consider extending duration rather than leveraging?

Nahtanoj
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

aristotelian wrote:
Mon Aug 26, 2019 11:16 am
How do you get the numbers going back to 1955 on Portfoliovisualizer?

50% Large Cap US/50% Long Term Treasuries going back to 1972 gives you a higher CAGR with lower Standard Deviation and lower max drawdown than your portfolio #2. Did you consider extending duration rather than leveraging?
To get data going back to 1955, I uploaded monthly return data to PV and made my own ticker symbols.

As for STT vs LTT...you need to compare data over the same time period. My data was since 1955 and you are looking at data since 1972. Below is a comparison of both since 1972. The version with leveraged STT had higher volatility over the time period, but it also had a higher return and sharpe ratio than the version with LTT.

Topic Author
EfficientInvestor
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Nahtanoj wrote:
Mon Aug 26, 2019 11:20 am
And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.
It depends which products you use. I'm also a DIY retail investor and I'm currently using futures contracts to obtain leverage. There are some finer details involved, but the borrowing cost associated with using futures contracts is close to the 3-month T-Bill rate that is reflected by the negative CASHX position in PV.

RandomWord
Posts: 57
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Mon Aug 26, 2019 1:40 pm
Nahtanoj wrote:
Mon Aug 26, 2019 11:20 am
And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.
It depends which products you use. I'm also a DIY retail investor and I'm currently using futures contracts to obtain leverage. There are some finer details involved, but the borrowing cost associated with using futures contracts is close to the 3-month T-Bill rate that is reflected by the negative CASHX position in PV.
I'm doing the same.

The results this year have been great (after a terrible year last year). But, I am a bit worried by the inverted yield curve. According to https://www.cmegroup.com/tools-informat ... ytics.html, right now we are actually paying more to borrow the bonds than the actual yield of the bonds. (as I write this, the Implied Repo Rate is 1.83% and the 2-year yield is only 1.4%.) Basically we're just counting on interest rates to continue dropping, which makes me uneasy. It seems like pure speculation, rather than the term premium that I'd like.

That said, when the yield curve was upward my treasury futures lost money, and now that it's downward they've been making money, so clearly I know nothing.

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

RandomWord wrote:
Mon Aug 26, 2019 2:00 pm
EfficientInvestor wrote:
Mon Aug 26, 2019 1:40 pm
Nahtanoj wrote:
Mon Aug 26, 2019 11:20 am
And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.
It depends which products you use. I'm also a DIY retail investor and I'm currently using futures contracts to obtain leverage. There are some finer details involved, but the borrowing cost associated with using futures contracts is close to the 3-month T-Bill rate that is reflected by the negative CASHX position in PV.
I'm doing the same.

The results this year have been great (after a terrible year last year). But, I am a bit worried by the inverted yield curve. According to https://www.cmegroup.com/tools-informat ... ytics.html, right now we are actually paying more to borrow the bonds than the actual yield of the bonds. (as I write this, the Implied Repo Rate is 1.83% and the 2-year yield is only 1.4%.) Basically we're just counting on interest rates to continue dropping, which makes me uneasy. It seems like pure speculation, rather than the term premium that I'd like.

That said, when the yield curve was upward my treasury futures lost money, and now that it's downward they've been making money, so clearly I know nothing.
I've thought about this a bunch as well. But I mainly come back to the following thoughts to make myself feel ok about it:

1. The yield curve has inverted many times since 1955 (the extent of my data) and the results over the long term say I should stick to the plan.
2. Over the long run, investors receive return above the risk-free rate for taking on equity (stock) and term (treasury bond) risk. So even though the yield of the bonds may dip below the risk-free (borrowing) rate from time to time, my total expected return for the risk I'm taking on (stocks + bonds) still exceeds that risk-free rate over the long run.

robertmcd
Posts: 509
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

RandomWord wrote:
Mon Aug 26, 2019 2:00 pm
EfficientInvestor wrote:
Mon Aug 26, 2019 1:40 pm
Nahtanoj wrote:
Mon Aug 26, 2019 11:20 am
And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.
It depends which products you use. I'm also a DIY retail investor and I'm currently using futures contracts to obtain leverage. There are some finer details involved, but the borrowing cost associated with using futures contracts is close to the 3-month T-Bill rate that is reflected by the negative CASHX position in PV.
I'm doing the same.

The results this year have been great (after a terrible year last year). But, I am a bit worried by the inverted yield curve. According to https://www.cmegroup.com/tools-informat ... ytics.html, right now we are actually paying more to borrow the bonds than the actual yield of the bonds. (as I write this, the Implied Repo Rate is 1.83% and the 2-year yield is only 1.4%.) Basically we're just counting on interest rates to continue dropping, which makes me uneasy. It seems like pure speculation, rather than the term premium that I'd like.

That said, when the yield curve was upward my treasury futures lost money, and now that it's downward they've been making money, so clearly I know nothing.
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.

Lee_WSP
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Location: Arizona

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Does the strategy require leveraging individual or packaged zero coupon bonds?

I ask because if you use futures, you don't receive the dividends right? And if dividends represent the bulk of a bond funds returns, leveraging with futures make sense there right?

Horton
Posts: 290
Joined: Mon Jan 21, 2008 3:53 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Leverage seems to be all the rage around here lately
"You must know that there is nothing higher and stronger and more wholesome and good for life in the future than some good memory, especially a memory of childhood, of home." - Dostoyevsky

RandomWord
Posts: 57
Joined: Tue Jun 18, 2019 1:12 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

robertmcd wrote:
Mon Aug 26, 2019 2:14 pm
RandomWord wrote:
Mon Aug 26, 2019 2:00 pm
EfficientInvestor wrote:
Mon Aug 26, 2019 1:40 pm
Nahtanoj wrote:
Mon Aug 26, 2019 11:20 am
And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.
It depends which products you use. I'm also a DIY retail investor and I'm currently using futures contracts to obtain leverage. There are some finer details involved, but the borrowing cost associated with using futures contracts is close to the 3-month T-Bill rate that is reflected by the negative CASHX position in PV.
I'm doing the same.

The results this year have been great (after a terrible year last year). But, I am a bit worried by the inverted yield curve. According to https://www.cmegroup.com/tools-informat ... ytics.html, right now we are actually paying more to borrow the bonds than the actual yield of the bonds. (as I write this, the Implied Repo Rate is 1.83% and the 2-year yield is only 1.4%.) Basically we're just counting on interest rates to continue dropping, which makes me uneasy. It seems like pure speculation, rather than the term premium that I'd like.

That said, when the yield curve was upward my treasury futures lost money, and now that it's downward they've been making money, so clearly I know nothing.
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.
That's an interesting idea. I have to admit, I don't really understand how futures would work for fed funds or eurodollars. What's the underlying there, a hypothetical money market account that doesn't actually exist? Also, at some point the cost of actually trading the contracts becomes significant, when you're trying to eek out a small term premium and constantly rolling all the contracts.

RandomWord
Posts: 57
Joined: Tue Jun 18, 2019 1:12 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Mon Aug 26, 2019 2:11 pm
RandomWord wrote:
Mon Aug 26, 2019 2:00 pm
EfficientInvestor wrote:
Mon Aug 26, 2019 1:40 pm
Nahtanoj wrote:
Mon Aug 26, 2019 11:20 am
And what does the leverage cost? For those of us who are do it yourself retail investors, I have to presume the cost will be substantial - maybe exceeding 100% of the total return on the leveraged asset in some cases.
It depends which products you use. I'm also a DIY retail investor and I'm currently using futures contracts to obtain leverage. There are some finer details involved, but the borrowing cost associated with using futures contracts is close to the 3-month T-Bill rate that is reflected by the negative CASHX position in PV.
I'm doing the same.

The results this year have been great (after a terrible year last year). But, I am a bit worried by the inverted yield curve. According to https://www.cmegroup.com/tools-informat ... ytics.html, right now we are actually paying more to borrow the bonds than the actual yield of the bonds. (as I write this, the Implied Repo Rate is 1.83% and the 2-year yield is only 1.4%.) Basically we're just counting on interest rates to continue dropping, which makes me uneasy. It seems like pure speculation, rather than the term premium that I'd like.

That said, when the yield curve was upward my treasury futures lost money, and now that it's downward they've been making money, so clearly I know nothing.
I've thought about this a bunch as well. But I mainly come back to the following thoughts to make myself feel ok about it:

1. The yield curve has inverted many times since 1955 (the extent of my data) and the results over the long term say I should stick to the plan.
2. Over the long run, investors receive return above the risk-free rate for taking on equity (stock) and term (treasury bond) risk. So even though the yield of the bonds may dip below the risk-free (borrowing) rate from time to time, my total expected return for the risk I'm taking on (stocks + bonds) still exceeds that risk-free rate over the long run.
Yeah, I'm basically just trusting in the wisdom of the market to correctly price the futures contracts. Seems like everyone is very sure that the interest rates are going to continue dropping this year.

I know it's hard to get data from the past, but I would be very interested to see how leveraged bonds would have done pre-1955, since that's the last time interest rates were this low. It's hard to judge much from post-1955 because it's just been one big cycle- rising rates from 1955-1981, falling rates ever since then. My prediction/hope for the future is that interest rates simply remain low, not moving up or down too much.

Kevin M
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

robertmcd wrote:
Mon Aug 26, 2019 2:14 pm
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.
The need for higher leverage for shorter maturities and the 3m Tbill having the "longest way to fall" are conflicting statements, aren't they?

If constant maturity 3m at 1.97% falls to 0% the gain is 0.49%.

If 2y at 1.51% falls to 0% the gain is 3.02%.

If 10y at 1.52% falls to 0% the gain is 15.20%.

If 20y at 1.82% falls to 0% the gain is 36.40%.

So it's really the duration that matters much more than how far it has to fall before hitting 0%.

Kevin
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Kevin M
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Mon Aug 26, 2019 1:37 pm
To get data going back to 1955, I uploaded monthly return data to PV and made my own ticker symbols.
What is your data source for short-term Treasuries (STT) back to 1955? I assume you're using simulated returns of some sort for the older returns. I know we have simulated annual STT returns back further than that in the Simba/siamond backtest spreadsheet, which rely on longinvest's simulated 2-4 year bond ladder prior to 1976.

Kevin
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robertmcd
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Kevin M wrote:
Mon Aug 26, 2019 3:08 pm
robertmcd wrote:
Mon Aug 26, 2019 2:14 pm
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.
The need for higher leverage for shorter maturities and the 3m Tbill having the "longest way to fall" are conflicting statements, aren't they?

If constant maturity 3m at 1.97% falls to 0% the gain is 0.49%.

If 2y at 1.51% falls to 0% the gain is 3.02%.

If 10y at 1.52% falls to 0% the gain is 15.20%.

If 20y at 1.82% falls to 0% the gain is 36.40%.

So it's really the duration that matters much more than how far it has to fall before hitting 0%.

Kevin
That is why you use leverage to gain duration equivalence. Historically the shorter terms have fallen more on a yields only basis than the longer terms. This is what you are looking for at any point in the curve, then you use leverage to match the volatility of the longer term issues or too achieve risk parity with stocks, etc. For example:

40% VTI & 60% TLT (20+ yr treasuries) - long term risk parity according to hedgefundie's backtests

10% VTI & 90% 2 yr treasuries - risk parity, but my stock allocation and expected return is too low

40% VTI & 60% 2 yr treasury futures leveraged 6x

ThrustVectoring
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Lee_WSP wrote:
Mon Aug 26, 2019 2:26 pm
Does the strategy require leveraging individual or packaged zero coupon bonds?

I ask because if you use futures, you don't receive the dividends right? And if dividends represent the bulk of a bond funds returns, leveraging with futures make sense there right?
The treasury futures market is very thickly traded and highly efficient. If the underlying would predictably make more money than the futures contract, then arbitrageurs would buy the underlying and short the futures contract and take a risk-free profit.

In short, even though you "don't get" the coupon payments from the underlying bonds, the futures contract is cheaper by an amount that makes the two strategies equivalent.
Current portfolio: 60% VTI / 40% VXUS

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Kevin M wrote:
Mon Aug 26, 2019 3:16 pm
EfficientInvestor wrote:
Mon Aug 26, 2019 1:37 pm
To get data going back to 1955, I uploaded monthly return data to PV and made my own ticker symbols.
What is your data source for short-term Treasuries (STT) back to 1955? I assume you're using simulated returns of some sort for the older returns. I know we have simulated annual STT returns back further than that in the Simba/siamond backtest spreadsheet, which rely on longinvest's simulated 2-4 year bond ladder prior to 1976.

Kevin
I am using data from siamond and I believe it is based on longinvest’s models, as you suggested. I believe it is the same data that was used as the basis for the 3x Leveraged ETFs that are the basis for Hedgefundie’s backtest.
Last edited by EfficientInvestor on Mon Aug 26, 2019 7:18 pm, edited 1 time in total.

MotoTrojan
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

You can also use EDV to get leverage-esque exposure to duration without all the drawbacks. I am building a holding in 43/57 UPRO/EDV for example.

Kevin M
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Contact:

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

robertmcd wrote:
Mon Aug 26, 2019 3:22 pm
Kevin M wrote:
Mon Aug 26, 2019 3:08 pm
robertmcd wrote:
Mon Aug 26, 2019 2:14 pm
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.
The need for higher leverage for shorter maturities and the 3m Tbill having the "longest way to fall" are conflicting statements, aren't they?

If constant maturity 3m at 1.97% falls to 0% the gain is 0.49%.

If 2y at 1.51% falls to 0% the gain is 3.02%.

If 10y at 1.52% falls to 0% the gain is 15.20%.

If 20y at 1.82% falls to 0% the gain is 36.40%.

So it's really the duration that matters much more than how far it has to fall before hitting 0%.

Kevin
That is why you use leverage to gain duration equivalence. Historically the shorter terms have fallen more on a yields only basis than the longer terms. This is what you are looking for at any point in the curve, then you use leverage to match the volatility of the longer term issues or too achieve risk parity with stocks, etc. For example:

40% VTI & 60% TLT (20+ yr treasuries) - long term risk parity according to hedgefundie's backtests

10% VTI & 90% 2 yr treasuries - risk parity, but my stock allocation and expected return is too low

40% VTI & 60% 2 yr treasury futures leveraged 6x
Yeah, I get the leverage part. I just don't get the relevance of "longest way to fall" bit.
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zaboomafoozarg
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Haha I was thinking the same thing yesterday - it seemed that half of the first page of TN&G was about leveraging.

Valuethinker
Posts: 38567
Joined: Fri May 11, 2007 11:07 am

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

zaboomafoozarg wrote:
Mon Aug 26, 2019 8:52 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Haha I was thinking the same thing yesterday - it seemed that half of the first page of TN&G was about leveraging.
I am reminded of the lead up to October 1987. Individual investor leveraging was all the rage then, too - there was a lot of margin debt out there.

And portfolio insurance was a form of leveraging, as I understood it. Requiring selling into falling markets.

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Valuethinker wrote:
Tue Aug 27, 2019 3:58 am
zaboomafoozarg wrote:
Mon Aug 26, 2019 8:52 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Haha I was thinking the same thing yesterday - it seemed that half of the first page of TN&G was about leveraging.
I am reminded of the lead up to October 1987. Individual investor leveraging was all the rage then, too - there was a lot of margin debt out there.

And portfolio insurance was a form of leveraging, as I understood it. Requiring selling into falling markets.
With all due respect, please understand that I'm not promoting the use of excessive leverage. It would be one thing to promote the leveraging up of all your stock holdings because I think the bull market still has some room left to run (or something like that). Generally, I think the use of leverage on stocks alone is just a form of gambling you can do without having to go to Vegas. In this case, I am promoting the use of leverage in a way that has shown to minimize risk in the past (including in 1987), not increase your risk. The link below is a backtest showing what would have happened since June 1986 had you applied this coin flip principle using stocks and long term treasury bonds (used here due to available data). The long term treasuries have enough leverage applied so their portion of risk is equal to stocks. Does Portfolio 1, which flips two coins every year, have more or less risk than the use of just one coin (the S&P 500 benchmark)? If it is widely accepted to have a portfolio in 100% stock, why can't it be widely accepted to use moderate amounts of leverage to create a portfolio that can generate similar returns with substantially less risk? Check out the Drawdowns and Rolling Returns tabs of the backtest. Flipping two coins every year instead of just one really has its advantages.

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

June 1986 - Present
50% S&P 500/75% LTT - CAGR = 10.5%, SD = 10.0%, Max DD = -18.5%
100% S&P 500 - CAGR = 10.1%, SD = 14.9%, Max DD = -51.0%

robertmcd
Posts: 509
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Kevin M wrote:
Mon Aug 26, 2019 6:21 pm
robertmcd wrote:
Mon Aug 26, 2019 3:22 pm
Kevin M wrote:
Mon Aug 26, 2019 3:08 pm
robertmcd wrote:
Mon Aug 26, 2019 2:14 pm
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.
The need for higher leverage for shorter maturities and the 3m Tbill having the "longest way to fall" are conflicting statements, aren't they?

If constant maturity 3m at 1.97% falls to 0% the gain is 0.49%.

If 2y at 1.51% falls to 0% the gain is 3.02%.

If 10y at 1.52% falls to 0% the gain is 15.20%.

If 20y at 1.82% falls to 0% the gain is 36.40%.

So it's really the duration that matters much more than how far it has to fall before hitting 0%.

Kevin
That is why you use leverage to gain duration equivalence. Historically the shorter terms have fallen more on a yields only basis than the longer terms. This is what you are looking for at any point in the curve, then you use leverage to match the volatility of the longer term issues or too achieve risk parity with stocks, etc. For example:

40% VTI & 60% TLT (20+ yr treasuries) - long term risk parity according to hedgefundie's backtests

10% VTI & 90% 2 yr treasuries - risk parity, but my stock allocation and expected return is too low

40% VTI & 60% 2 yr treasury futures leveraged 6x
Yeah, I get the leverage part. I just don't get the relevance of "longest way to fall" bit.
In the past 2 recessions, (drop in 2 yr yield x duration)/(volatility) has been higher than (drop in 30 yr yield x duration)/(volatility). Thus if you leverage the 2 yr up to the volatility of the 30 yr, you would have gotten a higher NAV gain than using 30 yr bonds. The 2 yr treasury yield also has a higher sharpe ratio than the 30 yr, so when you build portfolios you can see that 6x leveraged 2 yr treasuries perform better than TLT (20+ yr treasuries) in a portfolio of 50% VTI 50% bonds, even though they have the same volatility.

MotoTrojan
Posts: 5825
Joined: Wed Feb 01, 2017 8:39 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Tue Aug 27, 2019 6:06 am
Valuethinker wrote:
Tue Aug 27, 2019 3:58 am
zaboomafoozarg wrote:
Mon Aug 26, 2019 8:52 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Haha I was thinking the same thing yesterday - it seemed that half of the first page of TN&G was about leveraging.
I am reminded of the lead up to October 1987. Individual investor leveraging was all the rage then, too - there was a lot of margin debt out there.

And portfolio insurance was a form of leveraging, as I understood it. Requiring selling into falling markets.
With all due respect, please understand that I'm not promoting the use of excessive leverage. It would be one thing to promote the leveraging up of all your stock holdings because I think the bull market still has some room left to run (or something like that). Generally, I think the use of leverage on stocks alone is just a form of gambling you can do without having to go to Vegas. In this case, I am promoting the use of leverage in a way that has shown to minimize risk in the past (including in 1987), not increase your risk. The link below is a backtest showing what would have happened since June 1986 had you applied this coin flip principle using stocks and long term treasury bonds (used here due to available data). The long term treasuries have enough leverage applied so their portion of risk is equal to stocks. Does Portfolio 1, which flips two coins every year, have more or less risk than the use of just one coin (the S&P 500 benchmark)? If it is widely accepted to have a portfolio in 100% stock, why can't it be widely accepted to use moderate amounts of leverage to create a portfolio that can generate similar returns with substantially less risk? Check out the Drawdowns and Rolling Returns tabs of the backtest. Flipping two coins every year instead of just one really has its advantages.

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

June 1986 - Present
50% S&P 500/75% LTT - CAGR = 10.5%, SD = 10.0%, Max DD = -18.5%
100% S&P 500 - CAGR = 10.1%, SD = 14.9%, Max DD = -51.0%
This has been exhausted extensively in the hedgefundie excellent adventure thread, but uncorrelation is NOT what boosted performance from 1986-present for portfolios that utilize LTT, it was the LTT's incredible performance alone due to falling yields. Looking at 1955-present would give a much better picture since rates climbed and then returned to their current range (a full rate cycle). You can still get a better risk-adjusted return (and thus a higher return for equal risk, if you leverage) but this timeframe is flawed to look at in isolation, unless you are market timing and believe rates will go deeply negative.

I believe the rebalancing bonus between S&P500 and LTT at risk-parity for your timeframe was on the order of 0.5%; this would be the contribution due to uncorrelation.

Note I say all this as someone holding a position in UPRO & EDV (as well as a smaller position that utilizes TMF). I am hoping for closer to 1% CAGR over the S&P500 long-term for the UPRO/EDV variation, with similar risk.

Kevin M
Posts: 10967
Joined: Mon Jun 29, 2009 3:24 pm
Contact:

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

robertmcd wrote:
Tue Aug 27, 2019 9:14 am
Kevin M wrote:
Mon Aug 26, 2019 6:21 pm
robertmcd wrote:
Mon Aug 26, 2019 3:22 pm
Kevin M wrote:
Mon Aug 26, 2019 3:08 pm
robertmcd wrote:
Mon Aug 26, 2019 2:14 pm
If you want to avoid this negative spread, you can use Fed funds futures or eurodollar futures to go shorter than 2 yrs. You will need to up the leverage higher than 6x due to the shorter duration. Also think in terms of change in yield, the 3 mo t bill has the longest way to fall as of right now, and in the event we have stocks drop 50%, very good chance it goes to 0, and possibly beyond if people are scrambling for liquidity.
The need for higher leverage for shorter maturities and the 3m Tbill having the "longest way to fall" are conflicting statements, aren't they?

If constant maturity 3m at 1.97% falls to 0% the gain is 0.49%.

If 2y at 1.51% falls to 0% the gain is 3.02%.

If 10y at 1.52% falls to 0% the gain is 15.20%.

If 20y at 1.82% falls to 0% the gain is 36.40%.

So it's really the duration that matters much more than how far it has to fall before hitting 0%.

Kevin
That is why you use leverage to gain duration equivalence. Historically the shorter terms have fallen more on a yields only basis than the longer terms. This is what you are looking for at any point in the curve, then you use leverage to match the volatility of the longer term issues or too achieve risk parity with stocks, etc. For example:

40% VTI & 60% TLT (20+ yr treasuries) - long term risk parity according to hedgefundie's backtests

10% VTI & 90% 2 yr treasuries - risk parity, but my stock allocation and expected return is too low

40% VTI & 60% 2 yr treasury futures leveraged 6x
Yeah, I get the leverage part. I just don't get the relevance of "longest way to fall" bit.
In the past 2 recessions, (drop in 2 yr yield x duration)/(volatility) has been higher than (drop in 30 yr yield x duration)/(volatility). Thus if you leverage the 2 yr up to the volatility of the 30 yr, you would have gotten a higher NAV gain than using 30 yr bonds. The 2 yr treasury yield also has a higher sharpe ratio than the 30 yr, so when you build portfolios you can see that 6x leveraged 2 yr treasuries perform better than TLT (20+ yr treasuries) in a portfolio of 50% VTI 50% bonds, even though they have the same volatility.
OK, but that still has nothing to do with what has the "longest way to fall", and that's the only part I'm questioning.

If you're using historical returns from two recessions to determine which maturity to leverage to provide highest expected return in a recession, then your most recent explanation makes sense. I don't see any relationship to how far the yield can fall before hitting 0% though.

Kevin
||.......|| Suggested format for Asking Portfolio Questions (edit original post)

trueblueky
Posts: 1557
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Mon Aug 26, 2019 6:40 am
Below is the text from a blog post I recently published regarding the use of leveraged bonds. There are a few active threads that I have been wanting to present this concept to (viewtopic.php?f=10&t=288192, viewtopic.php?f=10&t=273666), but it just made more sense to write out my full narrative and start a new thread. Here goes:

One of my favorite investing books is William Bernstein’s, The Intelligent Asset Allocator. If you haven’t read the book, I highly recommend you grab a copy. In the book, Bernstein introduces us to Uncle Fred and his coin that determines the annual return of an investment. He then shows how if you have two identical coins that have similar but uncorrelated return and risk profiles, you receive a diversification benefit that results in better risk-adjusted returns. The following analysis is a recreation of Bernstein’s concept, but I use different numbers to better align with the denomination of the various coins in Uncle Fred’s pocket. I also take it a step further to make a case for the asset (leveraged bonds) that should represent Uncle Fred’s second coin.

As in Bernstein’s book, let’s assume you have an Uncle Fred that has a coin (we will say it’s a quarter) that dictates the annual return of your investments. When it flips heads, you get a 25% return (because a quarter is \$0.25). When it flips tails, you get a -5% return. The average of these two outcomes is 10% while the standard deviation is 15%. It just so happens that these metrics are similar to the long term average and standard deviation of the S&P 500.

Now, let’s assume Uncle Fred has a second coin that produces the same +25%/-5% results and the outcome of this second coin is completely independent from the first. In order to spread your bets, you decide to split your investments between the outcome of both coins equally. The result is that you now have four potential outcomes instead of just two. If both coins flip heads, you get +25%. If the first is heads and the second is tails, you get 10%. Likewise, if the first is tails and the second is heads, you get 10%. Lastly, if both are tails, you get -5%. Overall, your average of the four outcomes is still 10%. However, the standard deviation is now reduced to only 10.6%.

For those that are a little rusty on statistics, standard deviation helps you determine how often occurrences fall within a certain range of the average. 68% of outcomes occur within one standard deviation of the average, 95% occur within two standard deviations, and 99.7% occur within three standard deviations. When it comes to investing, I like to look at three standard deviation events (to the downside) to determine the type of worst case scenario that could be expected. For stocks, a three standard deviation event would result in a return of -35%. It just so happens that this was near the return in 2008 when the stock market crashed. Alternatively, if you look at the returns of the two-coin asset allocation, the three standard deviation event is -21.6%. Therefore, you get the same long term average returns of being 100% stock but do so with much less downside risk.

So now you are probably thinking, “I really like this concept in theory, but what asset could represent the second coin.” If we do a quick overview of various asset types, we can see that there isn’t really anything else that provides the same kind of returns as the stock market while being completely uncorrelated. Real estate can have the same potential returns as the stock market, but it has shown to be highly correlated to the market in the past. Commodities (e.g. gold) lack correlation to stocks, but you can’t expect much real return from them over the long run because they are ultimately just keeping up with inflation. That mainly leaves us with bonds.

Bonds lack correlation with stocks, but they don’t generally have the same kind of return potential. In fact, if bonds were to be represented by one of Uncle Fred’s coins, it would need to be a dime. On heads, you get a 10% return. On tails, you get a 2% return. In other words, you could expect a long term average of 6% with a standard deviation of 4%. But, what would the return and risk profile look like if we added some leverage?

It just so happens that if you apply leverage to bonds (via the use of futures, options, leveraged ETFs, etc.), you can approximate the return and risk profile of stocks. Since 1955, had you leveraged 2-year treasury bonds by a factor of 6, you would have produced an annualized return of around 9% and a standard deviation of 14.4%. Portfolio 1 in the Portfolio Visualizer results at the bottom of the page shows these results. Over this same time period, the stock market had an annualized return of 10.3% and a standard deviation of 14.5%. Had you split your bets evenly between stocks and leveraged bonds over this time period, you would have had an annualized return of 10.3% , a standard deviation of 10.5%, and a worst year of only -10.5% in 1969 (see Portfolio 2). You would have had similar returns to being 100% stock, but with substantially less risk!

It is quite fascinating how similar these real world results are to the theoretical results represented by the coin flips. What is even more fascinating is that you can take it a step further. Through the use of leverage, you don’t have to just limit yourself to splitting your results between the two coin flips. You can add the results of both coin flips. Since 1955, had you invested 100% in stocks AND 600% in 2-year treasuries, you would have generated an annualized return of 15.1%, a standard deviation of 21.8%, and a worst year of -28.8% in 1974 (see Portfolio 3). In this instance, your volatility is much greater than being all stock, but your return is (in my opinion) well worth the added volatility.

In summary, I would like to reiterate that “leverage” does not need to be a bad word. Most (if not all) companies you invest in use leverage to produce better returns and increase their stock price. Therefore, most investors are already comfortable with the idea of investing with leverage, they just don’t know they are. By applying leverage to bonds, you are essentially just trying to keep pace with what is already happening on the equity side of your portfolio. By applying leverage to bonds, you are creating a second coin flip that helps you spread your bets as an investor and better balance risk across the assets in which you invest.

I wish -35% were a three standard deviation event for stocks! That's three years out of 1,000.
Instead we had three years in the last 90 years (1931, 1937, 2008).

Conclusion: stock returns are not normally distributed.

Random Musings
Posts: 5412
Joined: Thu Feb 22, 2007 4:24 pm
Location: Pennsylvania

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Indeed, this thread, the 90/60, Hedgefundie and so on. Everything is foolproof until a black swan hits. Nah, that will only happen to LTCM.

Leverage is not a free lunch. Just because interest rate trends over the past 35 plus years have been kind toward leveraged bond strategies, I would be surprised if that will continue in the decades to come. If it does, there may be bigger issues to deal with if rates are super low/negative.

RM
I figure the odds be fifty-fifty I just might have something to say. FZ

MotoTrojan
Posts: 5825
Joined: Wed Feb 01, 2017 8:39 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Random Musings wrote:
Tue Aug 27, 2019 8:36 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Indeed, this thread, the 90/60, Hedgefundie and so on. Everything is foolproof until a black swan hits. Nah, that will only happen to LTCM.

Leverage is not a free lunch. Just because interest rate trends over the past 35 plus years have been kind toward leveraged bond strategies, I would be surprised if that will continue in the decades to come. If it does, there may be bigger issues to deal with if rates are super low/negative.

RM
Even the fully leveraged 55/45 version (hedgefundie's adventure allocation) would've beaten the S&P500 from 1955-2018 by almost 3% CAGR, so no it does not rely on 35 plus years of kind bond years (in fact it worked fine with one of the worst periods ever, and a full rate cycle).

I still prefer only leveraging the equity side and using EDV (43/57 UPRO/EDV).

HEDGEFUNDIE
Posts: 3262
Joined: Sun Oct 22, 2017 2:06 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Random Musings wrote:
Tue Aug 27, 2019 8:36 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Indeed, this thread, the 90/60, Hedgefundie and so on. Everything is foolproof until a black swan hits. Nah, that will only happen to LTCM.

Leverage is not a free lunch. Just because interest rate trends over the past 35 plus years have been kind toward leveraged bond strategies, I would be surprised if that will continue in the decades to come. If it does, there may be bigger issues to deal with if rates are super low/negative.

RM
Could there be a black swan that kills my strategy? Sure.

Am I willing to bet that no such event will happen over the next 20 years, and my \$100k turns into \$10M? Absolutely.

Forester
Posts: 360
Joined: Sat Jan 19, 2019 2:50 pm
Location: UK

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

The US has negative real interest rates; could be risky.

we1
Posts: 14
Joined: Tue Jul 30, 2019 12:24 am

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

HEDGEFUNDIE wrote:
Wed Aug 28, 2019 12:01 am
Random Musings wrote:
Tue Aug 27, 2019 8:36 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Indeed, this thread, the 90/60, Hedgefundie and so on. Everything is foolproof until a black swan hits. Nah, that will only happen to LTCM.

Leverage is not a free lunch. Just because interest rate trends over the past 35 plus years have been kind toward leveraged bond strategies, I would be surprised if that will continue in the decades to come. If it does, there may be bigger issues to deal with if rates are super low/negative.

RM
Could there be a black swan that kills my strategy? Sure.

Am I willing to bet that no such event will happen over the next 20 years, and my \$100k turns into \$10M? Absolutely.
Do you really think your strategy can return 25%+ annualized for 20 years? Sorry if you’ve answered that in the HEDGEFUNDIE thread. I stopped keeping up with it. The concept is ok but far fetched if you expect 100x in 20 years.

HEDGEFUNDIE
Posts: 3262
Joined: Sun Oct 22, 2017 2:06 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

we1 wrote:
Wed Aug 28, 2019 12:21 am
HEDGEFUNDIE wrote:
Wed Aug 28, 2019 12:01 am
Random Musings wrote:
Tue Aug 27, 2019 8:36 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Indeed, this thread, the 90/60, Hedgefundie and so on. Everything is foolproof until a black swan hits. Nah, that will only happen to LTCM.

Leverage is not a free lunch. Just because interest rate trends over the past 35 plus years have been kind toward leveraged bond strategies, I would be surprised if that will continue in the decades to come. If it does, there may be bigger issues to deal with if rates are super low/negative.

RM
Could there be a black swan that kills my strategy? Sure.

Am I willing to bet that no such event will happen over the next 20 years, and my \$100k turns into \$10M? Absolutely.
Do you really think your strategy can return 25%+ annualized for 20 years? Sorry if you’ve answered that in the HEDGEFUNDIE thread. I stopped keeping up with it. The concept is ok but far fetched if you expect 100x in 20 years.
Over the past 10 years it has delivered 33% CAGR:

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

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

MotoTrojan wrote:
Tue Aug 27, 2019 12:16 pm
EfficientInvestor wrote:
Tue Aug 27, 2019 6:06 am
Valuethinker wrote:
Tue Aug 27, 2019 3:58 am
zaboomafoozarg wrote:
Mon Aug 26, 2019 8:52 pm
Horton wrote:
Mon Aug 26, 2019 2:41 pm
Leverage seems to be all the rage around here lately
Haha I was thinking the same thing yesterday - it seemed that half of the first page of TN&G was about leveraging.
I am reminded of the lead up to October 1987. Individual investor leveraging was all the rage then, too - there was a lot of margin debt out there.

And portfolio insurance was a form of leveraging, as I understood it. Requiring selling into falling markets.
With all due respect, please understand that I'm not promoting the use of excessive leverage. It would be one thing to promote the leveraging up of all your stock holdings because I think the bull market still has some room left to run (or something like that). Generally, I think the use of leverage on stocks alone is just a form of gambling you can do without having to go to Vegas. In this case, I am promoting the use of leverage in a way that has shown to minimize risk in the past (including in 1987), not increase your risk. The link below is a backtest showing what would have happened since June 1986 had you applied this coin flip principle using stocks and long term treasury bonds (used here due to available data). The long term treasuries have enough leverage applied so their portion of risk is equal to stocks. Does Portfolio 1, which flips two coins every year, have more or less risk than the use of just one coin (the S&P 500 benchmark)? If it is widely accepted to have a portfolio in 100% stock, why can't it be widely accepted to use moderate amounts of leverage to create a portfolio that can generate similar returns with substantially less risk? Check out the Drawdowns and Rolling Returns tabs of the backtest. Flipping two coins every year instead of just one really has its advantages.

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

June 1986 - Present
50% S&P 500/75% LTT - CAGR = 10.5%, SD = 10.0%, Max DD = -18.5%
100% S&P 500 - CAGR = 10.1%, SD = 14.9%, Max DD = -51.0%
This has been exhausted extensively in the hedgefundie excellent adventure thread, but uncorrelation is NOT what boosted performance from 1986-present for portfolios that utilize LTT, it was the LTT's incredible performance alone due to falling yields. Looking at 1955-present would give a much better picture since rates climbed and then returned to their current range (a full rate cycle). You can still get a better risk-adjusted return (and thus a higher return for equal risk, if you leverage) but this timeframe is flawed to look at in isolation, unless you are market timing and believe rates will go deeply negative.

I believe the rebalancing bonus between S&P500 and LTT at risk-parity for your timeframe was on the order of 0.5%; this would be the contribution due to uncorrelation.

Note I say all this as someone holding a position in UPRO & EDV (as well as a smaller position that utilizes TMF). I am hoping for closer to 1% CAGR over the S&P500 long-term for the UPRO/EDV variation, with similar risk.
I agree. I was hesitant to post a backtest that only included times of falling interest rates. But I wanted to post something that anyone could click on and see the results (as opposed to my initial results that were based on my own data sets). I was mainly just trying to point out that it is possible to use appropriate amounts of leverage and not get burned.

As for LTTs, I prefer not to use them due to the additional term risk. I prefer to use shorter term treasuries with additional leverage.

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

trueblueky wrote:
Tue Aug 27, 2019 3:57 pm
I wish -35% were a three standard deviation event for stocks! That's three years out of 1,000.
Instead we had three years in the last 90 years (1931, 1937, 2008).

Conclusion: stock returns are not normally distributed.
I agree with your conclusion of stocks not being normally distributed and I was mindful of that when making my original post. However, I didn't want to get too in the weeds on that topic when I was generally just trying to present the concept of determining what a potential worst case scenario might be. It's just that in the case of stocks, that worst case scenario happens more often that it should.

MotoTrojan
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Joined: Wed Feb 01, 2017 8:39 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Wed Aug 28, 2019 6:12 am

As for LTTs, I prefer not to use them due to the additional term risk. I prefer to use shorter term treasuries with additional leverage.
Can you help me understand this? If you leverage 2yr to have the same effective duration as 20yr, how is your risk/performance vastly different?

robertmcd
Posts: 509
Joined: Tue Aug 09, 2016 9:06 am

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

MotoTrojan wrote:
Wed Aug 28, 2019 9:23 am
EfficientInvestor wrote:
Wed Aug 28, 2019 6:12 am

As for LTTs, I prefer not to use them due to the additional term risk. I prefer to use shorter term treasuries with additional leverage.
Can you help me understand this? If you leverage 2yr to have the same effective duration as 20yr, how is your risk/performance vastly different?
2 yr has higher sharpe ratio, and it also outperforms during recessions in terms of sharpe ratio when compared to long term. The leverage increases the volatility, thus increasing the returns.

https://www.portfoliovisualizer.com/bac ... sisResults

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

MotoTrojan wrote:
Wed Aug 28, 2019 9:23 am
EfficientInvestor wrote:
Wed Aug 28, 2019 6:12 am

As for LTTs, I prefer not to use them due to the additional term risk. I prefer to use shorter term treasuries with additional leverage.
Can you help me understand this? If you leverage 2yr to have the same effective duration as 20yr, how is your risk/performance vastly different?
I guess I would explain it by saying that effective duration (generated by leverage) is not the same as actual duration. If you are just holding long term treasuries, you are taking on long-term term risk. When you are leveraging short term treasuries, you are taking on short-term term risk, but doing it many times and counting on the short term returns exceeding your borrowing rate. The best data set we can look at to show performance during an extended rising interest rate environment is 1955 - 1981. As the image below shows, leveraged short term bonds performed better than unleveraged long term bonds. The amount of leverage used on the STT was chosen so that the St Dev would equal that of LTT.

vineviz
Posts: 5054
Joined: Tue May 15, 2018 1:55 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Wed Aug 28, 2019 12:37 pm
. The best data set we can look at to show performance during an extended rising interest rate environment is 1955 - 1981. As the image below shows, leveraged short term bonds performed better than unleveraged long term bonds. The amount of leverage used on the STT was chosen so that the St Dev would equal that of LTT.
During this time period LTTs were callable, which seriously distorts the payoff curve. Compound this with a different policy regime (the Fed was targeting interest rates instead of inflation) and you get a reconstructed data series that defies logical interpretation.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

Topic Author
EfficientInvestor
Posts: 200
Joined: Thu Nov 01, 2018 7:02 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

vineviz wrote:
Wed Aug 28, 2019 12:55 pm
EfficientInvestor wrote:
Wed Aug 28, 2019 12:37 pm
. The best data set we can look at to show performance during an extended rising interest rate environment is 1955 - 1981. As the image below shows, leveraged short term bonds performed better than unleveraged long term bonds. The amount of leverage used on the STT was chosen so that the St Dev would equal that of LTT.
During this time period LTTs were callable, which seriously distorts the payoff curve. Compound this with a different policy regime (the Fed was targeting interest rates instead of inflation) and you get a reconstructed data series that defies logical interpretation.
Ah...good point about the time period chosen. I have to admit I'm not well versed in the affects that callability had on bonds back then. However, as robermcd stated, I still am of the opinion that leveraging the STT (which generally have a higher sharpe ratio) is preferred over using LTT.

MotoTrojan
Posts: 5825
Joined: Wed Feb 01, 2017 8:39 pm

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

robertmcd wrote:
Wed Aug 28, 2019 11:15 am
MotoTrojan wrote:
Wed Aug 28, 2019 9:23 am
EfficientInvestor wrote:
Wed Aug 28, 2019 6:12 am

As for LTTs, I prefer not to use them due to the additional term risk. I prefer to use shorter term treasuries with additional leverage.
Can you help me understand this? If you leverage 2yr to have the same effective duration as 20yr, how is your risk/performance vastly different?
2 yr has higher sharpe ratio, and it also outperforms during recessions in terms of sharpe ratio when compared to long term. The leverage increases the volatility, thus increasing the returns.

https://www.portfoliovisualizer.com/bac ... sisResults
It has outperformed is what you meant to say. Using futures to leverage the 2yr will expose you to the price change, but not the income, no? I'd rather get the income of EDV or even TMF.

robertmcd
Posts: 509
Joined: Tue Aug 09, 2016 9:06 am

### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

MotoTrojan wrote:
Wed Aug 28, 2019 1:11 pm
robertmcd wrote:
Wed Aug 28, 2019 11:15 am
MotoTrojan wrote:
Wed Aug 28, 2019 9:23 am
EfficientInvestor wrote:
Wed Aug 28, 2019 6:12 am

As for LTTs, I prefer not to use them due to the additional term risk. I prefer to use shorter term treasuries with additional leverage.
Can you help me understand this? If you leverage 2yr to have the same effective duration as 20yr, how is your risk/performance vastly different?
2 yr has higher sharpe ratio, and it also outperforms during recessions in terms of sharpe ratio when compared to long term. The leverage increases the volatility, thus increasing the returns.

https://www.portfoliovisualizer.com/bac ... sisResults
It has outperformed is what you meant to say. Using futures to leverage the 2yr will expose you to the price change, but not the income, no? I'd rather get the income of EDV or even TMF.
You will earn the spread between the implied financing rate (usually around the 3 mo T bill) and the 2 yr yield, multiplied by your leverage. Right now for example you are earning a negative spread, multiplied by your leverage. It sucks to think about that, but historically it has paid off to have that exposure to the short end of the curve vs. the long end.

vineviz
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Wed Aug 28, 2019 1:10 pm
However, as robermcd stated, I still am of the opinion that leveraging the STT (which generally have a higher sharpe ratio) is preferred over using LTT.
I think using leveraged STT is possibly a very reasonable strategy, though it sounds to me very much like an attempt at arbitrage. And I generally am skeptical of arbitrage opportunities unless the limits preventing other market participants from profiting from it are incredibly persuasive. Maybe that's the case here, though, I don't know.

It's not hard to find times in the recent past where STTs had lower Sharpe ratio than LTTs (July 2016 to October 2018, when interest rates were still rising, for instance) which makes me think it's likely to be very period dependent.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

Lee_WSP
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

How would one achieve 6 or even 3x leverage on STT?

MotoTrojan
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Lee_WSP wrote:
Wed Aug 28, 2019 3:53 pm
How would one achieve 6 or even 3x leverage on STT?
Futures.

Topic Author
EfficientInvestor
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

MotoTrojan wrote:
Wed Aug 28, 2019 4:05 pm
Lee_WSP wrote:
Wed Aug 28, 2019 3:53 pm
How would one achieve 6 or even 3x leverage on STT?
Futures.
2-year treasury (/ZT) futures contracts primarily. You could also use options on SHY, but they aren't very liquid.

Random Musings
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

EfficientInvestor wrote:
Wed Aug 28, 2019 6:15 am
trueblueky wrote:
Tue Aug 27, 2019 3:57 pm
I wish -35% were a three standard deviation event for stocks! That's three years out of 1,000.
Instead we had three years in the last 90 years (1931, 1937, 2008).

Conclusion: stock returns are not normally distributed.
I agree with your conclusion of stocks not being normally distributed and I was mindful of that when making my original post. However, I didn't want to get too in the weeds on that topic when I was generally just trying to present the concept of determining what a potential worst case scenario might be. It's just that in the case of stocks, that worst case scenario happens more often that it should.
The 73-74 bear market is another, don't believe having a large downdraft outside one calendar year makes a difference. 2000 is another, SV and are REITS held up better, but the leveraged funds touted would have felt the pain as well.

RM
I figure the odds be fifty-fifty I just might have something to say. FZ

coingaroo
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Awesome post and lovely intuitive explanation.

Investing is about bearing risk to realise a return. Without leverage, your asset allocation is constrained to risk levels provided by underlying assets. This can get you very far, but what if you could scale underlying risk levels?

The main limitation of leverage for individual investors is that it’s hard to access this cheaply. Futures are the most efficient mechanism except taxes (which is a big one), and the overhead of rolling contracts. There are also minimum position size requirements, even with equity index minis. It could be better.

If you prefer something buy and hold, leveraged ETFs charge management fees of close to 1%, and is subject to greater volatility decay with daily resets.

Margin funding by brokers often apply a 1.5%++ pa markup at best. This sucks and destroys the improved sharpe of leveraging among the CAPM line.

For example: IBKR will charge you 3.62% on \$100k of margin funding. The Fed cash rate is 2.00%. You can see the problem. And IBKR is the cheapest retail broker.

So really, your option is futures and paying the futures tax rates. As an Australian, we don’t even get the 60/40 tax rate split, it’s all ordinary income tax

Tyler Aspect
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

I agree there are more postings about leveraging this year compared to last year. Unsure about the significance of this trend.
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.

coingaroo
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

Tyler Aspect wrote:
Fri Aug 30, 2019 12:22 am
I agree there are more postings about leveraging this year compared to last year. Unsure about the significance of this trend.
Appetite for leverage linearly increases based on number of years since the last recession.

MotoTrojan
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### Re: Uncle Fred’s Second Coin – The Case for Leveraged Bonds

coingaroo wrote:
Fri Aug 30, 2019 12:40 am
Tyler Aspect wrote:
Fri Aug 30, 2019 12:22 am
I agree there are more postings about leveraging this year compared to last year. Unsure about the significance of this trend.
Appetite for leverage linearly increases based on number of years since the last recession.
Leveraged bonds would seem to do well in said recession so kind of counter to that.