Understanding using treasury futures for leverage to implement risk parity

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BTTFutures
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Joined: Sat Sep 07, 2019 4:27 pm

Re: Understanding using treasury futures for leverage to implement risk parity

Post by BTTFutures » Mon Oct 07, 2019 10:32 pm

DonIce wrote:
Mon Oct 07, 2019 10:24 pm
BTTFutures wrote:
Mon Oct 07, 2019 10:20 pm
Thanks this makes sense but now I don't see how futures can help with leverage per the above Kessler article. If you are allocating the same amount of money ($640 margin + $215,360 Cash) how are they creating a 3.3x leveraged portfolio? The 2 yr futures plus excess cash in t bills returns 4% on average annually which is not much better than margin borrow rates so a 2x leverage in a margin account would be impractical. This would only be possible for mutual fund managers that can borrow at extremely low rates, correct?

Basically, if everything you say is accurate this whole approach with futures is wrong and the leveraged ETFs are the best approach. The 2 yr futures over the long-run returns less than 1% on average (CAGR) with a negative sharp ratio. Which is of course a terrible approach for long term investing.
The point is that you don't actually need to keep around $215,360 in cash. You COULD do that, but more likely you would just keep around a few thousand in cash, and invest the rest of your capital elsewhere. You might, for example, only have $10k of capital to begin with and you can still do this.
Yes, but the money you are investing in the 2-year future is ill-advised unless you know how interest rates will move. You are essentially 88x leveraging a terrible long term investment with a far greater stdv than returns.

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DonIce
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by DonIce » Mon Oct 07, 2019 10:37 pm

BTTFutures wrote:
Mon Oct 07, 2019 10:32 pm
Yes, but the money you are investing in the 2-year future is ill-advised unless you know how interest rates will move. You are essentially 88x leveraging a terrible long term investment with a greater stdv than returns.
You have to look at it from the standpoint of an overall portfolio. Treasuries have a low (or even negative) correlation with equities. By adding a treasury future position to an equity-heavy portfolio, you may be able to smooth out the ride without lowering expected return. So instead of being 100% equity, you might be 90% equity and 10% cash as collateral for 1000% in 2-year futures, for example.

rascott
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Mon Oct 07, 2019 11:35 pm

BTTFutures wrote:
Mon Oct 07, 2019 10:20 pm
rascott wrote:
Mon Oct 07, 2019 9:16 pm
BTTFutures wrote:
Mon Oct 07, 2019 8:50 pm
rascott wrote:
Fri Sep 13, 2019 3:49 pm
BTTFutures wrote:
Sat Sep 07, 2019 5:09 pm
I read through this thread and decided to test the theory using quandl data (https://www.quandl.com/databases/SCF/documentation). I used the backwards ratio adjusted open interest switch method with CME TU continuous futures( CME_TU1_OR). I found that open interest switch vs. first day of expire month switch method had very similar results. I then put the rolling futures data (daily settle value and date) in PV and found that the comparison was quite different. See below PV output. Can anyone help explain this difference and if I need to change my approach?

When using SPUST2TR (https://us.spindices.com/indices/fixed- ... turn-index) the results look great but these rolling futures results, with seemingly real futures data, have me worried. Any thoughts would be greatly appreciated!
Image

I assume you aren't accounting for putting all the excess cash in t bills?

See here

https://www.advisorperspectives.com/art ... res-market
A couple of follow up questions:
1. Can you explain how I put excess cash in t bills? Is this something that occurs automatically in my trading account? I'm not quite following the actual mechanics of how it works and why it isn't part of the quoted value.

2. Also, I'm not sure how I would simulate this. Do you use this rate?: https://fred.stlouisfed.org/series/DTB3 What is the total one day return from 10/3/2019 close to 10/4/2019 close for example?

Thanks for the help

One 2 year future contract is currently at roughly $216k notional value. You only need $640 in your account to actually take this position. And you must maintain that amount in your cash account at all times. If you took the remaining $215,360 and bought t bills.... your return should theoretically match just buying $216k of 2 year Treasuries.

No this doesn't happen automatically.... you'd need to decide how much to keep in your cash account to cover the daily cash settlements of your futures position.... and then go buy T- bills with the remainder.... so obviously that cash drag is going to make it so you aren't perfectly getting the returns of just holding the notes in full, as most brokers pay squat for cash. Obviously nobody is going to do such a thing... they are using futures for leverage and you'd take your remaining capital to go buy something else with a better expected return than t- bills.

In reality, you are going to get whatever the returns of the 2 year might be... minus the financing cost (usually around 3 month LIBOR). I'm guessing that's what you are seeing when just looking at the returns of futures themselves. That means they are theoretically a money loser right now (LIBOR > 2 year yield) ...... however your gains/ losses are also going to be driven by what interest rates do.

Also it appears that LIBOR hasn't caught up yet with the Fed rate cut.... and as such we are still paying closer to 2% right now. But I imagine that's a short lived thing that should resolve itself within the next couple of weeks. I don't fully understand how the Fed Funds rate cut works its way through to T bills and LIBOR... but it historically does... just some degree of lag.

Using the CASHX position in PV should get you fairly close to simulating tbills.
Thanks this makes sense but now I don't see how futures can help with leverage per the above Kessler article. If you are allocating the same amount of money ($640 margin + $215,360 Cash) how are they creating a 3.3x leveraged portfolio? The 2 yr futures plus excess cash in t bills returns 4% on average annually which is not much better than margin borrow rates so a 2x leverage in a margin account would be impractical. This would only be possible for mutual fund managers that can borrow at extremely low rates, correct?

Basically, if everything you say is accurate this whole approach with futures is wrong and the leveraged ETFs are the best approach. The 2 yr futures over the long-run returns less than 1% on average (CAGR) with a negative sharp ratio. Which is of course a terrible approach for long term investing.

I'm not following what you are saying.... you seem to be confused. You can get as much leverage as you want....I mean you can have $216k in exposure for $640.... all borrowed at the 3 month LIBOR rate. That's extreme leverage. As I said.... putting all the notional cash in T bills would equate to just buying the note outright. But nobody would do that... there would be no point.... it's only to show that the futures are efficient in following the returns of the actual notes.

You would first define what level of leverage you want..... then determine how much to set aside into T bills to back into it the right allocation. If you only wanted 3x leverage... you'd deposit roughly $70k in your account. Buy the contract for $640... and put the rest in T bills or a money market fund. Now you have $216k in exposure for $70k. You've "borrowed" the full $216k.... but you are totally offsetting the first $70k in financing cost by investing it in a comparable return instrument.

If you use CASHX in PV as a negative amount for whatever leverage you want... this should come fairly close to approximating your return from rolling futures. It's not exact, but it's close enough to give you an idea.

For 3.3x leverage

330% SHY
-230% CASHX

rascott
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Mon Oct 07, 2019 11:40 pm

BTTFutures wrote:
Mon Oct 07, 2019 10:32 pm
DonIce wrote:
Mon Oct 07, 2019 10:24 pm
BTTFutures wrote:
Mon Oct 07, 2019 10:20 pm
Thanks this makes sense but now I don't see how futures can help with leverage per the above Kessler article. If you are allocating the same amount of money ($640 margin + $215,360 Cash) how are they creating a 3.3x leveraged portfolio? The 2 yr futures plus excess cash in t bills returns 4% on average annually which is not much better than margin borrow rates so a 2x leverage in a margin account would be impractical. This would only be possible for mutual fund managers that can borrow at extremely low rates, correct?

Basically, if everything you say is accurate this whole approach with futures is wrong and the leveraged ETFs are the best approach. The 2 yr futures over the long-run returns less than 1% on average (CAGR) with a negative sharp ratio. Which is of course a terrible approach for long term investing.
The point is that you don't actually need to keep around $215,360 in cash. You COULD do that, but more likely you would just keep around a few thousand in cash, and invest the rest of your capital elsewhere. You might, for example, only have $10k of capital to begin with and you can still do this.
Yes, but the money you are investing in the 2-year future is ill-advised unless you know how interest rates will move. You are essentially 88x leveraging a terrible long term investment with a far greater stdv than returns.

No that's not true at all.... you are borrowing at the 3 month rate and lending at the 2 year rate. If the yield curve was not inverted like it is now.... this would be certain to make money.... if you assumed rates didn't move at all. If rates went down you'd make even more money. If rates went up, you could lose money.

Go look at a fund like NTSX.... this is exactly what they are doing..... putting 90% of the money into SP500.... and then using the other 10% to buy Treasury future contracts to get to a 60% bond exposure.

rascott
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Tue Oct 08, 2019 10:37 am

Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html

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Steve Reading
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Steve Reading » Tue Oct 08, 2019 9:59 pm

rascott wrote:
Tue Oct 08, 2019 10:37 am
Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html
I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson

rascott
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Tue Oct 08, 2019 10:04 pm

305pelusa wrote:
Tue Oct 08, 2019 9:59 pm
rascott wrote:
Tue Oct 08, 2019 10:37 am
Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html
I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.


I had a gut that that was correct. Just by watching how much more volatile 1 ultra bond was, vs 7 two years. I priced it at 120k. I'll trade back out tomorrow to lower duration.

Nothing like actually doing to learn. Fortunately keep making money, while all my stocks keep failing, lol.

rascott
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Wed Oct 09, 2019 12:08 pm

305pelusa wrote:
Tue Oct 08, 2019 9:59 pm
rascott wrote:
Tue Oct 08, 2019 10:37 am
Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html
I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.
Seems the way to determine how many contracts one needs is most simply defined by using DV01 then, correct?

If I want 18.5 duration on $x of exposure.... then just calculate the DV01 for that amount.... and then just accumulate enough contracts that add up to that DV01 in sum.

Example....$100k exposure @18.5 duration....0.185%*$100k = $185 Futures DV01

Then just buy whatever contacts that add up to $185 DV01.

That sound right?

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Steve Reading
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Steve Reading » Wed Oct 09, 2019 12:22 pm

rascott wrote:
Wed Oct 09, 2019 12:08 pm
305pelusa wrote:
Tue Oct 08, 2019 9:59 pm
rascott wrote:
Tue Oct 08, 2019 10:37 am
Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html
I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.
Seems the way to determine how many contracts one needs is most simply defined by using DV01 then, correct?

If I want 18.5 duration on $x of exposure.... then just calculate the DV01 for that amount.... and then just accumulate enough contracts that add up to that DV01 in sum.

Example....$100k exposure @18.5 duration....0.185%*$100k = $185 Futures DV01

Then just buy whatever contacts that add up to $185 DV01.

That sound right?
I'm a little confused what you want. If you want 18.5 duration on $x of exposure, just buy enough contracts whose settlement price add up to $x.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson

rascott
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Joined: Wed Apr 15, 2015 10:53 am

Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Wed Oct 09, 2019 1:16 pm

305pelusa wrote:
Wed Oct 09, 2019 12:22 pm
rascott wrote:
Wed Oct 09, 2019 12:08 pm
305pelusa wrote:
Tue Oct 08, 2019 9:59 pm
rascott wrote:
Tue Oct 08, 2019 10:37 am
Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html
I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.
Seems the way to determine how many contracts one needs is most simply defined by using DV01 then, correct?

If I want 18.5 duration on $x of exposure.... then just calculate the DV01 for that amount.... and then just accumulate enough contracts that add up to that DV01 in sum.

Example....$100k exposure @18.5 duration....0.185%*$100k = $185 Futures DV01

Then just buy whatever contacts that add up to $185 DV01.

That sound right?
I'm a little confused what you want. If you want 18.5 duration on $x of exposure, just buy enough contracts whose settlement price add up to $x.
You'd need some combo of contacts that are lower duration... as we saw, even one Ultra 30 year (duration 18.5) is $195k exposure.

If I only want $100k exposure at that duration (18.5) I need what? Seems like a single regular 30 yr would come close.... which is 163k exposure at 12.4 duration, DV01 = $201.

User avatar
Steve Reading
Posts: 2032
Joined: Fri Nov 16, 2018 10:20 pm

Re: Understanding using treasury futures for leverage to implement risk parity

Post by Steve Reading » Wed Oct 09, 2019 1:53 pm

rascott wrote:
Wed Oct 09, 2019 1:16 pm
305pelusa wrote:
Wed Oct 09, 2019 12:22 pm
rascott wrote:
Wed Oct 09, 2019 12:08 pm
305pelusa wrote:
Tue Oct 08, 2019 9:59 pm
rascott wrote:
Tue Oct 08, 2019 10:37 am
Can someone help me out here with futures pricing.....

Is the futures price really relevant to what ones notional exposure really is? I'm looking through the CME's Treasury Analytics tool.... and it seems to me that the cash price of the cheapest to deliver (CTD) would be your exposure.

I'm looking at the 30 year Ultra Bond future.... the clean cash price of the CTD bond is $120.... there is a conversion factor of 0.61..... which gives us the current price of the futures contract of $196. (196 x 0.61 = 120)

If I buy one contract.... is my effective exposure $120k? Or $196k? My thinking is that's it's $120k... as that's the actual cash price of the bond that I'd be delivered.

Also the implied repo rates are all over the board depending upon which note/ bond future you are looking at.... ranging from 1.68% on the Ultra Bond (25+ year) to as high as 2.83% on the normal 30 yr.

https://www.cmegroup.com/tools-informat ... ytics.html
I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.
Seems the way to determine how many contracts one needs is most simply defined by using DV01 then, correct?

If I want 18.5 duration on $x of exposure.... then just calculate the DV01 for that amount.... and then just accumulate enough contracts that add up to that DV01 in sum.

Example....$100k exposure @18.5 duration....0.185%*$100k = $185 Futures DV01

Then just buy whatever contacts that add up to $185 DV01.

That sound right?
I'm a little confused what you want. If you want 18.5 duration on $x of exposure, just buy enough contracts whose settlement price add up to $x.
You'd need some combo of contacts that are lower duration... as we saw, even one Ultra 30 year (duration 18.5) is $195k exposure.

If I only want $100k exposure at that duration (18.5) I need what? Seems like a single regular 30 yr would come close.... which is 163k exposure at 12.4 duration, DV01 = $201.
I understand. Yes, your math looks correct.

Duration/10000 = Div Contract/notional dollar exposure

So if dollar exposure desired is, say 50k at a duration of 14.5, solve for DV01 Contract (72.5) and go long contracts that add to that. In theory you could sell contracts too in order to get more precise.

Two things to keep in mind:
1) Whike different contract set-ups might have the same overall DV01 as above, it's not clear to me that they would have the same reward characteristics. That's because the yield curve isn't linear. So there are contracts that have higher yield per unit of duration (this you know already).

2) DV01 of contracts changes with time, especially if the CTD changes. So I imagine you'd want to stay on top of this. These positions do not have a zero Gamma so to speak.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson

rascott
Posts: 2147
Joined: Wed Apr 15, 2015 10:53 am

Re: Understanding using treasury futures for leverage to implement risk parity

Post by rascott » Wed Oct 09, 2019 2:28 pm

305pelusa wrote:
Wed Oct 09, 2019 1:53 pm
rascott wrote:
Wed Oct 09, 2019 1:16 pm
305pelusa wrote:
Wed Oct 09, 2019 12:22 pm
rascott wrote:
Wed Oct 09, 2019 12:08 pm
305pelusa wrote:
Tue Oct 08, 2019 9:59 pm


I imagine you want to know your notional exposure in regards to how much term risk you're exposed to right?

I believe the contract cost is the correct one (195k in this example). The reason is that rate changes that affect the CTD are magnified (by the CF) onto your contract (which gets marked-to-market). This is easy to confirm by looking at FUTURES DV01 (CASH DV01/TCF); which refers to how many dollars you lose/gain in your long futures position from a basis point change in interest rates.

This quantity is 361.16 right now. So a +0.01% change in interest rates inflict a 361.16/195k = 0.185% loss on your contract. In other words, a 1% rise in interest rates causes a 18.5% loss on your contract (a loss of 36k that you will have to cover that day). Hence, it is as though you have exposure to 195k in bonds with a duration of 18.5 years.
Seems the way to determine how many contracts one needs is most simply defined by using DV01 then, correct?

If I want 18.5 duration on $x of exposure.... then just calculate the DV01 for that amount.... and then just accumulate enough contracts that add up to that DV01 in sum.

Example....$100k exposure @18.5 duration....0.185%*$100k = $185 Futures DV01

Then just buy whatever contacts that add up to $185 DV01.

That sound right?
I'm a little confused what you want. If you want 18.5 duration on $x of exposure, just buy enough contracts whose settlement price add up to $x.
You'd need some combo of contacts that are lower duration... as we saw, even one Ultra 30 year (duration 18.5) is $195k exposure.

If I only want $100k exposure at that duration (18.5) I need what? Seems like a single regular 30 yr would come close.... which is 163k exposure at 12.4 duration, DV01 = $201.
I understand. Yes, your math looks correct.

Duration/10000 = Div Contract/notional dollar exposure

So if dollar exposure desired is, say 50k at a duration of 14.5, solve for DV01 Contract (72.5) and go long contracts that add to that. In theory you could sell contracts too in order to get more precise.

Two things to keep in mind:
1) Whike different contract set-ups might have the same overall DV01 as above, it's not clear to me that they would have the same reward characteristics. That's because the yield curve isn't linear. So there are contracts that have higher yield per unit of duration (this you know already).

2) DV01 of contracts changes with time, especially if the CTD changes. So I imagine you'd want to stay on top of this. These positions do not have a zero Gamma so to speak.
Thanks that was helpful

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Lock » Mon Nov 25, 2019 11:57 am

When implementing a levered futures strategy with a rebalancing component, is anyone else having difficulty with the line found between taxable and traditional/roth assets? For example, most of my equities are in tax sheltered accounts, whereas my futures contracts are in taxable accounts. I am concerned that the line and immobility of these two "compartments" could lead to rebalancing problems.

This specific problem has yet to occur, but I did catch a glimpse of the possibility with the bond blow-off this fall (i.e., I was running out of taxable equities to rebalance into levered treasuries; equities were trapped in tax sheltered accounts and I really didn't want to pick up bonds in tax sheltered).

Curious as to whether others have encountered this or strategies to mitigate these problems.

Cheers.

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by EfficientInvestor » Mon Nov 25, 2019 12:56 pm

Lock wrote:
Mon Nov 25, 2019 11:57 am
When implementing a levered futures strategy with a rebalancing component, is anyone else having difficulty with the line found between taxable and traditional/roth assets? For example, most of my equities are in tax sheltered accounts, whereas my futures contracts are in taxable accounts. I am concerned that the line and immobility of these two "compartments" could lead to rebalancing problems.

This specific problem has yet to occur, but I did catch a glimpse of the possibility with the bond blow-off this fall (i.e., I was running out of taxable equities to rebalance into levered treasuries; equities were trapped in tax sheltered accounts and I really didn't want to pick up bonds in tax sheltered).

Curious as to whether others have encountered this or strategies to mitigate these problems.

Cheers.
I just avoid the issue entirely by trying to achieve risk parity with each of my separate (taxable and tax-sheltered) accounts. If one of your accounts is too small to use futures, you could consider using options or leveraged ETFs until the account is large enough. But as long as you have at least $30k in each account, you should be able to do a mix of equities and 2-year treasury futures in each account (depending on the amount of leverage you are trying to achieve).

kim.gold
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by kim.gold » Sun Jan 19, 2020 8:34 am

I am looking into a 60% stock / 90% bond with 50% leverage portfolio https://www.portfoliovisualizer.com/bac ... ion3_1=-50

Let's assume that I want to put $100k into this.

- I would buy $60k of VFINX (or VTI)
- $90k shold go into futures equivalent to VUSTX

VUSTX has a duration of 17.4 and a DV01 of 156.6 for $90k. Looking at the treasury-analytics tool, I have ZN with a 82.5592788 DVI. That means that 2 ZN contracts with 165 DVI, is a good aproximation for $90k of VUSTX.

Is my calculation correct?

Wondering if anyone does this for real and can help. Thanks.

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by guyinlaw » Thu Feb 13, 2020 5:17 pm

DonIce wrote:
Mon Oct 07, 2019 10:37 pm
BTTFutures wrote:
Mon Oct 07, 2019 10:32 pm
Yes, but the money you are investing in the 2-year future is ill-advised unless you know how interest rates will move. You are essentially 88x leveraging a terrible long term investment with a greater stdv than returns.
You have to look at it from the standpoint of an overall portfolio. Treasuries have a low (or even negative) correlation with equities. By adding a treasury future position to an equity-heavy portfolio, you may be able to smooth out the ride without lowering expected return. So instead of being 100% equity, you might be 90% equity and 10% cash as collateral for 1000% in 2-year futures, for example.
Please share your experience if you are holding treasury futures..

I hold 2y and 5Y Treasury Futures.. The main reason for holding treasury Futures is because they have a negative correlation with stocks. The same reason for TMF with UPRO in the "excellent adventure."

The paper below suggests 2y treasury (or eurodollar) is best due to yield curve carry.. Are there other sources that discuss this and risks associated with this?

https://coexpartnersaig.files.wordpress ... -carry.pdf
Why limit the horizon to two years?
One reason to limit our horizon to two years stems from what we continue to learn about the behavior of carry in the U.S. dollar market. For whatever reasons, we have always found that most of the performance – both absolute and risk adjusted – is produced by the front end of the curve. These results are actually reinforced by the Sharpe ratio produced by the four Treasury contracts (See Exhibit 4). At first glance, it seems that all four contracts – from two-year notes to long-term Treasury bonds – produced satisfactory risk-adjusted returns. But if you try to improve the performance of the two-year note contract by adding five-year, 10-year, or long-term bond futures, you find that you cannot. For example, given the 0.92 correlation between returns on the two-year and five-year contracts, the five-year contract would need to deliver a Sharpe ratio of at least 0.85 before adding them to a portfolio of two-year contracts would produce a better risk-adjusted return. As it was, the five-year contract’s Sharpe ratio of 0.77 did not meet this minimum requirement. The same is true for the 10-year and long-term bond futures contracts.
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Time is your friend; impulse is your enemy. - John C. Bogle

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Uncorrelated » Thu Feb 13, 2020 5:32 pm

The sharpe ratio on lower duration bonds is much higher than the sharpe ratio on high duration bonds, this is caused by a beta-against-beta effect, sometimes called high-beta or low-volatility anomaly. This effect occurs in all asset classes.

However, it is not clear whether using shorter duration treasures at higher leverage is a better option than long duration treasuries at shorter leverage. Since execution and friction costs are proportional to leverage. Some users buy short duration treasuries and sell long duration treasuries in order to capitalize on the bet against beta effect, but I'm far from convinced such a strategy survives trading costs. I have not seen any analysis on trading costs, but it's safe to assume trading costs are a large part of the reason that the bet-against-beta anomaly exists in the first place.

Also, I would be very careful when using the assumption that bonds have negative correlation with stocks in your portfolio. Historically that has and hasn't been the case, depending on the time period tested.

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by syalams » Thu May 28, 2020 1:39 pm

Thanks to DonIce for starting this topic and the excellent responses so far.

I have an academic economics education but am a fairly new investor; a lot of the theory of (leveraged) risk-parity investment makes perfect sense to me, but I'm getting bogged down in the practical implementation aspects. As such, I'm writing out the totality of my understanding so far, which may help other newcomers to this thread. I also have some questions; for a few of them I think I know the answer to already but want to check my knowledge, whereas for a few others I am genuinely in the dark (in bold).

On page 3 of this thread, EfficientInvestor posted a link to this:

https://www.glynholton.com/notes/capital_market_line/

which makes sense to me. Essentially, the argument is that the risk-parity portfolio is the 'super efficient portfolio', obtaining the maximum possible Sharpe ratio within the achievable region. This is because of the inverse relationship between stocks and bonds, which is borne out historically and should be expected to continue in the future given the Fed's reaction function (raising rates when the economy is doing well).

Question (1): Assume equities and bonds (treasuries) are uncorrelated and equities have 3x the return and 3x the standard deviation as bonds. Does this imply the (unleveraged) super-efficient portfolio is 25/75 equities/treasuries? If not, how do we figure out what the super-efficient(risk-parity) portfolio is?

Question (2): An investor might have larger risk appetite. Following the principle that we should lever up the super-efficient portfolio at the risk free rate, an investor might instead want 50/150, or 75/225, or 90/270 exposure to stocks/bonds. Regardless, given the super-efficient portfolio in (1), it should always be in this 1:3 ratio, correct?

Question (3): The majority of this thread has discussed leveraged bond exposure through treasury futures, while leaving the equity potion in simple buy-and-hold stocks or equity ETFs. For example, an investor with $100k of capital might purchase treasury futures with a nominal value of ~$270k, at a margin maintenance requirement of <$10k, and invest the remaining $90k in equities. This achieves a 90/270 exposure without using equity futures. Some questions about obtaining leverage in this manner:

(3a): Using treasury futures is one of the best ways for a normal investor to borrow at the risk-free rate. Is this correct?
(3b): Using treasury futures instead of equity futures has two advantages: it's not possible to lever to the correct ratio using just equity futures and unlevered treasuries, and treasury futures benefit from the tax treatment of futures when the contracts are sold. Correct?
(3c): How does the term of the treasury futures affect the nominal exposure? I've seen mentions in this thread of how it's necessary to buy multiple short-term futures to get the same nominal exposure as one longer-term future contract, but I don't understand why this is the case? In general, for a given amount of desired nominal exposure (as calculated in question 2), how does one construct the required position in futures contracts?

Note: I don't sufficiently understand eurodollar strips, and I'm not sure how they can be used to also get cheap leverage, but I'm not super-invested in learning at this point - I intend to use short to medium (2-10 year) treasury futures. Although, please advise me if I'm overlooking something here (e.g., significant transaction costs, tax implications?)

Moving on to questions about practice instead of theory (and showing off my lack of experience with the mechanics of trading). For simplicity, ignore diversification issues and assume the only asset classes are S&P and treasuries.

Question (4): In practice, to get leveraged exposure to treasuries an investor would first decide what amount of nominal exposure and what term futures contracts are required (as in 3c). How does he put it into practice? I've done some reading into how futures contracts are quoted and traded, but am still a little confused. Would the following be how to go about doing it?
Suppose it's June 2020 and the investor wants leveraged (nominal) exposure of $1million through futures on 10-year treasuries. He would buy X(how many?) Sep-2020 futures, symbol /ZNU20. Would his nominal exposure then be X * $100,000? What if he was using 5-year or 2-year notes, how would this change, or what number of contracts would need to be purchased?

The price of /ZNU20 is quoted as 138'200 - i.e., $138,625 today for September delivery of $100,000 in face value of 10-year notes - but because margin requirements are exceedingly low for treasuries, the investor needs to only maintain about $3000 in cash per contract purchased.

(Side note: since the price is >100, does this indicate the market expects falling interest rates and low inflation?)

When the expiry for the September contracts approaches, the investor wants to roll these over to the December contracts, /ZNZ20. When is the ideal time, in terms of market liquidity, to sell /ZNU20 and buy /ZNZ20? What else should the investor be careful about, instead of blindly rolling the contracts every 3 months?

In the meantime, the rest of the investor's funds are in buy-and-hold equities. If the investor is targeting a 90/270 equity/bond split, this should be around $333,000 (1/3 of the $1million in nominal treasury exposure). These equities can be all S&P500 ETFs, or diversified into foreign and EM, etc., up to the investor's preference. But this part is bog-standard buy-and-hold Bogleheads investing.
Question (5): How does rebalancing work? It seems like the nominal treasury exposure is going to be in multiples of $100,000. How does the investor rebalance to hit the desired equity/bond split? And as the investor adds cash to the account, how does he calculate the leverage ratio of the portfolio?

Question (6): How can the investor achieve greater than 100% equity exposure? Suppose the desired exposure is 125/375, for a total of 5x leverage. Would he use stock futures such as S&P E-mini/micro E-mini (/ES and /MES) and do the same as for the treasuries? In other words, is the following exposition correct?
E.g., The investor has $150k in capital and wants a 200/600 exposure (this extreme leverage is only to make the math easier). This implies nominal exposure of $300k to equities and $900k to treasuries.

Equity side: S&P index is trading at 3000 in June 2020. Investor can buy either E-mini or micro E-mini. So he would purchase either 2 contracts of /ESU20 (S&P E-mini, Sep. delivery) or 20 contracts of /MESU20 (S&P micro E-mini, Sep. delivery). In either case, the margin requirement is around $26k.

Bond side: As in question (4), but obtaining a nominal exposure of $900k. This will probably require about $27k in margin requirement.

Come August, the investor would simply rollover both contracts to the December expiry contracts. I.e., sell ESU20 and buy ESZ20, sell ZNU20 and buy ZNZ20.

The investor has $150k in capital, and about $53k in margin requirement. All the $150k is held in the account, giving $97k in cash buffer for margin maintenence, held in money market or sweep.
Question (6b): Alternatively, given the extremely low margin rates available (around 1% on interactive brokers), is it simpler to just buy a S&P ETF on margin?

Question (7): In the above scenario, how does the investor monitor the amount of leverage? When is the right time to buy more E-mini/treasury future contracts?

Question (8): How should I be thinking about what a 'safe' amount of leverage is? Even in the extreme 8x leverage scenario in question (6) with 8x leverage, the investor has nearly 1/3 of the account as a buffer. Would a 5x leverage, 125/375 portfolio be 'too much' even for a young investor with high risk appetite? Otherwise, if there's too much risk in going more than 100% equity, it seems easier to just avoid the trouble of rebalancing and put the money in NTSX and forget about it.

Thanks for all the great thoughts upthread, and thank you in advance to future replies!

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Uncorrelated » Thu May 28, 2020 4:14 pm

syalams wrote:
Thu May 28, 2020 1:39 pm
Question (1): Assume equities and bonds (t-bills) are uncorrelated and equities have 3x the return and 3x the standard deviation as bonds. Does this imply the (unleveraged) super-efficient portfolio is 25/75 equities/t-bills? If not, how do we figure out what the super-efficient(risk-parity) portfolio is?
By definition, all portfolio's that are mixtures of t-bills (the risk free asset) and equities are efficient. In order to select an inefficient portfolio, you need more than 2 assets. Such as t-bills, bonds and equities.

The risk parity portfolio is on the mean-variance efficient frontier under the specific assumption that all assets have the same sharpe ratio. This assumption is false.

The efficient frontier idea can be extended to arbitrary numbers of assets. Commonly, risk factors such as market, size and value are used instead of asset classes. There is great debate to the extent one can expect these risk factors to persist in the future, as well as the question who should tilt. In a multi-factor world, all possible portfolio's are efficient, but a subset of portfolio's is mean-variance efficient.

For some theoretical background information you can refer to "Portfolio advice for a multifactor world" by John H. Cochrane.

My preferred approach to find the efficient portfolio for mean-variance investors is with mean-variance optimization. It appears this requires you to code your own. You may want to start here: viewtopic.php?f=10&t=305919 for some mathematical background that is required to select the correct ratio of stocks and bonds for your specific needs.
Question (2): An investor might have larger risk appetite. Following the principle that we should lever up the super-efficient portfolio at the risk free rate, an investor might instead want 50/150, or 75/225, or 90/270 exposure to stocks/bonds. Regardless, it should always be in this 1:3 ratio, correct?
In theory yes. In practice leverage isn't free, bonds can mean many different things, real investors are leverage constrained. It's not that simple.

According to research by me, leveraging equities is more expensive than leveraging treasuries. Although it is not possible to observe the borrow cost directly, I confirmed this using multiple different sources. The reason for this difference is not yet known.
viewtopic.php?p=4884654#p4884654

For equities you're looking at approx 0.5% above the risk free rate, treasury futures approx 0%, in some cases slightly negative. Because leveraging equities costs more, the optimal play for low-leverage portfolio's is to leverage treasuries and obtain as much as possible of your equity exposure with real unleveraged funds.
Question (3): The majority of this thread has discussed leveraged bond exposure through treasury futures, while leaving the equity potion in simple buy-and-hold stocks or equity ETFs. For example, an investor with $100k of capital might purchase treasury futures with a nominal value of ~$270k, at a margin maintenance requirement of <$10k, and invest the remaining $90k in equities. This achieves a 90/270 exposure without using equity futures. Some questions about obtaining leverage in this manner:

(3a): Using treasury futures is one of the best ways for a normal investor to borrow at the risk-free rate. Is this correct?
(3b): Using treasury futures instead of equity futures has two advantages: it's not possible to lever to the correct ratio using just equity futures and unlevered treasuries, and treasury futures benefit from the tax treatment of futures when the contracts are sold. Correct?
(3c): How does the term of the treasury futures affect the nominal exposure? I've seen mentions in this thread of how it's necessary to buy multiple short-term futures to get the same nominal exposure as one longer-term future contract, but I don't understand why this is the case? In general, for a given amount of desired nominal exposure (as calculated in question 2), how does one construct the required position in futures contracts?

Note: I don't sufficiently understand eurodollar strips, and I'm not sure how they can be used to also get cheap leverage, but I'm not super-invested in learning at this point - I intend to use short to medium (2-10 year) treasury futures. Although, please advise me if I'm overlooking something here (e.g., significant transaction costs, tax implications?)
3a depends on the rest of your portfolio and your total net worth. If your net worth is high enough it is probably the cheapest and most flexible option.
3b Don't know about the tax impact. The second part of the question is unanswerable because no "correct" ratio of equities to treasuries exist unless borrowing is free.
3c I think that refers to the normalized term (duration) exposure, rather than the nominal exposure. Generally, users are targeting "X years of duration exposure", rather than "a dollar amount of bond exposure". This is somewhat a leaky model, a portfolio of leveraged 2-year bonds behaves different than a portfolio of 10-year bonds leveraged to the same duration exposure.

The advantage of short term treasuries is that they have a higher sharpe ratio, the disadvantage of short term treasuries is that you need to leverage more to obtain the same duration exposure. Calculating the optimal amount of leverage for short term treasuries is very sensitive on the assumed borrowing costs and expected return, neither of which can be estimated which much accuracy.

Moving on to questions about practice instead of theory (and showing off my lack of experience with the mechanics of trading). For simplicity, ignore diversification issues and assume the only asset classes are S&P and treasuries.

Question (4): In practice, to get leveraged exposure to treasuries an investor would first decide what amount of nominal exposure and what term futures contracts are required (as in 3c). How, how does he put it into practice? I've done some reading into how futures contracts are quoted and traded, but am still a little confused. Would the following be how to go about doing it?
Suppose it's June 2020 and the investor wants leveraged (nominal) exposure of $1million through futures on 10-year treasuries. He would buy X(how many?) Sep-2020 futures, symbol /ZNU20. Would his nominal exposure then be X * $100,000? What if he was using 5-year or 2-year notes, how would this change, or what number of contracts would need to be purchased?

The price of /ZNU20 is quoted as 138'200 - i.e., $138,625 today for September delivery of $100,000 in face value of 10-year notes - but because margin requirements are exceedingly low for treasuries, the investor needs to only maintain about $3000 in cash per contract purchased.

(Side note: since the price is >100, does this indicate the market expects falling interest rates and low inflation?)

When the expiry for the September contracts approaches, the investor wants to roll these over to the December contracts, /ZNZ20. When is the ideal time, in terms of market liquidity, to sell /ZNU20 and buy /ZNZ20? What else should the investor be careful about, instead of blindly rolling the contracts every 3 months?

In the meantime, the rest of the investor's funds are in buy-and-hold equities. If the investor is targeting a 90/270 equity/bond split, this should be around $333,000 (1/3 of the $1million in nominal treasury exposure). These equities can be all S&P500 ETFs, or diversified into foreign and EM, etc., up to the investor's preference. But this part is bog-standard buy-and-hold Bogleheads investing.
I have no experience trading futures but that sounds about right. The contract size can be observed here: https://www.cmegroup.com/trading/why-fu ... tures.html

The average roll can be observed with the pace of roll tool: https://www.cmegroup.com/trading/intere ... oftheroll/. A free account might be necessary to use the tool. I believe it is customary to roll between two weeks and a few days before contract end.

In very rare cases (once every few years) the liquidity can be poor during the roll period, which can result in higher trading costs. For example, this happened during 9/11 and during the massive equities sell-off last march/april.
Question (5): How does rebalancing work? It seems like the nominal treasury exposure is going to be in multiples of $100,000. How does the investor rebalance to hit the desired equity/bond split? And as the investor adds cash to the account, how does he calculate the margin multiplier of the portfolio?
Never exceed your risk tolerance. As long as you don't do that, rebalancing when you roll is probably sufficient.

An alternative solution is to purchase TMF (3x leveraged 20 year treasuries ETF) instead.
Question (6): How can the investor achieve greater than 100% equity exposure? Suppose the desired exposure is 125/375, for a total of 5x leverage. Would he use stock futures such as S&P E-mini/micro E-mini (/ES and /MES) and do the same as for the treasuries? In other words, is the following exposition correct?
E.g., The investor has $150k in capital and wants a 200/600 exposure (this extreme leverage is only to make the math easier). This implies nominal exposure of $300k to equities and $900k to treasuries.

Equity side: S&P is trading at $300 in June 2020. Investor can buy either E-mini or micro E-mini which are both priced at 3k (I'm confused as to how futures prices are quoted here). So he would purchase either 6 contract of /ESU20 (S&P E-mini, Sep. delivery) or 60 contracts of /MESU20 (S&P micro E-mini, Sep. delivery). In either case, the margin requirement is around $80k.

Bond side: As in question (4), but obtaining a nominal exposure of $900k. This will probably require about $27k in margin requirement.

Come August, the investor would simply rollover both contracts to the December expiry contracts. I.e., sell ESU20 and buy ESZ20, sell ZNU20 and buy ZNZ20.

The investor has $150k in capital, and about $107k in margin requirement. All the $150k is held in the account, giving $43k in cash buffer for margin maintenence, held in money market or sweep.
A micro S&P500 future is 5x the index. A mini future is 50x the index. One can also leverage with options, which always trade in multiples of 100. The availability for international indices does suck. As a possible compromise, you can obtain US and treasury exposure with futures and international exposure with physical ETF's.

options and futures should cost the same, depending on your leverage target leveraged ETF's might be worthy of consideration. With both futures and options, the leverage increases when stocks go down which is very bad if you're not paying attention. I have calculated that above ~2.5x leverage, a 3x daily leveraged ETF results in higher certainty equivalent return than monthly rebalanced options or futures. The analysis above assumes all cash collateral is invested at t-bill rates.

Question (7): In the above scenario, how does the investor monitor the amount of leverage? When is the right time to buy more E-mini/treasury future contracts?
Same as treasuries. Rebalance regularly. Don't exceed your risk tolerance. This means you should rebalance quickly when markets go down.

It's tempting to not rebalance when stocks go down. Don't do that. This basically guarantees that you will get a margin call eventually. Even if that doesn't happen, it's suboptimal in the sense that there are strategies that offer higher return with equivalent risk. (the closer you are to constant leverage, the better the mean-variance optimality of your trading strategy is).

Question (8): How should I be thinking about what a 'safe' amount of leverage is? Even in the extreme 8x leverage scenario in question (6) with 8x leverage, the investor has nearly 1/3 of the account as a buffer. Would a 5x leverage, 125/375 portfolio be 'too much' even for a young investor with high risk appetite? Otherwise, if there's too much risk in going more than 100% equity, it seems easier to just avoid the trouble of rebalancing and put the money in NTSX and forget about it.
Based on my research (link), there is essentially no limit to the maximum amount of usable leverage. However due to practical considerations (higher leverage requires more frequent rebalancing), and a regulatory ban on leveraged ETF's above 3x, it appears that going above 3x callable equity leverage is impractical.

There are very good reasons to leverage. I believe NTSX is a good product for users with a risk tolerance supporting approximately 100% equities, but unsuited for users seeking higher return.

Be careful to avoid recency bias. Expected bond returns are much lower than the bond returns from the last 50 years. Despite what risk parity advocates are telling you, with my return assumptions most of the risk you take should be on the equity side.

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by syalams » Thu May 28, 2020 5:42 pm

Uncorrelated, thanks for your detailed reply. Looks like I still have quite a bit to learn...

With regard to mean-variance optimization, I definitely made some implicit assumptions in my previous post. For now, make the following simplifying assumption: the investor is constrained (by knowledge, effort, time, etc.) and is either unable or unwilling to sucesfully guess at risk factors or the correlation structure across assets.

Given the constraint, does it make sense for the investor to just view his options as between a single risky asset (e.g. the basket of all risky assets) and a riskless asset (e.g. treasuries)? Then, does it follow that he should simply construct a '2-fund portfolio', depending on his risk preference/curvature of his utility function?

For now, use the terminology that risky asset = equities. If the investor is simply making a choice of what split to make between equities and the riskless asset, doesn't that imply that the Sharpe ratio of all possible portfolios (under these constraints) is constant? I suppose this relates to what you said:
The risk parity portfolio is on the mean-variance efficient frontier under the specific assumption that all assets have the same sharpe ratio. This assumption is false.
This assumption is false, but if an individual investor is unable or unwilling to identify real risk factors/the correlation structure between risky assets, then the portfolio split between a basket of all the risky assets and the risk-free asset is an efficient solution to the constrained utility maximization problem for some γ, and each value of γ corresponds to exactly one such portfolio.

The bone of contention here is how reasonable are the constraints I've put on this investor. I think they're not too unreasonable for a Boglehead that has put in the effort to understand diversifiable vs. undiversifiable risk, but doesn't want to put in much more effort than is required to understand why a 2-fund portfolio of a 3-fund portfolio works. I.e., an investor who thinks (given the extensive and unsettled debate about risk factors) that the best they can do is assume all risky assets are uncorrelated. I'm happy to hear why this is a terrible assumption, and why there are proven risk factors that can improve the mean-variance of a portfolio easily.


----------------

Separately: I'm still unclear as to why investors target a duration exposure. What does it mean to have a particular duration exposure, and how does that 'convert' to a dollar exposure? And how are the other posters/practitioners in this thread deciding what is the 'right' amount of duration exposure for a given amount of equity exposure?

And finally,
There are very good reasons to leverage. I believe NTSX is a good product for users with a risk tolerance supporting approximately 100% equities, but unsuited for users seeking higher return.

Be careful to avoid recency bias. Expected bond returns are much lower than the bond returns from the last 50 years. Despite what risk parity advocates are telling you, with my return assumptions most of the risk you take should be on the equity side.
Maybe I should just invest in NTSX at 1.25 or 1.5x leverage with a margin account. M1 finance has a margin maintenance requirement of 25% and rates from 2-3.5%. It would make this a lot simpler :P

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by typical.investor » Thu May 28, 2020 7:27 pm

syalams wrote:
Thu May 28, 2020 5:42 pm

Separately: I'm still unclear as to why investors target a duration exposure. What does it mean to have a particular duration exposure, and how does that 'convert' to a dollar exposure?
Duration is sensitivity to interest rate changes. The idea is that greater duration exposure can help you offset equity volatility. For example, in the recent crash, rates were dropped to stimulate the economy. Longer duration bonds generally provide more ballast as you can see in the following:

Image
syalams wrote:
Thu May 28, 2020 5:42 pm
And how are the other posters/practitioners in this thread deciding what is the 'right' amount of duration exposure for a given amount of equity exposure?


I looked at backtests*** to offset 3X equity exposure. 3X intermediate didn't provide enough protection in my opinion in major equity drops. 3X long was better for that.

*** treasury backtests need to viewed realistically I think. Until the '80s, treasuries were callable which defeats their use as ballast and inflation wasn't really targeted by the Fed (which focused more on employment which turned to push inflation too high and ultimately hurt employment). And if you look at treasuries from the 80's, they are starting from a very high rate and sliding downward - great for returns but not really predictive of the future.

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Uncorrelated » Sat May 30, 2020 3:33 am

syalams wrote:
Thu May 28, 2020 5:42 pm
Uncorrelated, thanks for your detailed reply. Looks like I still have quite a bit to learn...
It makes sense to simplify the problem to something with only a risky asset and a riskless asset. This approach is employed by some people in the lifecycle investment thread. The argument is that limiting yourself to two assets simplifies the math and makes the strategy less sensitive to estimation errors. The disadvantage is that it's likely not optimal and there is potential for some calculation errors. iirc Ayres and Nalebuff use 10-year treasuries as the risk free asset in their models which appears to result in an over-estimation of borrow costs (at 3x leverage they assume you pay 3x the borrow cost, but with the right portfolio you pay it only twice).

The sharpe ratio is generally measured with t-bills as the risk-free asset, if you are choosing portfolio's with treasuries and equities, not all portfolio's have the same sharpe ratio. I think the sharpe ratio is a pretty useless measure that does not correspond to maximizing any particular utility function. If you perform an mean-variance optimization with the assumption all assets have the same sharpe ratio, you will find a risk parity portfolio (if you ignore borrow costs and different bond durations).

There is value in reducing complexity by ignoring some of the risk factors with low statistical confidence, but I don't see the value in assuming equities and treasuries have the same sharpe ratio. If you want to reduce complexity, it seems like a better idea to just throw out the idea of leveraging treasuries altogether. Portfolio optimization is complex. If you don't have a good enough view on the theory and data to know which assumptions are reasonable to make it's very likely that you will shoot yourself in the foot.

Risk parity is one of those things that novices use without really understanding the (unreasonable) assumptions that are hidden inside.


Separately: I'm still unclear as to why investors target a duration exposure. What does it mean to have a particular duration exposure, and how does that 'convert' to a dollar exposure? And how are the other posters/practitioners in this thread deciding what is the 'right' amount of duration exposure for a given amount of equity exposure?
Duration measures the sensitivity to interest rate risk. A 3x leveraged 10-year treasury bond will have the same duration as a 30-year treasury bond. If the interest rate changes by 1%, portfolio's will change a similar amount.

This is only an approximation because a 3x leveraged 10-year treasury bond has significantly higher sharpe than a 30-year treasury bond. Who buys the 30-year bond then? Leverage constrained investors and pension funds that have nominal liabilities far into the future.

The declining sharpe ratio as bond duration increases is known as the bet-against-beta effect.
And finally,
There are very good reasons to leverage. I believe NTSX is a good product for users with a risk tolerance supporting approximately 100% equities, but unsuited for users seeking higher return.

Be careful to avoid recency bias. Expected bond returns are much lower than the bond returns from the last 50 years. Despite what risk parity advocates are telling you, with my return assumptions most of the risk you take should be on the equity side.
Maybe I should just invest in NTSX at 1.25 or 1.5x leverage with a margin account. M1 finance has a margin maintenance requirement of 25% and rates from 2-3.5%. It would make this a lot simpler :P
Margin accounts are usually pretty costly. In addition to that, if you're only targeting a small amount of leverage, factor investing might be a better deal than leverage.

occambogle
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by occambogle » Sat May 30, 2020 4:18 am

Uncorrelated wrote:
Sat May 30, 2020 3:33 am
Duration measures the sensitivity to interest rate risk. A 3x leveraged 10-year treasury bond will have the same duration as a 30-year treasury bond. If the interest rate changes by 1%, portfolio's will change a similar amount.

This is only an approximation because a 3x leveraged 10-year treasury bond has significantly higher sharpe than a 30-year treasury bond. Who buys the 30-year bond then? Leverage constrained investors and pension funds that have nominal liabilities far into the future.

The declining sharpe ratio as bond duration increases is known as the bet-against-beta effect.
That's interesting. I'd played in PV with introducing a portion of TYD into Hedgefundie type portfolios and it's clear it can increase Sharpe and decrease STDev compared to TMF only. And the comparison with EDV is interesting, though noting EDV has lower expense ratio and lower turnover:

TYD vs EDV

What I can't get my head around is while the effective duration may be the same... isn't the re-investment risk/ability (and therefore ability to adjust to e.g. rising rates) different between the 3x 10-year vs the 30-year?

What are the implications of this for portfolios using long treasuries to partially balance equity risk? And why does TYD have such a tiny AUM and volume? Is it just the implementation that's bad?

occambogle
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by occambogle » Sat May 30, 2020 4:36 am

syalams wrote:
Thu May 28, 2020 5:42 pm
Maybe I should just invest in NTSX at 1.25 or 1.5x leverage with a margin account. M1 finance has a margin maintenance requirement of 25% and rates from 2-3.5%. It would make this a lot simpler :P
I've no idea if leveraging NTSX on margin is optimal (or not) compared to using more-leveraged ETFs in the first place. But if one were to do it it would seem advantageous to mix it with EDV to keep the volatility down....

(Jul 2011 - Apr 2020, ignoring margin costs)
P1: NTSX simulated
P2: NTSX SIM 150%, CASH -50%
P3: NTSX SIM 120%, EDV 30%, CASH -50%

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Uncorrelated » Sat May 30, 2020 5:17 am

occambogle wrote:
Sat May 30, 2020 4:18 am
Re-investment risk is not a thing unless you use bonds to match nominal or real liabilities completely, which almost nobody does. I would argue nobody should do that either, if you're at the age where it's possible to cover all your future liabilities, annuities are just a better deal.

It's very difficult to draw conclusions from portfolio visualizer. It just doesn't go back far enough. If you'll use simba's backtesting spreadsheet which contains data since 1955, you'll see that 3x ITT has higher returns and lower volatility than EDV (3.78%/20% vs 3.23%/24%, after expenses). This matches your observations, but that's mostly a coincidence. When estimated starting at 1934, ITT (7-10 year) has a sharpe ratio of .29, LTT (20 year) has a sharpe ratio of .20, and EDV has a sharpe ratio of .14. My mean variance optimizer almost always recommends total bond market and taking the risk on the equity side. For reference, equities have a sharpe ratio of .47 over the same time period.

TYD is a difficult product to use. Most investors suffer from recency bias which makes TMF look much more attractive. It has a high expense ratio, made worse by the fact you need more of it to reach the same duration as with TMF. The fact that you need more of it also hurts the equity side, I mentioned that leveraging equities is expense and using TMF just leaves more room for unleveraged equities (of factor funds, if you're into that). TYD is not a bad product in isolation but it's extremely difficult to put it to good use in a portfolio. The space argument also applies to EDV.

I tested many different bond funds in my mean-variance optimizer and the only ones that are used are total bond market and TMF. I have not tested treasuries, but I suspect that a mixture of different bond durations (like NTSX) is optimal. The problem with treasuries is that you can't implement it as efficient as the institutional investors because most brokers require cash collateral (institutional investors can use t-bills as collateral). Still, at today's rates beating TMF with treasuries does not appear to be particularly difficult.

Again don't use portfolio visualizer to draw conclusions about bond funds. You need data going back much farther than 1980 to arrive at sensible estimates.

occambogle
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by occambogle » Sat May 30, 2020 5:44 am

Uncorrelated wrote:
Sat May 30, 2020 5:17 am
Re-investment risk is not a thing unless you use bonds to match nominal or real liabilities completely, which almost nobody does. I would argue nobody should do that either, if you're at the age where it's possible to cover all your future liabilities, annuities are just a better deal.
I don't pretend to understand this. But say for the sake of argument we assumed TYD and EDV had exactly the same duration, and we bought $1000 of each today, and interest rates rose tomorrow. After 10 years wouldn't TYD have replaced all those lower-rate treasuries with higher rate ones... while EDV would only have done so after 30 years? Or is that not how it works?
Uncorrelated wrote:
Sat May 30, 2020 5:17 am
Again don't use portfolio visualizer to draw conclusions about bond funds. You need data going back much farther than 1980 to arrive at sensible estimates.
Is PV unreliable for bond funds only because of short periods and recency bias, or is it actually not accurately reflecting the funds somehow?
I don't doubt you... PV is just so much more user-friendly than spreadsheets.
Uncorrelated wrote:
Sat May 30, 2020 5:17 am
My mean variance optimizer almost always recommends total bond market and taking the risk on the equity side. For reference, equities have a sharpe ratio of .47 over the same time period.
But for balancing equity-heavy portfolios.... aren't LTT treasuries better than TBM because of the lower correlation? Doesn't using something like EDV actually allow you to take more risk on the equities side, through higher % equities and lower % bonds, because the LTTs are compensating in downturns more significantly/effectively than TBM?
Uncorrelated wrote:
Sat May 30, 2020 5:17 am
I tested many different bond funds in my mean-variance optimizer and the only ones that are used are total bond market and TMF. I have not tested treasuries, but I suspect that a mixture of different bond durations (like NTSX) is optimal. The problem with treasuries is that you can't implement it as efficient as the institutional investors because most brokers require cash collateral (institutional investors can use t-bills as collateral). Still, at today's rates beating TMF with treasuries does not appear to be particularly difficult.
Clearly institutions can do all of this far more effectively than individuals. I do find NTSX an appealing product and it's the bulk of my portfolio (roughly 65% NTSX, 20% VXUS, 15% EDV in taxable, with a very tiny Hedgefundie adventure in Roth). It would be interesting if they somehow did a version that was more akin to PSLDX level of leverage but I guess they would need to change strategy on that i.e. equities would have to be leveraged too. I've also always wondered how successful an institution might be at implementing a Hedgefundie strategy internally with internal rebalancing.

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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Uncorrelated » Sat May 30, 2020 7:27 am

occambogle wrote:
Sat May 30, 2020 5:44 am
Uncorrelated wrote:
Sat May 30, 2020 5:17 am
Re-investment risk is not a thing unless you use bonds to match nominal or real liabilities completely, which almost nobody does. I would argue nobody should do that either, if you're at the age where it's possible to cover all your future liabilities, annuities are just a better deal.
I don't pretend to understand this. But say for the sake of argument we assumed TYD and EDV had exactly the same duration, and we bought $1000 of each today, and interest rates rose tomorrow. After 10 years wouldn't TYD have replaced all those lower-rate treasuries with higher rate ones... while EDV would only have done so after 30 years? Or is that not how it works?
Neither funds hold treasuries until maturity. TYD holds treasuries with maturity 7-10 years, this implies that treasuries are held for a maximum of 3 years. EDV uses 20-30 year treasuries, this implies that treasuries are held for a maximum of 10 years.

Which treasuries are actually owned by the fund is not very relevant to the average investor. Whether the fund buys 10-year treasuries at 1% yield or 10-year treasuries at 5% yield, apart from some minor differences in effective duration, the expected return and volatility are the same.

The main difference between EDV and TYD is that EDV responds to yield changes in the 20-30 year range and TYD responds to yield changes in the 7-10 year range. Over a sufficiently large time horizon, this does not matter. Bond funds such as total bond market can benefit from diversification from different points on the yield curve.

In essence bonds are just simple investments with an expected return and volatility. The fact that they guarantee a certain payout stream is completely irrelevant for 99.99% of investors.
Uncorrelated wrote:
Sat May 30, 2020 5:17 am
Again don't use portfolio visualizer to draw conclusions about bond funds. You need data going back much farther than 1980 to arrive at sensible estimates.
Is PV unreliable for bond funds only because of short periods and recency bias, or is it actually not accurately reflecting the funds somehow?
I don't doubt you... PV is just so much more user-friendly than spreadsheets.
Recency bias. The time period since 1980 is simply not representative for future bond returns. For reference, from 1980 to 2020 10-year bonds returned approximately 4% real annually. Between 1900 and 1980 they returned less than 1% annually.
Uncorrelated wrote:
Sat May 30, 2020 5:17 am
My mean variance optimizer almost always recommends total bond market and taking the risk on the equity side. For reference, equities have a sharpe ratio of .47 over the same time period.
But for balancing equity-heavy portfolios.... aren't LTT treasuries better than TBM because of the lower correlation? Doesn't using something like EDV actually allow you to take more risk on the equities side, through higher % equities and lower % bonds, because the LTTs are compensating in downturns more significantly/effectively than TBM?
It's complicated. You're constantly trying to balance the total risk budget. If you use total bond market, you can simply fit more equities into the risk budget than with LTT or EDV. The difference in return between total bond market and LTT/EDV is quite modest:

excess return / excess volatility
total bond market: 1.68% / 4.94%
ITT 1.66% / 5.56%
LTT 2.06% / 9.8%
EDV 3.04% / 21.35%

With these numbers it's easy to imagine that it can be more attractive to spend the risk budget on equities instead of longer duration treasuries. The result is quite sensitive to estimation errors, if the estimated return on LTT was a little bit higher, the argument might swing the other way.

I don't see any evidence that long term bonds are effective in "compensating" down turns. Over sufficiently long time horizons there does not appear to be a meaningful negative correlation between stocks and bonds. IIRC the confidence intervals on negative correlation between market and value/profitability/investment are much better.

Wrench
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by Wrench » Sun Jun 14, 2020 8:59 am

New to this thread, but very interested in the topic. Here are my two cents:
For leveraged portfolio with 40% stock, in Simba backtesting (v19c) with
20% TSM
20% SCV
60% LTT
60% STT
-60% CASHX

Here are returns from 1940 - 2019 from Simba spreadsheet backtest:
https://www.dropbox.com/s/h36uvaif1zopd ... t.jpg?dl=0
(Note - account balance plotted on log scale)
I ignored depression years because of what today would be anomalous fed behavior (though even if you do include it, leveraged looks better)
There are clearly two regimes - 1940 - ~1968, and ~1972 - 2019. The latter has a higher slope than the former, i.e. better returns. Quantitatively, 1940-1968 has CAGR of 8.74, versus 13.52 for 1972-2019. This does make sense as in the earlier period interest rates were reasonably stable and/or increasing somewhat, while in the later period interest rates were very high initially and then declined steadily (i.e., a ~40 year bull bond market). A bond overweight portfolio should do better in a bond bull market! The important thing to me is that in both periods the returns were MUCH better than a 40% stock/60% LTT portfolio, by ~1.4% % in the earlier period and ~3% in the later period. And even more important, risk is lower in both periods by pretty much every measure. For example, Sharpe of 0.9 vs 0.7 for leveraged versus not in 1940-1968, and 0.84 versus 0.56 for 1972-2019. Draw downs for the leveraged portfolio in both periods are less than or worst case equal to the draw downs of the unleveraged portfolio. Worst draw down is ~9% in 1974; worst annual return of -7.9% is in 1969; and there are 8 years out of 80 (1940-2019) where the returns are negative (compared to 14 for the unleveraged).

All in all, leveraging the bond allocation looks almost to good to be true. And that worries me. Whenever I've seen things that look too good to be true, they usually are! :happy What am I missing?!

wrench

kim.gold
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Re: Understanding using treasury futures for leverage to implement risk parity

Post by kim.gold » Tue Jul 28, 2020 9:14 am

For the guys holding Sep futures and planing to roll them over, when do you plan to do the rollover? For Sep 20 contract, the First Notice Day is Aug 31 - https://www.barchart.com/futures/first- ... financials.

My broker (IBKR) would not let me open a long position after FND, although I am not sure if they would automatically close any existing long position. They do have a tendency to "cash settle" most of the future contracts.

My understanding is that any rollover needs to happen before FND. Can any of you guys confirm this? TIA.

Edit: Interest Rates Pace of the Roll Tool shows +$55 spread for 10Y and +$35 for 2Y today - this is money a contract holder would be paid for doing the rollover.

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