Understanding using treasury futures for leverage to implement risk parity

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
BTTFutures
Posts: 5
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.

Topic Author
DonIce
Posts: 719
Joined: Thu Feb 21, 2019 6:44 pm

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
Posts: 982
Joined: Wed Apr 15, 2015 10:53 am

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
Posts: 982
Joined: Wed Apr 15, 2015 10:53 am

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
Posts: 982
Joined: Wed Apr 15, 2015 10:53 am

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

User avatar
305pelusa
Posts: 881
Joined: Fri Nov 16, 2018 10:20 pm

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

Post by 305pelusa » 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.

rascott
Posts: 982
Joined: Wed Apr 15, 2015 10:53 am

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
Posts: 982
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 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?

User avatar
305pelusa
Posts: 881
Joined: Fri Nov 16, 2018 10:20 pm

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

Post by 305pelusa » 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.

rascott
Posts: 982
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
305pelusa
Posts: 881
Joined: Fri Nov 16, 2018 10:20 pm

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

Post by 305pelusa » 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.

rascott
Posts: 982
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

Post Reply