Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

constructor wrote: Tue Oct 19, 2021 9:17 pm
millennialmillions wrote: Mon Oct 18, 2021 9:55 pm
constructor wrote: Mon Oct 18, 2021 2:46 pm
millennialmillions wrote: Sun Oct 17, 2021 9:14 am Bentonkb linked to this CME paper, which describes how to calculate the Principal Invoice Price, a better representation of the market value.

"E.g., the conversion factor for delivery of the 2-3/8% T-note of Aug-24 vs. December 2017 10-year T-note futures is 0.8072. This suggests that a 2 3/8% security is approximately valued at 81% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625 expressed in decimal format), the principal invoice amount may be calculated as follows. Principal Invoice Price = 125.265625 x 0.8072 x $1,000 = $101,114.41 E.g., the conversion factor for delivery of the 1-7/8% T-note of Aug-24 vs. December 10-year T-note futures is 0.7807. This suggests that a 1-7/8% security is approximately valued at 78% as much as a 6% security. Assuming a futures price of 125-08+/32nds (or 125.265625), the principal invoice amount may be calculated as follows.
Principal Invoice Price
= 125.265625 x 0.7807 x $1,000
= $97,794.87
In order to arrive at the total invoice amount, one must of course further add any accrued interest since the last semi annual interest payment date to the principal invoice amount."

It looks like the current CTD underlying security has a conversion factor of 0.95. So I would calculate your current STT exposure as $109,245 * 0.95 CF * 2 (for $200,000 face value) * 4 contracts = $830,262.

Note it doesn't appear there is consensus on this calculation, but this seems to directly align with the CME paper, and I haven't seen a good reason to use any other number. Also, the conversion factor for STT is closer to 1 than ITT or LTT, so it doesn't have as much of an impact.
While I agree with you in terms understanding of the book/PDF in practice I found the conversion factor does not need to be taken account given these empirical observations. Let's use the most extreme example with UB which has a conversion factor of 0.6141 as per Treasury Analytics (https://www.cmegrou ... tics.html).

1. The volatility of UB is identical to TLT, and definitely not 0.6 times that of TLT. If the actual exposure is the "invoice price" which is 0.6 times the nominal value we would expect UB to be 0.6 times as volatile.
2. In the Treasury Analytics page there is DV01 for futures and DV01 for cash, and precisely Cash DV01 = 0.6 * Futures DV01. If the actual exposure is the invoice price then the DV01 would be identical.

Well basically these two points are the same point.

But I agree with you that it sounds like on delivery only 0.6 times the nominal amount of the underlying treasury would be delivered. Confusing... I wonder if I am understanding the delivery process incorrectly.

Edit: On page 12 it does say:
E .g ., if one held $10 million face value of the 2-3/8%-8/24 note, one might sell 81 December 2017 futures by reference to the conversion factor of 0 .8072 to execute a hedge .
So this confirms that the nominal value is correct, that one future contract hedges more than "one treasury", given the ration of (1 / conversion factor). Though my question remains how the delivery work, since this almost seems you might need to deliver fraction of a treasury, and what the invoice price really means in the delivery process.
Thank you for your reply. I'm amazed we haven't reached consensus on something so fundamental to this strategy...it should be important for everyone in this thread to have an answer to this.

I disagree with your reading of that section (page 9 of the CME PDF) and believe it actually confirms the opposite, that the futures price must be multiplied by the conversion factor to determine market value/market exposure. Look at this table:
Image

The cash price is the market value. Multiplying the futures price by the conversion factor gets us very close to this market value (and the difference is the basis, which is small enough to ignore for our purpose).

Ultimately, it doesn't matter that one futures contract hedges more than "one treasury". What matters is holding one futures contract gives you equivalent performance to investing $x directly in treasuries, or in a fund like TLT. This paper says that x ≈ futures price * CF.

The best way to settle this would be to use actual futures returns data compared against a fund to determine how much TLT is needed to replicate the results of 1 UB contract. Your point that "the volatility of UB is identical to TLT" doesn't answer this question of how much is needed.
Does this chart of UB divided by TLT convince you for the last point? Gaps are due to different quarter futures. Within each quarter the line is flat, or at least does not differ by a factor of 0.6.

Image

As I said I still don't fully understand the delivery process and thus would love to see discussion here, but I am convinced that the conversion factor is irrelevant if we only care about replicating exposure and not delivery. Empirically I ran HFEA with UB and MES for a while and the return appeared identical to what I would get from UPRO and TMF. Then I switched to ZN and ZF and it's all messed up now.
I agree, See my replies to mm and comeinvest above. Zf is 125k not 100k.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 6:40 pm I'm still suspicious of using standard deviations. Deviations may be the result of duration exposure, or, for example, fluctuations of demand and supply. The latter are not "risk" to me because the futures must converge to the CTD. Let me therefore calculate return per duration.

Modified duration comparisons:
Future / futures 5-y return / bond index 5-y return / CTD MD / S&P bond index MD / return per duration (CTD) / return per duration (bond index)
ZT / 1.33 / 1.44 / 1.90 / 1.91 / 0.7 / 0.75
ZF / 1.63% / 1.87% / 4.29 / 4.81 / 0.38 / 0.39
ZN / 2.01% / 2.34% / 6.20 / 6.62 / 0.324 / 0.353
TN / 2.38% / 2.01% / 8.77 / 9.22 / 0.271 / 0.218
ZB / 3.12% / 2.92% / 11.56 / 14.99 / 0.27 / 0.195
UB / 3.61% / 4.19% / 18.3 / 19.2 / 0.197 / 0.218


Striking it through because we don't know historic durations. But isn't it true that the CTD was always a bond with maturity close to the short end of the allowable range of deliverable bonds, since 10+ years ago when interest rates dropped below 6%?

I'm still not convinced of the standard deviation approach. Cash treasuries have lower volume than the futures market, right? If so, the fluctuations based on changes in liquidity - traders rushing to buy or sell on market turns, will be higher. Which would lead to higher standard deviations, but not to higher duration risk to me.
Did you see zkn did the max draw analysis above? I had missed it initially. The max draws for most of the cash indices were substantially higher. After adjusting there is little difference between cash and futures. I agree with zkn that max draw is a noisy measure and the remaining noise we see in the results is partially the noise of max draw. Some index may get lucky to have shorter duration during a max draw event relative to corresponding index. The good thing is there is no persistent bias for slippage.
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millennialmillions
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

constructor wrote: Tue Oct 19, 2021 9:17 pm Does this chart of UB divided by TLT convince you for the last point? Gaps are due to different quarter futures. Within each quarter the line is flat, or at least does not differ by a factor of 0.6.

Image

As I said I still don't fully understand the delivery process and thus would love to see discussion here, but I am convinced that the conversion factor is irrelevant if we only care about replicating exposure and not delivery. Empirically I ran HFEA with UB and MES for a while and the return appeared identical to what I would get from UPRO and TMF. Then I switched to ZN and ZF and it's all messed up now.
Appreciate everyone helping figure this out. I am coming around on using the futures price as the exposure amount rather than calculating the invoice price. However, a few things that still concern me (and since this makes a ~20% difference in treasury exposure, I think it's worth nailing down).

The above chart shows that $1 of UB is equivalent to $1 of TLT. But what does "$1 of UB" actually mean? It seems logical it would be the futures price, so 1 contract is ~$125,000, but do we have any confirmation of that?

I also can't explain this table from the CME paper. This seems to clearly show that the futures price must be multiplied by the conversion factor to get close to cash price/market value/market exposure of the underlying security. Maybe this is explained because more of the security needs to be delivered?
Image

Skier said:
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
I agree, this statement shows that 81M in futures contracts provides an exposure to 100M in face value in bonds. But face value is irrelevant, we want market value to determine how much cash we would have to invest directly in treasuries to get the results of 1 futures contract.

At this point after flipping back and forth, I feel 80% confident simply using the futures price is the right answer, and this post from skier was very helpful since I had not considered how the CF changes. If anyone can help explain the items above, I'll be very happy to move on and use the nice, simple solution of the price IB shows us as the exposure.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 8:43 pm Maybe I'm having some mental blockage, but taking a step back and trying to rationalize the math. Summary (UB as example):

Non-risk-adjusted slippage:
S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 4.3% (cash-secured futures index) / 5.04% (bond index) => slippage: 0.74%
5-year annualized returns: 3.61% (future) / 4.19% (bond index) => slippage: 0.58%
3-year: 9.99% / 10.72% => slippage: 0.73%
1-year: -8.44% / -8.35% => slippage: 0.09%

Risk-adjusted slippage: ("I compared the risk (annualized monthly standard deviation) for each index pair, and the annualized risk-adjusted returns")
S&P cash-secured ultra T-Bond future (25 years and 4 months) vs. the S&P U.S. Treasury Bond 20+ Year Index (26 years):
10 years: 11.54% / 12.10% => .33% / .37% => slippage .04%
5 years: 12.33% / 12.36% => .22% / .27% => slippage .05%
3 years: 13.94% / 13.93% => .62% / .67% => slippage .05%

Current duration comparison:
Future / futures 5-y return / bond index 5-y return / CTD MD / S&P bond index MD / return per duration (CTD) / return per duration (bond index)
UB / 3.61% / 4.19% / 18.3 / 19.2 / 0.197 / 0.218

Can it be that a mere 0.9 year shorter duration (18.3 vs. 19.2) justifies sacrificing a 0.7% annual return, when the total nominal return is only what - like 2%? We are talking about 35% or more of the (nominal) return. I know we don't know the historical durations, but still.

Another question: This thread is about leverage, i.e. most of us don't invest the cash collateral in T-bills. Instead, we are adding an overlay of a treasury allocation via futures on an equities portfolio, and we pay the funding rate (short-term rate + slippage).
The return generated from that overlay is much smaller than the nominal returns from treasuries. Our incremental return from the overlay is just the difference between long-term and short-term rates (term premium). Let's say 0.5%. (I'm forgetting rebalancing effects for this discussion.)
Shouldn't a fair "risk-adjusted return" be based on the incremental return that we are generating from that incremental addition of leveraged futures (with the implied funding cost already subtracted), instead of on the nominal return of only the positive part of that addition (the treasury without the funding cost)?
Example: assume expected term premium is 0.5%. This is our expected additional return from adding treasury futures to our portfolio. Basically what I'm saying is, shouldn't we use this all-in net return as input to the "annualized risk-adjusted returns" in zkn's "risk-adjusted slippage"?
An intuitive thought experiment using my example to support my thought: term premium 0.5%, 10-year nominal slippage 0.74% p.a., would you prefer to be invested in a portfolio with 0.5% - 0.74% = -0.24% expected return, or in one with 0.5% expected return, even if the latter has slightly higher standard deviations? Shouldn't we put the total incremental risk in relation to the total incremental return, instead of just the positive part of it?
There is definitely something about the UB future vs cash pairing. Even after adjusting for max-draw or stdev that one is way off. As zkn showed, the max draw on UB was actually larger than on the cash index. All the other duration pairings are nearly identical with almost no slippage. But the UB pairing is WAY off. Is it possible somehow one of indexes has shifted its duration at extremely innoportune times? Maybe but that's a huge slippage. Maybe we can find some papers about financing costs on UB being much higher than other contracts. One of us should also just double check zkn's math just to be sure.

Regarding your question on leverage, we are comparing two fully funded positions, one in cash, and one in futures. So it's a fair comparison. You are correct that we are not investing fully funded. So when we solve the optimization problems of what to invest in and how much leverage to use, we will need to use the lower unfunded return. This is done by subtracting out the fully funded portion that the SPGlobal indices hold in T-Bills. We can substitute VFITX for ZF+ZN SPGlobal because the returns are identical. We then subtract out the T-Bills held b ZF/ZN SPGlobal return series. We do this by subtracting CASHX in portfolio visualizer, or in Simba's backtesting spreadsheet. All the backtests already do this.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

millennialmillions wrote: Wed Oct 20, 2021 11:28 am
constructor wrote: Tue Oct 19, 2021 9:17 pm Does this chart of UB divided by TLT convince you for the last point? Gaps are due to different quarter futures. Within each quarter the line is flat, or at least does not differ by a factor of 0.6.

Image

As I said I still don't fully understand the delivery process and thus would love to see discussion here, but I am convinced that the conversion factor is irrelevant if we only care about replicating exposure and not delivery. Empirically I ran HFEA with UB and MES for a while and the return appeared identical to what I would get from UPRO and TMF. Then I switched to ZN and ZF and it's all messed up now.
Appreciate everyone helping figure this out. I am coming around on using the futures price as the exposure amount rather than calculating the invoice price. However, a few things that still concern me (and since this makes a ~20% difference in treasury exposure, I think it's worth nailing down).

The above chart shows that $1 of UB is equivalent to $1 of TLT. But what does "$1 of UB" actually mean? It seems logical it would be the futures price, so 1 contract is ~$125,000, but do we have any confirmation of that?

I also can't explain this table from the CME paper. This seems to clearly show that the futures price must be multiplied by the conversion factor to get close to cash price/market value/market exposure of the underlying security. Maybe this is explained because more of the security needs to be delivered?
Image

Skier said:
"E.g., if one were to buy the basis by buying $10 million
face value of the 2-3/8%-8/24 note, one might sell 81
December 2017 futures by reference to the conversion
factor of 0.8072."

This is the statement we should rely upon and its interpretation is indisputable. 81M in futures contracts provides an exposure to 100M in bonds when the CF is .81.
I agree, this statement shows that 81M in futures contracts provides an exposure to 100M in face value in bonds. But face value is irrelevant, we want market value to determine how much cash we would have to invest directly in treasuries to get the results of 1 futures contract.

At this point after flipping back and forth, I feel 80% confident simply using the futures price is the right answer, and this post from skier was very helpful since I had not considered how the CF changes. If anyone can help explain the items above, I'll be very happy to move on and use the nice, simple solution of the price IB shows us as the exposure.

I had confirmed, but should have posted, that in the example they were giving that the market value was very near the face value of 10M. In the example, the cash security had a price of 101,234 for 100k face value. See quote at end of this post or page 6 https://www.cmegroup.com/education/file ... utures.pdf

I also noticed a typo in the post you linked to which changes the meaning. I said originally:

"
Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the invoice price."

But of course what I meant was

"
Now we might say, OK but how did the invoice price change? The invoice price didn't change like a 125k bond because the invoice price is the futures price * the CF."

I've corrected it now so hopefully it's clearer. You probably knew what I meant anyways, and the key part is that the CF is changing along with the futures price. Both go up when interest rates drop.

However, the CF system is imperfect in practice as we find
that a particular security will tend to emerge as “cheapestto-deliver” (CTD) after studying the relationship between
cash security prices and principal invoice amounts

E.g., on October 10, 2017, one might have been able to
purchase the 2-3/8% of 8/24 at 101-07+ ($101,234.38
per $100,000 face value unit). The 1-7/8% of 8/24 was
valued at 98-01+ ($98,031.25 per $100,000 face value
unit). Compare these cash values to the principal invoice
amounts as follows.
jarjarM
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by jarjarM »

skierincolorado wrote: Wed Oct 20, 2021 8:45 am
jarjarM wrote: Tue Oct 19, 2021 9:44 pm
comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
Until we see a rules based backrest that significantly outperforms buy and hold ITT we should remain skeptical. It’s a market timing strategy which we should be inherently skeptical of given EMH. Even if such a backtest were provided, the rules are constantly changing and historical sources of alpha often do not persist. I would want to see it backtested over a very long period of 60+ years and that it has delivered alpha in each 20 year subset of the 60 years as well. I would probably also want a theoretical reason why the alpha has persisted (other than everybody else being to dumb to notice it).

Going long on the curve sounds like it makes sense when the curve is steep. But sometimes the steepness precedes a rise in rates across the whole curve. It would have been better to be in middle durations like 10 years in such a case where the carry and roll down is better.

Even when 10 y rates rise more than 30 y rates it will often have been better to be in the 10 y because the carry and roll is better. There are very few moments in history where it would have been better to be in the 30 y. The last few months happened to be one such case but in the big picture the benefit was minimal.

I’ve read a few papers on dynamic hedge fund strategies and none of them ever go farther than 10 years out on the curve. There’s a reason for this. The slope of the curve past ten years is pretty much always less steep.
Yes, the intent isn't going to dive in and starting to trade but more in depth study. Alpha always erodes as more market participants pick up the signal. It's there until it isn't due to efficient market.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

jarjarM wrote: Wed Oct 20, 2021 12:30 pm
skierincolorado wrote: Wed Oct 20, 2021 8:45 am
jarjarM wrote: Tue Oct 19, 2021 9:44 pm
comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
Until we see a rules based backrest that significantly outperforms buy and hold ITT we should remain skeptical. It’s a market timing strategy which we should be inherently skeptical of given EMH. Even if such a backtest were provided, the rules are constantly changing and historical sources of alpha often do not persist. I would want to see it backtested over a very long period of 60+ years and that it has delivered alpha in each 20 year subset of the 60 years as well. I would probably also want a theoretical reason why the alpha has persisted (other than everybody else being to dumb to notice it).

Going long on the curve sounds like it makes sense when the curve is steep. But sometimes the steepness precedes a rise in rates across the whole curve. It would have been better to be in middle durations like 10 years in such a case where the carry and roll down is better.

Even when 10 y rates rise more than 30 y rates it will often have been better to be in the 10 y because the carry and roll is better. There are very few moments in history where it would have been better to be in the 30 y. The last few months happened to be one such case but in the big picture the benefit was minimal.

I’ve read a few papers on dynamic hedge fund strategies and none of them ever go farther than 10 years out on the curve. There’s a reason for this. The slope of the curve past ten years is pretty much always less steep.
Yes, the intent isn't going to dive in and starting to trade but more in depth study. Alpha always erodes as more market participants pick up the signal. It's there until it isn't due to efficient market.
I will say comeinvest's timing has been impeccable thus far! Long rates up last few days while ITT rates hold steady right after he unloaded some UB.
Last edited by skierincolorado on Wed Oct 20, 2021 2:13 pm, edited 1 time in total.
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Bentonkb
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

skierincolorado wrote: Wed Oct 20, 2021 9:01 am I agree, See my replies to mm and comeinvest above. Zf is 125k not 100k.
If you bought a $100,000 par bond for $97,640 would you say you put $125,000 at risk? That doesn't make any sense.

One of the principles behind this strategy is that a long position in ZF is the risk equivalent of buying the CTD bond in the spot market. The price for today's CTD 5-year on Treasury Direct is $97,640. If the contract expired today, you would fork over (121-30.25 * 0.7999)=$97,544 to and get a 0.5% coupon bond maturing 2/28/2026.

I'm struggling to understand this, obviously. There are no circumstances where anyone has $125,000 at risk in this trade.

The thing that convinced me that $125,000 (or $121,945 in the example above) is not the right way to quantify the risk is thinking about what would happen if the conversion factor reference rate changed from 6% to, say, 0.5%. In the example above, the 0.5% coupon bond would have a CF of 1.00 and the futures price would be 97-17.41 but the trade risk would have remained the same. The 6% reference rate is totally arbitrary, so it can't have any effect on the trade risk. The CTC bond is divided by CF to get the futures price and the futures price is multiplied by CF to get the invoice price. No transactions take place at the futures price.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Bentonkb wrote: Wed Oct 20, 2021 1:41 pm
skierincolorado wrote: Wed Oct 20, 2021 9:01 am I agree, See my replies to mm and comeinvest above. Zf is 125k not 100k.
If you bought a $100,000 par bond for $97,640 would you say you put $125,000 at risk? That doesn't make any sense.

One of the principles behind this strategy is that a long position in ZF is the risk equivalent of buying the CTD bond in the spot market. The price for today's CTD 5-year on Treasury Direct is $97,640. If the contract expired today, you would fork over (121-30.25 * 0.7999)=$97,544 to and get a 0.5% coupon bond maturing 2/28/2026.

I'm struggling to understand this, obviously. There are no circumstances where anyone has $125,000 at risk in this trade.

The thing that convinced me that $125,000 (or $121,945 in the example above) is not the right way to quantify the risk is thinking about what would happen if the conversion factor reference rate changed from 6% to, say, 0.5%. In the example above, the 0.5% coupon bond would have a CF of 1.00 and the futures price would be 97-17.41 but the trade risk would have remained the same. The 6% reference rate is totally arbitrary, so it can't have any effect on the trade risk. The CTC bond is divided by CF to get the futures price and the futures price is multiplied by CF to get the invoice price. No transactions take place at the futures price.

See the post that MM linked to. The CME statement is very clear that 81 contracts hedges bonds with 10M face value and 10.1M market value. The theoretical/practical reason is tricky, I struggled with it for a while - it took up a bunch of my time the last couple days, but hopefully that post explains it.

It is very counterintuitive that the exposure is 125k when what is delivered is 100k and the invoice price is 100k. The contract however is for 100k of bonds with 6% interest, which has market value of 125k. That is literally what is being traded and what the invoice price reflects. That's probably not convincing on its own but perhaps an example will help. It didn't convince me until I went through an example, which the posts below should illustrate. Both the CF and the futures price go up when interest rates fall. I was like OK I get that when interest rates drop, the futures price will go up in proportion to 125k of bonds... but then we multiply by the CF to get back to the invoice price... so the change in invoice price would just be proportional to the 100k delivered. What I was missing is that the CF also goes up when interest rates drop. The invoice price changes are not CF * futures price, the invoice price changes are literally the same as the nominal changes in futures price.

If the futures price goes up by $1000, the invoice price does too. Not $1000 * CF. The full $1000, because the CF also goes up.

viewtopic.php?p=6284611#p6284611

viewtopic.php?p=6282815#p6282815

The final step is understanding why they did it like this. It is an attempt to make different bonds with different coupons all deliverable. It doesn't quite work perfectly so one usually ends up being CTD, but the CTD can change during a contact, and probabilities are assigned to each available bond as to which is most likely to be CTD at contract expiration. So it helps spread around the liquidity to other bonds with other coupons.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 8:59 am
cometqq wrote: Wed Oct 20, 2021 5:53 am So two ZFs give you an exposure to 250k ITT not 200k ITT. To have an exposure to 200k ITT, you'd buy one ZF and 75k VGIT. Is this correct? I feel that whether one ZF is an exposure to 125k or 100k ITT is important. The difference is certainly not negligible.
Correct. The quote from Cme confirms this. 10m hedged by only 81 contracts.
When you say 125k you mean approximately, right?
My IB TWS currently shows a Last price of 121'305 and a mark price of 121.9530 for ZF.
So if I wanted to determine my exposure to the underlying (I think commonly referred to as "notional value") accurately, one ZF gives me exposure to the underlying bond of $121,953 plus [expected coupon payments between now and contract expiration] - [implied financing cost between now and expiration], correct? Can you confirm my math? Basically I would have to look at the current price of the underlying CTD, correct?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Wed Oct 20, 2021 2:12 pm
skierincolorado wrote: Wed Oct 20, 2021 8:59 am
cometqq wrote: Wed Oct 20, 2021 5:53 am So two ZFs give you an exposure to 250k ITT not 200k ITT. To have an exposure to 200k ITT, you'd buy one ZF and 75k VGIT. Is this correct? I feel that whether one ZF is an exposure to 125k or 100k ITT is important. The difference is certainly not negligible.
Correct. The quote from Cme confirms this. 10m hedged by only 81 contracts.
When you say 125k you mean approximately, right?
My IB TWS currently shows a Last price of 121'305 and a mark price of 121.9530 for ZF.
So if I wanted to determine my exposure to the underlying (I think commonly referred to as "notional value") accurately, one ZF gives me exposure to the underlying bond of $121,953 plus [expected coupon payments between now and contract expiration] - [implied financing cost between now and expiration], correct? Can you confirm my math? Basically I would have to look at the current price of the underlying CTD, correct?
Yeah I was being approximate, 121953 is correct attm. I'm not sure about adding in coupon payments and subtracting financing cost. I think these would effect duration and expected return respectively, but not exposure.

It should be equivalent to buying a $121,953 bond with duration of whatever the futures duration is currently. If such a bond existed, which it doesn't, it would have a 6% coupon and 100k face value.
Last edited by skierincolorado on Wed Oct 20, 2021 2:29 pm, edited 1 time in total.
User avatar
Bentonkb
Posts: 83
Joined: Sun Mar 07, 2021 5:47 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

skierincolorado wrote: Wed Oct 20, 2021 1:54 pm
Bentonkb wrote: Wed Oct 20, 2021 1:41 pm
skierincolorado wrote: Wed Oct 20, 2021 9:01 am I agree, See my replies to mm and comeinvest above. Zf is 125k not 100k.
If you bought a $100,000 par bond for $97,640 would you say you put $125,000 at risk? That doesn't make any sense.

One of the principles behind this strategy is that a long position in ZF is the risk equivalent of buying the CTD bond in the spot market. The price for today's CTD 5-year on Treasury Direct is $97,640. If the contract expired today, you would fork over (121-30.25 * 0.7999)=$97,544 to and get a 0.5% coupon bond maturing 2/28/2026.

I'm struggling to understand this, obviously. There are no circumstances where anyone has $125,000 at risk in this trade.

The thing that convinced me that $125,000 (or $121,945 in the example above) is not the right way to quantify the risk is thinking about what would happen if the conversion factor reference rate changed from 6% to, say, 0.5%. In the example above, the 0.5% coupon bond would have a CF of 1.00 and the futures price would be 97-17.41 but the trade risk would have remained the same. The 6% reference rate is totally arbitrary, so it can't have any effect on the trade risk. The CTC bond is divided by CF to get the futures price and the futures price is multiplied by CF to get the invoice price. No transactions take place at the futures price.

See the post that MM linked to. The CME statement is very clear that 81 contracts hedges bonds with 10M face value and 10.1M market value. The theoretical/practical reason is tricky, I struggled with it for a while - it took up a bunch of my time the last couple days, but hopefully that post explains it.

It is very counterintuitive that the exposure is 125k when what is delivered is 100k and the invoice price is 100k. The contract however is for 100k of bonds with 6% interest, which has market value of 125k. That is literally what is being traded and what the invoice price reflects. That's probably not convincing on its own but perhaps an example will help. It didn't convince me until I went through an example, which the posts below should illustrate. Both the CF and the futures price go up when interest rates fall. I was like OK I get that when interest rates drop, the futures price will go up in proportion to 125k of bonds... but then we multiply by the CF to get back to the invoice price... so the change in invoice price would just be proportional to the 100k delivered. What I was missing is that the CF also goes up when interest rates drop. The invoice price changes are not CF * futures price, the invoice price changes are literally the same as the nominal changes in futures price.

If the futures price goes up by $1000, the invoice price does too. Not $1000 * CF. The full $1000, because the CF also goes up.

viewtopic.php?p=6284611#p6284611

viewtopic.php?p=6282815#p6282815

The final step is understanding why they did it like this. It is an attempt to make different bonds with different coupons all deliverable. It doesn't quite work perfectly so one usually ends up being CTD, but the CTD can change during a contact, and probabilities are assigned to each available bond as to which is most likely to be CTD at contract expiration. So it helps spread around the liquidity to other bonds with other coupons.
I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Kbg wrote: Wed Oct 20, 2021 8:07 am Relevant article to the discussion

https://www.simplify.us/blog/efficient- ... e=hs_email
"Let’s assume we can borrow at the 1-year Treasury rate" - He doesn't show us how to do this. That makes his graphs questionable. And it is ever more important to include realistic financing cost in the model.

"Third, implementation at the short end of the curve presents higher butterfly and twist basis risks than the middle of the curve (since further away from the long end of the curve)." - What are butterfly and twist risks?

"And fourth, the shorter end of the curve is generally more volatile on a duration-adjusted basis, thereby weakening the benefits of a short tenor strategy on a risk-adjusted basis." - True also for ITT vs LTT to a lesser extent, especially when the current slope is steep. I think the truth is somewhere in between a duration-ignorant model and a "per unit of duration" assumption. I think a dogmatic "risk = unit of duration" approach to optimization may lead to unrealistic results.
cometqq
Posts: 13
Joined: Mon Jul 20, 2020 7:36 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

Bentonkb wrote: Wed Oct 20, 2021 2:26 pm
skierincolorado wrote: Wed Oct 20, 2021 1:54 pm
Bentonkb wrote: Wed Oct 20, 2021 1:41 pm
skierincolorado wrote: Wed Oct 20, 2021 9:01 am I agree, See my replies to mm and comeinvest above. Zf is 125k not 100k.
If you bought a $100,000 par bond for $97,640 would you say you put $125,000 at risk? That doesn't make any sense.

One of the principles behind this strategy is that a long position in ZF is the risk equivalent of buying the CTD bond in the spot market. The price for today's CTD 5-year on Treasury Direct is $97,640. If the contract expired today, you would fork over (121-30.25 * 0.7999)=$97,544 to and get a 0.5% coupon bond maturing 2/28/2026.

I'm struggling to understand this, obviously. There are no circumstances where anyone has $125,000 at risk in this trade.

The thing that convinced me that $125,000 (or $121,945 in the example above) is not the right way to quantify the risk is thinking about what would happen if the conversion factor reference rate changed from 6% to, say, 0.5%. In the example above, the 0.5% coupon bond would have a CF of 1.00 and the futures price would be 97-17.41 but the trade risk would have remained the same. The 6% reference rate is totally arbitrary, so it can't have any effect on the trade risk. The CTC bond is divided by CF to get the futures price and the futures price is multiplied by CF to get the invoice price. No transactions take place at the futures price.

See the post that MM linked to. The CME statement is very clear that 81 contracts hedges bonds with 10M face value and 10.1M market value. The theoretical/practical reason is tricky, I struggled with it for a while - it took up a bunch of my time the last couple days, but hopefully that post explains it.

It is very counterintuitive that the exposure is 125k when what is delivered is 100k and the invoice price is 100k. The contract however is for 100k of bonds with 6% interest, which has market value of 125k. That is literally what is being traded and what the invoice price reflects. That's probably not convincing on its own but perhaps an example will help. It didn't convince me until I went through an example, which the posts below should illustrate. Both the CF and the futures price go up when interest rates fall. I was like OK I get that when interest rates drop, the futures price will go up in proportion to 125k of bonds... but then we multiply by the CF to get back to the invoice price... so the change in invoice price would just be proportional to the 100k delivered. What I was missing is that the CF also goes up when interest rates drop. The invoice price changes are not CF * futures price, the invoice price changes are literally the same as the nominal changes in futures price.

If the futures price goes up by $1000, the invoice price does too. Not $1000 * CF. The full $1000, because the CF also goes up.

viewtopic.php?p=6284611#p6284611

viewtopic.php?p=6282815#p6282815

The final step is understanding why they did it like this. It is an attempt to make different bonds with different coupons all deliverable. It doesn't quite work perfectly so one usually ends up being CTD, but the CTD can change during a contact, and probabilities are assigned to each available bond as to which is most likely to be CTD at contract expiration. So it helps spread around the liquidity to other bonds with other coupons.
I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
Yeah, I think you are right that CF is fixed during the span of the contract. The pdf file from CME is enormously confusing. I find this one explains things better: http://www.yieldcurve.com/mktresearch/l ... utures.pdf

On page 12, it says that "The price of the futures contract, over time, does not move tick-for-tick with the CTD bond (although it may on an intra-day basis) but rather by the amount of the change divided by the conversion factor. It is apparent therefore that to hedge a position in the CTD bond we
must hold the number of futures contracts equivalent to the value of bonds held multiplied by the conversion factor." Equation (8) on page 12 does seem to suggest that the bond exposure is the price of the futures contract times the CF.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

cometqq wrote: Wed Oct 20, 2021 3:01 pm
Bentonkb wrote: Wed Oct 20, 2021 2:26 pm
skierincolorado wrote: Wed Oct 20, 2021 1:54 pm
Bentonkb wrote: Wed Oct 20, 2021 1:41 pm
skierincolorado wrote: Wed Oct 20, 2021 9:01 am I agree, See my replies to mm and comeinvest above. Zf is 125k not 100k.
If you bought a $100,000 par bond for $97,640 would you say you put $125,000 at risk? That doesn't make any sense.

One of the principles behind this strategy is that a long position in ZF is the risk equivalent of buying the CTD bond in the spot market. The price for today's CTD 5-year on Treasury Direct is $97,640. If the contract expired today, you would fork over (121-30.25 * 0.7999)=$97,544 to and get a 0.5% coupon bond maturing 2/28/2026.

I'm struggling to understand this, obviously. There are no circumstances where anyone has $125,000 at risk in this trade.

The thing that convinced me that $125,000 (or $121,945 in the example above) is not the right way to quantify the risk is thinking about what would happen if the conversion factor reference rate changed from 6% to, say, 0.5%. In the example above, the 0.5% coupon bond would have a CF of 1.00 and the futures price would be 97-17.41 but the trade risk would have remained the same. The 6% reference rate is totally arbitrary, so it can't have any effect on the trade risk. The CTC bond is divided by CF to get the futures price and the futures price is multiplied by CF to get the invoice price. No transactions take place at the futures price.

See the post that MM linked to. The CME statement is very clear that 81 contracts hedges bonds with 10M face value and 10.1M market value. The theoretical/practical reason is tricky, I struggled with it for a while - it took up a bunch of my time the last couple days, but hopefully that post explains it.

It is very counterintuitive that the exposure is 125k when what is delivered is 100k and the invoice price is 100k. The contract however is for 100k of bonds with 6% interest, which has market value of 125k. That is literally what is being traded and what the invoice price reflects. That's probably not convincing on its own but perhaps an example will help. It didn't convince me until I went through an example, which the posts below should illustrate. Both the CF and the futures price go up when interest rates fall. I was like OK I get that when interest rates drop, the futures price will go up in proportion to 125k of bonds... but then we multiply by the CF to get back to the invoice price... so the change in invoice price would just be proportional to the 100k delivered. What I was missing is that the CF also goes up when interest rates drop. The invoice price changes are not CF * futures price, the invoice price changes are literally the same as the nominal changes in futures price.

If the futures price goes up by $1000, the invoice price does too. Not $1000 * CF. The full $1000, because the CF also goes up.

viewtopic.php?p=6284611#p6284611

viewtopic.php?p=6282815#p6282815

The final step is understanding why they did it like this. It is an attempt to make different bonds with different coupons all deliverable. It doesn't quite work perfectly so one usually ends up being CTD, but the CTD can change during a contact, and probabilities are assigned to each available bond as to which is most likely to be CTD at contract expiration. So it helps spread around the liquidity to other bonds with other coupons.
I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
Yeah, I think you are right that CF is fixed during the span of the contract. The pdf file from CME is enormously confusing. I find this one explains things better: http://www.yieldcurve.com/mktresearch/l ... utures.pdf

On page 12, it says that "The price of the futures contract, over time, does not move tick-for-tick with the CTD bond (although it may on an intra-day basis) but rather by the amount of the change divided by the conversion factor. It is apparent therefore that to hedge a position in the CTD bond we
must hold the number of futures contracts equivalent to the value of bonds held multiplied by the conversion factor." Equation (8) on page 12 does seem to suggest that the bond exposure is the price of the futures contract times the CF.
Ugh yes I was wrong that he CF changes. I thought it converted from market price to the reference bond.

But the statement from CME that 81 contracts hedges 10M in market value of bonds, and the statement you just quoted, both clearly indicate that the exposure is 100k/CF. This is the inverse of their statement that the number of futures contracts to hedge X thousand value in bonds is X * CF.

I am at a loss and will have to start all over again.
Last edited by skierincolorado on Wed Oct 20, 2021 3:30 pm, edited 2 times in total.
comeinvest
Posts: 2669
Joined: Mon Mar 12, 2012 6:57 pm

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 8:45 am
jarjarM wrote: Tue Oct 19, 2021 9:44 pm
comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
Until we see a rules based backrest that significantly outperforms buy and hold ITT we should remain skeptical. It’s a market timing strategy which we should be inherently skeptical of given EMH. Even if such a backtest were provided, the rules are constantly changing and historical sources of alpha often do not persist. I would want to see it backtested over a very long period of 60+ years and that it has delivered alpha in each 20 year subset of the 60 years as well. I would probably also want a theoretical reason why the alpha has persisted (other than everybody else being to dumb to notice it).

Going long on the curve sounds like it makes sense when the curve is steep. But sometimes the steepness precedes a rise in rates across the whole curve. It would have been better to be in middle durations like 10 years in such a case where the carry and roll down is better.

Even when 10 y rates rise more than 30 y rates it will often have been better to be in the 10 y because the carry and roll is better. There are very few moments in history where it would have been better to be in the 30 y. The last few months happened to be one such case but in the big picture the benefit was minimal.
I wouldn't generally disagree with everything you say, but consider that the short end of the curve is basically dictated by the fed, not determined by market forces. That's my understanding at least. The fed is thought to have "infinite" resources, i.e. even if we assume that many market participants detect a violation of the EMH, it would not move the market. Extreme example, to illustrate: If today the fed decides they need to "support the economy" and lower the short-term rates to -10%, while ITT and LTT (presumably determined by market forces) stay where they are, I would probably borrow at the short end, and move my long positions to the mid/longer end. I would not rely on EMH. The fed decided to redistribute wealth, and I and everyone else can either take advantage of it or be left out. Opinions?
skierincolorado wrote: Wed Oct 20, 2021 8:45 am I’ve read a few papers on dynamic hedge fund strategies and none of them ever go farther than 10 years out on the curve. There’s a reason for this. The slope of the curve past ten years is pretty much always less steep.
Agreed, but don't forget: I think you have to look at the logarithmic graph to compare slopes at different points on the curve.
cometqq
Posts: 13
Joined: Mon Jul 20, 2020 7:36 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

skierincolorado wrote: Wed Oct 20, 2021 3:26 pm
cometqq wrote: Wed Oct 20, 2021 3:01 pm
Bentonkb wrote: Wed Oct 20, 2021 2:26 pm
skierincolorado wrote: Wed Oct 20, 2021 1:54 pm
Bentonkb wrote: Wed Oct 20, 2021 1:41 pm

If you bought a $100,000 par bond for $97,640 would you say you put $125,000 at risk? That doesn't make any sense.

One of the principles behind this strategy is that a long position in ZF is the risk equivalent of buying the CTD bond in the spot market. The price for today's CTD 5-year on Treasury Direct is $97,640. If the contract expired today, you would fork over (121-30.25 * 0.7999)=$97,544 to and get a 0.5% coupon bond maturing 2/28/2026.

I'm struggling to understand this, obviously. There are no circumstances where anyone has $125,000 at risk in this trade.

The thing that convinced me that $125,000 (or $121,945 in the example above) is not the right way to quantify the risk is thinking about what would happen if the conversion factor reference rate changed from 6% to, say, 0.5%. In the example above, the 0.5% coupon bond would have a CF of 1.00 and the futures price would be 97-17.41 but the trade risk would have remained the same. The 6% reference rate is totally arbitrary, so it can't have any effect on the trade risk. The CTC bond is divided by CF to get the futures price and the futures price is multiplied by CF to get the invoice price. No transactions take place at the futures price.

See the post that MM linked to. The CME statement is very clear that 81 contracts hedges bonds with 10M face value and 10.1M market value. The theoretical/practical reason is tricky, I struggled with it for a while - it took up a bunch of my time the last couple days, but hopefully that post explains it.

It is very counterintuitive that the exposure is 125k when what is delivered is 100k and the invoice price is 100k. The contract however is for 100k of bonds with 6% interest, which has market value of 125k. That is literally what is being traded and what the invoice price reflects. That's probably not convincing on its own but perhaps an example will help. It didn't convince me until I went through an example, which the posts below should illustrate. Both the CF and the futures price go up when interest rates fall. I was like OK I get that when interest rates drop, the futures price will go up in proportion to 125k of bonds... but then we multiply by the CF to get back to the invoice price... so the change in invoice price would just be proportional to the 100k delivered. What I was missing is that the CF also goes up when interest rates drop. The invoice price changes are not CF * futures price, the invoice price changes are literally the same as the nominal changes in futures price.

If the futures price goes up by $1000, the invoice price does too. Not $1000 * CF. The full $1000, because the CF also goes up.

viewtopic.php?p=6284611#p6284611

viewtopic.php?p=6282815#p6282815

The final step is understanding why they did it like this. It is an attempt to make different bonds with different coupons all deliverable. It doesn't quite work perfectly so one usually ends up being CTD, but the CTD can change during a contact, and probabilities are assigned to each available bond as to which is most likely to be CTD at contract expiration. So it helps spread around the liquidity to other bonds with other coupons.
I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
Yeah, I think you are right that CF is fixed during the span of the contract. The pdf file from CME is enormously confusing. I find this one explains things better: http://www.yieldcurve.com/mktresearch/l ... utures.pdf

On page 12, it says that "The price of the futures contract, over time, does not move tick-for-tick with the CTD bond (although it may on an intra-day basis) but rather by the amount of the change divided by the conversion factor. It is apparent therefore that to hedge a position in the CTD bond we
must hold the number of futures contracts equivalent to the value of bonds held multiplied by the conversion factor." Equation (8) on page 12 does seem to suggest that the bond exposure is the price of the futures contract times the CF.
Ugh yes I was wrong that he CF changes. I thought it converted from market price to the reference bond.

But the statement from CME that 81 contracts hedges 10M in market value of bonds, and the statement you just quoted, both clearly indicate that the exposure is 100k/CF. This is the inverse of their statement that the number of futures contracts to hedge X thousand value in bonds is X * CF.

I am at a loss and will have to start all over again.
If you look at equation (8) on page 12 of the PDF file I quoted (I don't like the CME file, which i think is very hard to understand), the change in the futures contract price is approximately the change in the price of CTD bond divided by CF. Therefore, the exposure to bond is the price of futures contract multiplied by CF.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Wed Oct 20, 2021 3:29 pm
skierincolorado wrote: Wed Oct 20, 2021 8:45 am
jarjarM wrote: Tue Oct 19, 2021 9:44 pm
comeinvest wrote: Tue Oct 19, 2021 7:03 pm But I think hdas is basically playing with the idea of a dynamic allocation on the yield curve based on its current shape, particularly the current slope. Which according to some papers might generate excess returns. He says it's just a matter of time until the curve flattens, it has always flattened. So let's sit it out. It's not if, but when. Let's play the mean reversion. Let's tilt to longer maturities when there is some slope. Back to shorter when it's flat or inverts. Rinse and repeat.
Interesting, thanks to hdas and comeinvest on providing some idea on how to play the hike cycle. :beer
Until we see a rules based backrest that significantly outperforms buy and hold ITT we should remain skeptical. It’s a market timing strategy which we should be inherently skeptical of given EMH. Even if such a backtest were provided, the rules are constantly changing and historical sources of alpha often do not persist. I would want to see it backtested over a very long period of 60+ years and that it has delivered alpha in each 20 year subset of the 60 years as well. I would probably also want a theoretical reason why the alpha has persisted (other than everybody else being to dumb to notice it).

Going long on the curve sounds like it makes sense when the curve is steep. But sometimes the steepness precedes a rise in rates across the whole curve. It would have been better to be in middle durations like 10 years in such a case where the carry and roll down is better.

Even when 10 y rates rise more than 30 y rates it will often have been better to be in the 10 y because the carry and roll is better. There are very few moments in history where it would have been better to be in the 30 y. The last few months happened to be one such case but in the big picture the benefit was minimal.
I wouldn't generally disagree with everything you say, but consider that the short end of the curve is basically dictated by the fed, not determined by market forces. That's my understanding at least. The fed is thought to have "infinite" resources, i.e. even if we assume that many market participants detect a violation of the EMH, it would not move the market. Extreme example, to illustrate: If today the fed decides they need to "support the economy" and lower the short-term rates to -10%, while ITT and LTT (presumably determined by market forces) stay where they are, I would probably borrow at the short end, and move my long positions to the mid/longer end. I would not rely on EMH. The fed decided to redistribute wealth, and I and everyone else can either take advantage of it or be left out. Opinions?
skierincolorado wrote: Wed Oct 20, 2021 8:45 am I’ve read a few papers on dynamic hedge fund strategies and none of them ever go farther than 10 years out on the curve. There’s a reason for this. The slope of the curve past ten years is pretty much always less steep.
Agreed, but don't forget: I think you have to look at the logarithmic graph to compare slopes at different points on the curve.
Consider the 2 yr. If the 2-yr interest rates are made more volatile by the Fed, the market will demand a premium. Yes the FED can move the Fed Funds rate from 5% to 0%. But it cannot (completely) control whether the premium for the 2-yr is .25% or .5%. If the 2-yr always traded .5% higher than the T-Bill, the return on 2-yr bonds would be insanely good. Whereas if the premium is .25%, they would be more mundane. If the market knew that the 2-yr rate was going to get jacked up soon, the slope at 2-yrs would be extremely steep and the return from roll and carry could in fact dominate over the rate hiking.

Yeah the Fed can influence this premium too by buying 2-yr bonds directly. But the Fed buys buys more bonds proportional to the market at the long end. And ultimately, even though the Fed is a substantial portion of the market for all durations, market forces will ultimately dominate.

The steepness is basically why even though rates aren't going up I haven't really lost any money on ZF. If rates had gone up just a little slower, or the curve at 4.5 years had been a little steeper initially, the returns could easily have beaten UB, even though 5 year rates went up while 30 year rates did not. That wasn't the case the last 2 months as 4.5 year rates have just gone up too quickly. But it was certainly the case earlier this year. I was making money even as rates rose, because the steepness/roll was a bigger factor than the rate increases.

For example, if the 2pyr rate is 2% and the slope is 1%/year, then rates can rise up to 3% per year before you lose money. The rate increases would be exactly offset by the roll and carry.

In other words, the market can anticipate Fed rate increases, and this is reflected in the steepness. If the steepness at 2 years is great enough, the return can still be positive even in a rate increase cycle. That's what should happen theoretically and you'd really have to beat the market to do better.

Ultimately all that we really know is the backtest. And the backtest shows STT and ITT to have higher returns proportional to their stdev and max-draw.
Topic Author
skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

cometqq wrote: Wed Oct 20, 2021 3:32 pm
skierincolorado wrote: Wed Oct 20, 2021 3:26 pm
cometqq wrote: Wed Oct 20, 2021 3:01 pm
Bentonkb wrote: Wed Oct 20, 2021 2:26 pm
skierincolorado wrote: Wed Oct 20, 2021 1:54 pm


See the post that MM linked to. The CME statement is very clear that 81 contracts hedges bonds with 10M face value and 10.1M market value. The theoretical/practical reason is tricky, I struggled with it for a while - it took up a bunch of my time the last couple days, but hopefully that post explains it.

It is very counterintuitive that the exposure is 125k when what is delivered is 100k and the invoice price is 100k. The contract however is for 100k of bonds with 6% interest, which has market value of 125k. That is literally what is being traded and what the invoice price reflects. That's probably not convincing on its own but perhaps an example will help. It didn't convince me until I went through an example, which the posts below should illustrate. Both the CF and the futures price go up when interest rates fall. I was like OK I get that when interest rates drop, the futures price will go up in proportion to 125k of bonds... but then we multiply by the CF to get back to the invoice price... so the change in invoice price would just be proportional to the 100k delivered. What I was missing is that the CF also goes up when interest rates drop. The invoice price changes are not CF * futures price, the invoice price changes are literally the same as the nominal changes in futures price.

If the futures price goes up by $1000, the invoice price does too. Not $1000 * CF. The full $1000, because the CF also goes up.

viewtopic.php?p=6284611#p6284611

viewtopic.php?p=6282815#p6282815

The final step is understanding why they did it like this. It is an attempt to make different bonds with different coupons all deliverable. It doesn't quite work perfectly so one usually ends up being CTD, but the CTD can change during a contact, and probabilities are assigned to each available bond as to which is most likely to be CTD at contract expiration. So it helps spread around the liquidity to other bonds with other coupons.
I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
Yeah, I think you are right that CF is fixed during the span of the contract. The pdf file from CME is enormously confusing. I find this one explains things better: http://www.yieldcurve.com/mktresearch/l ... utures.pdf

On page 12, it says that "The price of the futures contract, over time, does not move tick-for-tick with the CTD bond (although it may on an intra-day basis) but rather by the amount of the change divided by the conversion factor. It is apparent therefore that to hedge a position in the CTD bond we
must hold the number of futures contracts equivalent to the value of bonds held multiplied by the conversion factor." Equation (8) on page 12 does seem to suggest that the bond exposure is the price of the futures contract times the CF.
Ugh yes I was wrong that he CF changes. I thought it converted from market price to the reference bond.

But the statement from CME that 81 contracts hedges 10M in market value of bonds, and the statement you just quoted, both clearly indicate that the exposure is 100k/CF. This is the inverse of their statement that the number of futures contracts to hedge X thousand value in bonds is X * CF.

I am at a loss and will have to start all over again.
If you look at equation (8) on page 12 of the PDF file I quoted (I don't like the CME file, which i think is very hard to understand), the change in the futures contract price is approximately the change in the price of CTD bond divided by CF. Therefore, the exposure to bond is the price of futures contract multiplied by CF.
Your statement is based off the equation, but directly contradicts the text of both documents. Both documents state that the to hedge bonds with market value of X thousand dollars, you would sell X * CF futures contracts.

In the example, to hedge 10M market value of bonds, you would sell just 81 futures contracts. The inverse is that buying 81 futures contracts are exposing you to the return of 10M in bonds.

I can't reconcile the text with the equation.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 1:11 pm I will say comeinvest's timing has been impeccable thus far! Long rates up last few days while ITT rates hold steady right after he unloaded some UB.
Thanks for the compliments. But rest assured, I messed up big time several times in my investing history. So don't try to imitate what I'm doing ;)
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millennialmillions
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

Bentonkb wrote: Wed Oct 20, 2021 2:26 pm I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
I've been convinced, so let me take a shot at explaining it. The futures price of ~$121,000 represents the price of a theoretical 5-year treasury with a $100,000 face value and 6% yield. Such a bond does not exist in practice. So for a given real treasury bond, the CF represents how much it is worth relative to this theoretical bond.

The exposure generated from the futures contract is not the same as the exposure generated by holding the CTD underlying security with the same face value. Instead, it is based on the theoretical asset mentioned above. Its price movement is equivalent to buying $121,000 worth of ITTs ("worth" meaning market value). This is verified by looking at constructor's graph and by the example from the CME paper skier provided.

So your exposure from holding a futures contract with $100,000 face value is greater than holding one underlying security with $100,000. At time of delivery, you couldn't just deliver a $100,000 face value treasury; you'd have to deliver more like $121,000 face value (in this case face value and market value are pretty close).
Last edited by millennialmillions on Wed Oct 20, 2021 7:07 pm, edited 2 times in total.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

millennialmillions wrote: Wed Oct 20, 2021 3:57 pm
Bentonkb wrote: Wed Oct 20, 2021 2:26 pm I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
I've been convinced, so let me take a shot at explaining it. The futures price of ~$121,000 represents the price of a theoretical 5-year treasury with a $100,000 face value and 6% yield. Such a bond does not exist in practice. So for a given treasury bond, you must multiply by the CF to determine how much it is worth. When such a bond is delivered, the invoice price of ~$98,000 is paid for this bond.

However, the exposure generated from the futures contract is not the same as the exposure generated by holding the CTD underlying security. Instead, it is based on the theoretical asset mentioned above. Its price movement is equivalent to buying $121,000 worth of ITTs ("worth" meaning market value). This is verified by looking at constructor's graph and by the example from the CME paper skier provided. So your exposure from holding one futures contract is greater than holding one underlying security that meets the delivery requirements.
The one thing I was wrong about though is that the CF does not change. So I'm trying to work through an example where the interest rate drops, what would happen to the futures price and invoice price.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 3:45 pm Consider the 2 yr. If the 2-yr interest rates are made more volatile by the Fed, the market will demand a premium. Yes the FED can move the Fed Funds rate from 5% to 0%. But it cannot (completely) control whether the premium for the 2-yr is .25% or .5%. If the 2-yr always traded .5% higher than the T-Bill, the return on 2-yr bonds would be insanely good. Whereas if the premium is .25%, they would be more mundane. If the market knew that the 2-yr rate was going to get jacked up soon, the slope at 2-yrs would be extremely steep and the return from roll and carry could in fact dominate over the rate hiking.

Yeah the Fed can influence this premium too by buying 2-yr bonds directly. But the Fed buys buys more bonds proportional to the market at the long end. And ultimately, even though the Fed is a substantial portion of the market for all durations, market forces will ultimately dominate.

The steepness is basically why even though rates aren't going up I haven't really lost any money on ZF. If rates had gone up just a little slower, or the curve at 4.5 years had been a little steeper initially, the returns could easily have beaten UB, even though 5 year rates went up while 30 year rates did not. That wasn't the case the last 2 months as 4.5 year rates have just gone up too quickly. But it was certainly the case earlier this year. I was making money even as rates rose, because the steepness/roll was a bigger factor than the rate increases.

For example, if the 2pyr rate is 2% and the slope is 1%/year, then rates can rise up to 3% per year before you lose money. The rate increases would be exactly offset by the roll and carry.

In other words, the market can anticipate Fed rate increases, and this is reflected in the steepness. If the steepness at 2 years is great enough, the return can still be positive even in a rate increase cycle. That's what should happen theoretically and you'd really have to beat the market to do better.

Ultimately all that we really know is the backtest. And the backtest shows STT and ITT to have higher returns proportional to their stdev and max-draw.
Thanks for your illustrations. How far out do you go for your options box financing? Exactly 1 year, a little shorter or longer, or depending on where the slope starts to steepen? We don't want to come close to the 2y point of the curve for options boxes, if the 2y has such good returns, as we would be paying what others earn. Also, do you happen to know an easy way to look up, or a chart that shows the current rolldown yields across the maturity range? Or do you calculate those manually when needed?
cometqq
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

skierincolorado wrote: Wed Oct 20, 2021 3:53 pm
cometqq wrote: Wed Oct 20, 2021 3:32 pm
skierincolorado wrote: Wed Oct 20, 2021 3:26 pm
cometqq wrote: Wed Oct 20, 2021 3:01 pm
Bentonkb wrote: Wed Oct 20, 2021 2:26 pm

I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
Yeah, I think you are right that CF is fixed during the span of the contract. The pdf file from CME is enormously confusing. I find this one explains things better: http://www.yieldcurve.com/mktresearch/l ... utures.pdf

On page 12, it says that "The price of the futures contract, over time, does not move tick-for-tick with the CTD bond (although it may on an intra-day basis) but rather by the amount of the change divided by the conversion factor. It is apparent therefore that to hedge a position in the CTD bond we
must hold the number of futures contracts equivalent to the value of bonds held multiplied by the conversion factor." Equation (8) on page 12 does seem to suggest that the bond exposure is the price of the futures contract times the CF.
Ugh yes I was wrong that he CF changes. I thought it converted from market price to the reference bond.

But the statement from CME that 81 contracts hedges 10M in market value of bonds, and the statement you just quoted, both clearly indicate that the exposure is 100k/CF. This is the inverse of their statement that the number of futures contracts to hedge X thousand value in bonds is X * CF.

I am at a loss and will have to start all over again.
If you look at equation (8) on page 12 of the PDF file I quoted (I don't like the CME file, which i think is very hard to understand), the change in the futures contract price is approximately the change in the price of CTD bond divided by CF. Therefore, the exposure to bond is the price of futures contract multiplied by CF.
Your statement is based off the equation, but directly contradicts the text of both documents. Both documents state that the to hedge bonds with market value of X thousand dollars, you would sell X * CF futures contracts.

In the example, to hedge 10M market value of bonds, you would sell just 81 futures contracts. The inverse is that buying 81 futures contracts are exposing you to the return of 10M in bonds.

I can't reconcile the text with the equation.
"Both documents state that the to hedge bonds with market value of X thousand dollars, you would sell X * CF futures contracts." This is actually consistent with the equation. So if I buy one zf, the price of which is about $125k, my bond exposure would be $125k * CF (CF is about .8 for zf). In other words, if I want an exposure to 100k ITT, I'd buy n = 100k/(125k * CF) futures contracts. I feel that millennialmillions and Bentonkb were right. Their explanation makes more sense to me.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Wed Oct 20, 2021 4:09 pm
skierincolorado wrote: Wed Oct 20, 2021 3:45 pm Consider the 2 yr. If the 2-yr interest rates are made more volatile by the Fed, the market will demand a premium. Yes the FED can move the Fed Funds rate from 5% to 0%. But it cannot (completely) control whether the premium for the 2-yr is .25% or .5%. If the 2-yr always traded .5% higher than the T-Bill, the return on 2-yr bonds would be insanely good. Whereas if the premium is .25%, they would be more mundane. If the market knew that the 2-yr rate was going to get jacked up soon, the slope at 2-yrs would be extremely steep and the return from roll and carry could in fact dominate over the rate hiking.

Yeah the Fed can influence this premium too by buying 2-yr bonds directly. But the Fed buys buys more bonds proportional to the market at the long end. And ultimately, even though the Fed is a substantial portion of the market for all durations, market forces will ultimately dominate.

The steepness is basically why even though rates aren't going up I haven't really lost any money on ZF. If rates had gone up just a little slower, or the curve at 4.5 years had been a little steeper initially, the returns could easily have beaten UB, even though 5 year rates went up while 30 year rates did not. That wasn't the case the last 2 months as 4.5 year rates have just gone up too quickly. But it was certainly the case earlier this year. I was making money even as rates rose, because the steepness/roll was a bigger factor than the rate increases.

For example, if the 2pyr rate is 2% and the slope is 1%/year, then rates can rise up to 3% per year before you lose money. The rate increases would be exactly offset by the roll and carry.

In other words, the market can anticipate Fed rate increases, and this is reflected in the steepness. If the steepness at 2 years is great enough, the return can still be positive even in a rate increase cycle. That's what should happen theoretically and you'd really have to beat the market to do better.

Ultimately all that we really know is the backtest. And the backtest shows STT and ITT to have higher returns proportional to their stdev and max-draw.
Thanks for your illustrations. How far out do you go for your options box financing? Exactly 1 year, a little shorter or longer, or depending on where the slope starts to steepen? We don't want to come close to the 2y point of the curve for options boxes, if the 2y has such good returns, as we would be paying what others earn. Also, do you happen to know an easy way to look up, or a chart that shows the current rolldown yields across the maturity range? Or do you calculate those manually when needed?
For roll down I calculate manually although I've seen a graph or two online, I haven't found a source that updates with this data.

I usually just do a rough calc, like see how much the price of a 5 year bond would go up if its rate fell to the current 4 year rate. To be more precice we'd want the slope exactly at 5 years, and then annualize. Of course roll assumes the curve is static, which it isn't.

I think you're right that for boxes, shorter durations are better, but there's also the bid-ask spread to consider. I don't do many boxes so I am lazy and do more than a year usually.
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

cometqq wrote: Wed Oct 20, 2021 4:19 pm
skierincolorado wrote: Wed Oct 20, 2021 3:53 pm
cometqq wrote: Wed Oct 20, 2021 3:32 pm
skierincolorado wrote: Wed Oct 20, 2021 3:26 pm
cometqq wrote: Wed Oct 20, 2021 3:01 pm

Yeah, I think you are right that CF is fixed during the span of the contract. The pdf file from CME is enormously confusing. I find this one explains things better: http://www.yieldcurve.com/mktresearch/l ... utures.pdf

On page 12, it says that "The price of the futures contract, over time, does not move tick-for-tick with the CTD bond (although it may on an intra-day basis) but rather by the amount of the change divided by the conversion factor. It is apparent therefore that to hedge a position in the CTD bond we
must hold the number of futures contracts equivalent to the value of bonds held multiplied by the conversion factor." Equation (8) on page 12 does seem to suggest that the bond exposure is the price of the futures contract times the CF.
Ugh yes I was wrong that he CF changes. I thought it converted from market price to the reference bond.

But the statement from CME that 81 contracts hedges 10M in market value of bonds, and the statement you just quoted, both clearly indicate that the exposure is 100k/CF. This is the inverse of their statement that the number of futures contracts to hedge X thousand value in bonds is X * CF.

I am at a loss and will have to start all over again.
If you look at equation (8) on page 12 of the PDF file I quoted (I don't like the CME file, which i think is very hard to understand), the change in the futures contract price is approximately the change in the price of CTD bond divided by CF. Therefore, the exposure to bond is the price of futures contract multiplied by CF.
Your statement is based off the equation, but directly contradicts the text of both documents. Both documents state that the to hedge bonds with market value of X thousand dollars, you would sell X * CF futures contracts.

In the example, to hedge 10M market value of bonds, you would sell just 81 futures contracts. The inverse is that buying 81 futures contracts are exposing you to the return of 10M in bonds.

I can't reconcile the text with the equation.
"Both documents state that the to hedge bonds with market value of X thousand dollars, you would sell X * CF futures contracts." This is actually consistent with the equation. So if I buy one zf, the price of which is about $125k, my bond exposure would be $125k * CF (CF is about .8 for zf). In other words, if I want an exposure to 100k ITT, I'd buy n = 100k/(125k * CF) futures contracts. I feel that millennialmillions and Bentonkb were right. Their explanation makes more sense to me.
That's not what the text says though. It says that 10M in bonds is hedged by 81 contracts. It's saying bond exposure is just the futures price. 81 contracts have a futures price of 10M. Not 100 contracts.

There is also this from CME. Profit or loss is just change in futures price. Futures price is the change in price of a reference 6% bond which would have value of 100k/CF. Our profit and loss is the same as if we owned 100k/CF in marketable value of bonds.

Example 1: A trader believes that the U.S. economy is strengthening and intermediate Treasury yields will increase (5-Yr and 10-Yr).

This trader sells 10 contracts of March 2019 5-year T-Note futures at 114 25/32.

The trader’s view proves correct. The economic numbers continue to show that the US economy is strengthening. 5-Yr Treasury yields rise, and the March 2019 5-year T-Note futures price declines. The trader buys back the 10 March 2019 5-year T-Note futures contracts at 114 03/32.

Profit on this example trade = 10 * (114 25/32 – 114 03/32) * $1000 = $6,875

(Profit or Loss = Number of contracts* Change in price * $1000)
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 2:16 pm
comeinvest wrote: Wed Oct 20, 2021 2:12 pm When you say 125k you mean approximately, right?
My IB TWS currently shows a Last price of 121'305 and a mark price of 121.9530 for ZF.
So if I wanted to determine my exposure to the underlying (I think commonly referred to as "notional value") accurately, one ZF gives me exposure to the underlying bond of $121,953 plus [expected coupon payments between now and contract expiration] - [implied financing cost between now and expiration], correct? Can you confirm my math? Basically I would have to look at the current price of the underlying CTD, correct?
Yeah I was being approximate, 121953 is correct attm. I'm not sure about adding in coupon payments and subtracting financing cost. I think these would effect duration and expected return respectively, but not exposure.

It should be equivalent to buying a $121,953 bond with duration of whatever the futures duration is currently. If such a bond existed, which it doesn't, it would have a 6% coupon and 100k face value.
I thought it's the same as for equity index futures, isn't it? At expiration of the futures contract, you get the underlying. You could alternatively buy the underlying now instead of the futures contract, and borrow the money for that via margin or box spreads. You would end up with the exact same asset at time of expiration, i.e. your risk exposure is exactly the same. But the futures quotation has financing cost and any cash flows to/from the underlying between now and expiration, all "baked in". So the "notional value" i.e. your exposure to the underlying, should be the currently quoted futures price, adjusted for expected cash flows to/from the underlying (= coupon payments) and implied financing rate, correct? We could also just say, your exposure is the current quote of the underlying, that is the current spot price of the CTD, unless the CTD changes. (When I say CTD, I mean CTD with all the conversion factor math applied. I didn't follow this part of our discussion. I just mean that the current futures price is not exactly the exposure or notional value, but needs to be adjusted.)

It won't make too much difference because the contract period is only 3 months, but I just want to be sure I got it right if I want to be accurate.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 4:22 pm
comeinvest wrote: Wed Oct 20, 2021 4:09 pm Thanks for your illustrations. How far out do you go for your options box financing? Exactly 1 year, a little shorter or longer, or depending on where the slope starts to steepen? We don't want to come close to the 2y point of the curve for options boxes, if the 2y has such good returns, as we would be paying what others earn. Also, do you happen to know an easy way to look up, or a chart that shows the current rolldown yields across the maturity range? Or do you calculate those manually when needed?
For roll down I calculate manually although I've seen a graph or two online, I haven't found a source that updates with this data.

I usually just do a rough calc, like see how much the price of a 5 year bond would go up if its rate fell to the current 4 year rate. To be more precice we'd want the slope exactly at 5 years, and then annualize. Of course roll assumes the curve is static, which it isn't.

I think you're right that for boxes, shorter durations are better, but there's also the bid-ask spread to consider. I don't do many boxes so I am lazy and do more than a year usually.
I got 0.58% today for a box of exactly 1 year. About 0.08% higher than for my 3-month boxes lately. In case you are interested in this data point. Eventually, the steepening will squeeze near-zero boxes to shorter and shorter lengths, until they will evaporate.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

That's the beauty of /ZT. It doesn't really matter with a CF of 0.95!

I joke. Let me know when y'all work it out!
55% VUG - 20% VEA - 20% EDV - 5% BNDX
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skierincolorado
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Tue Oct 19, 2021 7:03 pm
cometqq wrote: Wed Oct 20, 2021 4:19 pm

"Both documents state that the to hedge bonds with market value of X thousand dollars, you would sell X * CF futures contracts." This is actually consistent with the equation. So if I buy one zf, the price of which is about $125k, my bond exposure would be $125k * CF (CF is about .8 for zf). In other words, if I want an exposure to 100k ITT, I'd buy n = 100k/(125k * CF) futures contracts. I feel that millennialmillions and Bentonkb were right. Their explanation makes more sense to me.
millennialmillions wrote: Wed Oct 20, 2021 3:57 pm
I've been convinced, so let me take a shot at explaining it. The futures price of ~$121,000 represents the price of a theoretical 5-year treasury with a $100,000 face value and 6% yield. Such a bond does not exist in practice. So for a given treasury bond, you must multiply by the CF to determine how much it is worth. When such a bond is delivered, the invoice price of ~$98,000 is paid for this bond.

However, the exposure generated from the futures contract is not the same as the exposure generated by holding the CTD underlying security. Instead, it is based on the theoretical asset mentioned above. Its price movement is equivalent to buying $121,000 worth of ITTs ("worth" meaning market value). This is verified by looking at constructor's graph and by the example from the CME paper skier provided. So your exposure from holding one futures contract is greater than holding one underlying security that meets the delivery requirements.
Bentonkb wrote: Wed Oct 20, 2021 2:26 pm I'm not convinced. If the futures price goes up by $1000, the invoice price does not go up by $1000. It only changes by $1000*CF. The CF does not change, it is fixed during the span of the contract. It is true that the CTD bond might change during the span of the contract. The short pays a small premium for the implied option represented by that choice of deliverable, but that is not a significant part of the risk calculation.

The principle stands. The long contract holder and his counterparty have opposite and nearly equal risk. Neither party has a risk that is proportional to CF. The quoted daily price is just the bond cash price divided by CF and the invoice price is just the quoted price multiplied by CF. The conversion factor cancels out and nobody has any risk associated with the hypothetical 6% yielding bond. That is why it doesn't really matter that the world has not seen a 6% treasury in a long time - it is just an arbitrary number.

The reference rate used to be 8%. It wouldn't make any difference if they changed it back. All the quoted prices would change, but the risk associated with the contract would remain the same.
OK I think I've figured it out (again). While I was wrong about the CF changing, there has to be an explation of CMEs statement that 10M market value/face value of bonds is hedged with only 81 contracts. Or that profit and loss is just change in futures price - not change in invoice price. Hopefully we can all agree and consider the issue resolved. This statement is clear as day and it is repeated across several sources I've looked at. 81 contracts = 10M in bonds when CF is .81. Thats ~125k in bonds per contract.

I think I was thinking about the issue wrong. The delivery process doesn't matter until the end. WHen you enter into the contract what matters is the futures price. The futures price is marked to market every day until expiry. So if the futures price goes up $1000, the exchange literally takes $1000 from you, and gives it to the short. Thus up until expriy, the futures price is what matters and what determines your gains and losses. This is part of the contract and the process. The delivery process is what ties the futures price to real securities, so that the futures prices are actually based upon something real. But your gains and losses are based on changes in the futures price. If you buy a ZF when ZF is 124,000, and it falls to 123,000 the next day, you just lost $1000. Which is like obvious when you look at your account, but maybe not so obvious if you are thinking about the contract simply in terms of the delivery process. The delivery process is what ties it all together at the end and ties the futures contract to real bonds, but up until that expiration, what is being traded and marked to market is a 6% bond with 100k face value.

At first I was confused because I was like, well if my ZF goes down $1000 in futures price, why don't I just hold until expiry, and I'll only lose ~$800? But I can't because every day CME is marking it to market and I already lost $1000. They literally took it from me and gave it to the short. But then I started wondering, well why does the ZF go down by $1000, when the CTD bond only lost $800? Well because if it didn't, then the short position would be screwed at expiration, so the shorts sell until the ZF futures price is down the full $1,000. Then at the end of the day this $1000 lower settlement price is used to mark the shorts and longs positions to market.

If expiration was tomorrow, and if the CTD went down $800, and the futures price only went down $800, the longs would all sell. They'd be like great I'll take my $800 loss and walk because when it expires, I'm going to lose another $200. They would be forced to pay an invoice price of 101.2k for just 101k of bonds (hypothetical #s). No fair! So they sell. The futures price drops another $200. The invoice price drops to 101k. This selling action drives the futures price down the full $1,000. At that point the longs may reenter the market because there is no gain or loss at expiration anymore (ignoring financing), because the invoice price is actually equal to what is being delivered.

This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

LTCM wrote: Wed Oct 20, 2021 5:37 pm That's the beauty of /ZT. It doesn't really matter with a CF of 0.95!

I joke. Let me know when y'all work it out!
Figured it out for real this time (I think) see post one above.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

I mean even if we didn't understand the reason why, although I think I do now (see above), we should go with CMEs statement that when the CF is .81, each contract gives exposure and has the same price movement as ~125k in bonds.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

skierincolorado wrote: Wed Oct 20, 2021 6:04 pm
LTCM wrote: Wed Oct 20, 2021 5:37 pm That's the beauty of /ZT. It doesn't really matter with a CF of 0.95!

I joke. Let me know when y'all work it out!
Figured it out for real this time (I think) see post one above.
so my 4xZF contracts are worth ~$880k or ~$835k?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

LTCM wrote: Wed Oct 20, 2021 6:44 pm
skierincolorado wrote: Wed Oct 20, 2021 6:04 pm
LTCM wrote: Wed Oct 20, 2021 5:37 pm That's the beauty of /ZT. It doesn't really matter with a CF of 0.95!

I joke. Let me know when y'all work it out!
Figured it out for real this time (I think) see post one above.
so my 4xZF contracts are worth ~$880k or ~$835k?
expose you to 880k
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

Alrighty. Thanks.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by millennialmillions »

skierincolorado wrote: Wed Oct 20, 2021 5:45 pm
OK I think I've figured it out (again). While I was wrong about the CF changing, there has to be an explation of CMEs statement that 10M market value/face value of bonds is hedged with only 81 contracts. Or that profit and loss is just change in futures price - not change in invoice price. Hopefully we can all agree and consider the issue resolved. This statement is clear as day and it is repeated across several sources I've looked at. 81 contracts = 10M in bonds when CF is .81. Thats ~125k in bonds per contract.

I think I was thinking about the issue wrong. The delivery process doesn't matter until the end. WHen you enter into the contract what matters is the futures price. The futures price is marked to market every day until expiry. So if the futures price goes up $1000, the exchange literally takes $1000 from you, and gives it to the short. Thus up until expriy, the futures price is what matters and what determines your gains and losses. This is part of the contract and the process. The delivery process is what ties the futures price to real securities, so that the futures prices are actually based upon something real. But your gains and losses are based on changes in the futures price. If you buy a ZF when ZF is 124,000, and it falls to 123,000 the next day, you just lost $1000. Which is like obvious when you look at your account, but maybe not so obvious if you are thinking about the contract simply in terms of the delivery process. The delivery process is what ties it all together at the end and ties the futures contract to real bonds, but up until that expiration, what is being traded and marked to market is a 6% bond with 100k face value.

At first I was confused because I was like, well if my ZF goes down $1000 in futures price, why don't I just hold until expiry, and I'll only lose ~$800? But I can't because every day CME is marking it to market and I already lost $1000. They literally took it from me and gave it to the short. But then I started wondering, well why does the ZF go down by $1000, when the CTD bond only lost $800? Well because if it didn't, then the short position would be screwed at expiration, so the shorts sell until the ZF futures price is down the full $1,000. Then at the end of the day this $1000 lower settlement price is used to mark the shorts and longs positions to market.

If expiration was tomorrow, and if the CTD went down $800, and the futures price only went down $800, the longs would all sell. They'd be like great I'll take my $800 loss and walk because when it expires, I'm going to lose another $200. They would be forced to pay an invoice price of 101.2k for just 101k of bonds (hypothetical #s). No fair! So they sell. The futures price drops another $200. The invoice price drops to 101k. This selling action drives the futures price down the full $1,000. At that point the longs may reenter the market because there is no gain or loss at expiration anymore (ignoring financing), because the invoice price is actually equal to what is being delivered.

This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
I agree with the conclusion but think there is a simpler explanation. I edited my above post, restating here:

The futures price of ~$121,000 represents the price of a theoretical 5-year treasury with a $100,000 face value and 6% yield. Such a bond does not exist in practice. So for a given real treasury bond, the CF represents how much it is worth relative to this theoretical bond.

The exposure generated from the futures contract is not the same as the exposure generated by holding the CTD underlying security with the same face value. Instead, it is based on the theoretical asset mentioned above. Its price movement is equivalent to buying $121,000 worth of ITTs ("worth" meaning market value). This is verified by looking at constructor's graph and by the example from the CME paper skier provided.

So your exposure from holding a futures contract with $100,000 face value is greater than holding one underlying security with $100,000. At time of delivery, you couldn't just deliver a $100,000 face value treasury; you'd have to deliver more like $121,000 face value (in this case face value and market value are pretty close).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

millennialmillions wrote: Wed Oct 20, 2021 7:07 pm
skierincolorado wrote: Wed Oct 20, 2021 5:45 pm
OK I think I've figured it out (again). While I was wrong about the CF changing, there has to be an explation of CMEs statement that 10M market value/face value of bonds is hedged with only 81 contracts. Or that profit and loss is just change in futures price - not change in invoice price. Hopefully we can all agree and consider the issue resolved. This statement is clear as day and it is repeated across several sources I've looked at. 81 contracts = 10M in bonds when CF is .81. Thats ~125k in bonds per contract.

I think I was thinking about the issue wrong. The delivery process doesn't matter until the end. WHen you enter into the contract what matters is the futures price. The futures price is marked to market every day until expiry. So if the futures price goes up $1000, the exchange literally takes $1000 from you, and gives it to the short. Thus up until expriy, the futures price is what matters and what determines your gains and losses. This is part of the contract and the process. The delivery process is what ties the futures price to real securities, so that the futures prices are actually based upon something real. But your gains and losses are based on changes in the futures price. If you buy a ZF when ZF is 124,000, and it falls to 123,000 the next day, you just lost $1000. Which is like obvious when you look at your account, but maybe not so obvious if you are thinking about the contract simply in terms of the delivery process. The delivery process is what ties it all together at the end and ties the futures contract to real bonds, but up until that expiration, what is being traded and marked to market is a 6% bond with 100k face value.

At first I was confused because I was like, well if my ZF goes down $1000 in futures price, why don't I just hold until expiry, and I'll only lose ~$800? But I can't because every day CME is marking it to market and I already lost $1000. They literally took it from me and gave it to the short. But then I started wondering, well why does the ZF go down by $1000, when the CTD bond only lost $800? Well because if it didn't, then the short position would be screwed at expiration, so the shorts sell until the ZF futures price is down the full $1,000. Then at the end of the day this $1000 lower settlement price is used to mark the shorts and longs positions to market.

If expiration was tomorrow, and if the CTD went down $800, and the futures price only went down $800, the longs would all sell. They'd be like great I'll take my $800 loss and walk because when it expires, I'm going to lose another $200. They would be forced to pay an invoice price of 101.2k for just 101k of bonds (hypothetical #s). No fair! So they sell. The futures price drops another $200. The invoice price drops to 101k. This selling action drives the futures price down the full $1,000. At that point the longs may reenter the market because there is no gain or loss at expiration anymore (ignoring financing), because the invoice price is actually equal to what is being delivered.

This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
I agree with the conclusion but think there is a simpler explanation. I edited my above post, restating here:

The futures price of ~$121,000 represents the price of a theoretical 5-year treasury with a $100,000 face value and 6% yield. Such a bond does not exist in practice. So for a given real treasury bond, the CF represents how much it is worth relative to this theoretical bond.

The exposure generated from the futures contract is not the same as the exposure generated by holding the CTD underlying security with the same face value. Instead, it is based on the theoretical asset mentioned above. Its price movement is equivalent to buying $121,000 worth of ITTs ("worth" meaning market value). This is verified by looking at constructor's graph and by the example from the CME paper skier provided.

So your exposure from holding a futures contract with $100,000 face value is greater than holding one underlying security with $100,000. At time of delivery, you couldn't just deliver a $100,000 face value treasury; you'd have to deliver more like $121,000 face value (in this case face value and market value are pretty close).
I agree with your first 3 paragraphs for sure. But I'm not sure about the last paragraph. What is actually delivered is definitely a 100k face value bond with market value also very close to 100k. And what is paid is also very close to 100k.

I think your first three paragraphs basically explain it though. What is being traded is the hypthetical 100k face with 6% yield. I think my post explains how this relates to the whole delivery process though and how the two are tied together. And why even though what is delivered and paid at expiration have market value very near 100k, the holder of the future gets the returns of ~121k in bonds for ZF currently.

I also confirmed in my IB account. I bought and sold at a particular futures price and my return was the difference. The invoice price didn't enter into the equation at all. Pretty simple and obvious in the end.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Kbg wrote: Wed Oct 20, 2021 8:07 am Relevant article to the discussion

https://www.simplify.us/blog/efficient- ... e=hs_email
Every decade in those charts had overall falling interest rates, except the 70ies. The chart for the 70ies is the only one that shows LTT better than STT and part of ITT. Any concern that the results will reverse if the interest rate trend reverts to rising?

Image
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

I know skier is fond of the ZF; but if I wanted to hedge my bets by diversifying across ZF/ZN/TN/ZB (omitting UB for the moment as it seems like it's considered a sin in this thread) - I cannot decide should I use roughly equal dollar amounts (like NTSX), or roughly equal duration risk in each bucket for diversification. Thoughts?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Wed Oct 20, 2021 11:23 pm I know skier is fond of the ZF; but if I wanted to hedge my bets by diversifying across ZF/ZN/TN/ZB (omitting UB for the moment as it seems like it's considered a sin in this thread) - I cannot decide should I use roughly equal dollar amounts (like NTSX), or roughly equal duration risk in each bucket for diversification. Thoughts?
You know what my answer will be haha. Would be a very solid plan IMO
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

skierincolorado wrote: Wed Oct 20, 2021 8:24 pm
millennialmillions wrote: Wed Oct 20, 2021 7:07 pm
skierincolorado wrote: Wed Oct 20, 2021 5:45 pm
OK I think I've figured it out (again). While I was wrong about the CF changing, there has to be an explation of CMEs statement that 10M market value/face value of bonds is hedged with only 81 contracts. Or that profit and loss is just change in futures price - not change in invoice price. Hopefully we can all agree and consider the issue resolved. This statement is clear as day and it is repeated across several sources I've looked at. 81 contracts = 10M in bonds when CF is .81. Thats ~125k in bonds per contract.

I think I was thinking about the issue wrong. The delivery process doesn't matter until the end. WHen you enter into the contract what matters is the futures price. The futures price is marked to market every day until expiry. So if the futures price goes up $1000, the exchange literally takes $1000 from you, and gives it to the short. Thus up until expriy, the futures price is what matters and what determines your gains and losses. This is part of the contract and the process. The delivery process is what ties the futures price to real securities, so that the futures prices are actually based upon something real. But your gains and losses are based on changes in the futures price. If you buy a ZF when ZF is 124,000, and it falls to 123,000 the next day, you just lost $1000. Which is like obvious when you look at your account, but maybe not so obvious if you are thinking about the contract simply in terms of the delivery process. The delivery process is what ties it all together at the end and ties the futures contract to real bonds, but up until that expiration, what is being traded and marked to market is a 6% bond with 100k face value.

At first I was confused because I was like, well if my ZF goes down $1000 in futures price, why don't I just hold until expiry, and I'll only lose ~$800? But I can't because every day CME is marking it to market and I already lost $1000. They literally took it from me and gave it to the short. But then I started wondering, well why does the ZF go down by $1000, when the CTD bond only lost $800? Well because if it didn't, then the short position would be screwed at expiration, so the shorts sell until the ZF futures price is down the full $1,000. Then at the end of the day this $1000 lower settlement price is used to mark the shorts and longs positions to market.

If expiration was tomorrow, and if the CTD went down $800, and the futures price only went down $800, the longs would all sell. They'd be like great I'll take my $800 loss and walk because when it expires, I'm going to lose another $200. They would be forced to pay an invoice price of 101.2k for just 101k of bonds (hypothetical #s). No fair! So they sell. The futures price drops another $200. The invoice price drops to 101k. This selling action drives the futures price down the full $1,000. At that point the longs may reenter the market because there is no gain or loss at expiration anymore (ignoring financing), because the invoice price is actually equal to what is being delivered.

This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.

https://us.etrade.com/knowledge/library ... -to-market
I agree with the conclusion but think there is a simpler explanation. I edited my above post, restating here:

The futures price of ~$121,000 represents the price of a theoretical 5-year treasury with a $100,000 face value and 6% yield. Such a bond does not exist in practice. So for a given real treasury bond, the CF represents how much it is worth relative to this theoretical bond.

The exposure generated from the futures contract is not the same as the exposure generated by holding the CTD underlying security with the same face value. Instead, it is based on the theoretical asset mentioned above. Its price movement is equivalent to buying $121,000 worth of ITTs ("worth" meaning market value). This is verified by looking at constructor's graph and by the example from the CME paper skier provided.

So your exposure from holding a futures contract with $100,000 face value is greater than holding one underlying security with $100,000. At time of delivery, you couldn't just deliver a $100,000 face value treasury; you'd have to deliver more like $121,000 face value (in this case face value and market value are pretty close).
I agree with your first 3 paragraphs for sure. But I'm not sure about the last paragraph. What is actually delivered is definitely a 100k face value bond with market value also very close to 100k. And what is paid is also very close to 100k.

I think your first three paragraphs basically explain it though. What is being traded is the hypthetical 100k face with 6% yield. I think my post explains how this relates to the whole delivery process though and how the two are tied together. And why even though what is delivered and paid at expiration have market value very near 100k, the holder of the future gets the returns of ~121k in bonds for ZF currently.

I also confirmed in my IB account. I bought and sold at a particular futures price and my return was the difference. The invoice price didn't enter into the equation at all. Pretty simple and obvious in the end.
skier, you said that 10M in bonds is hedged by just 81 contracts when the CF is .81. So one contract hedges 100M/CF worth of bonds. Because CF is fixed for a contract, does this mean your exposure to bond is fixed (i.e. 100M/CF) regardless of when you enter into the futures contract.

But you also said that the exposure to bond is the market value in IBKR, which changes over time. My exposure to Bond will be different if I enter into a zf contract today versus tomorrow.

I feel this becomes even more confusing. Really need some help here.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

skierincolorado wrote: Wed Oct 20, 2021 6:47 pm
LTCM wrote: Wed Oct 20, 2021 6:44 pm
skierincolorado wrote: Wed Oct 20, 2021 6:04 pm
LTCM wrote: Wed Oct 20, 2021 5:37 pm That's the beauty of /ZT. It doesn't really matter with a CF of 0.95!

I joke. Let me know when y'all work it out!
Figured it out for real this time (I think) see post one above.
so my 4xZF contracts are worth ~$880k or ~$835k?
expose you to 880k
Doe you mean 8xZF?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

No. Face value on ZF is 200k not 100k like all the others.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cometqq »

LTCM wrote: Thu Oct 21, 2021 12:34 am No. Face value on ZF is 200k not 100k like all the others.
But face value of ZF is 100k not 200k:

https://www.cmegroup.com/markets/intere ... Specs.html
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by LTCM »

Yes, my apologies. I meant the ZT. 2 year.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Oct 20, 2021 11:34 pm
comeinvest wrote: Wed Oct 20, 2021 11:23 pm I know skier is fond of the ZF; but if I wanted to hedge my bets by diversifying across ZF/ZN/TN/ZB (omitting UB for the moment as it seems like it's considered a sin in this thread) - I cannot decide should I use roughly equal dollar amounts (like NTSX), or roughly equal duration risk in each bucket for diversification. Thoughts?
You know what my answer will be haha. Would be a very solid plan IMO
You would favor equal duration risk per bucket. But then total returns would be dominated by the returns of the short end. Trying to look at it purely from a diversification point of view, considering the future might be different from the past.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bentonkb »

skierincolorado wrote: Wed Oct 20, 2021 5:45 pm This explains the statement by CME and others that 10M in bonds is hedged by just 81 contracts when the CF is .81. Or taking the inverse, 81 contracts has equal exposure to 10M in bonds. Not 8.1M.
I have a copy of the CME paper, but can you provide references to the "others" that you mention?

The example in the CME paper does answer the question unambiguously if it is correct. I've been thinking it was an error because the CME paper doesn't seem to be very well written.

Your explanation based on how the MTM process is based on futures price, which is inflated by the CF, matches my thinking six months ago when I first started looking into it. I've been going back and forth ever since. It is obviously a difficult thing to figure out, given the discussion. I'm fully prepared to accept that I need to switch back to my previous position. We have about a month before the next roll period. Hopefully I won't need all that time to get it figured out to my satisfaction. :?

On the topic of changing my point of view . . .
This thread and some PV models have convinced me to switch from ZB a shorter duration contract and some more leverage. Unfortunately, it looks like this might be pretty bad timing. What are your thoughts on the short term outlook for ZB vs ZF? I've read that the market has priced in two rate increases next year of 25 basis points each. Seems like a reasonable assumption at this point. The question, then, is whether this will result in a curve flattening or just an a 50 basis point rise across the whole curve. Curve flattening would favor sticking with ZB until things settle down. Of course, if the change is fully priced in it won't matter.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Kbg »

There's a series of videos on YouTube by Bionic Turtle that goes through all this stuff.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Kbg »

comeinvest wrote: Wed Oct 20, 2021 11:13 pm
Kbg wrote: Wed Oct 20, 2021 8:07 am Relevant article to the discussion

https://www.simplify.us/blog/efficient- ... e=hs_email
Every decade in those charts had overall falling interest rates, except the 70ies. The chart for the 70ies is the only one that shows LTT better than STT and part of ITT. Any concern that the results will reverse if the interest rate trend reverts to rising?

Image
That's a given. What these charts tell me is that ITTs are probably the place to be as they appear to be the most stable for someone who doesn't want to get into trying to time the market.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhh
Last edited by hdas on Tue Oct 26, 2021 6:40 pm, edited 1 time in total.
....
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