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

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

Post by nisiprius »

Forgive me both for butting into this thread, and for doing so in search of material to discourage someone from using leveraged ETFs in a naïve way--not in the way you all are... some of you may have leveraged ETF simulation tools.

The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?

As a very crude estimate, I tried using PortfolioVisualizer--month-to-month, monthly rebalancing, 200% QQQ, -100% CASHX and got a -98.34% drawdown, but I supposed it wouldn't have been that bad with daily rebalancing.

Source
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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 »

nisiprius wrote: Thu May 04, 2023 7:48 am Forgive me both for butting into this thread, and for doing so in search of material to discourage someone from using leveraged ETFs in a naïve way--not in the way you all are... some of you may have leveraged ETF simulation tools.

The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?

As a very crude estimate, I tried using PortfolioVisualizer--month-to-month, monthly rebalancing, 200% QQQ, -100% CASHX and got a -98.34% drawdown, but I supposed it wouldn't have been that bad with daily rebalancing.

Source
There's this python code for simulated 3x. Its max drawdown is 97%. The code could be modified to do 2x.
https://teddykoker.com/2019/04/simulati ... in-python/

I actually think just straight 2x leveraged etfs are sort of OK for a young investor with a good savings rate. The contributions reduce the volatility decay. The main issue I see with 2x LETFs isn't the volatility decay it's the high expense ratio. Leverage can be had cheaper through other means. 3x leverage experiences too much volatility decay to hold straight and needs to be rebalanced against a more stable asset. But 2x is fine for young investors and is in fact exactly what the book recommends. There's nothing particularly different between rebalancing daily or monthly. Rebalancing monthly can do better or worse.

My nephew actually holds 80% 3x leveraged equity etfs. The last 20% is basically cash to tone things back a bit. The end result is similar to a 2.5x equity letf. I actually think this is fine based on his age and savings. Using other means of leverage would only improve the expense ratio but would add complexity.

Obviously if they don't have the risk tolerance for 80%+ drawdown with 2x SP500 leverage (probably close to 90% with QQQ 2x leverage), then they shouldn't be so leveraged. But there's nothing inherently wrong with overall 2x leverage. Even 3x can be ok if contributions are large relative to investments.

It's also fine if it's just a portion of the portfolio because the rest of the portfolio acts as the balast the same way bond funds do in HFEA or mHFEA. So long as one rebalanced between the rest of the portfolio and the LETF. Without rebalancing, it's just inefficient and illogical (less leverage when the market is low and more leverage when market is high).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hydromod »

nisiprius wrote: Thu May 04, 2023 7:48 am The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?
You can use UOPIX to represent an expensive QLD. Inception date 12/1/1997, ER 1.47%.

Note that TQQQ is much better represented with 150 UOPIX/-50 CASHX than 300 QQQ/-200 CASHX.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by nisiprius »

Hydromod wrote: Thu May 04, 2023 10:00 am
nisiprius wrote: Thu May 04, 2023 7:48 am The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?
You can use UOPIX to represent an expensive QLD. Inception date 12/1/1997, ER 1.47%.

Note that TQQQ is much better represented with 150 UOPIX/-50 CASHX than 300 QQQ/-200 CASHX.
Thank you very much. I hadn't known about this fund. Then it is fair to say that UOPIX, like QLD, is a 2X leveraged Nasdaq-100 fund, and that it actually did experience a drawdown worse than -98% in 2000-2002. Source.

The effect of a 1.5% expense ratio on percent drawdown over that time period would not have been much. With a 0% expense ratio it would still have been worse than -98%. The fund would have dropped to something like, at best, $144 + 1.5% + 1.5% + 1.5% = $151.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hydromod »

nisiprius wrote: Thu May 04, 2023 10:15 am
Hydromod wrote: Thu May 04, 2023 10:00 am
nisiprius wrote: Thu May 04, 2023 7:48 am The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?
You can use UOPIX to represent an expensive QLD. Inception date 12/1/1997, ER 1.47%.

Note that TQQQ is much better represented with 150 UOPIX/-50 CASHX than 300 QQQ/-200 CASHX.
Thank you very much. I hadn't known about this fund. Then it is fair to say that UOPIX, like QLD, is a 2X leveraged Nasdaq-100 fund, and that it actually did experience a drawdown worse than -98% in 2000-2002. Source.

The effect of a 1.5% expense ratio on percent drawdown over that time period would not have been much. With a 0% expense ratio it would still have been worse than -98%. The fund would have dropped to something like, at best, $144 + 1.5% + 1.5% + 1.5% = $151.
I like to account for the irrational NASDAQ runup as well, which accentuated the drawdown. One can go back to 12/97 with RYOCX. Starting at that point, UOPIX finally recovered above RYOCX in 2021 for a year or so before dropping back.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

nisiprius wrote: Thu May 04, 2023 10:15 am
Hydromod wrote: Thu May 04, 2023 10:00 am
nisiprius wrote: Thu May 04, 2023 7:48 am The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?
You can use UOPIX to represent an expensive QLD. Inception date 12/1/1997, ER 1.47%.

Note that TQQQ is much better represented with 150 UOPIX/-50 CASHX than 300 QQQ/-200 CASHX.
Thank you very much. I hadn't known about this fund. Then it is fair to say that UOPIX, like QLD, is a 2X leveraged Nasdaq-100 fund, and that it actually did experience a drawdown worse than -98% in 2000-2002. Source.

The effect of a 1.5% expense ratio on percent drawdown over that time period would not have been much. With a 0% expense ratio it would still have been worse than -98%. The fund would have dropped to something like, at best, $144 + 1.5% + 1.5% + 1.5% = $151.
QQQ unlevered was down 81% so yeah 98% is not too surprising. Note that Nasdaq-100 was much smaller and less diversified back then. It's still not nearly as diversified as SPY of course and I think buying QQQ is a bad idea and leveraging it is even worse.

For SPY, monthly 2x gives an 87% drawdown, but daily leveraged drawdown was around 80% if I remember. So for 2x QQQ daily, you might see 97% instead of 98% drawdown in 2000-2002.

Again, I don't see anything wrong with a young investor with good savings rate using 2x daily LETF, but it should be SPY not QQQ. If it's not the whole portfolio, one should rebalance with the rest of the portfolio periodically. And it's a temporary solution until the sums invested become consequential because the expense ratio is a bit high for my taste.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

comeinvest wrote: Mon Nov 14, 2022 3:36 pm
unemployed_pysicist wrote: Mon Nov 14, 2022 3:26 pm
comeinvest wrote: Mon Nov 14, 2022 2:26 pm It is possible to concatenate performance with custom rebalancing / portfolio switch dates in PV? If not, we need a quarterly data source. I think Simba is only yearly. Spreadsheet would be better anyways.
I thought there was a simple way to switch assets in portfolio visualizer? I've never used that feature so I don't know for sure.

What do you mean by spreadsheet? Something like one column for the quarterly date, one column for the quarterly max carry maturity, one column for the assigned index fund corresponding to the max carry maturity (vfisx, vfitx, vustx, vedtx), one column for the quarterly return of the assigned index fund from the start date, one column for the 3 month Tbill, one column for excess return? Something like that?
I was just saying if we have a spreadsheet, it's better than PV because it's more customizable. I have not looked too much into data sources; I just started with simulations. I don't know if there is some quarterly data in Simba or elsewhere. I think Yahoo might have historical data for ETFs to download. At least free equities data is easier to come by than free futures data.
I can't remember, did I already share this plot with you?

Image

I used the max carry switch dates indicated in one of my previous posts.

From this, it does not look like the max carry strategy offered any better risk adjusted performance than just staying in VFISX the entire time. At least since 1992 using bond funds to approximate the duration of the max carry bond, and all the rest of the methodology discussed earlier.

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

Post by unemployed_pysicist »

comeinvest wrote: Fri Feb 24, 2023 1:06 pm
If unemployed physicist was still here, he could provide the absolute implied financing cost :)
I missed the last roll date, my apologies.

Isn't there a roll date coming up soon? :happy
I got these at around 2pm EST today.

Code: Select all

       
src_line_nbr	cusip 	contract_code	irr	irr_minus_closest_bill_yield                                                               
200           91282CGU9         tum23  3.715133                     -1.004867
210           91282CEU1         tuu23  4.828620                     -0.129380
222           91282CFK2         tuz23  5.359701                      0.851701
246           91282CGR6        3yrm23  5.194143                      0.474143
257           9128287B0        3yru23  4.890204                     -0.067796
266           912828YG9        3yrz23  4.738498                      0.230498
301           91282CFH9         fvm23  4.186921                     -0.533079
310           91282CFZ9         fvu23  5.078958                      0.120958
319           91282CGP0         fvz23  5.520237                      1.012237
364           91282CGB1         tym23  4.528257                     -0.039743
370           91282CGS4         tyu23  4.978276                      0.020276
374           91282CAE1         tyz23  3.907316                     -0.600684
445           912810QC5         usm23  4.022013                     -0.545987
445           912810QC5         usu23  5.021705                      0.063705
445           912810QC5         usz23  5.484231                      0.976231
592           912810SE9         ulm23  2.356156                     -2.221844
592           912810SE9         ulu23  4.573097                     -0.386903
595           912810SF6         ulz23  3.243784                     -1.266216
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

I thought readers of this thread might be interested in this related discussion: "Role of bonds - with no term premium" https://community.rationalreminder.ca/t ... mium/23280 . I think you have to register, but it's free.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Interesting seasonality of treasury returns from the paper "Seasonal Variation in Treasury Returns" https://tspace.library.utoronto.ca/bits ... eturns.pdf

Between February and April, on average you are guaranteed to lose according to this, even though the average term premium was positive between 1952 and 2007.

Perhaps lighten up on treasury futures next Spring?

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

Post by km91 »

comeinvest wrote: Thu May 18, 2023 4:02 am I thought readers of this thread might be interested in this related discussion: "Role of bonds - with no term premium" https://community.rationalreminder.ca/t ... mium/23280 . I think you have to register, but it's free.
What's your take on vineviz first reply. I tend to agree with his views on LTT generally, and would think that in a strategy with long term leverage and over 100% of NAV in equities having exposure to duration matched risk free asset is preferred, despite what the sharpe ratio might say. It introduces more volatility which might not be ideal depending on how much the investor is leveraged. But there's much stronger economic intuition underlying the low / negative correlation to equities of LTT vs ITT and it represents the true risk free asset for a long term investor
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

km91 wrote: Thu May 18, 2023 6:45 pm
comeinvest wrote: Thu May 18, 2023 4:02 am I thought readers of this thread might be interested in this related discussion: "Role of bonds - with no term premium" https://community.rationalreminder.ca/t ... mium/23280 . I think you have to register, but it's free.
What's your take on vineviz first reply. I tend to agree with his views on LTT generally, and would think that in a strategy with long term leverage and over 100% of NAV in equities having exposure to duration matched risk free asset is preferred, despite what the sharpe ratio might say. It introduces more volatility which might not be ideal depending on how much the investor is leveraged. But there's much stronger economic intuition underlying the low / negative correlation to equities of LTT vs ITT and it represents the true risk free asset for a long term investor
I think everything has been said in this and other threads. I personally don't care about duration matching my liabilities. First I don't know my futures liabilities; second my liabilities if and when they will arrive will be real not nominal; third my equities are already my long-term hedge with respect to future liabilities in real terms. Fourth, you can deliberate and try academic or philosophical reasoning and do all the liability matching you like all day long; but in the end I think skier and others showed in numerous simulations that STT and ITT have lower risk and higher returns in the long run. So what's the point. I signed out of that other BH thread that goes like why you should have 20% of fixed income in LTT. Those folks seem to be really passionate about micro-managing unknown future liabilities with unknown nominal LTT returns (?!); but I never understood the point of this exercise. If anything I rather try to optimize the probabilistic distribution of my future spending power. Just my two cents.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by km91 »

comeinvest wrote: Thu May 18, 2023 8:25 pm
km91 wrote: Thu May 18, 2023 6:45 pm
comeinvest wrote: Thu May 18, 2023 4:02 am I thought readers of this thread might be interested in this related discussion: "Role of bonds - with no term premium" https://community.rationalreminder.ca/t ... mium/23280 . I think you have to register, but it's free.
What's your take on vineviz first reply. I tend to agree with his views on LTT generally, and would think that in a strategy with long term leverage and over 100% of NAV in equities having exposure to duration matched risk free asset is preferred, despite what the sharpe ratio might say. It introduces more volatility which might not be ideal depending on how much the investor is leveraged. But there's much stronger economic intuition underlying the low / negative correlation to equities of LTT vs ITT and it represents the true risk free asset for a long term investor
I think everything has been said in this and other threads. I personally don't care about duration matching my liabilities. First I don't know my futures liabilities; second my liabilities if and when they will arrive will be real not nominal; third my equities are already my long-term hedge with respect to future liabilities in real terms. Fourth, you can deliberate and try academic or philosophical reasoning and do all the liability matching you like all day long; but in the end I think skier and others showed in numerous simulations that STT and ITT have lower risk and higher returns in the long run. So what's the point. I signed out of that other BH thread that goes like why you should have 20% of fixed income in LTT. Those folks seem to be really passionate about micro-managing unknown future liabilities with unknown nominal LTT returns (?!); but I never understood the point of this exercise. If anything I rather try to optimize the probabilistic distribution of my future spending power. Just my two cents.
I don't want to argue the point of matching liabilities per se. Maybe to rephrase I'd ask do LTTs de-risk a portfolio in a way that ITT and STT do not and that is not captured by the statistical risk metrics, is this risk reduction of value to a lifecycle investor, and are the lower supposed returns of LTTs worth the trade off. Swap nominals for TIPS to suit your preference

On the first point I would answer yes, LTTs are risk free in a way that volatility doesn't measure. If my investment horizon is 30 years, I can buy a 30yr bond or TIPS and know with 100% certainty the final value of my portfolio or I can buy equities and expect to earn a return above long term rates but with uncertainty. In this context the claim that ITT or STT are less risky than LTT is a bit dubious as there is no risk surrounding the final value of LTTs

On the second question my naïve intuition also says yes. If the goal of lifecycle investing is to better diversify risk exposure across time and to better align risk exposure with an investors capacity for risk taking, LTTs again seem preferable despite what risk adjusted returns might suggest. They align with the investors time frame and capacity to take on volatility risk, and they are a better diversifier of equity risk than ITT or STT. If an investor has a goal of optimizing the distribution of future purchasing power, LTTs would seem superior in that they narrow the distribution of outcomes

On the third question I don't know the answer but I suspect there is something to be gained by trading off higher return of ITT for the de-risking benefits of LTTs. At the very least we know that LTTs narrow the distribution of outcomes
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

km91 wrote: Fri May 19, 2023 12:51 pm
comeinvest wrote: Thu May 18, 2023 8:25 pm
km91 wrote: Thu May 18, 2023 6:45 pm
comeinvest wrote: Thu May 18, 2023 4:02 am I thought readers of this thread might be interested in this related discussion: "Role of bonds - with no term premium" https://community.rationalreminder.ca/t ... mium/23280 . I think you have to register, but it's free.
What's your take on vineviz first reply. I tend to agree with his views on LTT generally, and would think that in a strategy with long term leverage and over 100% of NAV in equities having exposure to duration matched risk free asset is preferred, despite what the sharpe ratio might say. It introduces more volatility which might not be ideal depending on how much the investor is leveraged. But there's much stronger economic intuition underlying the low / negative correlation to equities of LTT vs ITT and it represents the true risk free asset for a long term investor
I think everything has been said in this and other threads. I personally don't care about duration matching my liabilities. First I don't know my futures liabilities; second my liabilities if and when they will arrive will be real not nominal; third my equities are already my long-term hedge with respect to future liabilities in real terms. Fourth, you can deliberate and try academic or philosophical reasoning and do all the liability matching you like all day long; but in the end I think skier and others showed in numerous simulations that STT and ITT have lower risk and higher returns in the long run. So what's the point. I signed out of that other BH thread that goes like why you should have 20% of fixed income in LTT. Those folks seem to be really passionate about micro-managing unknown future liabilities with unknown nominal LTT returns (?!); but I never understood the point of this exercise. If anything I rather try to optimize the probabilistic distribution of my future spending power. Just my two cents.
I don't want to argue the point of matching liabilities per se. Maybe to rephrase I'd ask do LTTs de-risk a portfolio in a way that ITT and STT do not and that is not captured by the statistical risk metrics, is this risk reduction of value to a lifecycle investor, and are the lower supposed returns of LTTs worth the trade off. Swap nominals for TIPS to suit your preference

On the first point I would answer yes, LTTs are risk free in a way that volatility doesn't measure. If my investment horizon is 30 years, I can buy a 30yr bond or TIPS and know with 100% certainty the final value of my portfolio or I can buy equities and expect to earn a return above long term rates but with uncertainty. In this context the claim that ITT or STT are less risky than LTT is a bit dubious as there is no risk surrounding the final value of LTTs

On the second question my naïve intuition also says yes. If the goal of lifecycle investing is to better diversify risk exposure across time and to better align risk exposure with an investors capacity for risk taking, LTTs again seem preferable despite what risk adjusted returns might suggest. They align with the investors time frame and capacity to take on volatility risk, and they are a better diversifier of equity risk than ITT or STT. If an investor has a goal of optimizing the distribution of future purchasing power, LTTs would seem superior in that they narrow the distribution of outcomes

On the third question I don't know the answer but I suspect there is something to be gained by trading off higher return of ITT for the de-risking benefits of LTTs. At the very least we know that LTTs narrow the distribution of outcomes
Your 3 questions are kind of all the same, liability matching. Look. You cannot eat or consume a perceived, theoretical "liability match". You didn't show any evidence for your conclusion, other than a theoretical thought. Yes, if the 30y as well as the 10y and the 2y are at about 3.5% now, interest rates fall gradually between now and your retirement in 30 years from 3.5% now to 1% at all maturities, then theoretically it is possible that with STT or ITT you won't earn any money from valuation changes during those 30 years because the drop in yields is already priced in each time you have to roll your bond ladder or your futures; with a 30y LTT you are guaranteed to profit from the drop in yields, i.e. you can "lock in" your yield as a return, something you cannot do with leveraged STT or ITT, even if you leverage them to match the duration of the LTT. But in practice it doesn't work that way. All the backtests that were presented in this thread showed that STT and ITT have higher returns per duration due to higher term premia per duration, in that order STT -> ITT -> LTT. Read the paper that I posted that shows the results of Eurodollar futures of various maturities between 0 and 2 years in an equities portfolio, or the Newedge paper, or Carry Investing on the Yield Curve, or skier's backtests, or physicist's recent charts in the HFEA side discussion thread. Over 30 years, those additional returns and/or less drawdowns (depending on your leverage ratio) will compound, and you will be almost guaranteed to come out ahead - the longer your investment horizon, the higher the probability that you come out ahead with STT or ITT. Just like the longer your investment horizon, the more you are guaranteed to come out ahead of T-bills (or bonds) with equities - almost 100% likelihood after 20 years. Simulating 30 years, if you play a game 30 times in a row where the odds are staked more in your favor vs. a game where the odds are staked less in your favor, you are almost guaranteed to come out ahead with the first game, even when each individual round of the second game is less risky than the first game, and/or even if the second game promised you some low minimum boundary after 30 rounds. There are 2 free lunches in investing: 1. diversification of idiosyncratic risk (30+ different stocks, 2+ asset classes); 2. time diversification (end results will asymptotically gravitate towards the exponential function with the short-term risk premium as exponent; the passage of time will "fix" almost any short-term anomaly and deviation from this exponential growth). Therefore, for the investor with longer time horizon, the optimization target (best distribution of final outcomes) should translate to finding the portfolio with the highest sharpe ratio, which would then be leveraged to a leverage ratio to maximize returns after volatility decay. With the highest sharpe ratio, the exponent in the exponential function is highest, which means your portfolio will crush everything else with the passage of time - all you have to do is sit and wait.

Long story short - in the end, real life statistical distributions of final outcomes will prevail over your theoretical thought of how markets might behave but how they don't behave in real life, and over your perceived "safety". Define your correct optimization target function first, before you start optimizing towards a target. For me, "more money with 99%+ likelihood" equals "safer" - I have a great margin of safety, and my liabilities that I would have matched with an LTT (or equities+LTT, or T-bills, etc.) will be matched many times over with equities+STT+ITT, and then some more - simply because equities+STT+ITT has the highest sharpe ratio, and therefore the biggest number in the exponent of the exponential growth function.

If you read the posts and discussions earlier in this thread, there is some uncertainty as so the assumption that shorter maturities have higher risk-adjusted returns - there were times longer ago in history when this was not the case; it's not like a law of physics. But this is different from your argument. In modern history, the statistics was pretty consistent.
Last edited by comeinvest on Sat May 20, 2023 2:22 pm, edited 4 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

IRRs at around 4pm EST yesterday:
(Showing just the CTDs)

Code: Select all

src_line_nbr  cusip 	contract_code	irr  	irr_minus_closest_bill_yield                                                               
200           91282CGU9         tum23  3.747290                     -1.280710
210           91282CEU1         tuu23  4.881628                     -0.173372
222           91282CFK2         tuz23  5.350959                      0.735959
246           91282CGR6        3yrm23  5.052681                      0.019681
257           9128287B0        3yru23  4.906330                     -0.153670
266           912828YG9        3yrz23  4.998832                      0.378832
301           91282CFH9         fvm23  4.405474                     -0.627526
310           91282CFZ9         fvu23  5.305488                      0.245488
319           91282CGP0         fvz23  5.670068                      1.050068
364           91282CGB1         tym23  4.989822                      0.279822
370           91282CGS4         tyu23  5.248377                      0.193377
374           91282CAE1         tyz23  4.994062                      0.379062
442           912810QB7         usm23  4.911760                      0.201760
442           912810QB7         usu23  5.239649                      0.181649
442           912810QB7         usz23  5.488968                      0.870968
592           912810SE9         ulm23  1.201640                     -3.506360
592           912810SE9         ulu23  4.664552                     -0.393448
595           912810SF6         ulz23  4.071185                     -0.541815
Two year and three year note futures September contract IRR spread to Tbills still holding at around 0. I am curious to see how the IRRs hold up through this roll period.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Sat May 20, 2023 4:07 am IRRs at around 4pm EST yesterday:
(Showing just the CTDs)

Code: Select all

src_line_nbr  cusip 	contract_code	irr  	irr_minus_closest_bill_yield                                                               
200           91282CGU9         tum23  3.747290                     -1.280710
210           91282CEU1         tuu23  4.881628                     -0.173372
222           91282CFK2         tuz23  5.350959                      0.735959
246           91282CGR6        3yrm23  5.052681                      0.019681
257           9128287B0        3yru23  4.906330                     -0.153670
266           912828YG9        3yrz23  4.998832                      0.378832
301           91282CFH9         fvm23  4.405474                     -0.627526
310           91282CFZ9         fvu23  5.305488                      0.245488
319           91282CGP0         fvz23  5.670068                      1.050068
364           91282CGB1         tym23  4.989822                      0.279822
370           91282CGS4         tyu23  5.248377                      0.193377
374           91282CAE1         tyz23  4.994062                      0.379062
442           912810QB7         usm23  4.911760                      0.201760
442           912810QB7         usu23  5.239649                      0.181649
442           912810QB7         usz23  5.488968                      0.870968
592           912810SE9         ulm23  1.201640                     -3.506360
592           912810SE9         ulu23  4.664552                     -0.393448
595           912810SF6         ulz23  4.071185                     -0.541815
Two year and three year note futures September contract IRR spread to Tbills still holding at around 0. I am curious to see how the IRRs hold up through this roll period.
Thanks! Super interesting, and an important ingredient in validating the implementation of the mHFEA strategy. Please keep us posted frequently; I'm curious how stable the rates are over the course of a day and during the roll period, as well as outside the roll period. In you May 12 post, all maturities had a spread close to zero, except the 2y had ca. -0.13%; and the 30y also had a low -0.39%, almost identical to now.

A few thoughts:

- Spreads to treasuries may be unusually low and perhaps not meaningful on an absolute basis because treasuries are not considered risk-free these days because of the debt ceiling. See my post and the subsequent replies that I received: viewtopic.php?p=7259352#p7259352
Perhaps the spread to Term SOFR is more meaningful? 1 mo., 3 mo., and 6 mo. Term SOFR rates are published on the ICE web site; I don't know about the 4 mo.; perhaps you would have to intelligently interpolate it.

- The IRRs for June and December expirations are not meaningful because of the short time to expiration of the June contracts and the low trading volume of the Dec contracts, are they?

- I find the 0.35% - 0.4% difference between the 2y spread and the 5y and 10y spreads disturbing, because I use the 5y and 10y treasury futures.

- The favorable IRR of the ultra long bond future is remarkable. What are potential explanations for the different IRRs of different maturities? Dealers who have short futures positions will hedge with a long position in the underlying, and the different duration risk is reflected in the corresponding futures margin requirements as well as the bid/ask spreads; so the IRR should be about equal across maturities shouldn't it?
The ultra long bond future contract was cheaper (in terms of financing spread) in every one of your absolute IRR calcs, if I remember right, with spreads more favorable in comparison to ITT futures by often 0.5% p.a. or more; except on Oct 24 and on Nov 18 2022. If this is a pattern, might this change the rationale of mHFEA when implemented with futures? Backtest traditional HFEA with LTT and add 0.5% p.a.?
viewtopic.php?p=6930575&hilit=irr#p6930575
viewtopic.php?p=6936782&hilit=irr#p6936782
viewtopic.php?p=6969015&hilit=irr#p6969015
viewtopic.php?p=6979271&hilit=irr#p6979271
viewtopic.php?p=6983231&hilit=irr#p6983231
viewtopic.php?p=7264007&hilit=irr#p7264007

- I'm not sure if you are also following or analyzing SOFR futures let along using them; but spreads of SOFR futures would be another interesting metric for folks who implement mHFEA with SOFR futures - I think a meaningful comparison would be to implied treasury forward rates, or to swap rates?

- You can't add the 20y future to your calculation algo, can you?

Thanks again for sharing your data!!!
Last edited by comeinvest on Sun May 21, 2023 1:13 pm, edited 1 time in total.
unemployed_pysicist
Posts: 220
Joined: Sat Oct 09, 2021 2:32 pm
Location: Amsterdam

Re: SOFR futures

Post by unemployed_pysicist »

SCraw wrote: Thu Apr 13, 2023 5:44 am
comeinvest wrote: Thu Apr 13, 2023 5:11 am
SCraw wrote: Thu Apr 13, 2023 5:04 am If we term out SOFR vs the $ swaps curve we get the SOFR fixed at ~29bps tighter than USSWs. Based on the latest ISDA fallbacks, ED futures are converting to SFR futs at 26.1bps tighter tomorrow. The $ Swaps curve is broadly in line with the T actives curve save for the 20-30y space where spread widens to 45bps

Not exact equivalents, but I see EDH8 (Mar28) at 3.28 vs the 5y3m USSW forward of 3.44 and the 5y3m T fwd at 3.39. SFRH8 is 3.02 and I see 5y3m SOFR fwd at 3.15. All in line.
Not understanding everything you are saying at the moment; perhaps I need to study yield curve mathematics a little more or perhaps just grasp it intuitively better. But why are the interest rates implied by the IB quotes and mark prices for SOFR futures different from the SOFR forward rates in the chart? Isn't forward rate = 100 - [value of SOFR futures] by definition?
This might help understand - here are the actual forward curves

Edit: Stripping SFRH5 (Mar25) to SFRH8 below. I've roughly matched it with the tenors for actual 3m forwards for SOFR fixed/USD Swaps/Treasuries. There's a few things going on in this decomposition - there's a difference between Treasuries and the USSW (USD Swaps) actually used in FRAs, then a difference between termed SOFR and those USD swaps (should be 29bps as of now), and then also a gap between the SFR futures contracts I've used and the tenor I've matched it with.

Image
Thank you for sharing your expertise with the members of this thread.

I have an unrelated question regarding some abnormalities in the current yield curve. I was wondering if you could comment on the following chart:

Image

Specifically, the (sizeable) dips centered at the 2031-02-15, CUSIP: 91282CBL4, and 2029-11-15, CUSIP: 912828YS3. The dips have the telltale sign of a liquidity premium for being OTR, fails to deliver on the CTD, special in the repo market, or some other market dislocation.

However, upon inspection, these are not on-the-runs or even first off-the-runs, and they are not CTDs. 91282CBL4 is deliverable to all of the ten year note futures contracts, but its IRR is quite far from the IRR of the current CTD for all contracts. 912828YS3 does not appear to be deliverable to any futures contract. I don't know how to check if something is special in the repo market, but I don't see any compelling reason for why these issues would be special. The yield dips are also not a function of lower duration due to higher coupon; their durations are similar to the surrounding bonds. In fact, 912828YS3 has a 10 bps lower yield than the nearby 91282CFT3, yet 912828YS3 has the higher duration (by ~0.3).

These dips have been persistent in recent history; I first noticed them a week ago and the dips have been there whenever I check. I would like to hear your expert opinion on this phenomenon.

Thanks!
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unemployed_pysicist
Posts: 220
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

comeinvest wrote: Sat May 20, 2023 3:43 pm
unemployed_pysicist wrote: Sat May 20, 2023 4:07 am IRRs at around 4pm EST yesterday:
(Showing just the CTDs)

Code: Select all

src_line_nbr  cusip 	contract_code	irr  	irr_minus_closest_bill_yield                                                               
200           91282CGU9         tum23  3.747290                     -1.280710
210           91282CEU1         tuu23  4.881628                     -0.173372
222           91282CFK2         tuz23  5.350959                      0.735959
246           91282CGR6        3yrm23  5.052681                      0.019681
257           9128287B0        3yru23  4.906330                     -0.153670
266           912828YG9        3yrz23  4.998832                      0.378832
301           91282CFH9         fvm23  4.405474                     -0.627526
310           91282CFZ9         fvu23  5.305488                      0.245488
319           91282CGP0         fvz23  5.670068                      1.050068
364           91282CGB1         tym23  4.989822                      0.279822
370           91282CGS4         tyu23  5.248377                      0.193377
374           91282CAE1         tyz23  4.994062                      0.379062
442           912810QB7         usm23  4.911760                      0.201760
442           912810QB7         usu23  5.239649                      0.181649
442           912810QB7         usz23  5.488968                      0.870968
592           912810SE9         ulm23  1.201640                     -3.506360
592           912810SE9         ulu23  4.664552                     -0.393448
595           912810SF6         ulz23  4.071185                     -0.541815
Two year and three year note futures September contract IRR spread to Tbills still holding at around 0. I am curious to see how the IRRs hold up through this roll period.
Thanks! Super interesting, and an important ingredient in validating the implementation of the mHFEA strategy. Please keep us posted frequently; I'm curious how stable the rates are over the course of a day and during the roll period, as well as outside the roll period. In you May 12 post, all maturities had a spread close to zero, except the 2y had ca. -0.13%; and the 30y also had a low -0.39%, almost identical to now.

A few thoughts:

- Spreads to treasuries may be unusually low and perhaps not meaningful on an absolute basis because treasuries are not considered risk-free these days because of the debt ceiling. See my post and the subsequent replies that I received: viewtopic.php?p=7259352#p7259352
Perhaps the spread to Term SOFR is more meaningful? 1 mo., 3 mo., and 6 mo. Term SOFR rates are published in the ICE web site; I don't know about the 4 mo.; perhaps you would have to intelligently interpolate it.

- The IRRs for June and December expirations are not meaningful because of the short time to expiration of the June contracts and the low trading volume of the Dec contracts, are they?

- I find the 0.35% - 0.4% difference between the 2y spread and the 5y and 10y spreads disturbing, because I use the 5y and 10y treasury futures.

- The favorable IRR of the ultra long bond future is remarkable. What are potential explanations for the different IRRs of different maturities? Dealers who have short futures positions will hedge with a long position in the underlying, and the different duration risk is reflected in the corresponding futures margin requirements as well as the bid/ask spreads; so the IRR should be about equal across maturities shouldn't it?
The ultra long bond future contract was cheaper (in terms of financing spread) in every one of your absolute IRR calcs, if I remember right, with spreads more favorable in comparison to ITT futures by often 0.5% p.a. or more; except on Oct 24 and on Nov 18 2022. If this is a pattern, might this change the rationale of mHFEA when implemented with futures? Backtest traditional HFEA with LTT and add 0.5% p.a.?
viewtopic.php?p=6930575&hilit=irr#p6930575
viewtopic.php?p=6936782&hilit=irr#p6936782
viewtopic.php?p=6969015&hilit=irr#p6969015
viewtopic.php?p=6979271&hilit=irr#p6979271
viewtopic.php?p=6983231&hilit=irr#p6983231
viewtopic.php?p=7264007&hilit=irr#p7264007

- I'm not sure if you are also following or analyzing SOFR futures let along using them; but spreads of SOFR futures would be another interesting metric for folks who implement mHFEA with SOFR futures - I think a meaningful comparison would be to implied treasury forward rates, or to swap rates?

- You can't add the 20y future to your calculation algo, can you?

Thanks again for sharing your data!!!
- Spread to term SOFR seems reasonable. But I don't have a way to get them from the ICE website or interpolate the yields in place yet. I can already get the zero coupon curve for SOFR from the quarterly futures contracts. Maybe I could include the monthly SOFR contracts and find a way to interpolate. I should check to see how close my SOFR zero coupon yields are to the term SOFR rates.

- The december contracts appear to be thinly traded and there are few contracts, so I imagine those IRRs are not meaningful. I presume though that the IRR of the June contracts is meaningful to a basis trader. Although I wonder, if you consistently buy a futures contract at a positive IRR (futures are rich relative to the CTD cash bond) and sell at a negative IRR (futures are cheap relative to the CTD cash bond), doesn't this increase your cost of leverage? Maybe such an effect would be minimal, because the price of the CTD and the futures contract will have converged significantly when there's only ~1 month until the contract expires.

- I mentioned the IRR of the Tbond futures contract in the fed funds side thread. The IRR of the Tbond futures contract has gone through long periods where it was negative. I don't know the precise reason why the IRR spread of the Ultra-bond futures contract has been consistently negative recently. My gut feeling is that the negative spread is due to the high implied volatility in the bond market right now - and that maybe the IV is higher for longer durations. Perhaps the relatively higher demand for the five and ten year futures contracts means that futures contracts run a little richer than for the others. But there's no coherent overall pattern for the spread for all the maturities. In short: I don't know. I'm not sure if I'm ready to add 0.5% p.a. to LTT just yet, since maybe this current phenomenon is... transitory :P

- I have my code that bootstraps the zero coupon curve from SOFR futures contracts. It is not fully clear to me yet how to calculate the implied financing of a SOFR futures contract. I will look into it.

- Unfortunately, I am unable to add the twenty year bond contract with the current setup since I get my quotes from Marketwatch. They do not offer information for the twenty year or ultra ten year contracts. I know that it is possible to get quotes from CME, but I have never been able to do so successfully.

I originally made the code out of curiosity - I would like to develop some additional analytics/dashboard for the forward curves, option-adjusted basis, probability to be CTD, etc. Nowadays I mostly just run it to share the numbers with this thread :happy
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comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Sun May 21, 2023 10:45 am - I mentioned the IRR of the Tbond futures contract in the fed funds side thread. The IRR of the Tbond futures contract has gone through long periods where it was negative. I don't know the precise reason why the IRR spread of the Ultra-bond futures contract has been consistently negative recently. My gut feeling is that the negative spread is due to the high implied volatility in the bond market right now - and that maybe the IV is higher for longer durations. Perhaps the relatively higher demand for the five and ten year futures contracts means that futures contracts run a little richer than for the others. But there's no coherent overall pattern for the spread for all the maturities. In short: I don't know. I'm not sure if I'm ready to add 0.5% p.a. to LTT just yet, since maybe this current phenomenon is... transitory :P
The rationale behind mHFEA is the opposite - that there is higher demand for LTT than for ITT. If for futures the opposite is the case, that would be disturbing.

However over the last 10 years, Apr 30 3013 to Apr 28 2023, the S&P Ultra T-Bond Futures Index https://www.spglobal.com/spdji/en/indic ... /#overview which is a funded index with the collateral invested in T-bills had a total return of 152.24 / 147.2 -> 3.4% while VGLT https://www.portfoliovisualizer.com/bac ... ion1_1=100 had a total return of 15087 / 13621 -> 10.8%. That's 7.4 percentage points or about 0.74% p.a. less for the future (linearized calculation). The calc is not precise because we don't have the historical durations of either the futures or VGLT; but because beginning and end index values are close over that period, the durations shouldn't make a big difference.

Let me however check if your absolute futures IRR calcs are consistent with the futures returns vs VGLT between Sep 30 2022 and Apr 30 2023:
Your IRR calcs - I'm taking the front month contract outside roll periods, and the back month contract during roll periods:
Oct 24 2022: ulz22: -0.552575 viewtopic.php?p=6930575&hilit=irr#p6930575
Oct 28 2022: ulz22: -1.352876 viewtopic.php?p=6936782&hilit=irr#p6936782
Nov 18 2022: ulz22: -0.316717 / ulh23: 0.259291 viewtopic.php?p=6969015&hilit=irr#p6969015
Nov 25 2022: ulh23: -0.645270 viewtopic.php?p=6979271&hilit=irr#p6979271
Nov 28 2022: ulh22: -0.544727 viewtopic.php?p=6983231&hilit=irr#p6983231
May 12 2023: ulm23: -2.221844 / ulu23: -0.386903 viewtopic.php?p=7264007&hilit=irr#p7264007
May 20 2023: ulm23: -3.506360 / ulu23: -0.393448 viewtopic.php?p=7275703#p7275703
Ultra futures: 152.24 / 144.92 -> 1.0505
VGLT: 15087 / 14246 -> 1.059
Ultra future CTD duration per 05/19/2023: 16.7312
VGLT duration per 04/30/2023: 16.1
VGLT return adjusted to ultra futures duration: 1 + (0.059 / 16.1 * 16.7312) -> 1.0613
Ultra futures minus VGLT adjusted return: 1.0505 - 1.0613 = -0.0108 -> annualized: -0.0108 / 7 * 12 -> -0.0185 p.a.
We don't have very much data to reconcile the data sets, but based on your IRR data from Nov 18 2022, the Nov 2022 roll would have cost ca. 0.35% p.a. (accounting for the different times to expiration left of the ulz22 and the ulh23), in comparison to the drag of 1.85% p.a. per the S&P data.

Image

Image

Image
Last edited by comeinvest on Sun May 21, 2023 1:06 pm, edited 1 time in total.
Alpha4
Posts: 175
Joined: Tue Apr 17, 2012 8:47 pm

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

Post by Alpha4 »

skierincolorado wrote: Thu May 04, 2023 8:23 am
nisiprius wrote: Thu May 04, 2023 7:48 am Forgive me both for butting into this thread, and for doing so in search of material to discourage someone from using leveraged ETFs in a naïve way--not in the way you all are... some of you may have leveraged ETF simulation tools.

The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?

As a very crude estimate, I tried using PortfolioVisualizer--month-to-month, monthly rebalancing, 200% QQQ, -100% CASHX and got a -98.34% drawdown, but I supposed it wouldn't have been that bad with daily rebalancing.

Source
There's this python code for simulated 3x. Its max drawdown is 97%. The code could be modified to do 2x.
https://teddykoker.com/2019/04/simulati ... in-python/

I actually think just straight 2x leveraged etfs are sort of OK for a young investor with a good savings rate. The contributions reduce the volatility decay. The main issue I see with 2x LETFs isn't the volatility decay it's the high expense ratio. Leverage can be had cheaper through other means. 3x leverage experiences too much volatility decay to hold straight and needs to be rebalanced against a more stable asset. But 2x is fine for young investors and is in fact exactly what the book recommends. There's nothing particularly different between rebalancing daily or monthly. Rebalancing monthly can do better or worse.

My nephew actually holds 80% 3x leveraged equity etfs. The last 20% is basically cash to tone things back a bit. The end result is similar to a 2.5x equity letf. I actually think this is fine based on his age and savings. Using other means of leverage would only improve the expense ratio but would add complexity.

Obviously if they don't have the risk tolerance for 80%+ drawdown with 2x SP500 leverage (probably close to 90% with QQQ 2x leverage), then they shouldn't be so leveraged. But there's nothing inherently wrong with overall 2x leverage. Even 3x can be ok if contributions are large relative to investments.

It's also fine if it's just a portion of the portfolio because the rest of the portfolio acts as the balast the same way bond funds do in HFEA or mHFEA. So long as one rebalanced between the rest of the portfolio and the LETF. Without rebalancing, it's just inefficient and illogical (less leverage when the market is low and more leverage when market is high).
Did that Python simulation back to 1980 include the actual cost of leverage as well (not just the simulated ER but the actual assumed cost to borrow so as to go 2X or 3X long each day)? If not, it will severely overstate the returns during any period that isn't low/zero interest rates (ZIRP) like we basically had from 2009 to 2016 or 2017. Rates were very high from 1979 to 1984 or so.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Sun May 21, 2023 10:45 am I originally made the code out of curiosity - I would like to develop some additional analytics/dashboard for the forward curves, option-adjusted basis, probability to be CTD, etc.
That would be terrific! Thanks for sharing your data and your charts!
Last edited by comeinvest on Sun May 21, 2023 1:44 pm, edited 1 time 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 »

unemployed_pysicist wrote: Sun May 21, 2023 10:45 am
comeinvest wrote: Sat May 20, 2023 3:43 pm - I'm not sure if you are also following or analyzing SOFR futures let along using them; but spreads of SOFR futures would be another interesting metric for folks who implement mHFEA with SOFR futures - I think a meaningful comparison would be to implied treasury forward rates, or to swap rates?
- I have my code that bootstraps the zero coupon curve from SOFR futures contracts. It is not fully clear to me yet how to calculate the implied financing of a SOFR futures contract. I will look into it.
SOFR futures have no implied repo rate per se, because they don't have an investable bond as underlying; so I think a meaningful comparison would be to implied treasury forward rates, or to swap rates?
The difference between the SOFR forward rate (as per the SOFR future) and the treasury forward rate would of course not be an implied financing rate, because (at expiration) instantaneous SOFR rates are not equal to instantaneous treasury rates; but deviations of that spread over time from the long-term average would indicate cheapness or richness, right? Another indication of cheapness or richness might be variations of the spread with the term if you plot the spread vs. the time to expiration, similar to this https://www.chathamfinancial.com/techno ... ard-curves , except I'm trying to wrap my head around where is the SOFR forward (not the Term SOFR) and where is the 3 mo. T-bill forward or Fed forward?! The 3-mo SOFR is NOT the 3-mo Term SOFR is it? No it's not, because the SOFR settles to realized rates, while the Term SOFR is a forward rate based on futures or other derivatives?

Image
comeinvest
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Re: SOFR futures

Post by comeinvest »

unemployed_pysicist wrote: Sun May 21, 2023 9:23 am Specifically, the (sizeable) dips centered at the 2031-02-15, CUSIP: 91282CBL4, and 2029-11-15, CUSIP: 912828YS3. The dips have the telltale sign of a liquidity premium for being OTR, fails to deliver on the CTD, special in the repo market, or some other market dislocation.

However, upon inspection, these are not on-the-runs or even first off-the-runs, and they are not CTDs. 91282CBL4 is deliverable to all of the ten year note futures contracts, but its IRR is quite far from the IRR of the current CTD for all contracts. 912828YS3 does not appear to be deliverable to any futures contract. I don't know how to check if something is special in the repo market, but I don't see any compelling reason for why these issues would be special. The yield dips are also not a function of lower duration due to higher coupon; their durations are similar to the surrounding bonds. In fact, 912828YS3 has a 10 bps lower yield than the nearby 91282CFT3, yet 912828YS3 has the higher duration (by ~0.3).

These dips have been persistent in recent history; I first noticed them a week ago and the dips have been there whenever I check. I would like to hear your expert opinion on this phenomenon.

Thanks!
I can't chime in on your question; but you are implying that CTDs might justify a liquidity premium in the market. I think somebody said very early in this thread that CTDs have no measurable premium; if untrue, what is your estimate of CTD liquidity yield premia?
unemployed_pysicist
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Location: Amsterdam

Re: SOFR futures

Post by unemployed_pysicist »

comeinvest wrote: Sun May 21, 2023 5:14 pm
unemployed_pysicist wrote: Sun May 21, 2023 9:23 am Specifically, the (sizeable) dips centered at the 2031-02-15, CUSIP: 91282CBL4, and 2029-11-15, CUSIP: 912828YS3. The dips have the telltale sign of a liquidity premium for being OTR, fails to deliver on the CTD, special in the repo market, or some other market dislocation.

However, upon inspection, these are not on-the-runs or even first off-the-runs, and they are not CTDs. 91282CBL4 is deliverable to all of the ten year note futures contracts, but its IRR is quite far from the IRR of the current CTD for all contracts. 912828YS3 does not appear to be deliverable to any futures contract. I don't know how to check if something is special in the repo market, but I don't see any compelling reason for why these issues would be special. The yield dips are also not a function of lower duration due to higher coupon; their durations are similar to the surrounding bonds. In fact, 912828YS3 has a 10 bps lower yield than the nearby 91282CFT3, yet 912828YS3 has the higher duration (by ~0.3).

These dips have been persistent in recent history; I first noticed them a week ago and the dips have been there whenever I check. I would like to hear your expert opinion on this phenomenon.

Thanks!
I can't chime in on your question; but you are implying that CTDs might justify a liquidity premium in the market. I think somebody said very early in this thread that CTDs have no measurable premium; if untrue, what is your estimate of CTD liquidity yield premia?
As I understand it, if there is a liquidity premium for CTDs, it is largely negligible on average. But when there is a shortage of the CTD notes to deliver into a futures contract, there can be a significant premium attatched to the CTD and nearby notes. See figure 6 in Gurkaynak et. al., 2006 for a historical example. Eyeballing the figure, I'd estimate that the premium was a 0.2% yield in that case, though that was a pretty extreme example.
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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 »

Alpha4 wrote: Sun May 21, 2023 12:41 pm
skierincolorado wrote: Thu May 04, 2023 8:23 am
nisiprius wrote: Thu May 04, 2023 7:48 am Forgive me both for butting into this thread, and for doing so in search of material to discourage someone from using leveraged ETFs in a naïve way--not in the way you all are... some of you may have leveraged ETF simulation tools.

The question is: if QLD--ProShares Ultra QQQ, 2X daily-rebalanced Nasdaq-1000 index--had existed from 2000 through 2002, how deep a drawdown would it have experienced?

As a very crude estimate, I tried using PortfolioVisualizer--month-to-month, monthly rebalancing, 200% QQQ, -100% CASHX and got a -98.34% drawdown, but I supposed it wouldn't have been that bad with daily rebalancing.

Source
There's this python code for simulated 3x. Its max drawdown is 97%. The code could be modified to do 2x.
https://teddykoker.com/2019/04/simulati ... in-python/

I actually think just straight 2x leveraged etfs are sort of OK for a young investor with a good savings rate. The contributions reduce the volatility decay. The main issue I see with 2x LETFs isn't the volatility decay it's the high expense ratio. Leverage can be had cheaper through other means. 3x leverage experiences too much volatility decay to hold straight and needs to be rebalanced against a more stable asset. But 2x is fine for young investors and is in fact exactly what the book recommends. There's nothing particularly different between rebalancing daily or monthly. Rebalancing monthly can do better or worse.

My nephew actually holds 80% 3x leveraged equity etfs. The last 20% is basically cash to tone things back a bit. The end result is similar to a 2.5x equity letf. I actually think this is fine based on his age and savings. Using other means of leverage would only improve the expense ratio but would add complexity.

Obviously if they don't have the risk tolerance for 80%+ drawdown with 2x SP500 leverage (probably close to 90% with QQQ 2x leverage), then they shouldn't be so leveraged. But there's nothing inherently wrong with overall 2x leverage. Even 3x can be ok if contributions are large relative to investments.

It's also fine if it's just a portion of the portfolio because the rest of the portfolio acts as the balast the same way bond funds do in HFEA or mHFEA. So long as one rebalanced between the rest of the portfolio and the LETF. Without rebalancing, it's just inefficient and illogical (less leverage when the market is low and more leverage when market is high).
Did that Python simulation back to 1980 include the actual cost of leverage as well (not just the simulated ER but the actual assumed cost to borrow so as to go 2X or 3X long each day)? If not, it will severely overstate the returns during any period that isn't low/zero interest rates (ZIRP) like we basically had from 2009 to 2016 or 2017. Rates were very high from 1979 to 1984 or so.
This particuoar sim doesn't include cost of leverage but does include ER. Simba sim does include both. I was using this because it is daily so shows the larger max drawdown. The long term result prior to 2009 won't be accurate though. It doesn't change the conclusion though. 3x leverage is too much unless you are making large contributions relative to the amount invested (very early career). 2x is more acceptable for early to mid career. The daily of LETFs vs monthly rebalancing of other methods doesn't make much difference. Less frequent rebalancing will lead to some worse drawdowns during big rapid market drops.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Fri May 12, 2023 1:45 pm
comeinvest wrote: Mon Nov 14, 2022 3:36 pm
unemployed_pysicist wrote: Mon Nov 14, 2022 3:26 pm
comeinvest wrote: Mon Nov 14, 2022 2:26 pm It is possible to concatenate performance with custom rebalancing / portfolio switch dates in PV? If not, we need a quarterly data source. I think Simba is only yearly. Spreadsheet would be better anyways.
I thought there was a simple way to switch assets in portfolio visualizer? I've never used that feature so I don't know for sure.

What do you mean by spreadsheet? Something like one column for the quarterly date, one column for the quarterly max carry maturity, one column for the assigned index fund corresponding to the max carry maturity (vfisx, vfitx, vustx, vedtx), one column for the quarterly return of the assigned index fund from the start date, one column for the 3 month Tbill, one column for excess return? Something like that?
I was just saying if we have a spreadsheet, it's better than PV because it's more customizable. I have not looked too much into data sources; I just started with simulations. I don't know if there is some quarterly data in Simba or elsewhere. I think Yahoo might have historical data for ETFs to download. At least free equities data is easier to come by than free futures data.
I can't remember, did I already share this plot with you?

Image

I used the max carry switch dates indicated in one of my previous posts.

From this, it does not look like the max carry strategy offered any better risk adjusted performance than just staying in VFISX the entire time. At least since 1992 using bond funds to approximate the duration of the max carry bond, and all the rest of the methodology discussed earlier.

Any thoughts?
Sorry for the delay, I was busy. Excellent chart!
I assume this is based on a constant duration exposure over the entire period?
Ok let's discuss this and do some sanity checks!

- The max carry is the STT most of the time.
- The max carry strategy correctly timed / anticipated the rise in short-term rates between ca. 2006 and 2008.
- The max carry was NOT the STT between ca. 2011 and 2014. The 2y was at ca. 0.25% between ca. 2012 and 2014. Good job, max carry strategy!
- Max carry was again STT between ca. 2016 and 2019, even though 2y rates were climbing but still below 1% until ca. 2016. Despite the low short-term rates, STT did not underperform longer tenors. Good job, max carry!
- The biggest bang for max carry vs STT came from the switch to LTT in 2019 and later ITT in 2020. In that period, LTT dropped from ca. 3% to ca. 1.5%; STT dropped from ca. 3% to ca. zero. LTT dropped to ca. 2% in 2019, and ITT dropped from ca. 3% to ca. 2% in 2019, and then from ca. 2% to ca. 1% in 2020. That means max carry timed the bigger drop of ITT vs LTT in 2020 correctly. I'm a bit lost why max carry outperformed vs. STT so much during the 2 years 2019-2020, when STT had a bigger percentage drop in rates. I know I'm just looking at yield changes here; but over the short time frame the yield changes should dominate differences in carry returns. (We are talking about ca. 17% outperformance of max here during 2019 and 2020 !) Any explanation? Double-check the data?

EDIT: The outperformance of max carry took place in 2019 only. In 2019, 2y rates dropped from 3% to 1.5%; 10y rates dropped from 3% to 2%; 30y rates from 3% to 2%. I'm still lost; theoretically 2y should have won in 2019, and even more so in the entire 2-year period 2019-2020.

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

Post by unemployed_pysicist »

comeinvest wrote: Sun May 21, 2023 8:01 pm
I assume this is based on a constant duration exposure over the entire period?
Whoops! As far as I recall, I did not use a contant duration exposure for this. Might be easier for me to do this with the zeros instead of funds, since we dont know exactly what the duration of the funds were. Another benefit would be the ability to go further back in time with zeros (to 1961).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Mon May 22, 2023 3:50 am
comeinvest wrote: Sun May 21, 2023 8:01 pm
I assume this is based on a constant duration exposure over the entire period?
Whoops! As far as I recall, I did not use a contant duration exposure for this. Might be easier for me to do this with the zeros instead of funds, since we dont know exactly what the duration of the funds were. Another benefit would be the ability to go further back in time with zeros (to 1961).
Two more comments on your max carry chart:
- The much higher stddev and lower sharpe of max carry vs. STT doesn't seem to be reflected in higher "real life" risk looking at the chart. Perhaps use a more meaningful scale (less frequent data points) for stddev calc, to reflect real economic risk? - Even the drawdowns of max carry in 2020 and 2021 are not significantly bigger than the drop of both max carry and STT in 2021-2022.
- How does your result reconcile with the Carry Investing on the Yield Curve paper which I think demonstrated relatively consistent outperformance of max carry by quite some margin? Different methodology?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

IRRs for futures contracts, just showing the CTDs. Please forgive the European formatting of the numbers. I think it might be helpful for historical purposes to record the clean price, dirty price and the futures price. This should permit direct calculation of the realized financing rate, provided the CTD doesn't change between roll dates. I have prices for almost all the other treasuries in the delivery basket, which are not shown, but have been recorded.

Code: Select all

src	cusip	contract_code	irr	irr_minus_closest_bill_yield	treasury_clean_price	treasury_dirty_price	futures_scrape_price
200	91282CGU9	tum23	2,781680308	-2,148319692		99,05759547		99,62869803		102,508
210	91282CEU1	tuu23	4,620025652	-0,462974348		97,23670737		98,49998442		103,137
222	91282CFK2	tuz23	5,140716049	0,440716049		98,50042874		99,16564034		103,766
246	91282CGR6	3yrm23	4,436393172	-0,496606828		101,6497194		102,5287542		105,285
257	9128287B0	3yru23	4,597175461	-0,487824539		93,97602235		94,72158426		105,82
266	912828YG9	3yrz23	4,464455123	-0,235544877		92,83926671		93,07877021		106,035
301	91282CFH9	fvm23	3,806449414	-1,126550586		97,2325667		97,95389782		108,695
310	91282CFZ9	fvu23	5,107751891	0,022751891		100,3409572		102,2033456		109,289
319	91282CGP0	fvz23	4,955158087	0,255158087		101,0582992		101,9816101		109,711
364	91282CGB1	tym23	4,164492699	-0,310507301		100,7425709		102,2834158		113,625
370	91282CGS4	tyu23	5,051742075	-0,033257925		99,41186559		99,9461606		114,391
374	91282CAE1	tyz23	3,130325304	-1,569674696		80,73087103		80,89997648		114,672
445	912810QC5	usm23	4,037102494	-0,437897506		107,5111122		108,7286779		126,906
442	912810QB7	usu23	4,943783811	-0,139216189		104,4894948		104,5928388		127,094
442	912810QB7	usz23	5,234320592	0,536320592		104,4651535		104,5685189		127,313
592	912810SE9	ulm23	0,292847924	-4,182152076		89,15712811		89,23922783		134,4375
592	912810SE9	ulu23	4,362728563	-0,720271437		89,15712264		89,23922783		134,9375
595	912810SF6	ulz23	2,349677136	-2,350322864		83,30266665		84,11443271		134,65625

I checked a few selected clean prices; they are very close to the mid-point that I see from my broker. Let me know if anything looks off. Note that identical cusips can have different prices, because they were scraped at different times. Some of the december contracts have no open interest (from what I see), so I would ignore the futures prices and IRRs for those.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Tue May 23, 2023 5:19 pm IRRs for futures contracts, just showing the CTDs. Please forgive the European formatting of the numbers. I think it might be helpful for historical purposes to record the clean price, dirty price and the futures price. This should permit direct calculation of the realized financing rate, provided the CTD doesn't change between roll dates. I have prices for almost all the other treasuries in the delivery basket, which are not shown, but have been recorded.

Code: Select all

src	cusip	contract_code	irr	irr_minus_closest_bill_yield	treasury_clean_price	treasury_dirty_price	futures_scrape_price
200	91282CGU9	tum23	2,781680308	-2,148319692		99,05759547		99,62869803		102,508
210	91282CEU1	tuu23	4,620025652	-0,462974348		97,23670737		98,49998442		103,137
222	91282CFK2	tuz23	5,140716049	0,440716049		98,50042874		99,16564034		103,766
246	91282CGR6	3yrm23	4,436393172	-0,496606828		101,6497194		102,5287542		105,285
257	9128287B0	3yru23	4,597175461	-0,487824539		93,97602235		94,72158426		105,82
266	912828YG9	3yrz23	4,464455123	-0,235544877		92,83926671		93,07877021		106,035
301	91282CFH9	fvm23	3,806449414	-1,126550586		97,2325667		97,95389782		108,695
310	91282CFZ9	fvu23	5,107751891	0,022751891		100,3409572		102,2033456		109,289
319	91282CGP0	fvz23	4,955158087	0,255158087		101,0582992		101,9816101		109,711
364	91282CGB1	tym23	4,164492699	-0,310507301		100,7425709		102,2834158		113,625
370	91282CGS4	tyu23	5,051742075	-0,033257925		99,41186559		99,9461606		114,391
374	91282CAE1	tyz23	3,130325304	-1,569674696		80,73087103		80,89997648		114,672
445	912810QC5	usm23	4,037102494	-0,437897506		107,5111122		108,7286779		126,906
442	912810QB7	usu23	4,943783811	-0,139216189		104,4894948		104,5928388		127,094
442	912810QB7	usz23	5,234320592	0,536320592		104,4651535		104,5685189		127,313
592	912810SE9	ulm23	0,292847924	-4,182152076		89,15712811		89,23922783		134,4375
592	912810SE9	ulu23	4,362728563	-0,720271437		89,15712264		89,23922783		134,9375
595	912810SF6	ulz23	2,349677136	-2,350322864		83,30266665		84,11443271		134,65625

I checked a few selected clean prices; they are very close to the mid-point that I see from my broker. Let me know if anything looks off. Note that identical cusips can have different prices, because they were scraped at different times. Some of the december contracts have no open interest (from what I see), so I would ignore the futures prices and IRRs for those.
Summary of your IRR calcs for /UL so far - I'm taking the front month contract outside roll periods, and the back month contract during roll periods. I'm too lazy to do the same for the other contracts right now. If you do this several decades and keep the results, you will have a nice data set for mHFEA implementations and roll strategies ;)
Oct 24 2022: ulz22: -0.552575 viewtopic.php?p=6930575#p6930575
Oct 28 2022: ulz22: -1.352876 viewtopic.php?p=6936782#p6936782
Nov 18 2022: ulz22: -0.316717 / ulh23: 0.259291 viewtopic.php?p=6969015#p6969015
Nov 25 2022: ulh23: -0.645270 viewtopic.php?p=6979271#p6979271
Nov 28 2022: ulh22: -0.544727 viewtopic.php?p=6983231#p6983231
May 12 2023: ulm23: -2.221844 / ulu23: -0.386903 viewtopic.php?p=7264007#p7264007
May 20 2023: ulm23: -3.506360 / ulu23: -0.393448 viewtopic.php?p=7275703#p7275703
May 23 2023: ulm23: -4,182152076 / ulu23: -0,720271437 viewtopic.php?p=7281226#p7281226
Last edited by comeinvest on Sat May 27, 2023 12:47 pm, edited 2 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

IRRs for futures contracts at around 3:30-4pm EST on 2023-05-24, showing just the CTD:

Code: Select all

src_line_nbr  cusip 	contract_code       irr  irr_minus_closest_bill_yield  dirty_price  clean_price  intra_day_price                                                                                                          
200           91282CGU9         tum23  2.704570                     -2.203430    99.497677    98.916432        102.35500
210           91282CEU1         tuu23  4.682998                     -0.407002    98.351182    97.080338        102.98800
222           91282CFK2         tuz23  5.387614                      0.647614    99.002838    98.328515        103.73400
246           91282CGR6        3yrm23  4.920742                      0.012742   102.312983   101.421910        105.10900
257           9128287B0        3yru23  4.706593                     -0.383407    94.538589    93.788066        105.64100
266           912828YG9        3yrz23  4.839547                      0.099547    92.900058    92.656302        106.05900
303           91282CFM8         fvm23  3.847107                     -1.060893   101.574468   100.955700        108.47700
310           91282CFZ9         fvu23  5.119166                      0.029166   102.014916   100.142334        109.07000
319           91282CGP0         fvz23  5.443160                      0.703160   101.760281   100.826562        109.78100
364           91282CGB1         tym23  4.723279                      0.285279   102.001684   100.450589        113.35900
370           91282CGS4         tyu23  5.249597                      0.159597    99.662659    99.118880        114.12500
374           91282CAE1         tyz23  3.777757                     -0.962243    80.694959    80.524200        114.81300
445           912810QC5         usm23  3.963553                     -0.474447   108.326615   107.097145        126.40600
442           912810QB7         usu23  5.084004                     -0.005996   104.226476   104.112058        126.68800
445           912810QC5         usz23  5.905147                      1.165147   108.351542   107.122005        127.37500
592           912810SE9         ulm23  0.959148                     -3.478852    88.868628    88.777728        133.96875
592           912810SE9         ulu23  4.473754                     -0.616246    88.868628    88.777721        134.40625
595           912810SF6         ulz23  3.517187                     -1.222813    83.729019    82.909297        134.96875
Intra_day_price refers to the futures price at scrape time. Looks like there was a CTD change for the usz23 contract, but it's a December contract so maybe not so useful information. CME treasury analytics page says 912810QB7 is the CTD, but the IRRs of 912810QB7 and 912810QC5 are very close for the december contract. The IRR for 912810QD3 is also close to these two for the december contract.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Thu May 25, 2023 2:07 am ...
Thanks, physicist!
The spreads seem to be quite persistent for each tenor.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by director84 »

This will be my first time rolling treasury futures. As I understand, today and tomorrow should be the best days to do so. I'm curious what spread people expect when doing so. Do you set a limit of just enter a market order after volume ramps up?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

director84 wrote: Thu May 25, 2023 6:48 am This will be my first time rolling treasury futures. As I understand, today and tomorrow should be the best days to do so. I'm curious what spread people expect when doing so. Do you set a limit of just enter a market order after volume ramps up?
I do market orders and I expect the minimum spread. For ZF futures, that's $7.8125 per contract (source: https://www.cmegroup.com/markets/intere ... Specs.html).

Make sure to do a rollover order rather than selling and buying as two separate orders.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Why are June boxes at 6%? They don't have the same default risk as treasuries. FFR and sofrs are still 5%
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

DMoogle wrote: Thu May 25, 2023 8:43 am
director84 wrote: Thu May 25, 2023 6:48 am This will be my first time rolling treasury futures. As I understand, today and tomorrow should be the best days to do so. I'm curious what spread people expect when doing so. Do you set a limit of just enter a market order after volume ramps up?
I do market orders and I expect the minimum spread. For ZF futures, that's $7.8125 per contract (source: https://www.cmegroup.com/markets/intere ... Specs.html).

Make sure to do a rollover order rather than selling and buying as two separate orders.
I think for futures, the benefit of using limit orders per "patient trading" paradigm is bigger than for equities, because it's a central market which is more fair as every participant (except block trades) is on the same order book and has the same price increments. But I would agree that if you are not a control freak like myself, the $7.8125 (or part of it) are not worth it; it's a very small amount in comparison to the notional values.
Another thing to note is that if you use limit orders, I think you want to put your entire position that you want to roll over in one single order, because for futures spreads it's not a strict time priority, but everybody gets slice of matching orders prorated to the order size.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Thu May 25, 2023 1:17 pm Why are June boxes at 6%? They don't have the same default risk as treasuries. FFR and sofrs are still 5%
I bought back 06/30 expiration SPX boxes (multiples of $100k) on 05/22 for 5.19% APY (always without commissions), and on 05/24 for 5.20%, walking up the limit each time. Term SOFR estimated/interpolated to the expiration of the SPX boxes were about 5.10% and 0.12%. Unfortunately I failed to check boxtrades.com at the time of my trades, and I also don't have any contemporaneous SPX box "sell" order for reference myself.

My last SPX box "sell" trade was for 06/30 expiration on 05/15, $50k box, at 5.41%. Estimated Term SOFR was at 5.07% at that time. I did not bother recording T-bill rates, because of the debt ceiling craziness.
In another account I also bought a 06/30 expiration box on 05/15 at 5.08%. Obviously I didn't like the spread between my two trades.

boxtrades.com has 06/16 expiration, but doesn't show 06/30 expirations.
Prevailing rates per boxtrades.com on 05/15 were between ca. 5.3% and 5.6%.
Prevailing rates per boxtrades.com on 05/22 were between ca. 5.4% and 5.9%.
Prevailing rates per boxtrades.com on 05/24 were between ca. 5.8% and 6.05%.
On 05/23 they were ca. 5.8% - 5.9% in the early morning and evening, and 4.9% - 5.2% in between. The 4.9% trade was a 76.5M floor trade. The morning and afternoon trades were 100M, 80M, and 20M among others. Both the 3m Mar-Jun SOFR future and the 1m Jun30 expiration SOFR future didn't budge almost at all on 05/23.

1m Term SOFR moved steadily from ca. 5.07% to 5.15% between 05/15 and 05/25. https://www.theice.com/marketdata/reports/281 (Don't forget though that I think this is a spot rate, i.e. the period covered shifted by 10 days between 05/15 and 05/25.)

What is the takeaway?

SOFR was stable between 05/15 and 05/25.
It looks like I got hosed with my "buy" box trades on 05/22 and 05/24 in comparison to other box trades (although my trades were 06/30 expiration); but the spread to SOFR was ok. By implication, it looks like the effective APY spreads between filled buy and ask box trades was large.
It looks like the SPX box spread market was chaotic with a wide spread between effective filled APYs on 05/22 and 05/23.
And finally, it looks like the spread between SPX box APYs and Term SOFR and SOFR futures increased by ca. 0.4 percentage points (0.1% increase for SOFR, 0.5% increase for SPX boxes).

In short words, box spread financing got more expensive during this time, but box spread investing was relatively stable.

I have no explanation for all of this. Perhaps it is connected to the debt ceiling, or the rising rates, although I don't think the rates rose particularly fast in this time frame.

Related discussion: viewtopic.php?p=7283900#p7283900

I'm not sure why today IB doesn't show the red and green dots for real time data during extended trading hours. I am subscribed to market data.

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Last edited by comeinvest on Fri May 26, 2023 4:06 pm, edited 1 time in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

On another note, we are approaching peak ITT interest rates again.
There is some steepening between ITT and LTT. My layman interpretation is that this suggests higher term premia; but don't take my word for it. I think the slope in this segment is more important than in the STT/ITT segment which is governed by short-term fed policy and economic expectations.
The curiosity of the local peak around 20y still exists.
I didn't rebalance or adjust my exposure in relation to NAV when ITT rates oscillated between 3.3 (?) and 4% - should I have? I plan on adjusting when ITT rates drop below 3% and 2% thresholds.

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

Post by comeinvest »

Following up on my previous post about box spreads

I'm typing this in a hurry so please someone verify the numbers and my ad-hoc conclusions.

Today an attempt to "buy" a $100k June 30 expiration SPX box @ 5.36% APY (adjusted for the holiday 34 days to expiration of settled cash, if I'm not mistaken) failed to fill.
As a reminder, the last few days ca. 5.2% "buy" orders filled.

June 15 T-bill BID yield is at about 5.8%. June 29 T-bill BID yield is at about 5.5%.

1 mo. Term SOFR is at ca. 5.15%.

I think based on the boxtrades diagram in me previous box spread post we can say that SPX box "sell" orders currently fill at ca. 0.2% above the T-bill bid yields (the elevated T-bill rates due to the debt ceiling), instead of ca. 0.2% - 0.35% above.
"Buy" orders fill at T-bill BID yields (mid June expiration) or at ca. 0.3% below T-bill bid yields (June 30 expiration), and at about 0.1% above Term SOFR (usually ca. 0.15% above Term SOFR according to my statistics).
"Buy" orders seem to be almost "normal" in relation to Term SOFR. The effective spread between filled SPX box buy and sell orders seems to be larger than usual. "Sell" orders seem to fill at elevated yields; but don't forget that the time to expiration is only ca. 3 weeks, which I think is when yields typically start fluctuating more - look at the fluctuations on 02/24 and even on 02/17 here for example: https://www.boxtrades.com/SPX/17MAR23 and compare to here where there are no corresponding fluctuations on those days: https://fred.stlouisfed.org/series/DGS1MO
Nevertheless before the debt ceiling drama I used to occasionally get some very good yields close to T-bill rates selling SPX boxes ca. 3 weeks before expiration.

Mid July T-bill BID yields are ca. 5.2%. 1.5 month Term SOFR (interpolated by me from available 1 mo and 3 mo values) is ca. 5.2%. SPX 07/21 boxes are at 5.4% - 5.5% https://www.boxtrades.com/SPX/21JUL23
July T-bill BID yields seem to be about 0.2 percentage points higher than usual in relation to Term SOFR. July box yields seem to be almost normal in relation to T-bills, but lower than usual in relation to Term SOFR (usually ca. 0.15% higher than Term SOFR according to my statistics). So either the Term SOFR seems to be the anomaly, or T-bills and SPX boxes together are an anomaly.
June and July 1-mo. SOFR futures are at ca. 5.2% if I interpret the quotations correctly - almost identical to the /ZQ fed fund futures. That seems to be normal - further out 1 mo. SOFR and fed fund futures are also almost identical to each other.
So in summary, the July T-bills and SPX box spreads both seem to have elevated yields.
It would appear that for whatever reason, SPX box spreads mimic T-bill anomalies (e.g. debt ceiling) to some extent.

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Last edited by comeinvest on Fri May 26, 2023 7:46 pm, edited 2 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

STT and /ZF people once again getting hosed more than 10y people.

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

Post by comeinvest »

unemployed_pysicist wrote: Thu May 25, 2023 2:07 am IRRs for futures contracts at around 3:30-4pm EST on 2023-05-24, showing just the CTD:

Code: Select all

src_line_nbr  cusip 	contract_code       irr  irr_minus_closest_bill_yield  dirty_price  clean_price  intra_day_price                                                                                                          
200           91282CGU9         tum23  2.704570                     -2.203430    99.497677    98.916432        102.35500
210           91282CEU1         tuu23  4.682998                     -0.407002    98.351182    97.080338        102.98800
222           91282CFK2         tuz23  5.387614                      0.647614    99.002838    98.328515        103.73400
246           91282CGR6        3yrm23  4.920742                      0.012742   102.312983   101.421910        105.10900
257           9128287B0        3yru23  4.706593                     -0.383407    94.538589    93.788066        105.64100
266           912828YG9        3yrz23  4.839547                      0.099547    92.900058    92.656302        106.05900
303           91282CFM8         fvm23  3.847107                     -1.060893   101.574468   100.955700        108.47700
310           91282CFZ9         fvu23  5.119166                      0.029166   102.014916   100.142334        109.07000
319           91282CGP0         fvz23  5.443160                      0.703160   101.760281   100.826562        109.78100
364           91282CGB1         tym23  4.723279                      0.285279   102.001684   100.450589        113.35900
370           91282CGS4         tyu23  5.249597                      0.159597    99.662659    99.118880        114.12500
374           91282CAE1         tyz23  3.777757                     -0.962243    80.694959    80.524200        114.81300
445           912810QC5         usm23  3.963553                     -0.474447   108.326615   107.097145        126.40600
442           912810QB7         usu23  5.084004                     -0.005996   104.226476   104.112058        126.68800
445           912810QC5         usz23  5.905147                      1.165147   108.351542   107.122005        127.37500
592           912810SE9         ulm23  0.959148                     -3.478852    88.868628    88.777728        133.96875
592           912810SE9         ulu23  4.473754                     -0.616246    88.868628    88.777721        134.40625
595           912810SF6         ulz23  3.517187                     -1.222813    83.729019    82.909297        134.96875
Intra_day_price refers to the futures price at scrape time. Looks like there was a CTD change for the usz23 contract, but it's a December contract so maybe not so useful information. CME treasury analytics page says 912810QB7 is the CTD, but the IRRs of 912810QB7 and 912810QC5 are very close for the december contract. The IRR for 912810QD3 is also close to these two for the december contract.
I think we should also compare to Term SOFR. Term SOFR (interpolated) until mid September is currently ca. 5.29%. Mid September maturity T-bills are at ca. 5.15 - 5.2% (interpolated). The difference between the two seems to be slightly on the low side compared to my historical statistics, but close to normal.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

comeinvest wrote: Fri May 26, 2023 7:53 pm I think we should also compare to Term SOFR. Term SOFR (interpolated) until mid September is currently ca. 5.29%. Mid September maturity T-bills are at ca. 5.15 - 5.2% (interpolated). The difference between the two seems to be slightly on the low side compared to my historical statistics, but close to normal.
IRRs for futures contracts at around 3:30-4pm EST on 2023-05-26, showing just the CTD:

Code: Select all

src_line_nbr	cusip 	contract_code       irr  irr_minus_closest_bill_yield  irr_minus_sofr  dirty_price  clean_price  intra_day_price                                                                                                                           
200           91282CGU9         tum23  2.707286                     -2.100714       -2.463370    99.148753    98.546409        101.97700
210           91282CEU1         tuu23  4.682481                     -0.430519       -0.610233    97.982417    96.695833        102.56600
222           91282CFK2         tuz23  5.629793                      0.819793        0.349547    98.595956    97.902679        103.41800
246           91282CGR6        3yrm23  4.196790                     -0.611210       -0.973866   101.847089   100.930968        104.50800
257           9128287B0        3yru23  4.759500                     -0.353500       -0.533214    94.020919    93.260073        105.04700
266           912828YG9        3yrz23  4.910034                      0.100034       -0.370212    92.357227    92.104622        105.44900
301           91282CFH9         fvm23  3.484766                     -1.323234       -1.685890    97.080249    96.333859        107.64100
310           91282CFZ9         fvu23  5.191659                      0.078659       -0.101055   101.289101    99.395298        108.26600
319           91282CGP0         fvz23  5.463066                      0.653066        0.182820   101.027901   100.072515        108.94500
364           91282CGB1         tym23  4.189081                     -0.185919       -0.969181   101.336106    99.763673        112.51600
370           91282CGS4         tyu23  5.353544                      0.240544        0.062973    98.985377    98.421853        113.34400
374           91282CAE1         tyz23  3.641262                     -1.168738       -1.644197    80.087446    79.913245        113.82800
445           912810QC5         usm23  4.693710                      0.318710       -0.464553   107.879123   106.624870        125.93800
445           912810QC5         usu23  5.521505                      0.408505        0.230933   107.879123   106.624840        126.28100
445           912810QC5         usz23  4.984318                      0.174318       -0.301141   107.879123   106.624809        126.06300
592           912810SE9         ulm23  1.108414                     -3.266586       -4.049848    88.922823    88.813640        134.06250
592           912810SE9         ulu23  4.766229                     -0.346771       -0.524343    88.922823    88.813632        134.59375
595           912810SF6         ulz23  1.715748                     -3.094252       -3.569711    83.837098    83.000853        133.65625
I just used linear interpolation for the term SOFR rate. I am open to using cubic splines if you prefer:

Image

No extrapolation was used for the cubic spline, which you can see with the last point. I used the following rates: [5.06 , 5.15 , 5.276, 5.315, 5.156] for the terms: [ 0, 30, 91, 182, 365] days. So the first element of the rates array is 5.06, the SOFR rate from thursday. FRED did not have the friday rate when I checked. In the future I could use the FRBNY website if they update more frequently than FRED. I use this as the zero day rate; probably more precise to make it 1 day instead of 0, but the impact on the rate interpolation is probably very small.

An advantage of interpolating the term SOFR is that now we can have a reference rate that coincides with the expiration of the futures contract. With the closest bill method, I just took the T-bill that matured closest to contract expiration, with no interpolation.

Here are the interpolated sofr values and bill yields in case you want to check the interpolated SOFR values themselves. Let me know if anything looks off.

Code: Select all

src_line_nbr	contract_code	irr  interpolated_sofr	closest_bill_yield	closest_bill_maturity last_delivery_date closest_bill                                                                                                            
200                  tum23  2.707286           5.170656               4.808            2023-07-11         2023-07-06    912797FX0
210                  tuu23  4.682481           5.292714               5.113            2023-10-05         2023-10-04    912796YJ2
222                  tuz23  5.629793           5.280246               4.810            2024-01-25         2024-01-04    912796ZY8
246                 3yrm23  4.196790           5.170656               4.808            2023-07-11         2023-07-06    912797FX0
257                 3yru23  4.759500           5.292714               5.113            2023-10-05         2023-10-04    912796YJ2
266                 3yrz23  4.910034           5.280246               4.810            2024-01-25         2024-01-04    912796ZY8
301                  fvm23  3.484766           5.170656               4.808            2023-07-11         2023-07-06    912797FX0
310                  fvu23  5.191659           5.292714               5.113            2023-10-05         2023-10-04    912796YJ2
319                  fvz23  5.463066           5.280246               4.810            2024-01-25         2024-01-04    912796ZY8
364                  tym23  4.189081           5.158262               4.375            2023-07-05         2023-06-30    912797FR3
370                  tyu23  5.353544           5.290571               5.113            2023-10-05         2023-09-29    912796YJ2
374                  tyz23  3.641262           5.285459               4.810            2024-01-25         2023-12-29    912796ZY8
445                  usm23  4.693710           5.158262               4.375            2023-07-05         2023-06-30    912797FR3
445                  usu23  5.521505           5.290571               5.113            2023-10-05         2023-09-29    912796YJ2
445                  usz23  4.984318           5.285459               4.810            2024-01-25         2023-12-29    912796ZY8
592                  ulm23  1.108414           5.158262               4.375            2023-07-05         2023-06-30    912797FR3
592                  ulu23  4.766229           5.290571               5.113            2023-10-05         2023-09-29    912796YJ2
595                  ulz23  1.715748           5.285459               4.810            2024-01-25         2023-12-29    912796ZY8
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Sat May 27, 2023 6:05 am I just used linear interpolation for the term SOFR rate. I am open to using cubic splines if you prefer:
The most accurate way would be to use 1 mo. SOFR futures to determine the interpolated or shall we say observed SOFR forward rates between the published Term SOFR dates, as Term SOFR is based on derivatives, isn't it? But the difference is small for the interesting period up to 4 months.

The Dec contracts are not interesting, are they? They have bid/ask spreads of about 4.

What date are you taking as date of delivery for the implied interest calculation again?

Are your T-bill rates BID or ASK yields?
Last edited by comeinvest on Sat May 27, 2023 1:14 pm, edited 1 time in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Sat May 27, 2023 6:05 am Here are the interpolated sofr values and bill yields in case you want to check the interpolated SOFR values themselves. Let me know if anything looks off.
...
Thanks. The spread of the September contracts increases monotonously with maturity, except the dropoff at the ulu23.

Summary:
Oct 24 2022: viewtopic.php?p=6930575#p6930575
Oct 28 2022: viewtopic.php?p=6936782#p6936782
Nov 18 2022: viewtopic.php?p=6969015#p6969015
Nov 25 2022: viewtopic.php?p=6979271#p6979271
Nov 28 2022: viewtopic.php?p=6983231#p6983231
May 12 2023: viewtopic.php?p=7264007#p7264007
May 20 2023: viewtopic.php?p=7275703#p7275703
May 23 2023: viewtopic.php?p=7281226#p7281226
May 26 2023: viewtopic.php?p=7286044#p7286044

The roll of the TY (2y) is not quite as cheap as it seems when you just look at the back month contracts. The front month contract seems to cheapen even more than the back month contract during roll period. We had a private conversation about roll cost. I'm not sure what the remaining economic time to expiration expected delivery of the front month contract is, but I think when you roll a long position in the contract you effectively "receive" the front month IRR (i.e. you pay, if negative) for the remainder of the economic time to delivery that the underlying is implicitly financed for whoever buys the front month contract from you, whatever it is. To determine the cheapness or richness of the roll and the implied financing cost for the person rolling a "continuous" contract, we would have to subtract the front month "cost" from the back month "cost", right?

In other words, if a contract, for example the TY, were perpetually undervalued for whatever reason, during the entire time period when you hold it, then the undervaluation wouldn't serve you. Surely the question arises why does it not converge to the underlying as expiration delivery approaches. I think the entire complicated physical delivery system of treasury futures is so that the contracts cannot be manipulated, but are tied to economic reality - the underlying bond. Perhaps double-check the data or look for some systematic error in our logic?

Nov 18 2022 where the front month was very expensive is the exception.

Nov 18 2022:
91282CFN6 tuz22 0.746103
91282CDN8 tuh23 0.045028
Nov 25 2022:
91282CFN6 tuz22 -1.501449
91282CDN8 tuh23 -0.728838
Nov 28 2022:
91282CFN6 tuz22 -1.608820
91282CDN8 tuh23 -0.659999
May 12 2023:
91282CGU9 tum23 -1.004867
91282CEU1 tuu23 -0.129380
May 20 2023:
91282CGU9 tum23 -1.280710
91282CEU1 tuu23 -0.173372
May 23 2023:
91282CGU9 tum23 -2,148319692
91282CEU1 tuu23 -0,462974348
May 27 2023:
91282CGU9 tum23 -2.100714
91282CEU1 tuu23 -0.430519

In light of this, the financing cost of the UL also no longer seems so favorable:

Nov 18 2022:
912810SA7 ulz22 -0.316717
912810SC3 ulh23 0.259291
Nov 25 2022:
912810SA7 ulz22 -4.345900
912810SC3 ulh23 -0.645270
Nov 28 2022:
912810SA7 ulz22 -3.472110
912810SC3 ulh23 -0.544727
May 12 2023:
912810SE9 ulm23 -2.221844
912810SE9 ulu23 -0.386903
May 20 2023:
912810SE9 ulm23 -3.506360
912810SE9 ulu23 -0.393448
May 23 2023:
912810SE9 ulm23 -4,182152076
912810SE9 ulu23 -0,720271437
May 27 2023:
912810SE9 ulm23 -3.266586
912810SE9 ulu23 -0.346771
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by unemployed_pysicist »

comeinvest wrote: Sat May 27, 2023 12:32 pm
unemployed_pysicist wrote: Sat May 27, 2023 6:05 am I just used linear interpolation for the term SOFR rate. I am open to using cubic splines if you prefer:
The most accurate way would be to use 1 mo. SOFR futures to determine the interpolated or shall we say observed SOFR forward rates between the published Term SOFR dates, as Term SOFR is based on derivatives, isn't it? But the difference is small for the interesting period up to 4 months.

The Dec contracts are not interesting, are they? They have bid/ask spreads of about 4.

What date are you taking as date of delivery for the implied interest calculation again?

Are your T-bill rates BID or ASK yields?
I have my code that calculates the zero-coupon curve from 3 month SOFR. Shouldn't a term SOFR position be equivalent to a zero-coupon curve extracted from futures prices? Perhaps I could try including the 1 month contracts to fill in the rest of the curve, but this will take time and testing. My current algorithm gives forward rates very close to the Chatham website, but not exactly the same. If I had to put a number on it, I'd say it's within +/- 10 basis points, is that accurate enough for you?

I do not think that the information about the December contracts are useful. When I check marketwatch, some of them do not even have any open interest. I can remove the furthest back month contract from my output if you think it will make the output less cluttered; I just leave it in there when I filter the output by cheapest to deliver. Maybe it is not worth the time to retrieve this data in the first place; I could save some time this way.

I use the last delivery date of the futures contract for all my Implied repo rate calculations. I think this generally makes sense for normal, upward sloping yield curves. However, when the yield curve is inverted, every day is a drain on the long basis position, so it makes sense to deliver earlier. Should I include an option to adjust the delivery date based on yield curve shape?

Unfortunately, all of my bill/note/bond price data comes from the midpoint of the bid ask spread. This is a wrinkle in the implied repo rate calculations, and in the comparison to Tbills. It would be better to have this information, but I do not know of a source of free data that has this on demand and up to the minute for all bills/notes/bonds. However, there are the end of day prices on the WSJ website and prices at the US Treasury website. I do not know the details of the prices on the US Treasury website, i.e., where the quotes are sourced from, I will have to look into it, but maybe this is a feasible option for the option of using end of day bond data. I suspect they may even have an API for their data, which would be very helpful. As I recall, WSJ gets their quotes from Tullet Prebon, which is ultimately the same source I that I use, except I do not have bid ask data. When I wrote the code, I wanted to get recent price data (time=now, not end of day) from a freely available source, so I optimized for that use-case. But an end-of-day bid/ask treasury prices feature could be another possible method if we want to eliminate this source of uncertainty.

Just a quick comment about basis optionality, since I am trying to explore this more quantitatively. It's in the CME literature, how a low duration bond is like a put option and a long duration bond is like a call option, but for me it is easier to understand with something more concrete. For my own understanding, I wanted to reproduce something like the payoff diagrams in figures 2.7 and 2.8 from Burghardt et. al. for a current-day, relevant example: the front month 10 year note futures.

Here are the payoff diagrams that would exist if 91282CGM7 (the highest duration bond in the basket, IRR=-49.26%!) and 91282CGB1 (the lowest duration bond in the basket, IRR=4.19%, and the current cheapest to deliver) were the only bonds deliverable to the TYM23 contract. If this were the case, 91282CGB1 will be the cheapest to deliver for yields below 6%, and 91282CGM7 will be the cheapest to deliver for yields above 6%. Interpret the yield axis as a result of parallel shifts to the curve - I do not include the likely scenario of curve flattening for an increasing yield, etc. because this is just meant as a simplified, illustrative example. These are the payoff curves for time=now, i.e., if these yield curve changes happened immediately, not at some later date. Therefore, the profit/loss from carry is ignored and is excluded. For simplicity, I set the futures price resulting from yield changes as just equal to the relevant CTD divided by its conversion factor. I show the payoff in terms of $100 face value - the profit in the position divided by the cost to enter the position by buying cash bonds and shorting a conversion factor number of futures contracts.

Image

In this picture, you can see payoff curves reminiscent of a call option (91282CGM7-high duration) and a put option (91282CGB1-low duration). As you can see, as yields explode to ridiculous values (~20%!), the long basis position in 91282CGB1 generates a decent profit. Neat, huh? If yields were to fall by a significant amount tomorrow, a long position in 91282CGM7 would begin to make a profit, even though it has a very negative IRR.

As the current cheapest to deliver with a positive IRR, a long basis position in 91282CGB1 generates a profit: 4.19% if held to the last delivery date. It's less than the corresponding T-bill or term SOFR, but it is still a profit. If yields were to dramatically increase tomorrow, a long basis position starts making an additional profit from a change in the basis because of its put option characteristics. It seems like it is nice to own something with a guaranteed payout, that generates an even greater profit if yields were to increase dramatically. Surely this put option characteristic is worth something, and the futures market should attach a price to this optionality. In times of greater rate uncertainty (volatility), I would expect that this optionality is worth more, and a negative spread to T-bills or SOFR seems justified.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Mon May 29, 2023 6:08 am ...
Thanks, very interesting. Unfortunately I cannot answer all your questions. But based on the summary of the front and back month contracts in my previous post before the one you cited, I suspect that there is a systematic error in the IRR calcs - as the front months don't seem to converge to the underlyings. Perhaps you didn't accurately factor in the timing option, as you say, and/or the wildcard option of the short position? It might be more complicated than it seems, to arrive at fair values for the calendar roll price or even at absolute futures pricing. Thanks for sharing your work, though, it's very insightful. I also hope you comment on my posts on your charts in the side discussion thread - the carry based strategies and the risk/return per zero coupon maturity exposure.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Illustration of equities, bonds, and commodity futures returns from the 2023 Credit Suisse yearbook

Notice the long interest rate cycles - although the term premium was positive after the 1960ies even during mean-reverting interest rate cycles, as we showed earlier in this thread. Not sure about the 1871-1930 period.

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

Post by comeinvest »

Some of the readers of this thread use MSCI futures for international equities leverage.

https://www.theice.com/pace-of-roll/MSC ... 6-20230915 shows 4.84% as SOFR. But overnight SOFR is 5.05%, and the probably most relevant reference for the futures implied financing cost, 3 months Term SOFR, is 5.24% https://www.cmegroup.com/market-data/cm ... -sofr.html
I'm curious why ICE puts 4.84% into their spreadsheet.
Also curious how reliable the dividend estimates are.

If (and only if) their dividend estimates are correct consensus estimates, then their spreads to SOFR are about 0.4% overstated.

Meanwhile, CME U.S. large cap futures have an implied rate of 5.5%, mid and small cap 5.2%, and Yen denominated Nikkei 225 futures have a financing spread of close to 0% as usual (unclear to which reference). Sep 14 maturity T-bills are at ca. 5.15%, ca. 0.1% below 3-months Term SOFR.

Image

Image

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

Post by unemployed_pysicist »

comeinvest wrote: Mon May 29, 2023 3:59 pm I also hope you comment on my posts on your charts in the side discussion thread - the carry based strategies and the risk/return per zero coupon maturity exposure.
I just want to mention that I have not forgotten about the various bond backtests we discussed in the sidethread. Until now, I have I been using a script to compare the duration-equivalent returns for various coupon and non-coupon bond tenors. I want to make something easier to use and maintain. Refactoring will give me the chance to perform some additional error testing along the way. The generation of the zero coupon and coupon bond returns, duration, etc. already works quite well, so I want to replicate that kind of process for the backtesting part (factory method pattern).
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

unemployed_pysicist wrote: Sun Jun 11, 2023 3:40 pm
comeinvest wrote: Mon May 29, 2023 3:59 pm I also hope you comment on my posts on your charts in the side discussion thread - the carry based strategies and the risk/return per zero coupon maturity exposure.
I just want to mention that I have not forgotten about the various bond backtests we discussed in the sidethread. Until now, I have I been using a script to compare the duration-equivalent returns for various coupon and non-coupon bond tenors. I want to make something easier to use and maintain. Refactoring will give me the chance to perform some additional error testing along the way. The generation of the zero coupon and coupon bond returns, duration, etc. already works quite well, so I want to replicate that kind of process for the backtesting part (factory method pattern).
Great, looking forward to it! I'm kind of stuck right now trying to define my STT/ITT allocation in a sensical and consistent way, and I think only a duration-neutral backtest can give more insight. I'm using SOFR futures up to ca. 4 years (up to ca. 2 years in other accounts), /ZF, and /ZN, and I'm realizing somehow this doesn't make sense, because those are not independent random variables, in fact they are highly dependent as per the expectations hypothesis: both /ZF and /ZN already reflect unexpected interest rate changes in the 0-2 year segment, and an equal-duration allocation between STT, ZF, and ZN results in not much diversification but is almost entirely dependent on the 0-2 year segment. I suspect that the forward rates e.g. represented by the individual SOFR futures are more independent random variables than the treasuries of different tenors. I hope that with duration and performance data, we gain more insight into risk and return and diversification benefits if any.
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