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

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zkn
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Joined: Thu Oct 14, 2021 12:45 pm

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

Post by zkn »

comeinvest wrote: Tue Nov 09, 2021 10:53 pm
zkn wrote: Tue Nov 02, 2021 9:09 pm ...
There is about 50% difference in final after-tax outcome between TYD and ZF/ZN, over only 10 years, although TYD is more tax efficient than the futures with your assumptions. That sounds like a lot; do you have any explanation? Also, the new TYA would have about 1% less expense ratio, after tax that should result in about 0.75% p.a. advantage over TYD everything else being equal? But surely not enough to even come close to ZF/ZN, although TYA has only 0.15% expense ratio. I'm having a bit of a hard time reconciling the results.
I agree it sounds like a lot, and I was expecting TYD to do a lot better. I recalculated the results for TYD and ZN, but I was not able to find any error. https://i.postimg.cc/wMZbTmTD/ZN-vs-TYD.png

TYD holds IEF and IEF swaps, but has a lower Sharpe than IEF (.59 versus .67 during the life of TYD). It has lower arithmetic mean and higher SD than IEF leveraged 3x with CASHX. There could be some more embedded fees in TYD, or it could be daily rebalance did not work well in this time period. TMF similarly underperforms TLT leveraged 3x with CASHX. More analysis would probably be required to unpack this.

TYA uses futures and not swaps so it will not be as tax efficient as TYD.
Topic Author
skierincolorado
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Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

comeinvest wrote: Wed Nov 10, 2021 12:44 am
skierincolorado wrote: Tue Nov 09, 2021 11:11 pm The financing on SHY was much less than IEF. This is probably because someone selling the call option would actually have to allocate capital to mostly or totally hedge their position to get any risk free gain because the yield on IEF is higher. Simply writing a call on IEF would lose you money. You'd need to hedge the position to make money. Whereas one could simply write a call on SHY and expect to make money. Imagine if a call on SHY had the same 3% financing cost as IEF. You could just write call options on SHY all day long and have nearly guaranteed gains without even having to allocate capital to hedging your position. So the implied financing is brought down to 0.5%... roughly in line with the expected return of SHY. Still too high to be profitable for the buyer. Which is probably why there was only a few of these traded in total.
I'm lost with your rationale, can you please re-phrase? Are you saying that the return on SHY is predictable enough that an option writer doesn't need to hedge? I would say in either case, IEF or SHY, an option writer would probably hedge a DITM option by buying the actual IEF or SHY respectively.

If you are saying the balance sheet constraints or risk considerations of the option writer will allow the writer to write more SHY than IEF for the same amount of risk, I can see that I can not really see that because there is a perfect hedge in either case, or maybe the risk of a spot/derivative no-arbitrage violation is bigger in the IEF case. But why would the financing cost for IEF with options be higher than that for IIT futures - the options writer or futures short contract holder can achieve a perfect hedge by buying essentially the exact same underlying in either case (except for no-arbitrage violations). Maybe I should start my hedge fund and get into the futures and options writing and hedging business.

Independent of that, I think implementing an IIT stake with options on ETFs is not a good idea, because the ETF expense ratio would always come on top of the cost of financing that ETF, unless you can explain to me how the expense ratio could magically disappear from the equation just by virtue of using derivatives.
*If* SHY had 3% implied financing cost for the buyer, the seller absolutely would not need to waste all that capital hedging. They might lose 1% by not hedging if SHY does really well, but they're still collecting the 3% implied financing. If I could write calls on SHY and collect 3% financing, I would do it all day long unhedged. Thus they are willing to offer lower financing. Even with the current 0.55% implied financing I'd say the seller is likely to make money without hedging and the buyer is likely to lose money.

Take it back a year ago when SHY rates were even lower basicaly zero. SHY could literally only go down. You'd still waste capital hedging, or would you just sell as many calls as possible collecting the 3% finance cost? Even the current 0.55% finance cost would be pretty great.
Last edited by skierincolorado on Wed Nov 10, 2021 8:38 am, edited 1 time in total.
zkn
Posts: 67
Joined: Thu Oct 14, 2021 12:45 pm

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

Post by zkn »

adamhg wrote: Tue Nov 09, 2021 4:52 pm
skierincolorado wrote: Tue Nov 09, 2021 12:17 am For SHY, I do see that last of 5.9 which is intriguing. The underlying was at 85.87 at the time so we should use that instead of the 85.99 at the time of your post (down to 85.89 now).

85.9-85.87 = .03

foregone divs = .436

cost = .466

((.466 + 79.97) / 79.79) ^ (1/(403/365)) = .73%

So we'd be paying .73% on the 79.97 we borrowed. And the 79.97 we borrowed is currently yielding only .46% so it's a net money loser, maybe breakeven with roll return and *if* rates don't rise as expected. Better than IEF which is a for sure money loser at 3.3%.

And while there is that last price at 5.9... it's just one contract so I wonder if it was a fluke. Even so, it's still breakeven at best.
I went ahead and executed this trade today so I have quite a few data points. I think this really does make a compelling case for SHY LEAPs to get STT. I was able to buy 78C, 80C and 82C at between 0.0052 and 0.0057, with the lowest rates going to the largest size order, details below. This is even lower than box spread financing at the same tenor I'm finding from boxtrades.

Here are the four SHY trades I made today:

Code: Select all

dtes               402         402         402        402        
strike             78          80          82         82         
call price         7.99        6.02        4          3.98       
underlying price   85.955      85.9575     85.959     85.955     
yield              0.0046      0.0046      0.0046     0.0046     
                                                                 
foregone dividends 0.435175869 0.435188526 0.43519612 0.435175869
                                                                 
total cost         0.476675869 0.504188526 0.48269612 0.466675869
borrowed           77.965      79.9375     81.959     81.975     
                                                                 
implied rate       0.005549685 0.005725105 0.00534597 0.00516758 
I made sure to capture the exact underlying price at the time of trade and the total cost includes .065/100 to account for TDA's option fee. The first three were all single contracts, but the last 82C was a single 30 contract trade

I went into the LEAPs with about 60% of the account and UPRO with remaining 40%. With the 33ish leaps, that brings me to about 12x worth of STT and 1.2x worth of SPY for an overall eff leverage ratio of 1:10.1 SPY:STT.

Here's the backtest vs HFEA, 1:9 STT and 1:10.1 STT:

https://www.portfoliovisualizer.com/bac ... 10_3=-1248
An annualized rate of .5% is about .45% over CASHX, as CASHX is about .05. So that is the additional financing cost. With 1248% in CASHX, that gives an additional financing cost on the portfolio of .45*1248 = 5.62%. Since you used quarterly rebalancing, quarterly that is 1-1.0562^(1/4) = 1.38%. If we add a quarterly fixed withdraw of 1.38% in portfoliovisualizer, the CAGR reduces to 21.79% from 28.73%. This seems like an expensive way to get SHY exposure.
https://www.portfoliovisualizer.com/bac ... 10_1=-1248

SHY LEAPs are not exactly comparable to funding via futures though, because you have locked in the borrowing rate for 400 days. We could view the position as more like ~.30-.35% over treasurys, with exposure to interest rate risk between ~700 days (duration of SHY) and 400 days at the start, as the value of the embedded loan will counteract price moves in SHY due to interest rate changes < 400 days. Assuming you hold until expiry and SHY rebalances to maintain constant duration, the position would move towards exposure to interest rate risk between 700 days and 0 days as the position gets older. From this perspective, it makes more sense to me to try to borrow as short as possible to better harvest the term risk premium, especially because a premise of this thread is that rate risk at lower maturities has better Sharpe.

PS The CPI reading today. Ouch.
Last edited by zkn on Wed Nov 10, 2021 8:42 am, edited 1 time in total.
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

zkn wrote: Wed Nov 10, 2021 8:37 am
adamhg wrote: Tue Nov 09, 2021 4:52 pm
skierincolorado wrote: Tue Nov 09, 2021 12:17 am For SHY, I do see that last of 5.9 which is intriguing. The underlying was at 85.87 at the time so we should use that instead of the 85.99 at the time of your post (down to 85.89 now).

85.9-85.87 = .03

foregone divs = .436

cost = .466

((.466 + 79.97) / 79.79) ^ (1/(403/365)) = .73%

So we'd be paying .73% on the 79.97 we borrowed. And the 79.97 we borrowed is currently yielding only .46% so it's a net money loser, maybe breakeven with roll return and *if* rates don't rise as expected. Better than IEF which is a for sure money loser at 3.3%.

And while there is that last price at 5.9... it's just one contract so I wonder if it was a fluke. Even so, it's still breakeven at best.
I went ahead and executed this trade today so I have quite a few data points. I think this really does make a compelling case for SHY LEAPs to get STT. I was able to buy 78C, 80C and 82C at between 0.0052 and 0.0057, with the lowest rates going to the largest size order, details below. This is even lower than box spread financing at the same tenor I'm finding from boxtrades.

Here are the four SHY trades I made today:

Code: Select all

dtes               402         402         402        402        
strike             78          80          82         82         
call price         7.99        6.02        4          3.98       
underlying price   85.955      85.9575     85.959     85.955     
yield              0.0046      0.0046      0.0046     0.0046     
                                                                 
foregone dividends 0.435175869 0.435188526 0.43519612 0.435175869
                                                                 
total cost         0.476675869 0.504188526 0.48269612 0.466675869
borrowed           77.965      79.9375     81.959     81.975     
                                                                 
implied rate       0.005549685 0.005725105 0.00534597 0.00516758 
I made sure to capture the exact underlying price at the time of trade and the total cost includes .065/100 to account for TDA's option fee. The first three were all single contracts, but the last 82C was a single 30 contract trade

I went into the LEAPs with about 60% of the account and UPRO with remaining 40%. With the 33ish leaps, that brings me to about 12x worth of STT and 1.2x worth of SPY for an overall eff leverage ratio of 1:10.1 SPY:STT.

Here's the backtest vs HFEA, 1:9 STT and 1:10.1 STT:

https://www.portfoliovisualizer.com/bac ... 10_3=-1248
An annualized rate of .5% is about .45% over CASHX, as CASHX is about .05. So that is the additional financing cost. With 1248% in CASHX, that gives an additional financing cost on the portfolio of .45*1248 = 5.62%. Since you used quarterly rebalancing, quarterly that is 1-1.0562^(1/4) = 1.38%. If we add a quarterly fixed withdraw of 1.38% in portfoliovisualizer, the CAGR reduces to 21.79% from 28.73%. This seems like an expensive way to get SHY exposure.
https://www.portfoliovisualizer.com/bac ... 10_1=-1248

SHY LEAPs are not exactly comparable to funding via futures though, because you have locked in the borrowing rate for 400 days. We could view the position as more like ~.30-.35% over 1y treasury, with exposure to interest rate risk between ~700 days (duration of SHY) and 400 days at the start, as the value of the embedded loan will counteract price moves in SHY due to interest rate changes < 400 days. Assuming you hold until expiry and SHY rebalances to maintain constant duration, the position would move towards exposure to interest rate risk between 700 days and 0 days as the position gets older. From this perspective, it makes more sense to me to try to borrow as short as possible to better harvest the term risk premium, especially because a premise of this thread is that rate risk at lower maturities has better Sharpe.

PS The CPI reading today. Ouch.
In addition, I would expect the financing cost of SHY LEAPs to rise as the expected return rises. So even the backtest you've shown is likely very optimistic. I'd focus more on the fact that SHY LEAPs have 0.55% implied on something that is very likely to yield substantially less than 0.55% over the life of the contract. The expected value is negative. I'd expect a CAGR of around -3% on this portfolio.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

zkn wrote: Wed Nov 10, 2021 7:47 am TYD holds IEF and IEF swaps, but has a lower Sharpe than IEF (.59 versus .67 during the life of TYD). It has lower arithmetic mean and higher SD than IEF leveraged 3x with CASHX. There could be some more embedded fees in TYD, or it could be daily rebalance did not work well in this time period. TMF similarly underperforms TLT leveraged 3x with CASHX. More analysis would probably be required to unpack this.

TYA uses futures and not swaps so it will not be as tax efficient as TYD.
If TYD holds IEF, then the expense ratio of IEF comes on top of the fees of TYD. Or are embedded fees included. In any case, TYD seems like a bad product. TYA will be better, but I don't see a use case for any of them, if futures are available. Taxable accounts and IRAs have access to futures. My HSA has not, I don't know a HSA that has access to futures, but I'll put high beta other stuff into the HSA and leverage the accounts that have access to futures. I must say, I think futures are the best invention since sliced bread.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Nov 10, 2021 8:31 am *If* SHY had 3% implied financing cost for the buyer, the seller absolutely would not need to waste all that capital hedging. They might lose 1% by not hedging if SHY does really well, but they're still collecting the 3% implied financing. If I could write calls on SHY and collect 3% financing, I would do it all day long unhedged. Thus they are willing to offer lower financing. Even with the current 0.55% implied financing I'd say the seller is likely to make money without hedging and the buyer is likely to lose money.

Take it back a year ago when SHY rates were even lower basicaly zero. SHY could literally only go down. You'd still waste capital hedging, or would you just sell as many calls as possible collecting the 3% finance cost? Even the current 0.55% finance cost would be pretty great.
I did something similar until recently when I went short ZT while the 2-year was at 0.15%, Libor very similar to that, and the 3 months bill at 0.05%. I didn't verify, but I hope I collected 0.2% financing cost from somebody else, whoever that poor fellow was and whatever he was trying to accomplish ;)
adamhg
Posts: 218
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by adamhg »

skierincolorado wrote: Wed Nov 10, 2021 8:41 am
zkn wrote: Wed Nov 10, 2021 8:37 am An annualized rate of .5% is about .45% over CASHX, as CASHX is about .05. So that is the additional financing cost. With 1248% in CASHX, that gives an additional financing cost on the portfolio of .45*1248 = 5.62%. Since you used quarterly rebalancing, quarterly that is 1-1.0562^(1/4) = 1.38%. If we add a quarterly fixed withdraw of 1.38% in portfoliovisualizer, the CAGR reduces to 21.79% from 28.73%. This seems like an expensive way to get SHY exposure.
https://www.portfoliovisualizer.com/bac ... 10_1=-1248

SHY LEAPs are not exactly comparable to funding via futures though, because you have locked in the borrowing rate for 400 days. We could view the position as more like ~.30-.35% over 1y treasury, with exposure to interest rate risk between ~700 days (duration of SHY) and 400 days at the start, as the value of the embedded loan will counteract price moves in SHY due to interest rate changes < 400 days. Assuming you hold until expiry and SHY rebalances to maintain constant duration, the position would move towards exposure to interest rate risk between 700 days and 0 days as the position gets older. From this perspective, it makes more sense to me to try to borrow as short as possible to better harvest the term risk premium, especially because a premise of this thread is that rate risk at lower maturities has better Sharpe.

PS The CPI reading today. Ouch.
In addition, I would expect the financing cost of SHY LEAPs to rise as the expected return rises. So even the backtest you've shown is likely very optimistic. I'd focus more on the fact that SHY LEAPs have 0.55% implied on something that is very likely to yield substantially less than 0.55% over the life of the contract. The expected value is negative. I'd expect a CAGR of around -3% on this portfolio.
I followed you up until this point. I can accept that I'm financing at .52 with a current yield less than that, but I don't see how you get a -3% cagr from that.

I'm still not 100% convinced that DITM LEAPs can even be thought of as implied financing outside of the moment it's calculated. Once the price changes the next day, then my MTM implied financing changes? Today with a -0.15% change, by implied financing goes up by 40% (unlevered)? I sure I'm not thinking about that right, but I've found no literature to that effect outside of lifecycle investing. And if that were the case, why would anybody ever trade LEAPs with little to no extrinsic value rather than just borrow and buy the underlying? Yet there are thousands of open DITM contracts. They can't all be spreads and dumb money, can they?

Bonds are especially confusing since the underlying value is tied directly to interest rates, but if we look at equity, options are more or less priced by expected volatility. So while there is an interest rate component, my thesis is that the option has less to do with the actual interest rate and more due to the volatility of the underlying (like all other options not tied to bond ETFs). I expect the 2% IV of SHY to have a greater impact on the option price than the 0.45% 2yr treasury yield today:

Image
Image

Forgive the terrible quality, I don't have a better way to chart IV, but you can kind of match it up and see that it spikes during turmoil, even if the interest rate goes up. So the thesis is that options give me the leveraged exposure I'm looking for. When the market dumps, interest rates tank and bonds go up, but bond options go up even more because IV spikes at the same time and all options become even more disproportionally valuable and are an added tail risk hedge on top.

You both make very valid points otherwise and are probably right. Options are notoriously hard to back test. But this is a toy account that was sitting in cash anyways so I'm happy to let it continue sitting in effectively cash for a year or so to see what happens and share the results :)
Topic Author
skierincolorado
Posts: 2377
Joined: Sat Mar 21, 2020 10:56 am

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

Post by skierincolorado »

adamhg wrote: Wed Nov 10, 2021 2:13 pm
skierincolorado wrote: Wed Nov 10, 2021 8:41 am
zkn wrote: Wed Nov 10, 2021 8:37 am An annualized rate of .5% is about .45% over CASHX, as CASHX is about .05. So that is the additional financing cost. With 1248% in CASHX, that gives an additional financing cost on the portfolio of .45*1248 = 5.62%. Since you used quarterly rebalancing, quarterly that is 1-1.0562^(1/4) = 1.38%. If we add a quarterly fixed withdraw of 1.38% in portfoliovisualizer, the CAGR reduces to 21.79% from 28.73%. This seems like an expensive way to get SHY exposure.
https://www.portfoliovisualizer.com/bac ... 10_1=-1248

SHY LEAPs are not exactly comparable to funding via futures though, because you have locked in the borrowing rate for 400 days. We could view the position as more like ~.30-.35% over 1y treasury, with exposure to interest rate risk between ~700 days (duration of SHY) and 400 days at the start, as the value of the embedded loan will counteract price moves in SHY due to interest rate changes < 400 days. Assuming you hold until expiry and SHY rebalances to maintain constant duration, the position would move towards exposure to interest rate risk between 700 days and 0 days as the position gets older. From this perspective, it makes more sense to me to try to borrow as short as possible to better harvest the term risk premium, especially because a premise of this thread is that rate risk at lower maturities has better Sharpe.

PS The CPI reading today. Ouch.
In addition, I would expect the financing cost of SHY LEAPs to rise as the expected return rises. So even the backtest you've shown is likely very optimistic. I'd focus more on the fact that SHY LEAPs have 0.55% implied on something that is very likely to yield substantially less than 0.55% over the life of the contract. The expected value is negative. I'd expect a CAGR of around -3% on this portfolio.
I followed you up until this point. I can accept that I'm financing at .52 with a current yield less than that, but I don't see how you get a -3% cagr from that.

I'm still not 100% convinced that DITM LEAPs can even be thought of as implied financing outside of the moment it's calculated. Once the price changes the next day, then my MTM implied financing changes? Today with a -0.15% change, by implied financing goes up by 40% (unlevered)? I sure I'm not thinking about that right, but I've found no literature to that effect outside of lifecycle investing. And if that were the case, why would anybody ever trade LEAPs with little to no extrinsic value rather than just borrow and buy the underlying? Yet there are thousands of open DITM contracts. They can't all be spreads and dumb money, can they?

Bonds are especially confusing since the underlying value is tied directly to interest rates, but if we look at equity, options are more or less priced by expected volatility. So while there is an interest rate component, my thesis is that the option has less to do with the actual interest rate and more due to the volatility of the underlying (like all other options not tied to bond ETFs). I expect the 2% IV of SHY to have a greater impact on the option price than the 0.45% 2yr treasury yield today:

Image
Image

Forgive the terrible quality, I don't have a better way to chart IV, but you can kind of match it up and see that it spikes during turmoil, even if the interest rate goes up. So the thesis is that options give me the leveraged exposure I'm looking for. When the market dumps, interest rates tank and bonds go up, but bond options go up even more because IV spikes at the same time and all options become even more disproportionally valuable and are an added tail risk hedge on top.

You both make very valid points otherwise and are probably right. Options are notoriously hard to back test. But this is a toy account that was sitting in cash anyways so I'm happy to let it continue sitting in effectively cash for a year or so to see what happens and share the results :)
If we assume yields aren't going to rise at all, then something that yields .45% with financing of .55% is a net -.1%. Leveraging it 10x would be -1%. That's a big oversimplification though. In reality we have two other factors to consider 1) market based expectations of interest rate increases 2) rolll yield. The former isn't market timing since these expectations are already baked into the yield curve. 2 year bonds yield .45% (higher today) *because* interest rates are expected to rise. The rational investor in 2 year bonds should expect some interest rate increases, which the .55% yield should help compensate them for. We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond. On the other hand, you have roll yield which is adding around .5% to your return. So on net SHY is expected to return around 0.1% in the next year. Minus the .55% financing and you have a -.45% expected return. Leveraged 10x and you get -4.5%.

The breakeven is pretty close to 0.2% rate increase. If rates increase less than 0.2% you'll make money, if they increase more than 0.2% you'll lose money. Right now the market expects around 0.5%. If rates somehow don't increase at all, you'd make close to 1% on the underlying after roll yield. After financing this would be .45%. Leveraged 10x this would be a 4.5% return. But the odds of rates not increasing at all are very very low according to the market.


I don't think your implied financing changes day to day. You're just making or losing money. The implied financing is an abstraction on the day of purchase based on how much you are overpaying if the underlying returned nothing. You've locked in those costs unless you are able to sell to somebody else willing to incur similar costs. We could repeat the calculation based on today's trading price for the option and underlying. Are you saying that if I were to buy one today I'd have higher implied financing than you did buying a few days ago?

You are probably right that options could have an added benefit as a hedge due to the IV. It would be interesting to backtest. I still very much doubt it's worth it though because the only reason you're getting even semi-reasonable financing costs on SHY is because the expected return is so low. On anything with more expected return like IEF (or SHY in the future when expected return is higher), the implied financing cost is going to be much higher. Also I'm not sure how much IV we would capture being so DITM. The fact that there is essentially zero IV at this strike price is how we could justify call all of the costs "implied financing" rather than a premium we paid for IV. From the IEF I looked at there wasn't much IV until we got within ~$8 of the current price, but we were looking at something that was $23 DITM. The price would have to drop a lot and volatility increase before we picked up much IV.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Nov 10, 2021 2:44 pm ... We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond...
... except that the forward contracts include both rate expectations and the term premium, as we have discussed earlier. The composition of both is hard to reverse-engineer. I'm not sure how representative the FOMC members' expectations are, nor if their "judgement of the appropriate target level" are actual rate expectations (I assume they are, as the FOMC decides on the rates), but look at the dot plot: https://www.cmegroup.com/trading/intere ... -fomc.html
You can see that the futures implied rates are higher than the average dot plot rates. The median dot plot projection for end of 2022 is still near zero. Which to me indicates that the rate implied in the forward contracts and futures might be mostly term premium.
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 »

comeinvest wrote: Wed Nov 10, 2021 3:12 pm
skierincolorado wrote: Wed Nov 10, 2021 2:44 pm ... We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond...
... except that the forward contracts include both rate expectations and the term premium, as we have discussed earlier. The composition of both is hard to reverse-engineer. I'm not sure how representative the FOMC members' expectations are, nor if their "judgement of the appropriate target level" are actual rate expectations (I assume they are, as the FOMC decides on the rates), but look at the dot plot: https://www.cmegroup.com/trading/intere ... -fomc.html
You can see that the futures implied rates are higher than the average dot plot rates. The median dot plot projection for end of 2022 is still near zero.
Yep. trying to keep things simple. but given the term premium is near zero, it works out about the same. Interest rates are going to go up... just generally speaking you've got to factor that in somehow when investing in bonds. .5% on short term rates seems about right for a market based estimate.
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 »

We make money when interest rates go up right :)

another leg on today's monstrous rate increases in the last hour

glad I don't hold the 30 year today... 2.5% loss
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Nov 10, 2021 3:16 pm
comeinvest wrote: Wed Nov 10, 2021 3:12 pm
skierincolorado wrote: Wed Nov 10, 2021 2:44 pm ... We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond...
... except that the forward contracts include both rate expectations and the term premium, as we have discussed earlier. The composition of both is hard to reverse-engineer. I'm not sure how representative the FOMC members' expectations are, nor if their "judgement of the appropriate target level" are actual rate expectations (I assume they are, as the FOMC decides on the rates), but look at the dot plot: https://www.cmegroup.com/trading/intere ... -fomc.html
You can see that the futures implied rates are higher than the average dot plot rates. The median dot plot projection for end of 2022 is still near zero.
Yep. trying to keep things simple. but given the term premium is near zero, it works out about the same. Interest rates are going to go up... just generally speaking you've got to factor that in somehow when investing in bonds. .5% on short term rates seems about right for a market based estimate.
Isn't the term premium 0.5% for the next year, if we believe the dot plot? What again is your source for the term premium data?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Wed Nov 10, 2021 3:22 pm
skierincolorado wrote: Wed Nov 10, 2021 3:16 pm
comeinvest wrote: Wed Nov 10, 2021 3:12 pm
skierincolorado wrote: Wed Nov 10, 2021 2:44 pm ... We can get a sense of market expected interest rate increases from interest rate forwards contracts. Interest rates are expected to increase nearly 0.5% in the next year, which would knock nearly 1% off the price of a 2 year bond...
... except that the forward contracts include both rate expectations and the term premium, as we have discussed earlier. The composition of both is hard to reverse-engineer. I'm not sure how representative the FOMC members' expectations are, nor if their "judgement of the appropriate target level" are actual rate expectations (I assume they are, as the FOMC decides on the rates), but look at the dot plot: https://www.cmegroup.com/trading/intere ... -fomc.html
You can see that the futures implied rates are higher than the average dot plot rates. The median dot plot projection for end of 2022 is still near zero.
Yep. trying to keep things simple. but given the term premium is near zero, it works out about the same. Interest rates are going to go up... just generally speaking you've got to factor that in somehow when investing in bonds. .5% on short term rates seems about right for a market based estimate.
Isn't the term premium 0.5% for the next year, if we believe the dot plot? What again is your source for the term premium data?
The ACM model
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

zkn wrote: Wed Nov 10, 2021 8:37 am SHY LEAPs are not exactly comparable to funding via futures though, because you have locked in the borrowing rate for 400 days. We could view the position as more like ~.30-.35% over treasurys, with exposure to interest rate risk between ~700 days (duration of SHY) and 400 days at the start, as the value of the embedded loan will counteract price moves in SHY due to interest rate changes < 400 days. Assuming you hold until expiry and SHY rebalances to maintain constant duration, the position would move towards exposure to interest rate risk between 700 days and 0 days as the position gets older. From this perspective, it makes more sense to me to try to borrow as short as possible to better harvest the term risk premium, especially because a premise of this thread is that rate risk at lower maturities has better Sharpe.

PS The CPI reading today. Ouch.
1 year vs. 3 month term premium: https://fred.stlouisfed.org/graph/?g=ILpW
So yes 3-months financing will result in higher returns in the long run.
But that's not the whole story. The negative 12-month cash position (i.e. negative ultra-short bond position) would be negatively correlated with your long bonds (albeit positively with your equities).
If we really wanted to sort out the optimal financing term for optimal risk-adjusted returns, we would probably have to do backtesting with the leveraged equities/treasuries portfolio, i.e. determine which part of the yield curve is best to capture the term premium for the optimal risk-adjusted return on the portfolio level.
Futures are only liquid for the front month, so this is only relevant for box spread financing. (If we ruled out DITM options.)
I personally would do around 3 months financing with box spreads once the curve steepens, but if I can get the same risk-adjusted returns with 12 months financing, I would be glad to know and happy to reduce my workload.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Nov 10, 2021 3:26 pm The ACM model
Current estimated term premia are between -0.37% (1y) and peak in the 6-8 year range at about -0.17%, if I read the spreadsheet right. Ouch. Not pretty. https://www.newyorkfed.org/research/dat ... remia.html
Minus 0.2%-0.25% slippage with treasury futures.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhhh
Last edited by hdas on Tue Nov 23, 2021 12:32 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 skierincolorado »

hdas wrote: Wed Nov 10, 2021 4:08 pm
skierincolorado wrote: Wed Nov 10, 2021 3:18 pm We make money when interest rates go up right :)

another leg on today's monstrous rate increases in the last hour

glad I don't hold the 30 year today... 2.5% loss
I don't know if you are trolling or just unaware, but the carnage today was in the short end of the curve. Somebody that replaced their EDV or GOVZ or ZROZ with the apt amount of ZF is down 3.75%, today.....not even counting what has transpired since March.

It seems that many fellow travelers in this thread are just not aware of curve movements. H
It depends on what ratio of substitution you use. Yes if you used DV01 the hit was harder at the short end today. But most if not all in this thread are not swapping their LTT with ITT according to DV01. One must also consider that the short term rates are much more volatile so it is not wise to rely solely on DV01. The appropriate amount should rely mostly on the historical volatility and returns which would suggest much less ITT is needed than dv01 suggests. Swapping LTT with ITT at a 2:1 ratio historically has higher returns and lower volatility. Someone that owned half as much LTT lost much more money today. 30 y bond prices fell 2.1% by the close (similar for the 20y), while 5 year bond prices fell .7%. Even if I own twice as much 5 year, the losses are substantially less (1.4% vs 2.1%). I think you are a little behind on the thread again. Although I do remember explaining why DV01 was the wrong metric previously as well.
Last edited by skierincolorado on Wed Nov 10, 2021 5:12 pm, edited 10 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 »

hdas wrote: Wed Nov 10, 2021 4:08 pm
skierincolorado wrote: Wed Nov 10, 2021 3:18 pm We make money when interest rates go up right :)

another leg on today's monstrous rate increases in the last hour

glad I don't hold the 30 year today... 2.5% loss
I don't know if you are trolling or just unaware, but the carnage today was in the short end of the curve. Somebody that replaced their EDV or GOVZ or ZROZ with the apt amount of ZF is down 3.75%, today.....not even counting what has transpired since March.

It seems that many fellow travelers in this thread are just not aware of curve movements. H
P.S.: Skier created this thread, which is my favorite on the BH forum! He also selflessly keeps explaining his valuable findings to fellow investors. It is not his fault that ITTs dropped as of late.

It looks like although the carry of the 5y was equal or higher than that of longer maturities 6 months ago (even before adjusting for durations), ITTs dropped while LTTs rallied. This is because the curve flattened. 6 months ago, the 5y30y topped out at ca. 1.6%, the highest point for the last 7 years https://fred.stlouisfed.org/graph/?g=ILBc . Considering the generally declining interest rates trend, that was a very steep curve 6 months ago. Maybe not the best time to start a leveraged ITT strategy. Also, the belly of the curve was not very pronounced 6 months ago. Maybe a dynamic strategy based on slope and curvature would have helped. (There are various papers proposing strategies based on current carry, or on mean reversion of parameters like slope and curvature.) There is also a tail risk of the curve permanently flattening, that I mentioned a few times before. But later one is always wiser. Skier demonstrated in numerous posts that the ITT advantage is persistent in the medium to long run in various interest rate environments.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by zkn »

comeinvest wrote: Wed Nov 10, 2021 1:15 pm
zkn wrote: Wed Nov 10, 2021 7:47 am TYD holds IEF and IEF swaps, but has a lower Sharpe than IEF (.59 versus .67 during the life of TYD). It has lower arithmetic mean and higher SD than IEF leveraged 3x with CASHX. There could be some more embedded fees in TYD, or it could be daily rebalance did not work well in this time period. TMF similarly underperforms TLT leveraged 3x with CASHX. More analysis would probably be required to unpack this.

TYA uses futures and not swaps so it will not be as tax efficient as TYD.
If TYD holds IEF, then the expense ratio of IEF comes on top of the fees of TYD. Or are embedded fees included. In any case, TYD seems like a bad product. TYA will be better, but I don't see a use case for any of them, if futures are available. Taxable accounts and IRAs have access to futures. My HSA has not, I don't know a HSA that has access to futures, but I'll put high beta other stuff into the HSA and leverage the accounts that have access to futures. I must say, I think futures are the best invention since sliced bread.
I don't expect the expense ratio of IEF to be included in the expense ratio of TYD. Surely TYD will just receive the post-fees return from IEF like any other holder of IEF.

TMF does the same, holding TLT and swaps on TLT.

Cheers to skier for showing a better way :sharebeer

TYD and TMF are from Direxion. UPRO from ProShares seems better constructed: swaps on the SP500 index directly as well as holding the individual SP500 stocks rather than an ETF. It also currently has a little bit in ES, maybe just for logistical reasons as it would be more liquid than the swaps.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Nov 10, 2021 4:28 pm It depends on what ratio of substitution you use. Yes if you used DV01 the hit was harder at the short end today. But most if not all in this thread are not swapping their LTT with ITT according to DV01. One must also consider that the short term rates are much more volatile so it is not wise to rely solely on DV01. The appropriate amount should rely mostly on the historical volatility and returns which would suggest much less ITT is needed than dv01 suggests. Swapping LTT with ITT at a 2:1 ratio historically has higher returns and lower volatility. Someone that owned half as much LTT lost much more money today. 30 y bond prices fell 2.1% by the close (similar for the 20y), while 5 year bond prices fell .7%. Even if I own twice as much 5 year, the losses are substantially less (1.4% vs 2.1%). I think you are a little behind on the thread again. Although I do remember explaining why DV01 was the wrong metric previously as well.
Point well taken as a general guideline if one is agnostic of the current rates. However, I would argue that the "excess ITT risk", as defined by the excess risk due to rising ITT rates in relation to rising LTT rates (i.e. curve flattening risk) when moving from LTT to ITT, can be reasonably thought of as limited by the current ITT to LTT yield spread. ("Reasonably" means excluding rare yield curve inversion events. Per the chart below, the LTT rates seem to act as a reliable cap on the ITT fluctuations.) Also note that I am naturally only interested in the bond "downward volatility" (rates upward potential) as risk measure, not the "upward volatility" (or shall we better just look at "excess expected maximum drawdown" rather than "volatility").

For example, yesterday the 10y note future (ZN) had a yield of ca. 1.35%, the 30y one of ca. 1.85%, difference 0.5%. The durations are 6.2 and 18.6. The excess risk would be 0.5% * 18.6 = 9.3%. My replacement ratio of LTTs with ITTs would be 18.6 / 6.2 * (1 - 0.093) = ca. 2.7 without incurring extra risk under the assumptions. This calc is very pessimistic, because my 2.7 ZN's will harvest significantly more money than 1 UB in the next 2 years alone from the carry with slope, if the forward rates are only halfway accurate. UB currently suffers from negative slope, lol. I think with the current yield curve, the ITT vs LTT decision is almost like a free lunch. The only risk that I can see is a flattening of the entire curve into a horizontal line in the next year or two.

Image
The chart is from https://www.longtermtrends.net/us-treasury-yield-curve/
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

comeinvest wrote: Wed Nov 10, 2021 6:31 pm
skierincolorado wrote: Wed Nov 10, 2021 4:28 pm It depends on what ratio of substitution you use. Yes if you used DV01 the hit was harder at the short end today. But most if not all in this thread are not swapping their LTT with ITT according to DV01. One must also consider that the short term rates are much more volatile so it is not wise to rely solely on DV01. The appropriate amount should rely mostly on the historical volatility and returns which would suggest much less ITT is needed than dv01 suggests. Swapping LTT with ITT at a 2:1 ratio historically has higher returns and lower volatility. Someone that owned half as much LTT lost much more money today. 30 y bond prices fell 2.1% by the close (similar for the 20y), while 5 year bond prices fell .7%. Even if I own twice as much 5 year, the losses are substantially less (1.4% vs 2.1%). I think you are a little behind on the thread again. Although I do remember explaining why DV01 was the wrong metric previously as well.
Point well taken as a general guideline if one is agnostic of the current rates. However, I would argue that the "excess ITT risk", as defined by the excess risk due to rising ITT rates in relation to rising LTT rates (i.e. curve flattening risk) when moving from LTT to ITT, can be reasonably thought of as limited by the current ITT to LTT yield spread. ("Reasonably" means excluding rare yield curve inversion events. Per the chart below, the LTT rates seem to act as a reliable cap on the ITT fluctuations.) Also note that I am naturally only interested in the bond "downward volatility" (rates upward potential) as risk measure, not the "upward volatility" (or shall we better just look at "excess expected maximum drawdown" rather than "volatility").

For example, yesterday the 10y note future (ZN) had a yield of ca. 1.35%, the 30y one of ca. 1.85%, difference 0.5%. The durations are 6.2 and 18.6. The excess risk would be 0.5% * 18.6 = 9.3%. My replacement ratio of LTTs with ITTs would be 18.6 / 6.2 * (1 - 0.093) = ca. 2.7 without incurring extra risk under the assumptions. This calc is very pessimistic, because my 2.7 ZN's will harvest significantly more money than 1 UB in the next 2 years alone from the carry with slope, if the forward rates are only halfway accurate. UB currently suffers from negative slope, lol. I think with the current yield curve, the ITT vs LTT decision is almost like a free lunch. The only risk that I can see is a flattening of the entire curve into a horizontal line in the next year or two.

Image
The chart is from https://www.longtermtrends.net/us-treasury-yield-curve/
But what if both LTT and iTT rates rise substantially.. prices are not linearly related to interest rates. If rates rise 5%, 5 year prices will not fall 1/6th of 30 year prices. They’ll fall more. Think of it as the dv50. The dv50 suggests a much lower ratio of itt:ltt than the dv01.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Wed Nov 10, 2021 7:28 pm
comeinvest wrote: Wed Nov 10, 2021 6:31 pm Point well taken as a general guideline if one is agnostic of the current rates. However, I would argue that the "excess ITT risk", as defined by the excess risk due to rising ITT rates in relation to rising LTT rates (i.e. curve flattening risk) when moving from LTT to ITT, can be reasonably thought of as limited by the current ITT to LTT yield spread. ("Reasonably" means excluding rare yield curve inversion events. Per the chart below, the LTT rates seem to act as a reliable cap on the ITT fluctuations.) Also note that I am naturally only interested in the bond "downward volatility" (rates upward potential) as risk measure, not the "upward volatility" (or shall we better just look at "excess expected maximum drawdown" rather than "volatility").

For example, yesterday the 10y note future (ZN) had a yield of ca. 1.35%, the 30y one of ca. 1.85%, difference 0.5%. The durations are 6.2 and 18.6. The excess risk would be 0.5% * 18.6 = 9.3%. My replacement ratio of LTTs with ITTs would be 18.6 / 6.2 * (1 - 0.093) = ca. 2.7 without incurring extra risk under the assumptions. This calc is very pessimistic, because my 2.7 ZN's will harvest significantly more money than 1 UB in the next 2 years alone from the carry with slope, if the forward rates are only halfway accurate. UB currently suffers from negative slope, lol. I think with the current yield curve, the ITT vs LTT decision is almost like a free lunch. The only risk that I can see is a flattening of the entire curve into a horizontal line in the next year or two.
But what if both LTT and iTT rates rise substantially.. prices are not linearly related to interest rates. If rates rise 5%, 5 year prices will not fall 1/6th of 30 year prices. They’ll fall more. Think of it as the dv50. The dv50 suggests a much lower ratio of itt:ltt than the dv01.
Thank you, something I have not thought about. I would like to quantify the relative risk of ITT vs LTT based on the current interest rate differential and under the assumption that the LTT rates are a cap on the ITT rates, which I think the chart suggests relatively convincingly except very few and limited rate inversion episodes, to arrive at more accurate risk estimates.

I did the math (assuming zero coupon bonds for simplicity):
Assume interest rates rise from 1.35% (/ZN) and 1.85% (/UB) to 6% across the board tomorrow (i.e. instantaneously, with no time to harvest coupons and rolldown returns):
LTT (/UB, duration 18.6) allocation of 100: ((1 / 1.06^18.6) - (1 / 1.0185^18.6)) / (1 / 1.0185^18.6) * 100 = ca. -52 -> drawdown -52%
ITT (/ZN, duration 6.2):
naive duration-neutral equivalent allocation of 300: ((1 / 1.06^6.2) - (1 / 1.0135^6.2)) / (1 / 1.0135^6.2) * 300 = ca. -73 -> drawdown -73% of original LTT allocation
risk-neutral allocation under my assumptions: ((1 / 1.06^6.2) - (1 / 1.0135^6.2)) / (1 / 1.0135^6.2) * x = -52 => x = -52 / (((1 / 1.06^6.2) - (1 / 1.0135^6.2)) / (1 / 1.0135^6.2)) = ca. 214
=> 214 would be my ITT (here: /ZN) allocation with the same risk as 100 LTT allocation under my assumptions.

But I think in the end a curated backtest of the total portfolio would be needed to validate the return and risk of a dynamic strategy based on the slope of the curve or other parameters.
Last edited by comeinvest on Thu Nov 11, 2021 4:19 am, edited 9 times in total.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by hdas »

hhhhhh
Last edited by hdas on Tue Nov 23, 2021 12:33 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 »

hdas wrote: Wed Nov 10, 2021 8:31 pm
skierincolorado wrote: Wed Nov 10, 2021 4:28 pm The appropriate amount should rely mostly on the historical volatility and returns which would suggest much less ITT is needed than dv01 suggests.
This we can agree. But It's clear to me that really old data is useless, we already know that this trade changed dramatically since 2010, in fact, whatever statistical tool you use to compare the last 10 years vs the older past will tell you that both samples are significantly different.

In any case, the 6 to 1 ratio seems to work out so that the volatility of 5YR leveraged is comparable to EDV, GOVZ, ZROZ
Your 6:1 ratio is higher than the ratio of the durations of the two ETFs: 24.6 / 5.2 = 4.73.
Skier explained numerous times is that he takes into account the possibility of a 1955-1982 scenario into his return and risk assessments. That timeframe would probably be the deal breaker for higher ITT allocations. We should not fall victim to recency bias.
Last edited by comeinvest on Thu Nov 11, 2021 2:37 am, 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 »

Skier started this thread, which is my favorite in the BH forum. He is fond of the /ZF , which experienced the biggest jump in yield over the past 6 months compared to all other major treasury futures of both lower and higher maturities. I feel for him. Somehow the belly of the curve ("curvature") was too little pronounced 6 months ago. But his findings are very sound. I think the strategy has a high likelihood of coming out ahead in the long run. Skier and all other contributors, keep on the good work!

P.S.: Looking at the chart, how can it be that the 7y-10y-20y portion is a straight line. Something doesn't seem right, the 10y point looks overvalued. Is this some artifact that I'm not seeing, or is it a market anomaly?

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

Post by skierincolorado »

comeinvest wrote: Wed Nov 10, 2021 7:46 pm
skierincolorado wrote: Wed Nov 10, 2021 7:28 pm
comeinvest wrote: Wed Nov 10, 2021 6:31 pm Point well taken as a general guideline if one is agnostic of the current rates. However, I would argue that the "excess ITT risk", as defined by the excess risk due to rising ITT rates in relation to rising LTT rates (i.e. curve flattening risk) when moving from LTT to ITT, can be reasonably thought of as limited by the current ITT to LTT yield spread. ("Reasonably" means excluding rare yield curve inversion events. Per the chart below, the LTT rates seem to act as a reliable cap on the ITT fluctuations.) Also note that I am naturally only interested in the bond "downward volatility" (rates upward potential) as risk measure, not the "upward volatility" (or shall we better just look at "excess expected maximum drawdown" rather than "volatility").

For example, yesterday the 10y note future (ZN) had a yield of ca. 1.35%, the 30y one of ca. 1.85%, difference 0.5%. The durations are 6.2 and 18.6. The excess risk would be 0.5% * 18.6 = 9.3%. My replacement ratio of LTTs with ITTs would be 18.6 / 6.2 * (1 - 0.093) = ca. 2.7 without incurring extra risk under the assumptions. This calc is very pessimistic, because my 2.7 ZN's will harvest significantly more money than 1 UB in the next 2 years alone from the carry with slope, if the forward rates are only halfway accurate. UB currently suffers from negative slope, lol. I think with the current yield curve, the ITT vs LTT decision is almost like a free lunch. The only risk that I can see is a flattening of the entire curve into a horizontal line in the next year or two.
But what if both LTT and iTT rates rise substantially.. prices are not linearly related to interest rates. If rates rise 5%, 5 year prices will not fall 1/6th of 30 year prices. They’ll fall more. Think of it as the dv50. The dv50 suggests a much lower ratio of itt:ltt than the dv01.
Thank you, something I have not thought about. I would like to quantify the relative risk of ITT vs LTT based on the current interest rate differential and under the assumption that the LTT rates are a cap on the ITT rates, which I think the chart suggests relatively convincingly except very few and limited rate inversion episodes, to arrive at more accurate risk estimates.

I did the math (assuming zero coupon bonds for simplicity):
Assume interest rates rise from 1.35% (/ZN) and 1.85% (/UB) to 6% across the board tomorrow (i.e. instantaneously, with no time to harvest coupons and rolldown returns):
LTT (/UB, duration 18.6) allocation of 100: ((1 / 1.06^18.6) - (1 / 1.0185^18.6)) / (1 / 1.0185^18.6) * 100 = ca. -52 -> drawdown -52%
ITT (/ZN, duration 6.2):
naive duration-neutral equivalent allocation of 300: ((1 / 1.06^6.2) - (1 / 1.0135^6.2)) / (1 / 1.0135^6.2) * 300 = ca. -73 -> drawdown -73% of original LTT allocation
risk-neutral allocation under my assumptions: ((1 / 1.06^6.2) - (1 / 1.0135^6.2)) / (1 / 1.0135^6.2) * x = -52 => x = -52 / (((1 / 1.06^6.2) - (1 / 1.0135^6.2)) / (1 / 1.0135^6.2)) = ca. 214
=> 214 would be my ITT (here: /ZN) allocation with the same risk as 100 LTT allocation under my assumptions.

But I think in the end a curated backtest of the total portfolio would be needed to validate the return and risk of a dynamic strategy based on the slope of the curve or other parameters.
Yeah the 214:100 is close to 2:1... if I was substituting LTT for ITT I would use something like that based on the above sort of calculation and historical backtests. I think this might be part of the reason that duration is not linearly related to yield, but even at 2 or 2.5 : 1 you're getting much more return from ITT. The remaining effect is probably BAB.
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

skierincolorado wrote: Tue Sep 14, 2021 1:53 pm Remember, part of the reason financing costs on boxes are higher than futures at the present is because you are locking in a fixed rate for 1-3 years, and yields are expected to rise. 2 years from now, he could have a lower rate on his old box, than the you'll be paying on your futures.
A failure mode of HFEA is rising yields, causing bonds to struggle and the entire portfolio to underperform. Would you go so far as to say using boxes mitigates this to some extent as rising yields cause the present value of the money you owe to drop? Or is this a double-edged sword that will diminish the ability of the bonds to cushion a fall to exactly the same extent?
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by skierincolorado »

Hfearless wrote: Thu Nov 11, 2021 3:16 pm
skierincolorado wrote: Tue Sep 14, 2021 1:53 pm Remember, part of the reason financing costs on boxes are higher than futures at the present is because you are locking in a fixed rate for 1-3 years, and yields are expected to rise. 2 years from now, he could have a lower rate on his old box, than the you'll be paying on your futures.
A failure mode of HFEA is rising yields, causing bonds to struggle and the entire portfolio to underperform. Would you go so far as to say using boxes mitigates this to some extent as rising yields cause the present value of the money you owe to drop? Or is this a double-edged sword that will diminish the ability of the bonds to cushion a fall to exactly the same extent?
wouldn’t consider it a benefit really it’s just a reduction in total bond duration exposure. Instead of being long LtT or ITT and short cash you’re short the 2 year bond. So you’ve just reduced your bond exposure which will help when bonds lose money and hurt when they make money. Overall it will be a loss since generally speaking shorting the 2 year bond has been a loss since 2 year bonds have great returns.

I wouldn’t buy bonds on boxes though. For equities it makes some sense in taxable. If it weren’t for the tax drag of equity futures compared to equity indexes, we would prefer the futures which borrow at the 3 month rate over boxes that borrow at the ~2 year rate.
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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 Nov 11, 2021 10:01 am Yeah the 214:100 is close to 2:1... if I was substituting LTT for ITT I would use something like that based on the above sort of calculation and historical backtests. I think this might be part of the reason that duration is not linearly related to yield, but even at 2 or 2.5 : 1 you're getting much more return from ITT. The remaining effect is probably BAB.
... in the long run per the backtests, but not currently if you believe the current term premia per ACM, right? Current ACM term premia are ca. -0.2% for 5y, same for 10y. So with a somewhat higher allocation to the 5y we would get more negative return than with the 10y, with the same risk.
6 months ago the term premia were 0.13% (5y) and 0.53% (10y). Had we allocated our treasuries across the yield curve based on the ACM estimates, we would have done a lot better. Maybe worth using the highest riks-adjusted return per ACM?
P.S.: My understanding is the ACM term premia are a priori estimates / predictions.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Thu Nov 11, 2021 3:47 pm I wouldn’t buy bonds on boxes though. For equities it makes some sense in taxable. If it weren’t for the tax drag of equity futures compared to equity indexes, we would prefer the futures which borrow at the 3 month rate over boxes that borrow at the ~2 year rate.
I use boxes with 3-month lengths in taxable, no problem.
Bread Investor
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bread Investor »

I've read through this thread and the information here is amazing.

I'm finally going to adopt mHFEA, but am not very familiar with the ETF/Futures set up. Using UPRO/TYD (45/55) is the easier way out, but is not optimal (according to the back-tests in this thread) when compared to using Futures.

I have at least a 20-year horizon, and am planning to invest $100k into this (through interactive brokers). Can someone please advise on a ETF & Futures set up for the best risk-reward, in view of the current market conditions?

I saw the recommendation on the usage of UPRO/MES/ZF/ZN (I'm still trying to figure out on how to use futures), and if someone could provide advice on what allocation provides a good risk-reward, that'll be very much appreciated.
Last edited by Bread Investor on Thu Nov 11, 2021 7:06 pm, edited 1 time in total.
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

Bread Investor wrote: Thu Nov 11, 2021 7:05 pm I've read through this thread and the information here is amazing.

I'm finally going to adopt mHFEA, but am not very familiar with the ETF/Futures set up. Using UPRO/TYD (45/55) is the easier way out, but is not optimal (according to the back-tests in this thread) when compared to using Futures.

I have at least a 20-year horizon, and am planning to invest $100k into this (through interactive brokers). Can someone please advise on a ETF & Futures set up for the best risk-reward, in view of the current market conditions?

I saw the recommendation on the usage of UPRO/MES/ZF/ZN (I'm still trying to figure out on how to use futures), and if someone could provide advice on what allocation provides a good risk-reward, that'll be very much appreciated.
In your watchlist type ZN and hit enter. Then click on futures. Send 1 buy order. Can be market order it is very liquid during trading hours. The quotation is a bit weird. 130'125 means = (130 + 125/320)*1000. This will be your exposure. No money changes hands yet (other than small commission). So you are not really buying something. It is just exposure.
You'll need around 10 2k collateral to carry this position. It is called margin but it is not margin in the sense that you are borrowing. You are not borrowing if you have 10 2k cash. If you don't IBKR will use margin (the other kind of margin) to lend you 10 2k and you'll pay interest.

Futures are marked to marked every day. It means if you gained 2k, 2k cash will appear in your account in real time. same with losses. If your cash goes below the margin requirement (~10 2k) ibkr will lend you margin loan.

Maybe buy 1 /ZN and get used to futures first?
Last edited by klaus14 on Fri Nov 12, 2021 12:34 am, edited 3 times in total.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
Bread Investor
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Bread Investor »

Thanks for your reply.

I read that 165/400 Stock/ITT is a good mix. If I want to have a portfolio on that mix, would the following work: Buy $55k UPRO & 3 ZN, while keeping $45k as cash for collateral:
Image

For exposure:
Stock: 55.0% (of Portfolio) x 3 = 165%
ITT: 3 ZN = 3 x ((130 + 115/320)*1000) = 391,078. (391,078 / 100,000) = 391%
The above is roughly 165/400. Does it work that way?
avgunner
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by avgunner »

klaus14 wrote: Thu Nov 11, 2021 10:12 pm
Bread Investor wrote: Thu Nov 11, 2021 7:05 pm I've read through this thread and the information here is amazing.

I'm finally going to adopt mHFEA, but am not very familiar with the ETF/Futures set up. Using UPRO/TYD (45/55) is the easier way out, but is not optimal (according to the back-tests in this thread) when compared to using Futures.

I have at least a 20-year horizon, and am planning to invest $100k into this (through interactive brokers). Can someone please advise on a ETF & Futures set up for the best risk-reward, in view of the current market conditions?

I saw the recommendation on the usage of UPRO/MES/ZF/ZN (I'm still trying to figure out on how to use futures), and if someone could provide advice on what allocation provides a good risk-reward, that'll be very much appreciated.
In your watchlist type ZN and hit enter. Then click on it. Send 1 buy order. Can be market order it is very liquid during trading hours. The quotation is a bit weird. 130'125 means = (130 + 125/320)*1000. This will be your exposure. No money changes hands yet (other than small commission). So you are not really buying something. It is just exposure.
You'll need around 10k collateral to carry this position. It is called margin but it is not margin in the sense that you are borrowing. You are not borrowing if you have 10k cash. If you don't IBKR will use margin (the other kind of margin) to lend you 10k and you'll pay interest.

Futures are marked to marked every day. It means if you gained 2k, 2k cash will appear in your account in real time. same with losses. If your cash goes below the margin requirement (~10k) ibkr will lend you margin loan.

Maybe buy 1 /ZN and get used to futures first?
I thought a zn/zf/zb had an exposure of 100k of bonds despite the price listed. I understand (130 + 125/320)*1000 is much higher than 100k, but how are we looking at bond exposure here? At face value or actual bond amount were being exposed to?
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

Bread Investor wrote: Thu Nov 11, 2021 11:13 pm Thanks for your reply.

I read that 165/400 Stock/ITT is a good mix. If I want to have a portfolio on that mix, would the following work: Buy $55k UPRO & 3 ZN, while keeping $45k as cash for collateral:
Image

For exposure:
Stock: 55.0% (of Portfolio) x 3 = 165%
ITT: 3 ZN = 3 x ((130 + 115/320)*1000) = 391,078. (391,078 / 100,000) = 391%
The above is roughly 165/400. Does it work that way?
It should work. It is too much bonds for my tastes in this low yield environment. i wouldn't go over 150/300. (I personally do 80/55/15 stock/bond/gold for all my savings but i am close to my retirement target)

I checked the actual margin requirement for ZN and it is just $1833. This can change but $15k per contract is more than enough buffer. if you want to optimize further you can buy VGIT for $10k of it and sell some if necessary. But i think easiest is to hold this in your main account with your other holdings (ETFs, stocks etc.) so that IB can margin lend you money in case. And you can pay back with your new savings. This way you avoid cash drag.

If you are not concerned with capital gain taxes you can use /MES instead of UPRO and avoid volatility decay.
Last edited by klaus14 on Fri Nov 12, 2021 12:44 am, edited 5 times in total.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
klaus14
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by klaus14 »

avgunner wrote: Fri Nov 12, 2021 12:18 am
klaus14 wrote: Thu Nov 11, 2021 10:12 pm
Bread Investor wrote: Thu Nov 11, 2021 7:05 pm I've read through this thread and the information here is amazing.

I'm finally going to adopt mHFEA, but am not very familiar with the ETF/Futures set up. Using UPRO/TYD (45/55) is the easier way out, but is not optimal (according to the back-tests in this thread) when compared to using Futures.

I have at least a 20-year horizon, and am planning to invest $100k into this (through interactive brokers). Can someone please advise on a ETF & Futures set up for the best risk-reward, in view of the current market conditions?

I saw the recommendation on the usage of UPRO/MES/ZF/ZN (I'm still trying to figure out on how to use futures), and if someone could provide advice on what allocation provides a good risk-reward, that'll be very much appreciated.
In your watchlist type ZN and hit enter. Then click on it. Send 1 buy order. Can be market order it is very liquid during trading hours. The quotation is a bit weird. 130'125 means = (130 + 125/320)*1000. This will be your exposure. No money changes hands yet (other than small commission). So you are not really buying something. It is just exposure.
You'll need around 10k collateral to carry this position. It is called margin but it is not margin in the sense that you are borrowing. You are not borrowing if you have 10k cash. If you don't IBKR will use margin (the other kind of margin) to lend you 10k and you'll pay interest.

Futures are marked to marked every day. It means if you gained 2k, 2k cash will appear in your account in real time. same with losses. If your cash goes below the margin requirement (~10k) ibkr will lend you margin loan.

Maybe buy 1 /ZN and get used to futures first?
I thought a zn/zf/zb had an exposure of 100k of bonds despite the price listed. I understand (130 + 125/320)*1000 is much higher than 100k, but how are we looking at bond exposure here? At face value or actual bond amount were being exposed to?
Quoted price is your exposure.
My investment algorithm: https://www.bogleheads.org/forum/viewtopic.php?f=10&t=351899&p=6112869#p6112869
msun641
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by msun641 »

I've downloaded the ACM model data found here:
https://www.newyorkfed.org/research/dat ... remia.html

Can anyone help me make heads or tails out of it?

I know this has already been discussed a bit in the thread, but how does the current negative expected term premium affect this strategy?
cross123
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by cross123 »

I know Interactive Brokers allows futures and stocks in the same account. How does this work with margin?

For example, say you wanted 110% equity and 110% 10 Year Treasury exposure through futures (ZN). Knowing that the treasury futures require cash as collateral, how does this work? In order to get to 110% equity you will run through all cash that could be used as collateral for ZN.

The only way I can think to accomplish this is to open a separate account for the futures portion, where I could segregate the cash collateral, and go into margin in the other account for the 110% stocks.

What am I missing?

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

Post by Hfearless »

cross123 wrote: Fri Nov 12, 2021 7:47 am For example, say you wanted 110% equity and 110% 10 Year Treasury exposure through futures (ZN). Knowing that the treasury futures require cash as collateral, how does this work?
If you have spare cash, it will be used for collateral. If you do not, IBKR will happily lend it to you and charge the usual margin loan rates for it, this happens automatically. There are slight complications to this, because for regulatory reasons IBKR needs to keep securities and commodities separate, and you can end up in situations where you’ve closed all your futures positions but you still have loaned money sitting in the commodities part of your account. There’s an entry called Excess Funds Sweep in account settings, it controls this.
DMoogle
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

cross123 wrote: Fri Nov 12, 2021 7:47 am I know Interactive Brokers allows futures and stocks in the same account. How does this work with margin?

For example, say you wanted 110% equity and 110% 10 Year Treasury exposure through futures (ZN). Knowing that the treasury futures require cash as collateral, how does this work? In order to get to 110% equity you will run through all cash that could be used as collateral for ZN.

The only way I can think to accomplish this is to open a separate account for the futures portion, where I could segregate the cash collateral, and go into margin in the other account for the 110% stocks.

What am I missing?

Thanks.
Several options, in rough order of preference:
  • Use futures on stock to achieve the needed leverage (using ES or MES). E.g. use 90% of your portfolio cash to buy ETFs directly, then the remaining amount as collateral in the treasury/stock futures. This is the cheapest based on implied financing rates in the futures (although know that rates on stock futures are higher than on treasury futures).
  • Use options box spreads to gain extra funds in your account. There's another thread floating around here that gives detail on how to execute. I do this personally. This is a little more expensive than futures on stocks (but still very low rates), but more tax efficient because the "interest" you pay on the spreads is counted as a loss. It also gives you flexibility to choose whatever ETF you want with the funds, rather than being locked to the S&P500 with ES/MES.
  • Use margin. Very easy, simple, and straightforward. I used this for years in low amounts. However, financing is more expensive than the previous two, and you can only deduct the interest if you're already itemizing deductions on your taxes.
  • Put the needed portion of your portfolio in daily rebalanced LETFs (SSO or UPRO). This is expensive given the expense ratios are added onto whatever their own financing costs are for the leverage. Plus, not sure if it sits well to have your equity exposure daily rebalanced while your treasury portion is manually rebalanced.
Last edited by DMoogle on Fri Nov 12, 2021 9:03 am, edited 1 time in total.
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 »

Bread Investor wrote: Thu Nov 11, 2021 11:13 pm Thanks for your reply.

I read that 165/400 Stock/ITT is a good mix. If I want to have a portfolio on that mix, would the following work: Buy $55k UPRO & 3 ZN, while keeping $45k as cash for collateral:
Image

For exposure:
Stock: 55.0% (of Portfolio) x 3 = 165%
ITT: 3 ZN = 3 x ((130 + 115/320)*1000) = 391,078. (391,078 / 100,000) = 391%
The above is roughly 165/400. Does it work that way?
I'm assuming you have high risk tolerance and a long time horizon. Even so, 165/400 is too bondy. At most I would go 165/300, and personally I would go 165/275 even if I was in my mid-twenties and high risk tolerance with low net worth but high income. This would still beat HFEA (55/45 UPRO/TMF) in a backtest. But it's a little less bond risk which given todays very low rates makes some sense. There were a number of other reasons justifying a lower ratio of stock : bond discussed in the thread - try to skim it if you can. People in this thread are generally choosing ratios between 1:1 and 1:2 with a mean around 1:1.5. 165/400 is actually significanly more bond risk than HFEA which would not do well in a rising rate scenario.

You can test in PV by modifying the backtests in this thread. But also backtest in Simba's spreadsheet which takes you back to 1955 to see how it would do in a rising rate environment.
DMoogle
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by DMoogle »

skierincolorado wrote: Fri Nov 12, 2021 9:01 amI'm assuming you have high risk tolerance and a long time horizon. Even so, 165/400 is too bondy. At most I would go 165/300, and personally I would go 165/275 even if I was in my mid-twenties and high risk tolerance with low net worth but high income. This would still beat HFEA (55/45 UPRO/TMF) in a backtest. But it's a little less bond risk which given todays very low rates makes some sense. There were a number of other reasons justifying a lower ratio of stock : bond discussed in the thread - try to skim it if you can. People in this thread are generally choosing ratios between 1:1 and 1:2 with a mean around 1:1.5. 165/400 is actually significanly more bond risk than HFEA which would not do well in a rising rate scenario.

You can test in PV by modifying the backtests in this thread. But also backtest in Simba's spreadsheet which takes you back to 1955 to see how it would do in a rising rate environment.
Btw is the current thought to use all ZN, all ZF, or some mix of the two to achieve the ITT portion? I'm in ZN right now, but not sure if I should switch next time I need to rebalance.
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 »

msun641 wrote: Fri Nov 12, 2021 5:04 am I've downloaded the ACM model data found here:
https://www.newyorkfed.org/research/dat ... remia.html

Can anyone help me make heads or tails out of it?

I know this has already been discussed a bit in the thread, but how does the current negative expected term premium affect this strategy?
My understanding is that if the term premium is actually zero the expected return of borrowing money to invest in bonds would also be zero. However, there still would be a rebalancing and risk-reduction benefit if the negative correlation with stocks continues. If the negative correlation with stocks did not continue, the term premium would theoretically rise because one of the primary benefits of bonds would be gone and investors would demand more premium.

However, the estimate of term premium is only an estimate and historically it appears to have been too low. For example, it first shows the term premium going negative since 2012, but in reality borrowing money to invest in bonds in 2012 would have worked out very nicely still. Maybe I am misunderstanding something, but the model seems to be overly pessimistic when disaggregating the term premium from market expected future interest rate increases.
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 »

DMoogle wrote: Fri Nov 12, 2021 9:08 am
skierincolorado wrote: Fri Nov 12, 2021 9:01 amI'm assuming you have high risk tolerance and a long time horizon. Even so, 165/400 is too bondy. At most I would go 165/300, and personally I would go 165/275 even if I was in my mid-twenties and high risk tolerance with low net worth but high income. This would still beat HFEA (55/45 UPRO/TMF) in a backtest. But it's a little less bond risk which given todays very low rates makes some sense. There were a number of other reasons justifying a lower ratio of stock : bond discussed in the thread - try to skim it if you can. People in this thread are generally choosing ratios between 1:1 and 1:2 with a mean around 1:1.5. 165/400 is actually significanly more bond risk than HFEA which would not do well in a rising rate scenario.

You can test in PV by modifying the backtests in this thread. But also backtest in Simba's spreadsheet which takes you back to 1955 to see how it would do in a rising rate environment.
Btw is the current thought to use all ZN, all ZF, or some mix of the two to achieve the ITT portion? I'm in ZN right now, but not sure if I should switch next time I need to rebalance.
Current thinking is to use at least two contracts, probably even better with 3. Upthread there was some excellent discussion comparing the returns of futures vs a cash position in the same duration vs a diversified bond etf. The discussion showed very low finance costs for futures because the returns were very similar to the cash position in the same duration. But the risk-adjusted returns of the diversified bond etfs were noticeably better, presumably because they hold multiple durations and are diversified. So at a minimum I would hold ZF and ZN. Those are pretty close in duration though so maybe it would be better to hold a pairing farther apart in duration such as ZF + TN, or ZT + ZN. Obviously one would adjust the size of the position relative to the duration (over twice as much ZF as TN) and even then I might lean most heavily on ZF and ZN (TN is a little long in duration the risk-adjusted returns start to drop off historically). Or one could use 3 durations, mostly ZF, with a little ZT and TN. Obviously simplicity is important too. Currently I just hold ZN and ZF, but might add a little TN or ZT, but need to develop a rules based plan so I am not introducing risk by jumping in and out of contracts. If I was holding 3 durations long-term it would be ZT, mostly ZF, and a smidge of TN, which would cover the whole curve under 10 years nicely.

The diversification benefit isn't huge so holding just ZF I think is fine too especially for smaller amounts early in the accumulation phase. If somebody finds the complexity of holding 2+ contracts prohibitive, they should just hold 1, and it will still be better than any other implementation (e.g. TYA/TYD).

The benefit is marginal. Like a 5 or 10% reduction in the standard deviation of returns.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Fri Nov 12, 2021 9:22 am
DMoogle wrote: Fri Nov 12, 2021 9:08 am
skierincolorado wrote: Fri Nov 12, 2021 9:01 amI'm assuming you have high risk tolerance and a long time horizon. Even so, 165/400 is too bondy. At most I would go 165/300, and personally I would go 165/275 even if I was in my mid-twenties and high risk tolerance with low net worth but high income. This would still beat HFEA (55/45 UPRO/TMF) in a backtest. But it's a little less bond risk which given todays very low rates makes some sense. There were a number of other reasons justifying a lower ratio of stock : bond discussed in the thread - try to skim it if you can. People in this thread are generally choosing ratios between 1:1 and 1:2 with a mean around 1:1.5. 165/400 is actually significanly more bond risk than HFEA which would not do well in a rising rate scenario.

You can test in PV by modifying the backtests in this thread. But also backtest in Simba's spreadsheet which takes you back to 1955 to see how it would do in a rising rate environment.
Btw is the current thought to use all ZN, all ZF, or some mix of the two to achieve the ITT portion? I'm in ZN right now, but not sure if I should switch next time I need to rebalance.
Current thinking is to use at least two contracts, probably even better with 3. Upthread there was some excellent discussion comparing the returns of futures vs a cash position in the same duration vs a diversified bond etf. The discussion showed very low finance costs for futures because the returns were very similar to the cash position in the same duration. But the risk-adjusted returns of the diversified bond etfs were noticeably better, presumably because they hold multiple durations and are diversified. So at a minimum I would hold ZF and ZN. Those are pretty close in duration though so maybe it would be better to hold a pairing farther apart in duration such as ZF + TN, or ZT + ZN. Obviously one would adjust the size of the position relative to the duration (over twice as much ZF as TN) and even then I might lean most heavily on ZF and ZN (TN is a little long in duration the risk-adjusted returns start to drop off historically). Or one could use 3 durations, mostly ZF, with a little ZT and TN. Obviously simplicity is important too. Currently I just hold ZN and ZF, but might add a little TN or ZT, but need to develop a rules based plan so I am not introducing risk by jumping in and out of contracts. If I was holding 3 durations long-term it would be ZT, mostly ZF, and a smidge of TN, which would cover the whole curve under 10 years nicely.

The diversification benefit isn't huge so holding just ZF I think is fine too especially for smaller amounts early in the accumulation phase. If somebody finds the complexity of holding 2+ contracts prohibitive, they should just hold 1, and it will still be better than any other implementation (e.g. TYA/TYD).

The benefit is marginal. Like a 5 or 10% reduction in the standard deviation of returns.
I personally currently hold ZF, ZN, TN, and ZB, with amounts decreasing in that order. I think ZB might be a good diversifier for longer periods and might possibly lessen drawdowns, even if it has less expected return, as it often moves in the opposite direction than the other futures. Maybe we can verify or refute that some day with some backtest.

I agree that a rigorous rules-based system should be in place for rebalancing, especially if multiple futures are used. I would probably go for a strict duration-neutral approach in addition to some other rules to accomplish the rebalancing target, that way I would not introduce artifacts from changes in the level of the yield curve, but just from changes in the slope and curvature, which should offset and be neutral in the long run if rules-based. That way only the risk (if we assume that shorter durations have more risk when strictly duration adjusted) might ever so slightly change on a rebalancing event; but you cannot have all.
comeinvest
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

skierincolorado wrote: Fri Nov 12, 2021 9:14 am
msun641 wrote: Fri Nov 12, 2021 5:04 am I've downloaded the ACM model data found here:
https://www.newyorkfed.org/research/dat ... remia.html

Can anyone help me make heads or tails out of it?

I know this has already been discussed a bit in the thread, but how does the current negative expected term premium affect this strategy?
My understanding is that if the term premium is actually zero the expected return of borrowing money to invest in bonds would also be zero. However, there still would be a rebalancing and risk-reduction benefit if the negative correlation with stocks continues. If the negative correlation with stocks did not continue, the term premium would theoretically rise because one of the primary benefits of bonds would be gone and investors would demand more premium.

However, the estimate of term premium is only an estimate and historically it appears to have been too low. For example, it first shows the term premium going negative since 2012, but in reality borrowing money to invest in bonds in 2012 would have worked out very nicely still. Maybe I am misunderstanding something, but the model seems to be overly pessimistic when disaggregating the term premium from market expected future interest rate increases.
I think you cannot expect that any model or forecaster could have predicted in 2012 the global race to zero of interest rates, let alone negative nominal rates and negative real rates of several percentage points. On the other hand, I have not seen any comment or study on the confidence range of the ACM or other models. I think interest rates, along with term premia, are notoriously difficult to predict. Absent a crystal ball, I think we should be prepared that the future might be different from the entire history. There is no guarantee or law of nature that there must be a positive term premium, and I don't even think there is a theoretical justification. All theories around the yield curve or term premia that I came across seem to be rather descriptive-explanatory than predictive or fundamentally-explanatory. However I have seen papers with explanations why the term premia might be generally muted or negative in the future. The explanations are generally centered around shifts in supply and demand for capital in an aging, post-industrial world. I personally don't have the highest expectations. If the strategy happens to work out during my investment horizon, I see it as icing on the cake.
Hfearless
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by Hfearless »

Regarding rebalance, I took the duration estimates from this thread and the current market prices and tried to figure out how hard is it to maintain a certain ratio of equities to bonds, given the lumpy nature of futures. From the data

Code: Select all

UB 18.6y $196k
ZB 11.5y $161k
TN  8.8y $145k
ZN  6.2y $130k
ZF  4.3y $121k
it turns out that as long as desired exposure to bonds is greater than the equivalent of $460k worth of ZF, the relative steps between different combinations are at most 10%, so it’s always possible to be within 5% of the desired ratio. Or within 10% starting with $270k. That’s neglecting the diversification aspect and solely trying to get a particular duration-adjusted exposure.
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 »

Hfearless wrote: Fri Nov 12, 2021 4:35 pm Regarding rebalance, I took the duration estimates from this thread and the current market prices and tried to figure out how hard is it to maintain a certain ratio of equities to bonds, given the lumpy nature of futures. From the data

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UB 18.6y $196k
ZB 11.5y $161k
TN  8.8y $145k
ZN  6.2y $130k
ZF  4.3y $121k
it turns out that as long as desired exposure to bonds is greater than the equivalent of $460k worth of ZF, the relative steps between different combinations are at most 10%, so it’s always possible to be within 5% of the desired ratio. Or within 10% starting with $270k. That’s neglecting the diversification aspect and solely trying to get a particular duration-adjusted exposure.
When combined with vgit it should be possible to get exactly the desired duration in bonds down to about 50k of equity. Below 100k equity might involve switching between zf and zn. I personally would feel comfortable owning a single ZF down to about 30k of equity although you do lose the rebalance flexibility below 50k (assuming 200% allocation to 5 yr duration)
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Re: Modified versions of HFEA with ITT and Futures / Lifecycle Investing with Modern Portfolio Theory

Post by comeinvest »

Hfearless wrote: Fri Nov 12, 2021 4:35 pm Regarding rebalance, I took the duration estimates from this thread and the current market prices and tried to figure out how hard is it to maintain a certain ratio of equities to bonds, given the lumpy nature of futures. From the data

Code: Select all

UB 18.6y $196k
ZB 11.5y $161k
TN  8.8y $145k
ZN  6.2y $130k
ZF  4.3y $121k
it turns out that as long as desired exposure to bonds is greater than the equivalent of $460k worth of ZF, the relative steps between different combinations are at most 10%, so it’s always possible to be within 5% of the desired ratio. Or within 10% starting with $270k. That’s neglecting the diversification aspect and solely trying to get a particular duration-adjusted exposure.
We still have to figure out the optimal rebalancing strategies for mHFEA. If I remember right, the HFEA threads have some comparison of the effects of rebal frequencies or the size of rebalancing bands, somewhere on the 279 pages of the two threads ;)
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