skierincolorado wrote: ↑Tue Nov 16, 2021 3:36 pm
comeinvest wrote: ↑Tue Nov 16, 2021 3:23 pm
skierincolorado wrote: ↑Tue Nov 16, 2021 3:02 pm
comeinvest wrote: ↑Tue Nov 16, 2021 2:38 pm
I am totally lost with your reasoning. "Duration weighted duration" almost sounds like a parody to me. ZF has duration of about 4.5 if I remember right; ZB has about 11.5. So his 484:161 ratio is already *more* than a duration-adjusted allocation, i.e. his ZF position has already more duration risk than his ZB allocation. And that is setting aside the fact that, as you discovered in the course of this thread, the actual relative risks as you move along the maturities are less than what a strict duration based risk model would suggest, because the interest rates of shorter durations fluctuate more. But regardless of the specific model, his treasury portfolio interest rate sensitivity wold be about 6.5, not 8. Weighting durations by duration to come up with a weighted average duration makes zero sense to me. It's like double dipping. And what would be the meaning of that number.
Let's also look at it from another angle. Say in a given hypothetical future time period, the curve flattens and interest rates generally increase - stagflation with decreasing term premia because of little demand for capital - a tail risk scenario that we want to hedge by diversifying across the yield curve. Say ZF returns -10%, and ZB returns -1% during that period. With $484k in ZF and $161 in ZB, your treasury portfolio return would be -7.8%. An equi-distribution based on notional values would have a treasury portfolio return of -5.5%, a significantly smaller drawdown. By the way, your equities tank during that hypothetical period because of stagflation. All this is just one example. ZB could also increase in value all the while ZF drops, which is what happened in the past 6 months.
I know, my equi-distribution based on notional values has lower expected return based on your historical backtests. But it is more diversified. What you are suggesting would make the diversification effect minuscule if not irrelevant. ZF and ZN are very close to each other, and even with DMoogle's proposal would already have 3/4 of the assets. Do you move 75% of your equities to Australia, just because the Australian stock market had the highest risk-adjusted returns historically?
Might be interesting to actually backtest a diversified-ITT (ZF/ZN/TN/ZB with either duration-adjusted or notional value based weights) vs. a short-maturity-ITT portfolio during a historical rising rate plus flattening period, or compare returns and drawdowns over a full cycle.
The situation you have described for its diversificatoin benefit - a 10% drop in ZF and a 1% drop in ZB.. would amount to a 2.5% rate increase for ZF and a .1% rate increase for ZB. The yield curve would be insanely inverted with 4.5 year rates of 3.75% and 11.5 year rates of 1.8%.
Note that the 11.5 year rate increased 25x more than the 4.5 year rate (2.5% vs .1%).
Let's try the reverse scenario. What if the 11.5 year rate increases 25x more than the 4.5 year rate. The ZB would lose 23%. ZF would lose 0.5%. But the return of the portfolio would be completely dominated by the single ZB contract.
While both scenarios are extremely unlikely bordering on impossible, I'd still argue the second is more likely than the former since a 2.5-3% spread between 11y vs 4.5y has actually happened before while a 2% inversion has not.
My example was just an ad hoc example to demonstrate the benefit of diversification. Tweak the numbers to your liking or make them more realistic.
The return in a steepening or flattening scenario will always be dominated by the maturity where the rate changed more. That effect is a wash.
Although I think the theoretical rationale is shaky, I could follow your argument for a weighting based on duration risk (which would be based on an assumption of an equal probability of steepening vs. flattening by the same nominal interest rate change), or at least based on "modified" duration risk that reflects the bigger fluctuations of rates at shorter maturities. But I'm lost with your concept of going beyond that.
You also sometimes tend to allude to mean reversion based on current valuations, as in "this can only continue so long"; while other times you say you only consider strict rules based allocations based on simple rules. I would generally not disagree with either one approach. But firstly, you have to reflect drawdowns based on temporary dislocations in your risk model, even if they "can only continue so long". Secondly, there are not only theoretical, but also real scenarios that are happening in other parts of the world - permanent flattening -, where longer maturities would benefit, and as a result, diversification would benefit vs putting all your eggs in one basket.
I edited to include the fact that the loss on the ZB in my 2.5% widening was nearly as large on all those ZFs in your 2.5% inversioning (I won't even call that a flattening haha so I am making up a word). This is what I mean by he has equal risk at each duration.
Ignoring the fact that a 2.5% widening is probably more likely than a 2.5% inversioning, we still should tilt towards the lower duration because the roll and carry is better. If there is no flattening or widening, the ZF wins substantially. Only if we believe flattening/inversioning will be rapid at high probability would we want equal risk. That's the breakeven. Otherwise we tilt to the one with the better roll and carry and historical returns.
If widening/flattening was a normal distribution centered at zero... we would pick ZF and zero TN or ZB. It's not centered at zero though.. slight flattening is probably a bit more likely than widening. But not enough to push us into equal risk in ZB.
How about a more realistic scenario where 4.5 year rates increase 3% and 11.5 year rates increase 2.5%. The yield curve would still be inverted. But one would of course have been much better off in the shorter durations 1) because we can have less duration risk (I'd replace each ZB with 1.5 ZFs) and 2) unless this happened overnight we'd be getting the much better roll and carry of the shorter durations every single day that interest rates didn't rise
Again I don't generally disagree, but I would also question, or at least not blindly follow, the approach to estimating expected returns and risk based on simplistic interest rates models and simplistic relationships. It's a nice and valuable exercise, but in the end, we are dealing with financial markets, which are governed by preferences of market participants, some of which theoretically have the same information or more information than we have. The BAB effect is hard to quantify, and it may or may not persist. (Just like "value" risk-adjusted outperformance persisted for decades in the U.S. stock market, until it didn't for 2+ decades.)
"we would pick ZF and zero TN or ZB" - makes only sense if you think you can forecast the future with 100% accuracy in that ZF will outperform by virtue of its carry, and give 0% chance to alternate scenarios.
If we assume that whatever biases lead to ITT outperformance will persist, then I think the Simplify chart is one of the most valuable supporting an ITT based strategy. I am re-posting it. The chart shows the "carry", which I interpret to be an estimator of returns after removing the effect of changes in interest rate (which can only persist so long until they reverse).
The outperformance of ITT was on average ca. 2.5% in the 5-7 year range. If I understand the assumptions right that Simplify made, the chart does not reflect the futures slippage of ca. 0.2%, but then they use the 1-year treasury rate as funding rate and not a 3-month funding, so it might be a wash. But I think we might want to adjust the expected future outperformance or ITT vs LTT by dividing it by a "compression factor" of maybe 2 or 3 to reflect the generally lower interest rate level at the long end of maturities compared to history, that I think must eventually result in lower term premiums across the yield curve, as we have less "vertical space" on the y-axis of the yield curve to work with.
Also note that the chart is based on duration-adjusted allocations, not risk-adjusted allocations that we determined to be somewhat lower.
https://www.simplify.us/blog/efficient- ... -investing