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

[skierincolorado]

I would agree with all of this. But I would argue that both the time in the market and the reduced risk aversion conditions are likely fulfilled for most people reading this thread and seriously taking care of their financial independence; so the formula given is obsolete in most cases. I don't mean to make statements that include or exclude more or less affluent readers; but I think what matters is the savings rate relative to current consumption (which b.t.w. is often worse for very affluent people, who occasionally also go broke). That is simply because the savings grow exponentially, while the earnings from your career typically just grow with inflation after the first few years. Someone with less than 15-20 years time in the market can use the formula; probably for less than 15 only, because the yellow or blue curve with the earlier upswings would apply. 15-20 years is probably also the minimum to seriously benefit from of mHFEA. Probably not coincidentally, 15 years is about the maximum that momentum or "trending" market dislocations of valuation ratios last, or at least before the exponential function "wins" and dominates the returns.

I agree with most of this but want to point out that decreasing RRA (relative risk aversion) with higher wealth is an argument for less leverage not more. Decreasing RRA with high wealth is equivalent to having smaller changes in utility from relative changes in wealth. For example, doubling from 5M to 10M or halving from 10M to 5M have very little difference in utility. Taking risk today (for someone with no future additional savings) can help increase the odds of very high wealth, but if there is little additional utility there is little incentive. A person with decreasing RRA at high wealth must have increasing RRA at low wealth. Taking lots of leverage increases the risk of very large loss at long horizons. If the person has increasing RRA at lower wealth they would view these outcomes extremely negatively.

I think a potential argument against using RRA to calculate samuelson share is that RRA actually decreases at low wealth for most people. To take it to an extreme, losing half your money when you have $2 isn't as bad as losing half when you have $2M. Risk Aversion is both absolute and relative.

Because samuelaon assumes risk aversion is relative and constant, the worst case scenarios cost more utility than they would for most people. Even if the assumption of normality isn't perfect, the odds of losing 99% of your money are surely higher over 20 years than 1 year. Assuming constant RRA of 1 means that losing 99% instead of 98% has the same effect on utility as doubling your money (in opposite directions). I don't think that's true.

We are getting on slippery slopes here. I would disagree that a person with $100k has less risk aversion than someone with $2M; I know people in either category. But it is rather irrelevant for the topic at hand.
You are repeating your thesis "losing 99% of your money are surely higher over 20 years" that contradicts your charts (for moderate leverage). History has no precedence for either losing 99% in one year or in 20 or 30 years; in fact not only the probability of a 99% loss, but even the probability of a 1% loss was zero for ca. 20 year or longer horizons and no or moderate leverage, if I read your chart right. So you are wildly speculating here on something with no factual support whatsoever. The question becomes, what would the world look like if that were to happen. In many such catastrophic scenarios I think your portfolio would outlive you, in which case the utility of $1, $100k, and $1M would all be zero; you could then argue the $2M -> $4M increment, which you would likely realize in case a global catastrophic event does not happen, has more utility, even if the additional utility is small. (Obviously not saving at all, but consuming everything might have been best in this case in a catastrophic scenario; but that is off topic.) Another scenario that I could imagine that you would survive is political upheaval with a full or partial expropriation of property, in which case the utility of any amounts of assets is pure speculation. To stay on topic, the question whether a loss larger than historical precedence over your investment horizon can happen although the system survives, is also speculation. There are a lot of empirical and theoretical arguments that the capital will keep growing exponentially in the long run, as long as the system survives; although of course I would always use leverage ratios way below the historical optimal. Other than that, the empirical evidence per your charts is that the risk of loss (and/or the retirement target shortfall risk, if applicable) decreases with increasing time after 15-20 years.
Can you still answer my question about the ratios in your charts please?

Your first sentence mixes up risk aversion and relative risk aversion. All the people i know with 50k have much less relative risk aversion than I do. Their loss or utility from losing half their money is much less than mine. This is because loss aversion is not just relative, it is absolute. They have more risk aversion of losing 50k than I do. I've lost 50 multiple times and not even noticed. But their relative risk aversion is surely higher.

It is also absolutely true that losing 99% is more likely over 20 years than 1 year. Both the charts I posted and common sense tell me this. The charts show loss of more than 0% rises at first and then falls. It establishes that returns are close (not perfectly) to the assumption of i.i.d. even at 20 years. If returns are i.i.d. the risk of losing 99% is much higher at 20 years than in 1 year. This also is just common sense I think. The risk of catastrophe over 20 years is higher than over 1 year. A way to visual it is that the 30th percentile goes down at first and then improves. The 10th percentile would go down longer, and then improve. The 5th percentile goes down even longer but eventually improves. Etc. This is backed mathematically under approximate assumption of normality, but also common sense. The higher risk of 99% loss at 20 years would be true even if returns are auto correlating. They would have to be extremely autocorrelating/mean reverting for it Not to be true. And the charts show that while there might be some autocorrelation/mean reversion by year 20 it is by no means extreme.

The higher probability of 99% loss at 20 years than 1 year is a big problem for risk taking and leverage IF relative risk aversion is constant. In other words, of the loss of utility from 100k to 50k is the same as the loss of utility from 1M to 500k. This is the part that I think is the bigger flaw. Relative Risk Aversion is surely lower for somebody with $10 than 1M.

At longer time horizons, proving the fallacy of time diversifcation relies more and more on very low probability events with extremely negative utility. But if the loss in utility has a lower bound, we start to care less about about these very low probability events and more about the 10th percentile, which is likely improving at 20 years even though the 99th percentile is still deteriorating.

So I think that's the bigger issue over longer horizons. The assumption of normality and the rising probability of 99% losses is likely pretty accurate but maybe the odds are a bit better on longer horizons but I'm not sure there's enough data on long horizons to be sure. On shorter horizons the returns of 15 yrars are quite close to what normality predicts.

What was your question about the ratios?

All your paragraphs except the second are implications of your assumption that the "final deathblow" after an already near complete wipeout has less negative utility than the same relative loss from a higher starting point. I'm not sure about that. I think many people who own "only" $100k would see that as a big safety buffer and source of possible spending and financial independence in excess of government benefits, with equal if not higher relative risk aversion. But that is subjective and everybody can make their own determination. I personally would want to avoid both a 90% and a 95% final wipeout at nearly all cost; so it is rather irrelevant to me. Let's go back to the objective part, your second paragraph.

Like I said, I find that extrapolating a mathematical formula to derive probabilities of a 90% or 99% or whatever drawdown over some time horizon, when that formula was a closed-end formula mathematical approximation of empirical data that showed 0% probability of even a 1% drawdown, let alone any larger drawdowns, is completely futile and pure speculation.
For this reason alone I'm tossing out almost all your sentences in your second paragraph.
Secondly and independently, I think the fact that the solid and the dashed lines in your chart show significant and consistent (across leverage ratios) divergence from each other after about 15-20 years, is prima facie evidence that the returns process is not i.i.d. (Loosely speaking the returns appear to have negative correlation with probably 5-10 year lags, with the negative cumulative correlation increasing from there to 15-20 year lags, before they probably become less correlated again as the exponential growth dominates the mean-reverting underlying components of returns; but that interpretation and analysis is rather irrelevant; your charts that show an important portfolio level "end user" risk metric speak for themselves.)
Not only the amount, but the directions of the solid and the dashed lines in the second chart become consistently opposite starting between ca. year 6 and year 17 depending on leverage. In short, the solid and dashed lines are diametrically opposed for investment horizons longer than ca. 15-20 years.
"They would have to be extremely autocorrelating/mean reverting for it Not to be true. And the charts show that while there might be some autocorrelation/mean reversion by year 20 it is by no means extreme." - I disagree. I acknowledge that the historical data points are few, which might prompt you to extrapolate the <15 years behavior. But the divergence after 15-20 years seems significant and consistent. Short of more sophisticated parameterization of the empirical data and more sophisticated statistical hypothesis tests, if anything I would extrapolate the divergent trend after 20 years. Plot the 35 year chart and it becomes more clear.
My conclusion is also consistent with the plots that show 10-year and 15-year returns against CAPE ratios for many decades worth of data. There would be no visible correlation if the return process were i.i.d. (It's more complex than this and not a direct proof, as I'm jumping from autocorrelation to CAPE ratios; but you get the general idea regarding the existence of mean-reverting components of the returns process.)
I think the yellow, blue, and red lines are the relevant ones, as nobody would leverage at, near, or above the Kelly optimal in the first place. I am magnifying the relevant parts of your charts.

Like I said, just like you, I would use leverage ratios way below the historical optimal, to reflect an unknown probability of tail risk that might have not been exposed in history. But that is completely independent of the evidence regarding the question at hand, that risk decreases with time horizon after ca. 15-20 years (less than 15 years for the low leverage yellow line), and that the return distributions are not i.i.d. but have some mean-reverting characteristics. You can create a chart of 30 or 35 years and it becomes even more evident. I think your mistake is jumping from < 15-20 years to > 15-20 years (less for no or lower leverage). For short periods, the returns appear almost i.i.d.; the non i.i.d. behavior is not evident. For longer investment horizons and lag times, the non i.i.d behavior shows and eventually dominates, or else the solid lines in your charts would not diverge and eventually turn to the opposite direction from the dashed lines in the average loss chart. An intuitive explanation is that the portfolio has more time to recover from a catastrophic event the longer the time horizon after ca. 15-20 years (less than 15 years for the yellow line), as the exponential growth will eventually dominate the end results. Economic downturns and surprise effects, as well as dislocations of financial valuation multiples, can develop some momentum or trend in the same direction, but typically last not more than a few years and are, loosely speaking, "naturally" range bound and mean-reverting. Another possible intuitive explanation would be that stocks as real assets cannot just "evaporate" into nothing or into almost nothing. I know reality is more complicated; there is book value and goodwill etc.; but you get the idea. I guess individual productive assets can become obsolete, but hardly the aggregate of productive assets.

My other question was:

I noticed that you selected the proportion of Kelly optimal leverage ratios (if I understand it right) for your legend. Is this because the charts would scale similarly for varying expected returns and volatilities, as long as this proportion stays constant? Could you please generate charts or explain how the charts would be different for our consensus 4% expected real returns, 20% volatility assumptions, and what would be the Kelly optimal leverage ratio in this case; or what leverage ratios do the ratios in your charts correspond to?

It's probably debatable whether the loss in utility from 1M to 500k or 100k to 50k is greater, but I think it would be tough to argue the loss from 10k to 5k is as great or from 2k to 1k. It some point the utility also relates to the absolute loss and not just the relative loss. The 99% loss scenarios that become more likely on longer horizons don't necessarily have the massive loss to utility indicated by RRA (RRA is a necessary assumption of Samuelsons proof).

There's really not enough data to say how much more likely (if any) a 95% or 99% loss become on longer time horizons. It's true the probability of loss diverges somewhat from the normal distribution after 15 years, but there are only 5 non-overlapping 20 year periods in the data. Anything regarding normality or autocorrelation beyond 10 or 15 years is speculation based on too little data.

However, I don't need data to tell me the probability of a 90% loss is greater over 30 years than it is over 5. The probability of a major natural disaster or social/political upheaval event is greater over 30 years than over 5. Maybe it's not exactly as more likely as extrapolating a normal distribution of returns would theorize. But I think the overall point is very much intact. I do agree with your point that real assets are unlikely to evaporate and would have some mean reverting properties. So it's not perfectly normal. But I'd also speculate that while the partial/total collapse of the U.S. government (let's say it is replaced with some sort of violent populist/fascist/socialist government that doesn't respect private property rights) only has a 1-5% chance in the next 5 years, the probability over the next 30 years might be as high as 10%. The probability of an asteroid large enough to mostly destroy the economy might be .1% in 5 years but 1% in 50 years (or maybe it's 0% for both and this is a bad exaple). The risk of extreme events large enough to mostly or totally destroy the stock market certainly increases over longer horizons.

At a certain point it stops mattering though and this is where I have more of an issue with Samuelson's assumptions. I don't know that I care that much about a 99% loss vs 98% loss (or 100% loss).

For your question about the chart, they're not my charts, here's the link below. The post says that 100% stock was .38 kelly crit. So the kelly crit was 2.63x leverage (1 kelly crit). The most leveraged line is about 5.5x leverage, while the least leveraged line is 0.65x stock allocation.

https://outcastbeta.com/time-diversific ... ventually/

[comeinvest]

However, I don't need data to tell me the probability of a 90% loss is greater over 30 years than it is over 5. The probability of a major natural disaster or social/political upheaval event is greater over 30 years than over 5. Maybe it's not exactly as more likely as extrapolating a normal distribution of returns would theorize. But I think the overall point is very much intact. I do agree with your point that real assets are unlikely to evaporate and would have some mean reverting properties. So it's not perfectly normal. But I'd also speculate that while the partial/total collapse of the U.S. government (let's say it is replaced with some sort of violent populist/fascist/socialist government that doesn't respect private property rights) only has a 1-5% chance in the next 5 years, the probability over the next 30 years might be as high as 10%. The probability of an asteroid large enough to mostly destroy the economy might be .1% in 5 years but 1% in 50 years (or maybe it's 0% for both and this is a bad exaple). The risk of extreme events large enough to mostly or totally destroy the stock market certainly increases over longer horizons.

At a certain point it stops mattering though and this is where I have more of an issue with Samuelson's assumptions. I don't know that I care that much about a 99% loss vs 98% loss (or 100% loss).

I think we are coming closer; but I still don't agree. The blue and yellow lines are based on about 10-15 independent periods, and yet the upswing and divergence of the solid from the dashed lines are what I would call consistent and significant.

Of course this doesn't tell us anything about very rare and very negative events. If we had enough time on hand, we could probably decompose the stock market returns into the effects of changes to risk-free rates, economic downturns, profit margins, valuation multiples / equity risk premia, and a few more; I'm sure others have done that already. This would probably make more sense than extrapolating a formula that never covered any single data point even close to such a scenario. Most if not all of these underlying parameters are "naturally" "soft" range bound and mean reverting. Then the question would become, think of a hypothetical scenario that can result in a drawdown, like > 90%, that the mean reverting characteristics and the growth of the exponential function cannot "heal" within 30 years.
Perhaps we can agree that if such an event happens at all, it would be a singular event during a 30 year period; the probability of two such events happening within 30 years is negligible (think of 2 independent asteroids in short sequence). Perhaps we can also agree that it would likely be an event with a root cause that is outside the normal economic and financial forces that until now governed the modern financial markets - a natural or man-made global disaster, or political upheaval; it would likely not be a slowly progressing or a series of several economic or valuation dislocations that would all go in the same direction, compound, and never end within a 30 year period; you can expand or compress things like valuation multiples, risk-free real rates, etc., only so much, until they either vehemently reverse or yield powerful carry returns.

So the question becomes with equal portfolio leverage, would you prefer a smaller chance of a singular catastrophic event happening during for example the next 10 years, with not enough time to recover by way of portfolio growth via exposure to the "regular" risk premia, or a somewhat bigger chance of the same catastrophic event happening during the next 30 years, with exponentially compounding growth during the remaining let's say 25-29 years.

I would tend to go with the second option, and I think the total loss after recovery from a singular catastrophic event would be less than it would be during a 10 year timeframe. Let's assume you start with $1M, ready to retire early with no future contributions expected, and let's ignore consumption for sake of simplicity; perhaps you have some semi-passive side income for living expenses, or perhaps it is a trust. Let's assume 4% equity risk premium (ignoring the asteroid), 5% annual geometric real return of mHFEA (ignoring the asteroid), and figuratively speaking an asteroid hitting and destroying 80% of Earth (substitute any other catastrophe of your imagination). Within 10 years you would end up with $1,000,000 * 1.05^10 * 0.2 -> $325,779. Within 30 years, you would end up with $1,000,000 * 1.05^30 * 0.2 -> $864,388 i.e. almost no loss. (Wait another 3 years or get some lazy side job, and you recovered your money, short of another asteroid hitting Earth.) Even though the likelihood of the same asteroid hitting was 3 times as high during 30 years as during 10 years, there would be no significant terminal portfolio loss in the 30 year scenario.

Now you may say ok but a 95% to 100% wipeout instead of an 80% wipeout would leave residual value with similar utility in both 10-year and 30-year scenarios, but at 3x the likelihood in the 30-year scenario. True, but what is the likelihood of yourself surviving such a scenario? So you would have to condition the scenario analysis and probabilities on your own survival.
Furthermore you would want to condition your analysis on the scenarios where a less leveraged portfolio than the one under consideration, or an unleveraged portfolio, would have survived with meaningful residual value. The scenarios where everything or almost everything on Earth that your portfolio assets might represent simply ceases to exist, constitute risks that are inherent in the passage of time, and not inherent in a particular portfolio, asset allocation, or leverage ratio.

In any case I think the model needs adjustments for rare events, not simplistic extrapolation. A 1929-1931 scenario repeating somewhere between 1931 and 1959 before the market recovered, was less likely than the initial 1929-1931 scenario, or perhaps impossible under any sensical economic assumptions; likewise the rates-driven 1968-1982 scenario repeating in 1982-1996 and combining to a 28-year long multiples compression period would arguably have been impossible, as stock market multiples were already extreme in 1982.

[sharukh]

Hello all,

Which brokerage do people who do mhfea use.
IIUC only 2 or 3 brokers support futures and options on futures in IRA
Brokers like Robinhood don't support SPX for borrowing in taxable or futures like MES.

Does mhfea followers do brokerage transfer bonus game

I did Robinhood bonus this January, immediately lost ability to do low cost mhfea. Any bonus is being used up for higher expenses of mhfea.

Or even for doing Merrill edge preferred rewards.. not sure if Merrill ed ge support short spx boxes.

I think Schwab don't support SOFR futures.

Can you consider sharing your setup?

Thank you

[comeinvest]

Interesting charts from Donald van Deventer's series or articles https://seekingalpha.com/article/472416 ... ield-curve . Notably his forward curve goes beyond the 10 years on the Chatham Financial site https://www.chathamfinancial.com/techno ... ard-curves

[comeinvest]

Hello all,

Which brokerage do people who do mhfea use.
IIUC only 2 or 3 brokers support futures and options on futures in IRA
Brokers like Robinhood don't support SPX for borrowing in taxable or futures like MES.

Does mhfea followers do brokerage transfer bonus game

I did Robinhood bonus this January, immediately lost ability to do low cost mhfea. Any bonus is being used up for higher expenses of mhfea.

Or even for doing Merrill edge preferred rewards.. not sure if Merrill ed ge support short spx boxes.

I think Schwab don't support SOFR futures.

Can you consider sharing your setup?

Thank you

You learned your lesson already the hard way, regarding chasing brokerage bonuses.

Schwab (with their ToS applications from former TdA) and IB seem to be the "real" thing, the main difference being that IB provides access to international equity and futures markets; but IB doesn't recall lent securities on dividend ex dates and you cannot avoid lending if you have a margin (negative cash) balance or negative options value, so you pay taxes at ordinary income rates on payments-in-lieu in taxable accounts; I'm not an E-Trade customer, but E-Trade seems to be ok although not quite up to par. TradeStation has good historical data, backtesting capabilities, and trading apps, but is a bit small and fee laden with nickel-and-diming, and has no combined equities+futures accounts, so you have to open separate accounts for each, with no automatic cash sweeps. Fidelity has no futures trading and is therefore not an option for mHFEA or portable alpha investors. Tastytrade is too small for my taste and lacks scale.
The rest of U.S. and all international (European, let alone Asian) retail brokers seem to be pure garbage compared to the above (no offense); I wasted my time trying some of them in the past.
So essentially only 2 serious options, as far as I can tell.

[sharukh]

Hello all,

Which brokerage do people who do mhfea use.
IIUC only 2 or 3 brokers support futures and options on futures in IRA
Brokers like Robinhood don't support SPX for borrowing in taxable or futures like MES.

Does mhfea followers do brokerage transfer bonus game

I did Robinhood bonus this January, immediately lost ability to do low cost mhfea. Any bonus is being used up for higher expenses of mhfea.

Or even for doing Merrill edge preferred rewards.. not sure if Merrill ed ge support short spx boxes.

I think Schwab don't support SOFR futures.

Can you consider sharing your setup?

Thank you

You learned your lesson already the hard way, regarding chasing brokerage bonuses.

Schwab (with their ToS applications from former TdA) and IB seem to be the "real" thing, the main difference being that IB provides access to international equity and futures markets; but IB doesn't recall lent securities on dividend ex dates and you cannot avoid lending if you have a margin (negative cash) balance or negative options value, so you pay taxes at ordinary income rates on payments-in-lieu in taxable accounts; I'm not an E-Trade customer, but E-Trade seems to be ok although not quite up to par. TradeStation has good historical data, backtesting capabilities, and trading apps, but is a bit small and fee laden with nickel-and-diming, and has no combined equities+futures accounts, so you have to open separate accounts for each, with no automatic cash sweeps. Fidelity has no futures trading and is therefore not an option for mHFEA or portable alpha investors. Tastytrade is too small for my taste and lacks scale.
The rest of U.S. and all international (European, let alone Asian) retail brokers seem to be pure garbage compared to the above (no offense); I wasted my time trying some of them in the past.
So essentially only 2 serious options, as far as I can tell.

Hi,

Thank you for sharing your experience. I had very good experience with E-Trade before moving to IB, only reason to leave E-Trade was it didn't support FOP, collateral had to be cash only.
Now I am 50% at IB, 50% at robinhood. Will probably move away from Robinhood soon.

[comeinvest]

Term premia per ACM are still all negative, despite the upward sloping yield curve except the expected short-term rate cuts.

[comeinvest]

September 2024 equity index futures roll a total disaster. Nikkei and MSCI EAFE futures cost of leverage is lower; they are the better value proposition in terms of cost of leverage, especially after considering foreign withholding taxes of an equivalent exposure via ETFs.

Implied rates of leverage with options are currently measurably lower.

The fools at ICE show the overnight SOFR instead of the 3-month term SOFR, so you have to add ca. 0.5% to the financing cost above SOFR shown.









MSCI EAFE:



MSCI Emerging Markets:

[unemployed_pysicist]

September 2024 equity index futures roll a total disaster. Nikkei and MSCI EAFE futures cost of leverage is lower; they are the better value proposition in terms of cost of leverage, especially after considering foreign withholding taxes of an equivalent exposure via ETFs.

Implied rates of leverage with options are currently measurably lower.

Which options have implied rates of leverage lower than which futures contracts? E.g., SPX options vs ES contracts, or something else?

[comeinvest]

September 2024 equity index futures roll a total disaster. Nikkei and MSCI EAFE futures cost of leverage is lower; they are the better value proposition in terms of cost of leverage, especially after considering foreign withholding taxes of an equivalent exposure via ETFs.

Implied rates of leverage with options are currently measurably lower.

Which options have implied rates of leverage lower than which futures contracts? E.g., SPX options vs ES contracts, or something else?

I'm not 100% sure if I understand your question, but if you are asking which actionable decisions it might affect, probably not many as your asset allocation mostly dictates your risk exposure, and your portfolio, account, and tax constraints dictate your use of futures and options; but you could for example use ETFs instead of U.S. futures if you have enough "space" in tax-deferred accounts, or use foreign futures instead of U.S. futures for leverage. Money is fungible, so it doesn't matter which risk exposure you leverage. The information can also be good to know simply for attribution of returns of your strategy, and monitoring the execution of your mHFEA implementation; for example emerging markets implemented with futures would have a ca. 1% drag lately (on top of risk-free rates if defined as 3 months term SOFR) compared to the emerging market index. It appears that most futures became more expensive lately, including SOFR and treasury futures as per my comments on the basis spread of treasury futures in the last few pages, and per the swap spread discussion earlier in this thread; only SPX options implied rates stayed about the same as the historical average, which I know because I maintain a spreadsheet with my entire history of SPX options trades. Notably the Nikkei futures went from ca. 0% financing spread to JPY risk-free rates where the spread has been for many years, to ca. 0.5%.

[unemployed_pysicist]

September 2024 equity index futures roll a total disaster. Nikkei and MSCI EAFE futures cost of leverage is lower; they are the better value proposition in terms of cost of leverage, especially after considering foreign withholding taxes of an equivalent exposure via ETFs.

Implied rates of leverage with options are currently measurably lower.

Which options have implied rates of leverage lower than which futures contracts? E.g., SPX options vs ES contracts, or something else?

I'm not 100% sure if I understand your question, but if you are asking which actionable decisions it might affect, probably not many as your asset allocation mostly dictates your risk exposure, and your portfolio, account, and tax constraints dictate your use of futures and options; but you could for example use ETFs instead of U.S. futures if you have enough "space" in tax-deferred accounts, or use foreign futures instead of U.S. futures for leverage. Money is fungible, so it doesn't matter which risk exposure you leverage. The information can also be good to know simply for attribution of returns of your strategy, and monitoring the execution of your mHFEA implementation; for example emerging markets implemented with futures would have a ca. 1% drag lately (on top of risk-free rates if defined as 3 months term SOFR) compared to the emerging market index. It appears that most futures became more expensive lately, including SOFR and treasury futures as per my comments on the basis spread of treasury futures in the last few pages, and per the swap spread discussion earlier in this thread; only SPX options implied rates stayed about the same as the historical average, which I know because I maintain a spreadsheet with my entire history of SPX options trades. Notably the Nikkei futures went from ca. 0% financing spread to JPY risk-free rates where the spread has been for many years, to ca. 0.5%.

Thank you for your detailed answer, but I was just curious if you had some kind of specific example on hand, like "SPX call option at X strike had an implified financing rate of Y percent at expiry D, whereas ES contract had an implied financing rate of Y+Z percent at expiry D".

I thought it was unusal for options to have a lower implied financing rate than futures, right? Such a regime seems notable, even if not necessarily actionable.

Note: I am referring to the implied financing of leverage using call options only, not the cost to leverage with box spreads.

[comeinvest]

Thank you for your detailed answer, but I was just curious if you had some kind of specific example on hand, like "SPX call option at X strike had an implified financing rate of Y percent at expiry D, whereas ES contract had an implied financing rate of Y+Z percent at expiry D".

I thought it was unusal for options to have a lower implied financing rate than futures, right? Such a regime seems notable, even if not necessarily actionable.

Note: I am referring to the implied financing of leverage using call options only, not the cost to leverage with box spreads.

I think only with box spreads you can easily determine the implied financing rates. For most other options it will be difficult to separate the components that make the price - options implied risk-free rate, implied volatility, and higher order derivatives of the volatility surface, if you look at only one options contract in isolation. But I would think that you might be able to go the opposite way and solve the equation from the known variables (intrinsic value and implied risk-free rate of options derived from box spreads) to calculate the implied volatility based on an options pricing formula. Disclaimer: I'm not an options professional.

The implied financing rate spreads of futures products generally increased after ca. 2013 for some equity index futures because of increased government regulations, and then again recently for equity index futures and treasury futures as well as the swap spread for SOFR futures. There are some papers on the subject that I still have to read. I hope that the implied rates don't stay permanently elevated as ETFs, mutual funds and perhaps pensions pile into leveraged or "return stacked" strategies using futures or using futures for "portable alpha" (i.e. HFEA and perhaps particularly mHFEA additionally exploiting the historical short-term/long-term treasuries anomaly become more popular).

[skierincolorado]

However, I don't need data to tell me the probability of a 90% loss is greater over 30 years than it is over 5. The probability of a major natural disaster or social/political upheaval event is greater over 30 years than over 5. Maybe it's not exactly as more likely as extrapolating a normal distribution of returns would theorize. But I think the overall point is very much intact. I do agree with your point that real assets are unlikely to evaporate and would have some mean reverting properties. So it's not perfectly normal. But I'd also speculate that while the partial/total collapse of the U.S. government (let's say it is replaced with some sort of violent populist/fascist/socialist government that doesn't respect private property rights) only has a 1-5% chance in the next 5 years, the probability over the next 30 years might be as high as 10%. The probability of an asteroid large enough to mostly destroy the economy might be .1% in 5 years but 1% in 50 years (or maybe it's 0% for both and this is a bad exaple). The risk of extreme events large enough to mostly or totally destroy the stock market certainly increases over longer horizons.

At a certain point it stops mattering though and this is where I have more of an issue with Samuelson's assumptions. I don't know that I care that much about a 99% loss vs 98% loss (or 100% loss).

I think we are coming closer; but I still don't agree. The blue and yellow lines are based on about 10-15 independent periods, and yet the upswing and divergence of the solid from the dashed lines are what I would call consistent and significant.

Of course this doesn't tell us anything about very rare and very negative events. If we had enough time on hand, we could probably decompose the stock market returns into the effects of changes to risk-free rates, economic downturns, profit margins, valuation multiples / equity risk premia, and a few more; I'm sure others have done that already. This would probably make more sense than extrapolating a formula that never covered any single data point even close to such a scenario. Most if not all of these underlying parameters are "naturally" "soft" range bound and mean reverting. Then the question would become, think of a hypothetical scenario that can result in a drawdown, like > 90%, that the mean reverting characteristics and the growth of the exponential function cannot "heal" within 30 years.
Perhaps we can agree that if such an event happens at all, it would be a singular event during a 30 year period; the probability of two such events happening within 30 years is negligible (think of 2 independent asteroids in short sequence). Perhaps we can also agree that it would likely be an event with a root cause that is outside the normal economic and financial forces that until now governed the modern financial markets - a natural or man-made global disaster, or political upheaval; it would likely not be a slowly progressing or a series of several economic or valuation dislocations that would all go in the same direction, compound, and never end within a 30 year period; you can expand or compress things like valuation multiples, risk-free real rates, etc., only so much, until they either vehemently reverse or yield powerful carry returns.

So the question becomes with equal portfolio leverage, would you prefer a smaller chance of a singular catastrophic event happening during for example the next 10 years, with not enough time to recover by way of portfolio growth via exposure to the "regular" risk premia, or a somewhat bigger chance of the same catastrophic event happening during the next 30 years, with exponentially compounding growth during the remaining let's say 25-29 years.

I would tend to go with the second option, and I think the total loss after recovery from a singular catastrophic event would be less than it would be during a 10 year timeframe. Let's assume you start with $1M, ready to retire early with no future contributions expected, and let's ignore consumption for sake of simplicity; perhaps you have some semi-passive side income for living expenses, or perhaps it is a trust. Let's assume 4% equity risk premium (ignoring the asteroid), 5% annual geometric real return of mHFEA (ignoring the asteroid), and figuratively speaking an asteroid hitting and destroying 80% of Earth (substitute any other catastrophe of your imagination). Within 10 years you would end up with $1,000,000 * 1.05^10 * 0.2 -> $325,779. Within 30 years, you would end up with $1,000,000 * 1.05^30 * 0.2 -> $864,388 i.e. almost no loss. (Wait another 3 years or get some lazy side job, and you recovered your money, short of another asteroid hitting Earth.) Even though the likelihood of the same asteroid hitting was 3 times as high during 30 years as during 10 years, there would be no significant terminal portfolio loss in the 30 year scenario.

Now you may say ok but a 95% to 100% wipeout instead of an 80% wipeout would leave residual value with similar utility in both 10-year and 30-year scenarios, but at 3x the likelihood in the 30-year scenario. True, but what is the likelihood of yourself surviving such a scenario? So you would have to condition the scenario analysis and probabilities on your own survival.
Furthermore you would want to condition your analysis on the scenarios where a less leveraged portfolio than the one under consideration, or an unleveraged portfolio, would have survived with meaningful residual value. The scenarios where everything or almost everything on Earth that your portfolio assets might represent simply ceases to exist, constitute risks that are inherent in the passage of time, and not inherent in a particular portfolio, asset allocation, or leverage ratio.

In any case I think the model needs adjustments for rare events, not simplistic extrapolation. A 1929-1931 scenario repeating somewhere between 1931 and 1959 before the market recovered, was less likely than the initial 1929-1931 scenario, or perhaps impossible under any sensical economic assumptions; likewise the rates-driven 1968-1982 scenario repeating in 1982-1996 and combining to a 28-year long multiples compression period would arguably have been impossible, as stock market multiples were already extreme in 1982.

I agree with much of this and if I am understanding correctly the only real point of contention remaining is that I may have argued that the higher probability of catastrophic events over 30 or 50 years is somehow a function or extrapolation of the near normality of returns over 10 or 15 years. I agree that to some extent that might not be true and I have argued for the higher probability of catastrophe over the long run from two independent and unrelated arguments. It sounds like we agree with the second argument that the probability of volcano or asteroid or political collapse is higher over 30 years is higher than 5. But you don't buy that the normality of returns over 10 is an argument for normality over 30 and that the first argument is totally unrelated to the second.

Id emphasize again we don't need perfect normality or anything close to perfect normality to conclude that the probability of catastrophe rises over time. Even distributions with high auto correlation show increasing probability of catastrophe over time. Anything with autocorrelation significantly higher than -1 will have this property. It's more simply a result of the basic intuition that getting multiple bad years in a row is only possible when you actually have more years. Even if there is autocorrelation well below zero (bad years tending to be followed by good years). This is one reason why so many phenomenon tend to fall into near normal distributions even when you don't expect them to. The bell curve and increasing probability of catastrophe are more like artifacts of nearly any distribution than strictly normal ones. They're mathematical artifacts of any event with an element of chance. Only pre-determined causative sequences of events would seriously defy the bell curve or increasing probability of catastrophe with more events.

I'd also argue that the near normality over 10-15 years and my inclination to extend semi-normality to 30+ years is not entirely unrelated to the intuition that asteroid/volcanoes/political collapse are more likely over 30+ years that 10. While we didn't experience a major asteroid in the data, there were a few political and economic shocks and upheaval in the data, like the great depression and ww2. Having 2 great depressions in 30 years is certainly possible and more likely over 30 years than 5. There are some aspects of the great depression and ww2 that are likely mean reverting (primarily valuations) but there are other aspects that are not mean reverting. It's pretty clear that global gdp was set back by the great depression and ww2 and did not mean revert compared to a hypothetical where the great depression and ww2 did not happen.

Global gdp per capita increased a mere 25% from 1930 to 1950 whereas normally it increases about 60% every 20 years. There was some acceleration after ww2 globally and especially in the U.S. but not nearly enough to make up for the poor growth from 1930-1945. These are real shocks to the real economy that do show up in the actual historical data and are part of the reason that the data is near normal. Arguing for semi-normality of returns or a lack of perfect autocorrelation or a lack of perfect mean reversion is, in practice, arguing that 2 great depression and ww2 are more likely in 30 years than 10. You could certainly argue that people's propensity for stupid economic policy and blowing each other up is autocorrelating/mean reverting and there might even be some truth to it but the argument is certainly not strong enough to completely discount the probability. If the probability of a great depression every 10 years is 1 in in 20 then the probability of two in 10 years would be about 1 in 400 if there is no autocorrelation. The probability in 40 years will be close to 4 in 400 though substantially greater.

And I concede from an equity market perspective much of the great depression could be mean reverting (valuations) but much or most of the effect on gdp was not.

I take your argument about mean reversion and I think there is some truth to it. Many of the less catastrophic events that effect returns over 10 years may be mean reverting over 30 (ie valuations). Some of these events are probably not mean reverting and thus the probability of catastrophe rises over time. But I think the weakest of Samuelsons assumption by far is the assumption that we care bout losing 95% vs 90% as much as we care about losing 50%. We've both argued against this in various ways. At a certain point the result is so bad you stop caring about investing

[comeinvest]

Current 1-month and 10-year forward discount rates. Source: https://seekingalpha.com/article/472553 ... r-how-long
The curve as of 09/30 is from before the payrolls report and is not concurrent with the numbers in the discount table.

[comeinvest]

I think we are coming closer; but I still don't agree. The blue and yellow lines are based on about 10-15 independent periods, and yet the upswing and divergence of the solid from the dashed lines are what I would call consistent and significant.

Of course this doesn't tell us anything about very rare and very negative events. If we had enough time on hand, we could probably decompose the stock market returns into the effects of changes to risk-free rates, economic downturns, profit margins, valuation multiples / equity risk premia, and a few more; I'm sure others have done that already. This would probably make more sense than extrapolating a formula that never covered any single data point even close to such a scenario. Most if not all of these underlying parameters are "naturally" "soft" range bound and mean reverting. Then the question would become, think of a hypothetical scenario that can result in a drawdown, like > 90%, that the mean reverting characteristics and the growth of the exponential function cannot "heal" within 30 years.
Perhaps we can agree that if such an event happens at all, it would be a singular event during a 30 year period; the probability of two such events happening within 30 years is negligible (think of 2 independent asteroids in short sequence). Perhaps we can also agree that it would likely be an event with a root cause that is outside the normal economic and financial forces that until now governed the modern financial markets - a natural or man-made global disaster, or political upheaval; it would likely not be a slowly progressing or a series of several economic or valuation dislocations that would all go in the same direction, compound, and never end within a 30 year period; you can expand or compress things like valuation multiples, risk-free real rates, etc., only so much, until they either vehemently reverse or yield powerful carry returns.

So the question becomes with equal portfolio leverage, would you prefer a smaller chance of a singular catastrophic event happening during for example the next 10 years, with not enough time to recover by way of portfolio growth via exposure to the "regular" risk premia, or a somewhat bigger chance of the same catastrophic event happening during the next 30 years, with exponentially compounding growth during the remaining let's say 25-29 years.

I would tend to go with the second option, and I think the total loss after recovery from a singular catastrophic event would be less than it would be during a 10 year timeframe. Let's assume you start with $1M, ready to retire early with no future contributions expected, and let's ignore consumption for sake of simplicity; perhaps you have some semi-passive side income for living expenses, or perhaps it is a trust. Let's assume 4% equity risk premium (ignoring the asteroid), 5% annual geometric real return of mHFEA (ignoring the asteroid), and figuratively speaking an asteroid hitting and destroying 80% of Earth (substitute any other catastrophe of your imagination). Within 10 years you would end up with $1,000,000 * 1.05^10 * 0.2 -> $325,779. Within 30 years, you would end up with $1,000,000 * 1.05^30 * 0.2 -> $864,388 i.e. almost no loss. (Wait another 3 years or get some lazy side job, and you recovered your money, short of another asteroid hitting Earth.) Even though the likelihood of the same asteroid hitting was 3 times as high during 30 years as during 10 years, there would be no significant terminal portfolio loss in the 30 year scenario.

Now you may say ok but a 95% to 100% wipeout instead of an 80% wipeout would leave residual value with similar utility in both 10-year and 30-year scenarios, but at 3x the likelihood in the 30-year scenario. True, but what is the likelihood of yourself surviving such a scenario? So you would have to condition the scenario analysis and probabilities on your own survival.
Furthermore you would want to condition your analysis on the scenarios where a less leveraged portfolio than the one under consideration, or an unleveraged portfolio, would have survived with meaningful residual value. The scenarios where everything or almost everything on Earth that your portfolio assets might represent simply ceases to exist, constitute risks that are inherent in the passage of time, and not inherent in a particular portfolio, asset allocation, or leverage ratio.

In any case I think the model needs adjustments for rare events, not simplistic extrapolation. A 1929-1931 scenario repeating somewhere between 1931 and 1959 before the market recovered, was less likely than the initial 1929-1931 scenario, or perhaps impossible under any sensical economic assumptions; likewise the rates-driven 1968-1982 scenario repeating in 1982-1996 and combining to a 28-year long multiples compression period would arguably have been impossible, as stock market multiples were already extreme in 1982.

I agree with much of this and if I am understanding correctly the only real point of contention remaining is that I may have argued that the higher probability of catastrophic events over 30 or 50 years is somehow a function or extrapolation of the near normality of returns over 10 or 15 years. I agree that to some extent that might not be true and I have argued for the higher probability of catastrophe over the long run from two independent and unrelated arguments. It sounds like we agree with the second argument that the probability of volcano or asteroid or political collapse is higher over 30 years is higher than 5. But you don't buy that the normality of returns over 10 is an argument for normality over 30 and that the first argument is totally unrelated to the second.

Id emphasize again we don't need perfect normality or anything close to perfect normality to conclude that the probability of catastrophe rises over time. Even distributions with high auto correlation show increasing probability of catastrophe over time. Anything with autocorrelation significantly higher than -1 will have this property. It's more simply a result of the basic intuition that getting multiple bad years in a row is only possible when you actually have more years. Even if there is autocorrelation well below zero (bad years tending to be followed by good years). This is one reason why so many phenomenon tend to fall into near normal distributions even when you don't expect them to. The bell curve and increasing probability of catastrophe are more like artifacts of nearly any distribution than strictly normal ones. They're mathematical artifacts of any event with an element of chance. Only pre-determined causative sequences of events would seriously defy the bell curve or increasing probability of catastrophe with more events.

I'd also argue that the near normality over 10-15 years and my inclination to extend semi-normality to 30+ years is not entirely unrelated to the intuition that asteroid/volcanoes/political collapse are more likely over 30+ years that 10. While we didn't experience a major asteroid in the data, there were a few political and economic shocks and upheaval in the data, like the great depression and ww2. Having 2 great depressions in 30 years is certainly possible and more likely over 30 years than 5. There are some aspects of the great depression and ww2 that are likely mean reverting (primarily valuations) but there are other aspects that are not mean reverting. It's pretty clear that global gdp was set back by the great depression and ww2 and did not mean revert compared to a hypothetical where the great depression and ww2 did not happen.

Global gdp per capita increased a mere 25% from 1930 to 1950 whereas normally it increases about 60% every 20 years. There was some acceleration after ww2 globally and especially in the U.S. but not nearly enough to make up for the poor growth from 1930-1945. These are real shocks to the real economy that do show up in the actual historical data and are part of the reason that the data is near normal. Arguing for semi-normality of returns or a lack of perfect autocorrelation or a lack of perfect mean reversion is, in practice, arguing that 2 great depression and ww2 are more likely in 30 years than 10. You could certainly argue that people's propensity for stupid economic policy and blowing each other up is autocorrelating/mean reverting and there might even be some truth to it but the argument is certainly not strong enough to completely discount the probability. If the probability of a great depression every 10 years is 1 in in 20 then the probability of two in 10 years would be about 1 in 400 if there is no autocorrelation. The probability in 40 years will be close to 4 in 400 though substantially greater.

And I concede from an equity market perspective much of the great depression could be mean reverting (valuations) but much or most of the effect on gdp was not.

I take your argument about mean reversion and I think there is some truth to it. Many of the less catastrophic events that effect returns over 10 years may be mean reverting over 30 (ie valuations). Some of these events are probably not mean reverting and thus the probability of catastrophe rises over time. But I think the weakest of Samuelsons assumption by far is the assumption that we care bout losing 95% vs 90% as much as we care about losing 50%. We've both argued against this in various ways. At a certain point the result is so bad you stop caring about investing

I argued more along the line that you might not survive a 95% wipeout i.e. your portfolio would outlast you, and that a very large catastrophe with no possibility of recovery in the longer timeframe would be almost certainly a singular event in both the shorter or the moderately longer timeframe, rather than that you are indifferent to a 5% vs. a 10% residual value, e.g. $200k vs. $400k of an initial $4M. But it probably doesn't matter as these scenarios and how they unfold are quite hypothetical.

Regarding your normality assumption and all that, I generally agree that the truth is somewhere between mean reversion and increased likelihood of ever more destructive events. We should however never forget the power of the exponential function that describes the geometric portfolio growth, which has the risk premium in the exponent. (Albert Einstein: "Compound interest is the eighth wonder of the world. He who understands it, earns it; he who doesn’t, pays it.")
The question is then how to account for the possibility of increasingly destructive events with increasing time horizon on one hand, and for the increasing power of the exponential function with increasing time horizon on the other hand.
Sometimes it is educational to consider boundary cases or asymptotic behavior. "If the probability of a great depression every 10 years is 1 in in 20 then the probability of two in 10 years would be about 1 in 400 if there is no autocorrelation. The probability in 40 years will be close to 4 in 400 though substantially greater." - None of that would matter as long as the risk premium is high enough such that the portfolio would recover during the average time between two catastrophic events, and also high enough to reflect the likelihood of one catastrophe of ever increasing magnitude happening with measurable likelihood, as the investment horizon increases. So let's look at the asymptotic behavior and pretend we have a 100 year or 200 year investment horizon. If you assume that the risk premium reflects a catastrophe of magnitude x happening within t (e.g. t = 30) years, then by your linear extrapolation it would also reflect 3.3 catastrophes of similar magnitude happening within 100 years, or 6.7 within 200 years. But in the 100 year scenario the portfolio has 3.3. times the time to recover, and 6.7 times the time in the 200 year scenario. 1.05 ^ 30 -> 4.3; 1.05 ^ 100 -> 132; 1.05 ^ 200 -> 17293. In the 200 year scenario it would take a 1/(1.05 ^ 200) -> 0.00006 residual value, or a 0.99994 (99.994% destruction) to suffer a terminal loss. Fair so say you would probably not survive a 99.994% destruction of global productive assets yourself, even after adjusting for financial leverage. In other words, eventually you can ignore ever smaller (per constant time horizon) likelihoods of every bigger catastrophes, even if their likelihood scales linearly with time horizon as per your normal distribution; all the while the exponential portfolio growth from the risk premium will eventually win over all the "moderate to very large" (short of global annihilation) catastrophes, if you just wait long enough.

We can also try to look at the problem from another angle, using reasoning by contradiction: What is the source of market risk premia, in particular the equity risk premium? I'm not exactly sure about the theoretical foundation, but I think it is fair to say it is a combination of 1. the risk of temporary drawdowns at times when you might have wanted to consume, i.e. uncertainty about the temporal evolution of the portfolio value; 2. the risk of terminal destruction. As long as (1.) is at least part of the risk premium that the market participants require for delayed consumption, we must conclude that whoever has the longer time horizon i.e. whoever has the luxury to sit out temporary drawdowns, will be at a structural game theoretic advantage over less patient "competitors" bidding for the same asset, as the drawdown risk is an attribute of the asset and not conditioned on its owner; by implication, the investor with the longer time horizon should have less total risk, as one of the two sources of risk premium does not apply to him, but he still collects the same premium per unit of time. The reasoning by contradiction is that temporary drawdowns would require no risk premia (equity risk premium), if the investor with the longer time horizon had higher risk of portfolio loss per unit of time and therefore per unit of risk premium collected.
Good luck finding the flaw in my reasoning. I acknowledge that it has a circular element (the assumption that the ERP is asymptotically positive over long time periods even after accounting for very rare but large realized losses, for which I provided no proof); but the catastrophic risk per unit of time (and therefore per expected risk premium to be collected), whether positive or negative after accounting for rare catastrophes, would apply to both the short-term and the long-term investor, and it seems natural that high volatility and large temporary drawdowns require a risk premium, as it seems to constrain your ability to consume at will, and as such it seems to constitute a microeconomic risk that deserves to be compensated.

Depending on what size ERP humans demand in relation to mathematical models of catastrophes of ever increasing size, infinite horizon wealth is probably either infinite or zero, but not anything in between. I would say asymptotic behavior is meaningless, as our sun will cease to illuminate Earth in about 5 billion years, at which time all financial assets are likely zero regardless of ERP. The answer to our original question (whether longer or shorter time horizons are safer for a given portfolio) will heavily depend on medium term assumptions on large catastrophes in relation to the ERP that humans demand; If the ERP is too low (perhaps due to human recency bias) to reflect rare but large catastrophes that humans would survive but not their portfolios, longer time horizons might pose higher risk than shorter ones; if the ERP is high enough, then I can argue that longer time horizons carry less risk than shorter ones, as recovery from conceivable catastrophes by virtue of the eighth wonder of the world is more likely. In any case, naive extrapolation of a simplistic model, whether i.i.d. or not, makes little to no sense in my opinion. Studies have shown that real property generally has survived hundreds of years and grown with positive geometric CAGR in countries where private property was not annihilated in its entirety, and notably has survived longer than cash; so it all comes down again to the choice of leverage ratio or beta exposure.

[comeinvest]

The astonishing divergence between treasury yields and SOFR swap rates, both sometimes referred to as "risk-free" rates

Some people say that treasuries can realistically only "fail" in form of high inflation, i.e. the government debt is inflated away. That doesn't seem to be consistent with what "the market" thinks, per the existence of credit default swaps which trade measurably above zero.

SOFR swap rates (plus a spread) are the rates at which borrowers can borrow money for a certain time; SOFR swap (OIS) rates represent the expected overnight SOFR rates and the term premium.
We have the option to use treasury futures or SOFR futures to implement leveraged duration risk exposure. Treasuries currently trade at higher rates than SOFR swaps; but are treasuries (and treasury futures) free of credit risk?
If the asset swap spread is a measure of a bond's credit risk, then compare the swap spread to the U.S. government credit default swap rate of 40.47 bps. (Germany for comparison has a CDS rate of 9.65 bps.)

[comeinvest]

I would like to cross-link this thread viewtopic.php?t=414623 which ponders lifetime asset allocation models, and an article https://elmwealth.com/earnings-yield-dy ... llocation/ (Haghani and White) referenced by it that ponders the possibility of dynamic stock/bond asset allocations based on relative valuations - earnings yield for stocks, and TIPS yields for bonds; further discussion also here viewtopic.php?p=8084984#p8084984 . We all know that there is a risk of parameter fitting, although the same could be said about mHFEA and just about every other asset allocation model. And yet, a rules based dynamic allocation like the relatively simple one that is presented in the article, looks intriguing. Below are two long-run charts and one table from the article. Note that although the first chart shows no excess returns (cumulative outperformance) of the dynamic asset allocation for the last 37 years, the Sharpe ratio was higher and the drawdowns less severe, which would lead to excess returns in scenarios where leverage is allowed. The decade-by-decade results seem robust, with some outliers some of which can be explained by unlucky endpoints (1989-1999) and might disappear in 15-year or 20-year segments.

[comeinvest]

Regarding our conversation about risk dependence on time horizon here viewtopic.php?p=8033425#p8033425 and on subsequent pages
Interesting paper ("Are Stocks Really Less Volatile in the Long Run?") here https://papers.ssrn.com/sol3/papers.cfm ... id=1136847
I have not read the entire paper yet. But on another note, I think in order to simulate and to optimize return distributions for an investment horizon, one would not want to optimize for an optimal static asset allocation (or leverage ratio) and the corresponding risk and return distribution over that horizon, but rather solve a functional analysis or control optimization problem for an allocation function based on then current net asset value and leftover time at any time between now and the finish line. In other words, for the current decision consider the optionality of conditional future decisions at all future points in time. This should result in a larger opportunity set. For example you need only one decently lucky subperiod, and once it arrives you may have lucked out and can reduce or eliminate leverage for the remaining time. Of course some catastrophic tail risk remains, especially if it were to happen before assets have sufficiently grown; but the optimal leverage ratios should be different than with static leverage ratios only based on the charts in the post that I linked above; I think the tail risk of rare catastrophic events over increasingly long investment horizons should be greatly reduced with the adaptive modeling approach.

[comeinvest]

Some musings on interest rates and term premia from here https://seekingalpha.com/article/472837 ... -6-percent

[comeinvest]

For whatever reason, the TIPS yield curve does not have the 20y-30y inversion. Source: WisdomTree Daily Market Snapshot 11/18/2024

[comeinvest]

Interesting
Changes in swap spreads as well as the level of swap spreads affect treasury returns (in relation to swap returns).

[unemployed_pysicist]

The CME Quickstrike treasury analytics tool no longer works for me, at least not without logging in with an account. Has anyone faced the same issue?

[Investing Lawyer]

The CME Quickstrike treasury analytics tool no longer works for me, at least not without logging in with an account. Has anyone faced the same issue?

Yes, you need to have an account to log in. The CME account is free.

[unemployed_pysicist]

The CME Quickstrike treasury analytics tool no longer works for me, at least not without logging in with an account. Has anyone faced the same issue?

Yes, you need to have an account to log in. The CME account is free.

Thank you for your answer. I had hoped the tool was somehow still available without having to log in, but I guess I will go ahead and make an account

[comeinvest]

I would like to cross-link this thread viewtopic.php?t=414623 which ponders lifetime asset allocation models, and an article https://elmwealth.com/earnings-yield-dy ... llocation/ (Haghani and White) referenced by it that ponders the possibility of dynamic stock/bond asset allocations based on relative valuations - earnings yield for stocks, and TIPS yields for bonds; further discussion also here viewtopic.php?p=8084984#p8084984 . We all know that there is a risk of parameter fitting, although the same could be said about mHFEA and just about every other asset allocation model. And yet, a rules based dynamic allocation like the relatively simple one that is presented in the article, looks intriguing. Below are two long-run charts and one table from the article. Note that although the first chart shows no excess returns (cumulative outperformance) of the dynamic asset allocation for the last 37 years, the Sharpe ratio was higher and the drawdowns less severe, which would lead to excess returns in scenarios where leverage is allowed. The decade-by-decade results seem robust, with some outliers some of which can be explained by unlucky endpoints (1989-1999) and might disappear in 15-year or 20-year segments.

Also see discussion in the new thread "Static vs Dynamic Asset Allocation" viewtopic.php?t=442753 for possible variations of mHFEA