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Anyone want to share their current leverage? Currently at 1.85 with IBKR. Planning to buy VOOG for 2.5x - 3x leverage if it dips to around 200. Need an extra couple mil for down payment next summer, and hoping the market dips in the coming months, then increase position to about 3x leverage, and then the market recovers by Spring 2024. Is this a terrible idea? I don't think I have a risk of margin call because I have large credit facilities available to me in case the market really drops. So is the only risk rising interest rates and larger margin interest on a 3x leverage position? I’m at around 3.2x leverage. But a large part of my position comes from QSPIX, which I estimate diversifies so well that I can get away with much higher levera...

Anyone want to share their current leverage? Currently at 1.85 with IBKR. Planning to buy VOOG for 2.5x - 3x leverage if it dips to around 200. Need an extra couple mil for down payment next summer, and hoping the market dips in the coming months, then increase position to about 3x leverage, and then the market recovers by Spring 2024. Is this a terrible idea? I don't think I have a risk of margin call because I have large credit facilities available to me in case the market really drops. So is the only risk rising interest rates and larger margin interest on a 3x leverage position? I’m at around 3.2x leverage. But a large part of my position comes from QSPIX, which I estimate diversifies so well that I can get away with much higher levera...

If you only put a small amount into a leveraged strategy, so that your whole portfolio is not net leveraged, what's the point? Why put (say) 60% into stocks and 10% into 2X leveraged stocks when you could just put 80% into stocks? If you dilute a leveraged holding aren't you wasting the leverage? You shouldn't dilute a leveraged holding with cash , I agree with you. It's silly to have 60% stocks, 10% 2x stocks and 30% cash. Better to just be 80% stocks, 20% cash. Agreed. However, it's perfectly reasonable to put a small portion of the account in leveraged investments (like, idk 10-25% into AQR long-short funds) if you're not holding an appreciable amount of cash. 80% TSM, 20% AQR long-short isn't "silly" like the above portfolio ...

A - Depends in what social circles you're in. Definitely not a Boglehead endorsed strategy... but the r/WallStreetBets crowd thrive on using options to make "bets" using options to essentially take synthetic leverage "to the moon!" I was talking about the trillions in derivatives and leveraged used by thousands of large institutional entities (hedge funds, insurance funds, etc). The stuff Buffett loves to rail against. Few advisors would say you put everything in a hedge fund for instance. But yeah, you could cherry-pick what some Reddit forum likes to do. But even there, few would recommend you actually do that so I stand by my statement even in those edge cases. B - That's what "diversification" is meant to ...

Valuethinker wrote: ↑Sun Feb 26, 2023 9:10 am

There is no such thing as a 100% sure thing when investing. Thus, the use of leverage is
dangerous. A string of wonderful numbers times zero will always equal zero. Don’t count
on getting rich twice.

https://www.berkshirehathaway.com/letters/2022ltr.pdf

There's a lot of very clever strategies involving leverage out there. They can all wind up with 0 as an outcome.

A) Few would say to put everything in those clever strategies.
B) Plenty of unleveraged strategies can also go to zero.
C) Buffett himself used plenty of leverage throughout his life.

Using debt (leverage) is just a tool of the investor. Used judiciously, it can be a net positive. Used recklessly, it can be a net negative.

VCMDX investor here, who betted VCMDX quite a bit before diving in. I invested in VCMDX, the Vanguard Commodities Strategy Fund, thinking that this fund would be a way to go long on commodities. However I understand Vanguard to have told me on a phone call today that this fund is long or short commodities depending entirely on the current judgment of fund management. VCMDX is long AND short commodities, with a target of about 100% long overall on average. That's why it uses BCOM as its index (which it has handily beaten since inception btw). It can be hard to judge exactly its notional exposure given the holdings because it uses swaps for a lot of the exposure. It looks like it's 131% long and 45% short right now, so maybe about 86% long ov...

1) "Labor market is always strong before a recession" A recession is generally characterized by a meaningful uptick in unemployment so unemployment tends to look lowest right before one. It's like saying "you're always asleep before you wake up". Isn't this obvious/expected/not insightful? 2) "Unemployment rate is the lowest since 1969, which was right before a recession." If an unemployment rate is historic low (like the 1969 low) then it must mean the unemployment rate the year after that historic low (1970) must have been higher than the historic low. Otherwise, then 1970 would have been the historic low and not 1969. So when you say "lowest unemployment rate since the previous low of 1969, which was fo...

1. Are there any situations where extreme market volatility may alter the price of the box to an extent that the portfolio crashes? I once had my account go +-50K every few seconds due to the marks on a box. It was gnarly. It was night time, I only noticed it by coincidence. I would've had about $2M in short boxes at that time. Idk if that's as bad as marks can get but if you're handling seven figures, make sure your excess liquidity is past $200K or so just in case. 2. What tax impact could he expect because of mark to market if he borrows 1,000,000 with a 5 year box? An IT treasury bond fund lost like 8% last year, so from regular market movements, maybe you see that $1M go up and down by 8% or so over a year in the worst case. Ex: If yo...

Note that the 117% was calculated for the period 1926 to 1984 which was a particularly low return high volatility for equities. Using the full dataset available to us, the KK is closer to 2x, and higher still if we diversify with foreign equities. Moreover, this concerns the investment of one's entire lifetime of capital and is unrelated to the subject at hand. When one is only able to invest a tiny portion of one's entire lifetime of capital, it should be leverage at or even above the KK. How do you compute "lifetime capital"? Who promised you (or anyone else) that you would actually receive your supposed "lifetime capital"? Merton and Samuelson Merton and Samuelson "promised you (or anyone else) that you would ac...

To clarify, no investor ever would have lost everything ("financial ruin"). That is, no decline of 50% or worse in a month. But "Market Timer" actually did . http://i496.photobucket.com/albums/rr326/markettimer/nw-37.jpg Ah sorry, i thought we were talking about the paper (2x leveraged, rebalanced monthly). MarkeTimer had much higher leverage (technically infinite since he had a negative net worth), wasn’t even earning/saving/contributing, didn’t rebalance at all until he actually got margin called, invested in individual companies (many which went to essentially zero) and sold puts through it all to short volatility (lots of money lost there obviously). Now THAT strategy definitely would have resulted in ruin MANY time...

nisiprius wrote: ↑Wed Feb 01, 2023 7:38 pm

Dry-Drink wrote: ↑Wed Feb 01, 2023 5:58 pm ..."Risk aversion" is what finance academics refer to as "risk tolerance". You can search "risk aversion" in that paper to understand better how risk aversion affects the optimal glidepath...

You are correct. My bad.

How do we go about measuring the "risk aversion" value for a particular investor, and what is the distribution of CRRA values across the population of young investors?

Do you have/read the book? Pages 137-148 go over exactly both those questions.

PotashDoggerd wrote: ↑Wed Feb 01, 2023 6:14 pm [If the issue was heart surgery instead of investing, and you wrote that something Dr. DeBakey wrote or said showed he "didn't understand" something about heart surgery as well as you did, I would have to go with Dr. DeBakey.

At first, perhaps. But upon closer inspection and reading, you find Dr.DeBakey said humans aren’t born with hearts and Ben Matthew said they definitely are but Dr.Debakey simply misheard the question.

At that point, would you still say Dr. DeBakey is probably correct? Even though he is demonstrably mistaken? Or would you agree with Ben, who is saying Dr. DeBakey simply misunderstood the question?

bobcat2 wrote: ↑Wed Feb 01, 2023 6:19 pm

Dry-Drink wrote: ↑Wed Feb 01, 2023 5:46 pm You are OK with someone leveraging by buying a call option but not OK with someone buying stock and either longing or shorting the risk-free asset via margin to get the same performance as that call option? What am I missing?

If you want to replicate a one year LEAPS option by continuously trading every few seconds for the next year a stock and a one year Tbill, then I say have at it, Dry-Drink.

BobK

Do you need to trade every few seconds to get close enough to a LEAP? Could you get “close enough” by rebalancing every few weeks, or just whenever your leverage hit your rebalancing bands (say 2.2x or 1.8x)?
Or at that point, it loses any sense of downside protection that an option contract gives?
Thanks.

They say that "we find there were at most five months in which margin calls would have led to portfolio liquidation." Which is another way of confirming that financial ruin was sometimes encountered in their simulations. To clarify, no investor ever would have lost everything ("financial ruin"). That is, no decline of 50% or worse in a month. As they said: "In our monthly data the stock market has never declined sufficiently to wipe out the preexisting investments of any cohort" However, assuming a 25% margin requirement, there were 5 months that would have triggered margin calls. That is, declines of 33% or worse in a month that would have forced rebalancing before month end. The phrase "risk tolerance&q...

I read once that a continuously-rebalanced stock portfolio can be made to mimic the performance of an option contract. That is, rebalancing is akin to shorting volatility so if you do it in a specific amount, the portfolio is identical to a call option. Is this true? And if so, it would make this distinction about "OK to buy call options, NOT ok to buy stocks on margin" pretty silly yes? Since one can be made to mimic the other. No that's not right. If you continuously trade, say at least every few seconds, then by following a set of rules for trading a stock (or a stock index etf) and the risk-free asset you can create a portfolio that produces the same payoff as the option. BTW, it was Robert Merton who discovered that. You are...

Ben Mathew wrote: ↑Wed Feb 01, 2023 2:15 pm

I read once that a continuously-rebalanced stock portfolio can be made to mimic the performance of an option contract. That is, rebalancing is akin to shorting volatility so if you do it in a specific amount, the portfolio is identical to a call option.

Is this true? And if so, it would make this distinction about "OK to buy call options, NOT ok to buy stocks on margin" pretty silly yes? Since one can be made to mimic the other.

Thanks

H.Hornblower wrote: ↑Tue Jan 31, 2023 4:11 pm According to my calculations Moraif will be buying back in tomorrow. His buy point is 3% above the S & P 200 day moving average. The average today was 3954.01. 3% above that is 4072.6303. The S & P 500 closed today at 4076.60.

At what price point did he sell? I know it’s higher than this reentry price but how much higher?

Why are we hung up on the unjustified and contradicting opinions of Samuelson, who never wrote a review or response, when we have the empirically and theoretically justified peer reviewed opinion of Ayres and Nalebuff? Imagine taking economics under Samuelson. Learning from him and Merton's lifecycle models. Putting together a paper that is consistent with their theory and that many other writers (like Campbell) expanded on. Then you name the asset allocation equation after Samuelson as a final tribute to him. And the dude glances at your paper, wrongly thinks it's about the fallacy of time diversification, which Samuelson furiously fought against for decades, and says it's junk. And then dies shortly after. It's kind of sad and kind of fu...

1) Long-dated nominal vehicles expose retirees to unnecessary risks in an fiat money world. Zvi Bodie emphatically agrees with that. Didn't Zvi Bodie recommend everyone invest in TIPs first and once retirement nest egg is set, THEN invest into stocks? If someone could win a prize for ignoring lifecycle finance, it would have to be Bodie lol. 2) Leveraged products are unwise at any stage, and one has to twist oneself into a pretzel to get Samuelson disagreeing with that. Samuelson would definitely disagree with you, no pretzels required. He actually thought it prudent: "... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necess...

I find the generally-higher dividend rate combined with the generally-lower QDI of International is enough of a tax drag for my bracket (22%) that the FTC doesn’t make up for it. So tax-advantaged it is for me.

You might find it’s the opposite for you so you could compute it for your situation.

Ok, got it. Thanks. If I plug in the numbers from 2008-present, my backtested portfolio has largest utility (compared to VFINX/QQQ/VBINX/FIGTX) up to RRA of 8, then FIGTX takes over. VFINX and QQQ go negative at RRA of 7 and 8, respectively. My portfolio goes to the largest negative utility starting at RRA = 10 or so. Over the last 8 years, similar story except my backtested portfolio has largest utility to 6, then VBINX takes over. Yeah you got it, that all sounds correct. Just to clarify one last thing: You're finding the above because you are forcing the investor to hold 100% of that asset/portfolio. So very risk averse people will prefer 100% VBINX, and those less risk averse will prefer stocks or your adaptive thing. However, I can in...

If an investor would select a portfolio with a given Sharpe/volatility ratio of a , why wouldn't that same investor be indifferent to switching to another portfolio that has the identical Sharpe/volatility ratio of a ? Investors are indifferent to switch between portfolios that have identical utility. Portfolios with identical Sharpe/volatility don’t provide identical utility to all investors of all risk aversions. (Just to be on the same page) Utility = E(x) - .5*Var(x)*RRA Try two portfolios with the same ratio Sharpe/volatility but different Sharpes and volatilities. Then plug those in to utility eqn using an arbitrary RRA (idk, maybe 2). Each portfolio will output a different utility so that investor isn’t indifferent to switching betw...

Am I correct that the Kelly criterion is arithmetic mean return divided by volatility squared? Which is the Sharpe ratio divided by volatility? *arithmetic mean return in excess of the risk-free asset. The ideal portfolio weight for a risky asset is Sharpe/(volatility*RRA). The term "RRA" is the coefficient of relative risk aversion. When you set risk aversion = 1 (that is, you are willing to take any additional volatility and risk as long as it still provides a higher compound return), then it simplifies to Sharpe/volatility. That is the Kelly Criterion. Any more leverage above KC requires a coefficient of risk aversion below 1 to be optimal for that investor. This is called "risk-seeking" (as opposed to "risk-ave...

I'm not sure it would beat Kelly either, although I think it might help some, but the main benefit is that if still making contributions it reduces variance based on lifecycle investing. I also doubt this "floating leverage" portfolio (one which doesn't rebalance if markets are down, but does if they're up) would be better for lifecycle investing (in any of the 3 phases) than a simple Kelly Criterion portfolio (adjusted by risk-aversion, if needed), where leverage is applied to current assets as well as discounted future cash flows. In fact, this whole idea of rebalancing in one direction but not in the other (because you're hoping you don't go bust) reeks of mental gymnastics and you don't have to think too hard to figure out in...

Am I correct that the Kelly criterion is arithmetic mean return divided by volatility squared? Which is the Sharpe ratio divided by volatility? *arithmetic mean return in excess of the risk-free asset. The ideal portfolio weight for a risky asset is Sharpe/(volatility*RRA). The term "RRA" is the coefficient of relative risk aversion. When you set risk aversion = 1 (that is, you are willing to take any additional volatility and risk as long as it still provides a higher compound return), then it simplifies to Sharpe/volatility. That is the Kelly Criterion. Any more leverage above KC requires a coefficient of risk aversion below 1 to be optimal for that investor. This is called "risk-seeking" (as opposed to "risk-ave...

It was mostly not mine but skier's idea of "floating" leverage that we discussed in the mHFEA and lifecycle threads. You are correct, there is an unquantifiable tail risk. But there is tail risk of going bust either way in case of a flash crash. With 1.4x initial leverage the max leverage after 1929 if you refuse to de-leverage would have been 2.3x. You could still deleverage if and when the leverage ratio ever gets higher. So absent a flash crash you will avoid going bust either way. Just to clarify: 1.4x isn’t the Kelly Criterion . In USA stocks, its around 2x historically. And 2x leverage without rebalancing on the way down would definitely have led to busts multiple times post 1929, in the USA alone (not to mention in many ot...

- With 1.4x leverage you didn't need to deleverage at any time since 1929. (The 2007-2009 showdown would have turned 1.4x into 2.3x with no action from your side.) So if I don't deleverage, like you often advocated, then my excess return from leverage should be approximately equal to the equity risk premium (5.55% - 3%) on the leveraged amount (40%) -> 2.55% * 0.4 = 1.02% p.a., or not? How would that reconcile with your result of 0.21% p.a. excess return from the Kelly formula? Kelly Criterion is the portfolio and leverage that maximizes CAGR. That is, no other portfolio beats it in growth over arbitrarily large time periods (thousands of years). For that to be the case, it clearly cannot go bust as it doesn’t matter your CAGR if you have ...

"You might wonder, though, whether value spreads are at extreme levels for a fundamental reason – which gets to our second lens: implied growth rates. In order to justify current valuation multiples from a fundamental perspective, expensive companies in developed markets would have to outgrow their cheap industry peers by approximately 90% over the next five years (Exhibit 3). This is 3-5x higher than analyst expectations and almost 2x the maximum growth differential seen in the historical sample. It's eerie that I recently complained AQR has been hammering home the concept of "value spreads" without addressing the difference in earnings that could account for a large portion of it: https://www.bogleheads.org/forum/viewtopic...

Saw an interesting tweet over the weekend. https://twitter.com/mkt_sentiment/status/1614249042745397251?s=46&t=Ms4mIiArpWAkHxp3vvGr4A Your average fund charging 1.5% management and 20% performance will have amassed more off your investment than your investment will be worth within 20 years. Even worse for the investor as you lengthen your time frame. Would like to see a similar study for a 1% management fee which I think is a little more common for the average Joe. Anyone have those numbers? Assuming the returns to YOU are reasonable post-fee (as this tweet shows) and the hedge fund in question is providing enough diversification to you to be worth including in your portfolio of index funds, then why does it matter how much they make? ...

Chik-fil-a closes on Sundays, which definitely doesn't maximize shareholder profits. There are thousands of similar examples out there. It's not clear that closing on Sundays doesn't maximize shareholder value. It aligns Chik-fil-a with a religious tradition, which could be argued is in shareholder interest. This one isn't so cut and dry. AFAIK, Cathy family owns all the shares but assuming some people do own some private shares of Chik-fil-a: If tomorrow, Cathy family decided to give away all food for free and wanted to drive Chik-fil-a to bankruptcy purposefully, can those people who own shares (that will soon be worthless) really not sue the Cathy family for deliberately driving the business to the ground? Board members of companies hav...

Agreed, fiduciary duty exists but what happens if the board members violate it (maybe because CEO is their personal friend)? I don't think it's a misdemeanor or felony. Yes typically shareholders have oversight of the board via voting. So board looks out for shareholder interests. It looks like you put a lot of importance and weight on voting as an oversight tool that I don't (because voting rarely goes against what board recommends any ways). And you put zero weight on civil lawsuits that I place a ton of weight on (since it appears to be by far the most common way to affect change/discourage non-fiduciary actions in public and private companies today). I can see how if that's your attitude, then Vanguard's structure would appear insurmou...

My understanding only, please correct if wrong: If, for example, the board votes to pay CEO Mortimer (Tim) Buckley an annual salary of $1 million, 10 million, 100 million or 1,000 million - you as a shareholder would have no knowledge or vote in any part of the process (not even election of board). Board members of companies have a fiduciary duty to maximize shareholder profits. If word ever got out that board members were not in fact doing so (such as, if they paid Tim $1B a year), you would sue them the way all other shareholders at other companies do. This is basically the main accountability mechanism for all companies afaik. It's rare that stocks vote against board recommendations, it's very rare that compensation packages aren't appro...

It's a rational strategy to commit 10% of one's inputs to moonshots with huge growth potential and 90% to safe assets. Isn't that what Taleb recommends? Of course it's rational. That portfolio comes from before Taleb though maybe he popularized it? I don't remember it in incerto but McMillan does talk about it in what most consider THE options bible ( Options as a Strategic Investment (2002, pg 413)), well before Taleb's Fooled by Randomness. Maybe Taleb popularized in an interview? In any case, both Taleb and McMillan would obviously have you rebalance. Not rebalancing is irrational and Taleb's whole thing is to be as rational as possible in finance-related topics (and OK to be irrational in other things). From McMillan's book: The strate...

It’s not goals, what you’re saying is just irrational. Think about it: You have $1M and put 10% in HFEA, never to rebalance. Then HFEA goes up 100% over a year but the rest of your assets go down 11.11%. Now, you still have $1M in total but now have 20% in HFEA. Do you see the problem? You, the same person, are investing the same quantity of dollars in two different ways depending on time. It’s fine to have a changing asset allocation based on wealth. Maybe as you have fewer assets, you put a lower % of capital in HFEA and vice-versa so your “losses aren’t actually unlimited”. But you would still REBALANCE at any point in time to have your desired allocation given your assets. No, I don't see issues with that at all. That's exactly how I p...

So the concept of good and bad money comes from recency bias. Recency bias simply does not work and is bad; the opposite might work. If you believe in reversion to the mean, then you'd hurry to throw money (good or bad) into your poor-performing investment. I hope that makes sense. I think our goals are different. My goal is to limit the downside of funny money and ensure that my max loss is X%. If I blow up 10%, refill another 10%, blow up again etc etc then my exposure is 10% but my losses aren't, they are actually unlimited. This is why I don't rebalance into the funny money space. Obviously you're free to manage differently. To each their own. It’s not goals, what you’re saying is just irrational. Think about it: You have $1M and put 1...

skierincolorado wrote: ↑Mon Jan 09, 2023 12:06 pm I wanted to apologize for getting the math wrong here. I was rushing through this on my phone. I think you are right in your calculations.

I accept your apology and appreciate it.

skierincolorado wrote: ↑Mon Jan 09, 2023 12:06 pm I My methodology would be to just use the historical number and add a percent of two as a buffer.

Idk if I mentioned it already but I like 18% because of that very reason (it’s the historical 16%, plus a buffer to account a little for the fat tails of stock distributions) and it is also the volatility for global stocks for the past 50 years. It feels to me like a better number to actually compute Kelly.

This is very important and true. As long as you rebalance in and out of HFEA to keep at around X% (say 10%), then the overbetting concern isn’t a problem. Imo you do NOT want to rebalance in and out of your "funny money" space. Rebalancing in is bad because you might end up throwing good money after bad. Rebalancing out is bad because you take the wind out of HFEA sails. The correct way imo is to do neither. I simply control the seed money for the funny money space. Regardless, I’m not claiming to do so or not. I mean, you should obviously do so but that wasn’t my point. My point is that you should stay below Kelly Criterion on your entire portfolio, not just a sliver. It can be ok to leverage 3x+ on a portion of your portfolio i...

The point that needs to be kept in mind is that the HFEA portfolio is not a 3x S&P portfolio, even though it uses 3x LETFs, as long as relatively frequent rebalancing is performed. A 55/45 UPRO/TMF portfolio is leveraging the S&P by 1.65x and LTT by 1.35x. Still risky, but well less than 2x S&P that the cited studies show as optimal. Lol you can’t think of it that way. That’s like taking 10 assets, making a 10x leveraged portfolio with them, and then claiming it’s not too much leverage because you only have 1x exposure to each asset. The correct way to do this is to look at the characteristic of a 55/45 SPX/TLT portfolio. And then see if 3x leverage is too much for THAT, regardless of how it is composed. 3x leverage is certainl...

The point that needs to be kept in mind is that the HFEA portfolio is not a 3x S&P portfolio, even though it uses 3x LETFs, as long as relatively frequent rebalancing is performed. A 55/45 UPRO/TMF portfolio is leveraging the S&P by 1.65x and LTT by 1.35x. Still risky, but well less than 2x S&P that the cited studies show as optimal. Lol you can’t think of it that way. That’s like taking 10 assets, making a 10x leveraged portfolio with them, and then claiming it’s not too much leverage because you only have 1x exposure to each asset. The correct way to do this is to look at the characteristic of a 55/45 SPX/TLT portfolio. And then see if 3x leverage is too much for THAT, regardless of how it is composed. 3x leverage is certainl...

Oh.. ok so it's 8.3%. I think I had a typo someplace. I guess the -3.9% price of cash is making leverage look not that attractive. Would you have a historical rate of the price of cash? I see people using CASHX negative on portfolio visualizer to model it. But it has been under 2% for the past year. Yeah, given those return assumptions by Vanguard, stock equity risk premium is just 3.3% while the bond premium is just 0.5%. These are much lower than historical (around 8.3% and 2.5% respectively, though it depends on the data set and exact time period). So compared to history, bonds and stocks are expensive compared to cash (or cash is cheap comparatively, whichever way you want to look at it). I use Ken French's data for cash returns. He ha...

Are you talking about this backtest where UPRO and SPX had virtually the same results: https://www.bogleheads.org/forum/viewtopic.php?p=4426328#p4426328 To clarify, I don't use nor care for backtests, don't know what I'll gain from putting one together. I don't invest with the rearview mirror. I use forward-looking estimates. That said, I did want to know why YOU had UPRO beating SPX going forward 3-4%. And I have my answer, you believed that's what would have happened in the past and hence, believe it will occur in the future. I had my question answered so I'm all set, thanks :) I ran my own backtest using the S&P500 data and 3x daily leverage. I don't remember the end date but probably a couple of years ago. This is something anyone ...

I don't think the volatility multiplies by 3. I think you do. Using your equation and assumption even 1.1x leverage has lower return than 1x. Idk what you're talking about: 1.1x leverage has return of 1.1*10% - 0.1*4% = 10.6% and vol of 1.1*18% = 19.8%. So CAGR is 10.6% - 19.8%^2/2 = 8.6% Which is higher than unleveraged stocks (was 8.4%). The fact that 5x more money remains from -75% than -95% is important. If the -95% were true, one would never recover. Having 5x more money remaining allows for the possibility of recovery. Whatever you say skier :sharebeer this strategy is too path dependent for your use of ensemble averages to be of much help. you're using annual averages of variance and return for unleveraged equities to model the long...

I don't think the volatility multiplies by 3. I think you do. Using your equation and assumption even 1.1x leverage has lower return than 1x. Idk what you're talking about: 1.1x leverage has return of 1.1*10% - 0.1*4% = 10.6% and vol of 1.1*18% = 19.8%. So CAGR is 10.6% - 19.8%^2/2 = 8.6% Which is higher than unleveraged stocks (was 8.4%). The fact that 5x more money remains from -75% than -95% is important. If the -95% were true, one would never recover. Having 5x more money remaining allows for the possibility of recovery. Whatever you say skier :sharebeer this strategy is too path dependent for your use of ensemble averages to be of much help. you're using annual averages of variance and return for unleveraged equities to model the long...

skierincolorado wrote: ↑Sun Jan 08, 2023 3:09 pm I don't think the volatility multiplies by 3.

I think you do.

skierincolorado wrote: ↑Sun Jan 08, 2023 3:09 pm Using your equation and assumption even 1.1x leverage has lower return than 1x.

Idk what you're talking about:
1.1x leverage has return of 1.1*10% - 0.1*4% = 10.6% and vol of 1.1*18% = 19.8%. So CAGR is 10.6% - 19.8%^2/2 = 8.6%

Which is higher than unleveraged stocks (was 8.4%).

skierincolorado wrote: ↑Sun Jan 08, 2023 3:09 pm The fact that 5x more money remains from -75% than -95% is important. If the -95% were true, one would never recover. Having 5x more money remaining allows for the possibility of recovery.

Whatever you say skier

skierincolorado wrote: ↑Sun Jan 08, 2023 2:39 pm From memory, I would expect 10% return with 4% financing would have a Kelly criterion between 2 and 2.5x.

If you assume stock vol of 16%, then yeah, Kelly Criterion is at 2.25x in that example above. So obv it depends on your volatility estimate, I like to use 18% because it's in line with global stock volatility for the past 50 years, and I want to err a little conservative when it comes to sizing a leveraged position.

But yeah, if you expect closer to 16%, then I would expect UPRO would eke SPX out by 2% or so. Comes down to your expectations.

Wait how? I have UPRO underperforming SPX long-term. 3x leverage is well past the Kelly Criterion, assuming cash return of 4% and stock average return of 10%, then 3x leveraged stocks underperform unleveraged stocks. You must be expecting higher stock returns than I am, but even mine are pretty optimistic I think. (Of course, math changes once you include bonds, but we're talking about SPX vs UPRO specifically above) My backtest was simply based off of S&P500 triple leveraged daily. 3x comes out ahead because we've had more bull markets than bear markets. Not sure why cash return of 4% is relevant here. Idk that it matters how many "bulls or bears" we have, even if you only have one big long bull with stocks exhibiting 10% av...

Marseille07 wrote: ↑Sun Jan 08, 2023 1:40 pm
Over the long term, my expectation of UPRO is more or less 3~4% higher than the SPX CAGR, and this is because we (hopefully) have more bull markets than bear markets.

Wait how? I have UPRO underperforming SPX long-term. 3x leverage is well past the Kelly Criterion, assuming cash return of 4% and stock average return of 10%, then 3x leveraged stocks underperform unleveraged stocks.

You must be expecting higher stock returns than I am, but even mine are pretty optimistic I think.

(Of course, math changes once you include bonds, but we're talking about SPX vs UPRO specifically above)

And while there isn’t a circuit beaker supporting TLT, the underlying bonds aren’t that volatile to move 33% in a single day (I may be misremembering some details on TLT/TMF). NYSE does have a circuit breaker for TLT as part of its Limit Up Limit Down program. They're talking about SPX going down -33% over time and UPRO pretty much goes down by -95% along the way. Yes, it's not going to be exactly 3x, but will be pretty close is what they're saying. It entirely depends on the overall loss of SPX. At very high losses (like -33%), UPRO will lose quite a bit less than your rule of thumb will suggest. For medium-ish losses, it will track your rule somewhat. You asked about SPX at -15%. In that case, UPRO will likely loss around -40%, assuming ...

skierincolorado wrote: ↑Sun Jan 08, 2023 12:29 pm You suggested it goes to -95%, which would be catastrophic. It doesn't. It went -75%

This is a funny sentence to me like "yeah -95% is catastrophic but it was only -75%" lmao.

Most people would call a 75% loss of an investment as completely catastrophic. That is well past what is considered a blow-up for a hedge fund, it's usually where distressed bonds of countries at war trade at (like Ukraine).

In fact, if someone is willing to put money at risk of 75% loss, it's usually money they're totally OK losing entirely (ex: play money). I suspect the 75% mark is enough of a loss for most that it's basically just considered as a total loss.

[The difference between the P/E of value and P/E of growth is called the "value spread". So we can look at the ratio P/E Growth to P/E Value to estimate the value spread. If value had become increasingly popular, value stocks would have become more expensive relative to growth and the ratio would be smaller. Instead we still see the value spread at about the 90th percentile of historic values. Check out the below chart from Cliff Asness of AQR. https://www.aqr.com/Insights/Perspectives/The-Bubble-Has-Not-Popped Dave Dave, As I said already, value spread is only one part. The earnings growth spread matters too. In Cliff's "Style Timing Value vs Growth" piece, he explains it all really well, including the math. Here's my ...