Options Nitpick: You can't use equity index* option prices as true probabilities because adding hedges to a portfolio makes the whole portfolio more valuable. People then buy options based on their value when added to the portfolio, not as individual investments.
The first reason option hedges make your portfolio more valuable is preferences: people don't just want to maximize their expected return, but also reduce the chance they go broke. People don't like risk and hedges reduce risk, ergo they pay more to get rid of risk. However you can't just subtract X vols to adjust as this "risk premia" isn't constant over time.
Secondly hedges maximize long term returns (or why you shouldn't sell options) You want to maximize your average geometric annual return not average annual return. You care about geometric averages because if for 3 years your returns were +75%, +75%, -100%, your don't have 50% more money then when you started but 0. The average of annual returns was 10.7% over the past 30 years, but if you'd invested in 1992 you'd've only compounded at 8.5% year till 2022.
Geometric returns are the the nth root of a product of n numbers and have the approximation = Average Annual Return - (variance/2). If you could reduce variance and not reduce Annual returns, your portfolio (market + hedges) would grow faster than the market.
These reasons are why despite the worst Annual return being -48% in 1931, you say there's a 5% chance of > -50% returns based on option markets.
*I'm specifically talking index options because that's the portfolio investors have (or something similar) and the total is what they care about. If you were to use prices as true probabilities for say a merger going through these reasons don't apply as much and would be more accurate.
PS. I've referred to investors as all having the same portfolio because most people do have highly correlated index holdings and it's at this level of generality you can think about investors as a class.
This would be useful as a comment on https://www.lesswrong.com/posts/xg3hXCYQPJkwHyik2/the-best-textbooks-on-every-subject, not sure of best way to update existing lists though.
new design without the quote looks fine.
I seem to be having a bug though/ironically am not able to solve it; I got the matrix that is F9 here https://www.dbglab.ru/en/slovar-dannykh/61/130/ (answer is 5)
My function f(x) = 5x³ + 14x² + 8x + 20 -> f'(x) + x = 15x² + 28x + 8 + x = 528 is being marked incorrect.
just pull something (and quickly) from the Flat Earth Society; https://www.extremetech.com/extreme/259821-flat-earth-society-trolls-elon-musk-claims-mars-round
is a prime example
No, it's lower than the normal "8%" you hear because I'm not averaging across time.
[+10%, + 1%, +9%, +20%, 15%] = 9% if you average the percentages, but this represents putting in $100 at the start of each year and selling any excess gains at year end. The way people invest of putting in $100 once and letting it compound* gives
1.1*1.01*1.09*1.2*1.15 = 1.6711662 total gain or
1.6711662^(1/5) = 10.8% annualized.
The technical terms for this is non-ergodic see https://jasoncollins.blog/ergodicity-economics-a-primer/ for a description.
*Actually people do even worse then this, particularly for hedge funds: individuals put money into hedge funds that recently outperformed but go on to reverse to the mean and underperform. So while the average annual returns are +30% -6% = 12% annualized, pretty good across time, but if you did 30% managing 100M and -6% on 1B then the dollar returns are net negative.
It seems deluk is investing with Bitfinex (blocked in US), which has lots of ongoing issues; see Patrick McKenzie on why the whole thing is a fraud that is down several hundred million and is likely to seize accounts https://www.kalzumeus.com/2019/10/28/tether-and-bitfinex/ .
IIRC some individual investors in Binance (also supposed to be blocked for US investors) were being targeted for investigation by CFTC; there's an aspect of lending that lead to Know Your Customer violations (very hazy on specifics).
A legal way to put on this trade is to short MicroStrategy (Co that bought bitcoin) and buy bitcoin yourself. https://www.coindesk.com/microstrategy-bitcoin-michael-saylor-valuation
That's a very selective term history; the exact bottom of the SP500 from Covid fear was March 20 2020, vs todays March 18th. Unless you put in everything on March 18th this is highly misleading. The true comparison would be your annualized dollar weighted average return (but for Schwab at least this isn't easily calculatable, as saving is counted as increasing portfolio weight, and buying increases the base investment, but without a proportional change in 'Total gain').
Since 2000 the average annual return of the SP-500 is 5.9%(6.1% for VTI since inception) and a reasonable approximation of what would be earned going forward.
There's a similar pattern in Rap music, the misanthropic self promotion. The message of basically every lyric is either "I'm super successful" or "I know no bounds in what I will do"; either case has the listener emphasize with the sentiment of being better than others/not caring about others. I stopped listening when I noticed the avarice it was promoting, how I could only fantasize about being a $MM success, which not having a path to improve toward just gives the fantasy of becoming $MM.
EDIT: NVM. This is just proof I didn't get enough neonatal iodine.
For Section 2 on transaction costs you write the calculation for probability of winning is:
100 / ( ( ( 100 / 0.40 ) * 0.9 ) + 10 )
Where does the extra +10 come from?
EDIT: It's so that you're not paying taxes on the amount of the original wager.
maximum_%_bet_on_P = bet_amount / (conditional_winnings - fees )
= bet_amount / (conditional_winnings(1-fee%) + bet_amount*fee%))
The 2000-2021 VIX has averaged 19.7, sp500 annualized vol 18.1.
From a 2ndary source: "The mean of the realistic volatility risk premium since 2000 has been 11% of implied volatility, with a standard deviation of roughly 15%-points" from https://www.sr-sv.com/realistic-volatility-risk-premia/ . So 1/3 of the time the premia is outside [-4%,26%], which swamps a lot of vix info about true expect vol.
-60% would the worst draw down ever, the prior should be <<1%. However, 8 years have been above 30% since 1928 (9%), seems you're using a non-symetric CI.
The reasoning for why there'd be such a drawdown is backwards in OP: because real rates are so low the returns for owning stocks has declined accordingly. If you expect 0% rates and no growth stocks are priced reasonably, yielding 4%/year more than bonds. Thinking in the level of rates not changes to rates makes more sense, since investments are based on current projected rates. A discounted cash flow analysis works regardless of how rates change year to year. Currently the 30yr is trading at 2.11% so real rates around the 0 bound is the consensus view.