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"the addicted mind will find a way to rationalize continued use at all costs" 

Alan Carr wrote a series of books:  "The easy way to quit X". I picked up one since I figured he had found a process to cure addictive behaviors if he could write across so many categories.  I highly recommend it. The main points are:

  1. Give you 200 pages explaining why you don't actually enjoy X. Not that it's making your life worse but gives you momentary pleasure, you do not enjoy it. 
    1. I assume it's hypnotizing you into an emotional revulsion to the activity, and then giving you reasons with which to remind yourself that you don't like it.
  2. Decide you will never do/consume X again. You don't like it remember? You will never even think if you should X, you've decided permanently.  
    1. If every day you decided not to X, you'd be draining will power till one day you'd give in. So make an irreversible decision and be done with it.

It's a process easily transferable to any other activity.

I found that installing 3 website blockers at once on my laptop worked for me: the same way you use multiple anti-biotics at once to combat resistance. I might’ve trained myself to disable 1, then disable 2, then disable 3 if I added another whenever I realized the blocking wasn’t working: but by adding all 3 at once I wasn’t going to unblock all 3. Now it’s been long enough I’ve probably forgotten what I’d even need to do to unblock it.

The one thing the duality section was connected to was Riesz representation theorem. Riesz states every finite linear functional φ has a unique vector f, such that for all v, φ(v) = <v,f>.  It gives an isomorphism from functionals to vectors for a given norm, as the function is just multiplication with the vector.  

It's not tied to the section on duals in the text, but the section on duals lets you appreciate the result more.

The converse of fast paced conversations leading people to say stupid things is: if someone says something foolish it maybe not be a lie nor a tendency to BS nor stupidity. They may have responded faster than they thought. You can correct them not by refuting what was said but allowing them a moment to reconsider. A liar, politician, and fool are hard to reform or work with. “Stopping to think” may be easier trained and much easier used to keep a conversation on track.

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 . 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.

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.

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 (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;

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 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.

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