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For those who are:

  • Mathematically literate, but
  • Not familiar with this particular analogy (of proofs <-> agents)

Do you know of a good reference for how to interpret discussions like this?

For example: " tries to prove that , and  tries to prove " -- If A and B are propositions, what does it mean for a proposition to try and prove another proposition?

(There might be more language that needs interpreting, but I got stuck there.)

As a follow-up: I did this for a while, but I've become convinced there are a couple effects that make this not as good as it sounds:

  • Futures have taxes paid in the year gains are made, which significantly reduces returns in simulations I've run.  In an ETF or mutual fund, you can instead let those gains ride.
  • Futures have an implicit financing cost, and portfolio performance is very sensitive to this cost if you're using a lot of leverage (e.g. for intermediate term bonds).
  • Leveraged ETFs fluctuate a lot, and need to be rebalanced with the rest of your portfolio.  This causes taxes like above.  If you don't rebalance, your leverage ratio changes which causes the portfolio to behave poorly as well.

With all of these effects accounted for, the gains from leveraging look very modest and depend a lot on what time period you look at.  Given the risks, I've decided against it for myself.

I've got no attachment to the phrase, I meant it in the sense of (From Wikipedia):

In simple terms, a negative externality is anything that causes an indirect cost to individuals.

I think e.g. paying for labor increases the demand for labor, thus increasing the price everyone else pays.  That's an indirect cost to them.  I didn't intend to make any claims about rights.

I disagree that believing there's a negative externality of production leads to the position you're arguing against -- for instance, I might think the negative externality is very small compared to the positive gains from trade.  But I appreciate you pointing out exactly where you disagree with my framing.

The part that is missing from your question is, in a parallel reality where you didn't buy the PS5, how did you spend the extra money

Correct, and intentionally so.  This is why I compare to setting the money on fire instead.  Maybe I have the wrong framing, but it seems valuable to me to look at the marginal value of a single spending act in isolation.  I might do many things with the money (like invest, spend, or donate it in various ways), and it would be interesting to know each of their values independently so I could compare them on even footing.

Maybe the parallel reality we should look at is the one where you worked less, got less money, and therefore didn't buy the PS5

Maybe!  I think if you're trying to influence social policy, you should definitely think about that.  But as an individual, I'm curious about the separate positive/negative effects of more work vs more spending.

some traditional alternatives are "you extort money from people at a gunpoint, then spend the money to buy PS5", which do not generate so much positive value for the others.

Thanks for bringing this up, it hadn't occurred to me.

I basically agree with the rest of your answer but, I'm still on the hunt for quantification!

I strong downvoted this, because it doesn't answer the question and instead seems to me to be making a political point.

Insanity Wolf would tell you you're absolutely right.

About what?  I don't think I believe any of the things you're arguing against.  I'm just wanting to get a quantitative sense, whether it supports or opposes the political point you're trying to make.

Thanks for this post, these kinds of details seem very useful for anyone wanting to attempt this path!

A worry I have: there are people who long for the imagined lifestyle and self-description of being an independent AI alignment/agency researcher.  I would categorize some of my past selves this way.

For many such people, trying to follow this path too enthusiastically would be bad for them -- but they might not have the memetic immunities that protect them from those bad decisions.  For instance, their social safety net might be insufficient for the level of financial risk, or the career tradeoffs might be very large.  This post is enthusiastic, but I think many people need to be urged caution when making major life changes -- especially around such high stakes causes, where emotions run high.

So for my past selves, I'd disclaim:

  • It's ok (and good) to prioritize your own financial and social safety net.  You can revisit your ability to contribute from a better position in the future.  The risks of things not going as well for you are very real.
  • When starting down such a path, you should have a clear fallback plan that does not involve immense suffering.  For instance, make effort for X time period before attempting to find an alternate job if you have not achieved Y income.  Do this only if you have confidence you will not take a too-large psychological hit from the failure.
Answer by tryactions90

For buy-and-hold strategies: leverage (borrowing to invest) can be used to increase returns.  The Sharpe ratio of a portfolio is a measure of it's risk/reward trade-off; there's a theorem that given a set of assets with fixed known distributions and ability to borrow at the risk-free rate, the Kelly optimal allocation is a leveraged version of the portfolio with highest Sharpe ratio.  You can calculate that optimal leverage in various ways.

In practice, we don't know future Sharpe ratios (only the past), we don't have assets with fixed known distributions (to the extent there is a distribution, it likely changes over time), and there's other idiosyncratic risks to leverage.

Using past data, however, is highly suggestive that at least some leverage is a great idea. For instance, a 40/60 stock/bond portfolio has higher Sharpe ratio than a 100% stock portfolio in almost all historical models since bonds and stocks have low correlation. It's not unreasonable to assume that low correlation will hold going forward.  If I leverage up a stock/bond portfolio to the same volatility as the corresponding 100% stock portfolio, I see a 2-4% increase in yearly returns depending on time period.  This is easily achievable by buying leveraged ETFs.

Naive Kelly models will usually recommend more risk than the stock market, so if your risk tolerance is even higher the (potentially naive and misleading) math is on your side. Be careful if you might need the money soon: these models assume you're never withdrawing!

My opinion: ~1.5-2.5x leverage on stock/bond portfolios looks reasonable for long-term investors, although it really depends on the assets -- short term treasuries for example are so stable that even 10x leveraging isn't crazy.

In the real world, you can leverage by:

  • Buying leveraged ETFs.  These work just like buying stocks or regular non-leveraged ETFs.  Vanguard doesn't allow these, so I use Fidelity.  I might recommend SSO and TMF, along with international + extended market diversification.  Since the leverage on these is set daily, they eliminate some of the tail risk of leveraging. Downsides: volatility decay in sideways markets and ETFs can simply fail to track their (leveraged) index.
  • Using margin accounts.  This is where your broker lends you money, using your other investments as collateral.  Rates are often really bad/not worth it -- be careful.  Also they'll sell your other investments if you become overly leveraged due to a downturn (a "margin call") -- which means forced selling during a downturn, which can cause you to miss out on any recovery.  I don't like this.
  • Directly taking on debt / counter-factually not paying off debt.  If you take out a mortgage instead of paying cash for a house, the money you saved can be considered to be "on loan" at the mortgage rate.  Investing it is then a form of leveraging.  This is bad if the rate is too high, but mortgage rates are really low right now.
  • Futures.  These allow higher leverage than ETFs and adoption of various strategies if you're willing to monitor them daily -- for instance, you can leverage/deleverage on a daily basis with no (additional) tax penalty.  Great for getting really high leverage, e.g. for stable investments like treasuries.  Downsides: your positions will be closed if you run out of margin -- which means you can be forced out of the market during a bad enough downturn, potentially missing the recovery.  For high-leverage strategies, this means you probably need to monitor daily and de-lever as appropriate.  Gains from futures are immediately taxed at 60% short-term 40% long-term capital gains, introducing tax drag that you wouldn't have with ETFs.
  • Options.  I don't know much about these.  Here's a book talking about passive indexing approaches using options, which I haven't read:
  • Other stuff (box spread financing?)

You can kind of backtest various strategies for yourself using e.g.:

Keep in mind that the past doesn't predict the future, and naive back-testing might not track historical reality perfectly or may be missing some idiosyncratic risks of leveraging certain ways.

For your maximal laziness, here's an ~1.9x leveraged ETF allocation I made up just now that's around 40/60 world stock market/long-term bonds: 36% TMF, 16% SSO, 8% VXF, 40% VXUS.  Full disclosure: Lots of people would think this is a terrible allocation since "everyone knows" the bond market is due to crash due to current low interest rates.

For increasing salary vs investing: do these really funge against each other?  Why not both?  Generically I'd think income should dominate before you have a lot invested, and then investment strategy becomes important once your yearly average investment returns become similar in scale to your yearly income.

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This is mentioned in the "don't screw up" section.  By market cap, crypto was 1.7% as big as the world stock market, and Bitcoin 1% as big, so those seem like good starting points -- adjust from there for your desired level of risk vs reward.

IMO, self picked stocks are dumb.  You give up diversification benefit for no reason, unless you think you know better than the market (which you don't).

Great point; I agree.  Also a great example of missing an obvious risk; I hadn't noticed that before linking.

The calculator here allows simulating withdrawal rates by asset allocation, although it only has data back to 1970 so is a bit limited.  I get the same safe withdrawal rate (4.3%) for 30 year retirees using either 100% US or 50/50 US/ex-US over that time frame.  100% Japan had a 1.5% safe withdrawal rate.

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