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also I very much think it's a language debate when you phrase it like this: twitter.com/danrobinson/st Let's say you go to your advisor. They say: "do you want X with an expected return of 50% in 5 years or Y with an expected return of 25% in 5 years?"

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Replying to @danrobinson @SBF_Alameda and 3 others

You wouldn’t rather invest your money with an asset manager where you expect a 5% annualized rate of return to one where you expect a 3% annualized rate of return? Your reaction would be “I might be interested in the 3% rate, although only if it’s RISKIER”? That seems unusual.

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"but", they say, "X is riskier". I don't think you'd immediately say "obviously I want you to take lim as t-->inf of returns^(1/t) and then take the EV of that and tell me" You might, if you like Kelly! But you tried to phrase it as _obvious_ that's what you'd ask.

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How do I try to learn what some fund's expected returns are? I'll probably at least look at historical returns, right? (NOT 👏 INVESTING 👏ADVICE) Suppose there is 50 years of history. I compute historical returns by averaging the actual annual returns, right?

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(OK, technically, I get a more accurate result if I average LOG returns, just as we do when measuring volatility. But no funny business—I'm never looking at log wealth! And my point will still stand if we use arithmetic mean of returns.)

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So, when I do this, what number is it going to approximate? It's going to approximate the time-average rate of growth of wealth, right?

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How do we know that Warren Buffett is a phenomenal investor? We look at his average annual return, right? We see that he has has returned, on average >20.3% per year since he started.

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That's the time-average growth rate, right?

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@GaussianProcess

nope, not if you're averaging the returns! to get what you're trying to call the time-average growth rate you have to *geometrically mean* the returns

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OK, and you're saying that arithmetic mean of annual returns is appropriate? What happens if you flip the coin not once a year, but once a day? Even faster growth in EV(wealth), right? But what happens to your arithmetic mean of annualized returns?

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(I could make the spreadsheet for you but you can probably guess that it's going to be -99.999999999%)

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@GaussianProcess

if you do _one single simulation of it_ then the median result will be very negative returns! but in fact the expected arithmetic mean of annualized returns is positive!

4:25 AM · Dec 4, 2020Twitter Web App

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But really a lot of my point is: twitter.com/danrobinson/st what you said there was literally false. what you _meant_ may have been true! But your whole point was some weird gotcha schtick involving a sentence you thought sounded bad for me. and actually it sounds bad for you!

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Replying to @SBF_FTX @SBF_Alameda and 3 others

How do I try to learn what some fund's expected returns are? I'll probably at least look at historical returns, right? (NOT

INVESTING

ADVICE) Suppose there is 50 years of history. I compute historical returns by averaging the actual annual returns, right?

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Which sentence is false?

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1) Run it as many times as you want and try to get a positive return. 2) There's no simulation. We're at the advisor's office. Here reality, what do we know about this strategy's historical performance? That it has never done better than -99.999% in any year ever.

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@GaussianProcess

1) sure I will, but it'll take a while :P 2) ok but you also didn't present the *real life thing* at the advisor's office. A *closer* version would be he shows you two sets of companies:

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