prioritarian wrote: Sun Oct 12, 2025 10:13 am
NiceUnparticularMan wrote: Sat Oct 11, 2025 9:40 amAgain, the “prediction” takes the form of an expected return.
This is the CAPM formula:
The E(Ri) is an expected return.
This is the definition of an expected return:
In this formula, each Ri is the return in scenario i, and the Pi is the probability of scenario i. Note ‘i” is being used differently in each of these formulas respectively.
OK, so the CAPM formula does not output a prediction of the form that the stock “will” return some particular amount, either in absolute terms or relative to the risk-free rate.
It outputs a probabilistic prediction, that the probability weighted returns in all possible scenarios adds up to that expected return.
I think it is very, very helpful to keep this distinction in mind.
And this is actually another of those things where the CAPM folks have not necessarily done themselves any favor with the jargon they use. To be fair, that definition of an “expected return” is not unique to CAPM, it is a general technical term coming out of standard probability theory.
But I think many people think something like, “If you say the expected return is 20%, you are telling me I should expect a return of 20%”. And, no, not in this case. What they actually mean is the probability-weighted average of possible returns ends up 20%, and that is not the same thing.
In fact, there are cases where the expected return would literally be impossible as an actual return. Like, if you bet $1 on a coin flip, heads you get $2, tails you get back your $1, then the expected return of this bet is $0.50. But that is not a possible outcome. Either you get $1 return, or $0 return, you can’t get $0.50.
Anyway, point being an “expected return” in this context does not mean a return you should expect. I know that is confusing, but understanding the difference is really critical.
Thank you for this lucid explanatory post that I can now refer to when forum participants complain about “missed” expected returns (often in response to Vanguard CAPM forecast threads).
Yes, Vanguard’s asset model is a great example of how even at 10 years, what you tend to get is sufficiently wide probability distributions such that even if the central estimate is A beats B, it may not be very unlikely for B to actually beat A instead.
The model doesn’t really care about such horse race things, that’s just another range of possible scenarios among many to it. But around here, calling the wrong “winner” of a well-watched horse race (sometimes even before 10 years is up!) is often deemed “proof” the model is bad.
A constant frustration to me, though, is the same people will then just assert it is safer to assume that something like a 20 year backtest is predictive of the next 20 years. That’s also a type of model, and it has a terrible track record! But as interested as they are in “proving” Vanguard’s model doesn’t always call the right “winners”, they seem uninterested in seriously assessing whether their alternative proposal would actually have worked better when used without the benefit of hindsight.
Oh well.
