Thanks for these numbers. Yes: holding expected returns equal, our propensity to invest should be decreasing in volatility.

But symmetric uncertainty about the long-run average rate of return—or to a lesser extent, as in your example, time-independent symmetric uncertainty about short-run returns at every period—increases expected returns. (I think this is the point I made that you’re referring to.) This is just the converse of your observation that, to keep expected returns equal upon introducing volatility, we have to lower the long-run rate from r to q = r – s^2/2.

Whether these increased expected returns mean that patient philanthropists should invest more or less than they would under certainty is in principle sensitive to (a) the shape of the function from resources to philanthropic impact and (b) the behavior of other funders of the things we care about; but on balance, on the current margin, I’d argue it implies that patient philanthropists should invest more. I’ll try writing more on this at some point, and apologies if you would have liked a deeper discussion about this on the podcast.

Thanks for the response. To clarify: in the second model both the drift and the diffusion term impact on the expected returns. If you substitute in a model return e^{q + sz}, with z a standard normal:

So, if we have fixed from some source that E[V(1)]=1.07=e^r then we cannot set q=r in the model with randomness while maintaining the equality. Where the equality cashes out as ‘the expected rate of return a year from now is 7%’.

Empirically estimated long run rates already take into account the effects of randomness since they are typically some sort of mean of observed returns. If this were not the case one would always have to, at least, quote the parameters in pairs (drift=such and such, vol=such and such) and perform a calculation in order to get out the expected returns.

Yup, no disagreement here. You’re looking at what happens when we introduce uncertainty holding the absolute expected return constant, and I was discussing what happens when we introduce uncertainty holding the expected annual rate of return constant.

So, what do you think of the idea that aiming for high expected returns in long term investments might not be the best thing to do, given the skewed distribution? This is, we want to ensure that most futures are ‘good’; not just a few that are ‘excellent’ lost in a mass of ‘meh’ or worse.

BTW, I did like the podcast—it does take something to make me tap out forum posts :)

In the model I’m working on, to try to weigh the main considerations, the goal is to maximize expected philanthropic impact, not to maximize expected returns. I do recommend spending more quickly than I would in a world where the goal were just to maximize expected returns. My tentative conclusion that long-term investing is a good idea already incorporates the conclusion that it will most likely just involve losing a lot of money.

That is, I argue that we’re in a world where the highest-expected-impact strategy (not just the highest-expect-return strategy) is one with a low probability of having a lot of impact and a high probability of having very little impact.

Ah, that’s interesting and the nub of a difference.

The way I see it, a ‘good’ impact function would upweight the impact of low probability downside events and, perhaps, downweight low probability upside events. Maximising the expectation of such a function would push one toward policies which more reliably produce good outcomes.

Hey, I know that episode : )

Thanks for these numbers. Yes: holding expected returns equal, our propensity to invest should be decreasing in volatility.

But symmetric uncertainty about the long-run average rate of return—or to a lesser extent, as in your example, time-independent symmetric uncertainty about short-run returns at every period—increases expected returns. (I think this is the point I made that you’re referring to.) This is just the converse of your observation that, to keep expected returns

equalupon introducing volatility, we have to lower the long-run rate from r to q = r – s^2/2.Whether these increased expected returns mean that patient philanthropists should invest more or less than they would under certainty is in principle sensitive to (a) the shape of the function from resources to philanthropic impact and (b) the behavior of other funders of the things we care about; but on balance, on the current margin, I’d argue it implies that patient philanthropists should invest more. I’ll try writing more on this at some point, and apologies if you would have liked a deeper discussion about this on the podcast.

Thanks for the response. To clarify: in the second model both the drift and the diffusion term impact on the expected returns. If you substitute in a model return e^{q + sz}, with z a standard normal:

E[V(1)] = E[e^{q + s z}] = E[e^{sz}]e^q = e^{s^2/2} e^q > e^q

So, if we have fixed from some source that E[V(1)]=1.07=e^r then we cannot set q=r in the model with randomness while maintaining the equality. Where the equality cashes out as ‘the expected rate of return a year from now is 7%’.

Empirically estimated long run rates already take into account the effects of randomness since they are typically some sort of mean of observed returns. If this were not the case one would always have to, at least, quote the parameters in pairs (drift=such and such, vol=such and such) and perform a calculation in order to get out the expected returns.

Yup, no disagreement here. You’re looking at what happens when we introduce uncertainty holding the absolute expected return constant, and I was discussing what happens when we introduce uncertainty holding the expected annual rate of return constant.

So, what do you think of the idea that aiming for high expected returns in long term investments might not be the best thing to do, given the skewed distribution? This is, we want to ensure that most futures are ‘good’; not just a few that are ‘excellent’ lost in a mass of ‘meh’ or worse.

BTW, I did like the podcast—it does take something to make me tap out forum posts :)

Glad you liked it!

In the model I’m working on, to try to weigh the main considerations, the goal is to maximize expected philanthropic impact, not to maximize expected returns. I do recommend spending more quickly than I would in a world where the goal were just to maximize expected returns. My tentative conclusion that long-term investing is a good idea already incorporates the conclusion that it will most likely just involve losing a lot of money.

That is, I argue that we’re in a world where the highest-expected-impact strategy (not just the highest-expect-return strategy) is one with a low probability of having a lot of impact and a high probability of having very little impact.

Ah, that’s interesting and the nub of a difference.

The way I see it, a ‘good’ impact function would upweight the impact of low probability downside events and, perhaps, downweight low probability upside events. Maximising the expectation of such a function would push one toward policies which more reliably produce good outcomes.