This is only 2.4 standard deviations assuming returns follow a normal distribution, which they don't.

No, 2.4 standard deviations is 2.4 standard deviations.

It's possible to have distributions for which what's more or less surprising.

For a normal distribution, this happens about one every 200 periods. I totally agree that this isn't a factor of 200 evidence against your view. So maybe saying "falsifies" was too strong.

But no distribution is 2.35 standard deviations below its mean with probability more than 18%. That's literally impossible. And no distribution is 4 standard deviations below its mean with probability >6%. (I'm just adopting your variance estimates here, so I don't think you can really object.)

This is not directly relevant to the investment strategies I talked about above, but if you use the really simple (and well-supported) expected return model of earnings growth plus dividends plus P/E mean reversion and plug in the current numbers for emerging markets, you get 9-11% real return (Research Affiliates gives 9%, I've seen other sources give 11%). This is not a highly concentrated investment of 50 stocks—it's an entire asset class. So I don't think expecting a 9% return is insane.

Have you looked at backtests of this kind of reasoning for emerging markets? Not of total return, I agree that is super noisy, but just the basic return model? I was briefly very optimistic about EM when I started investing, based on arguments like this one, but then when I looked at the data it just seems like it doesn't work out, and there are tons of ways that emerging market companies could be less appealing for investors that could explain a failure of the model. So I ended up just following the market portfolio, and using much more pessimistic returns estimates.

I didn't look into it super deeply. Here's some even more superficial discussion using numbers I pulled while writing this comment.

Over the decade before this crisis, it seems like EM earnings yields were roughly flat around 8%. Dividend yield was <2%. Real dividends were basically flat. Real price return was slightly negative. And I think on top of all of that the volatility was significantly higher than US markets.

Why expect P/E mean reversion to rescue future returns in this case? It seems like EM companies have lots of on-paper earnings, but they neither distribute those to investors (whether as buybacks or dividends) nor use them to grow future earnings. So their current P/E ratios seem justified, and expecting +5%/year returns from P/E mean reversion seems pretty optimistic.

Like I said, I haven't looked into this deeply, so I'm totally open to someone pointing out that actually the naive return model has worked OK in emerging markets after correcting for some important non-obvious stuff (or even just walking through the above analysis more carefully), and so we should just take the last 10 years of underperformance as evidence that now is a particularly good time to get in. But right now that's not my best guess, much less strongly supported enough that I want to take a big anti-EMH position on it (not to mention that betting against beta is one of the factors that seems most plausible to me and seems best documented, and EM is on the other side of that trade).

which explain why the authors believe their particular implementations of momentum and value have (slightly) better expected return.

I'm willing to believe that, though I'm skeptical that they get enough to pay for their +2% fees.

I don't overly trust backtests, but I trust the process behind VMOT, which is (part of the) reason to believe the cited backtest is reflective of the strategy's long-term performance.[2] VMOT projected returns were based on a 20-year backtest, but you can find similar numbers by looking at much longer data series

The markets today are a lot different from the markets 20 years ago. The problem isn't just that the backtests are typically underpowered, it's that markets become more sophisticated, and everyone gets to see that data. You write:

RAFI believes the value and momentum premia will work as well in the future as they have in the past, and some of the papers I linked above make similar claims. They offer good support for this claim, but in the interest of conservatism, we could justifiably subtract a couple of percentage points from expected return to account for premium degradation.

Having a good argument is one thing---I haven't seen one but also haven't looked that hard, and I'm totally willing to believe that one exists and I think it's reasonable to invest on the basis of such arguments. I also believe that premia won't completely dry up because smart investors won't want the extra volatility if the returns aren't there (and lots of people chasing a premium will add premium-specific volatility).

But without a good argument, subtracting a few percentage points from backtested return isn't conservative. That's probably what you should do with a good argument.

I haven't done a deep dive on this but I think futures are better than this analysis makes them look.

Suppose that I'm in the top bracket and pay 23% taxes on futures, and that my ideal position is 2x SPY.

In a tax-free account I could buy SPY and 1x SPY futures, to get (2x SPY - 1x interest).

In a taxable account I can buy 1x SPY and 1.3x SPY futures. Then my after-tax expected return is again (2x SPY - 1x interest).

The catch is that if I lose money, some of my wealth will take the form of taxable losses that I can use to offset gains in future years. This has a small problem and a bigger problem:

• Small problem: it may be some years before I can use up those taxable losses. So I'll effectively pay interest on the money over those years. If real rates were 2% and I had to wait 5 years on average to return to my high-water mark, then this would be an effective tax rate of (2% * 5 years) * (23%) ~ 2.3%. I think that's conservative, and this is mostly negligible.
• Large problem: if the market goes down enough, I could be left totally broke, and my taxable losses won't do me any good. In particular, if the market went down 52%, then my 2x leveraged portfolio should be down to around 23% of my original net worth, but that will entirely be in the form of taxable losses (losing $100 is like getting a $23 grant, to be redeemed only once I've made enough taxable gains).

So I can't just treat my taxable losses as wealth for the purpose of computing leverage. I don't know exactly what the right strategy is, it's probably quite complicated.

The simplest solution is to just ignore them when setting my desired level of leverage. If you do that, and are careful about rebalancing, it seems like you shouldn't lose very much to taxes in log-expectation (e.g. if the market is down 50%, I think you'd end up with about half of your desired leverage, which is similar to a 25% tax rate). But I'd like to work it out, since other than this futures seem appealing.

I'm surprised by (and suspicious of) the claim about so many more international shares being non-tradeable, but it would change my view.

I would guess the savings rate thing is relatively small compared to the fact that a much larger fraction of US GDP is inevestable in the stock market---the US is 20-25% of GDP, but the US is 40% of total stock market capitalization and I think US corporate profits are also ballpark 40% of all publicly traded corporate profits. So if everyone saved the same amount and invested in their home country, US equities would be too cheap.

I agree that under EMH the two bonds A and B are basically the same, so it's neutral. But it's a prima facie reason that A is going to perform worse (not a prima facie reason it will perform better) and it's now pretty murky whether the market is going to err one way or the other.

I'm still pretty skeptical of US equities outperforming, but I'll think about it more.

I haven't thought about the diversification point that much. I don't think that you can just use the empirical daily correlations for the purpose of estimating this, but maybe you can (until you observe them coming apart). It's hard to see how you can be so uncertain about the relative performance of A and B, but still think they are virtually perfectly correlated (but again, that may just be a misleading intuition). I'm going to spend a bit of time with historical data to get a feel for this sometime and will postpone judgment until after doing that.

I also like GMP, and find the paper kind of surprising. I checked the endpoints stuff a bit and it seems like it can explain a small effect but not a huge one. My best guess is that going from equities to GMP is worth like +1-2% risk-free returns.

I like the basic point about leverage and think it's quite robust.

But I think the projected returns for VMOT+MF are insane. And as a result the 8x leverage recommendation is insane, someone who does that is definitely just going to go broke. (This is similar to Carl's complaint.)

My biggest problem with this estimate is that it kind of sounds crazy and I don't know very good evidence in favor. But it seems like these claimed returns are so high that you can also basically falsify them by looking at the data between when VMOT was founded and when you wrote this post.

VMOT is down 20% in the last 3 years. This estimate would expect returns of 27% +- 20% over that period, so you're like 2.4 standard deviations down.

When you wrote this post, before the crisis, VMOT was only like 1.4 standard deviations below your expectations. so maybe we should be more charitable?

But that's just because it was a period of surprisingly high market returns. VMOT lagged VT by more than 35% between its inception and when you wrote this post, whereas this methodology expects it to outperform by more than 12% over that period. VMOT/VT are positively correlated, and based on your numbers it looks like the stdev of excess performance should be <10%. So that's like 4-5 standard deviations of surprising bad performance already.

Is something wrong with this analysis?

If that's right, I definitely object to the methodology "take an absurd backtest that we've already falsified out of sample, then cut a few percentage points off and call it conservative." In this case it looks like even the "conservative" estimate is basically falsified.

We could account for this by treating mean return and standard deviation as distributions rather than point estimates, and calculating utility-maximizing leverage across the distribution instead of at a single point. This raises a further concern that we don’t even know what distribution the mean and standard deviation have, but at least this gets us closer to an accurate model.

Why not just take the actual mean and standard deviation, averaging across the whole distribution of models?

What exactly is the "mean" you are quoting, if it's not your subjective expectation of returns?

(Also, I think the costs of choosing leverage wrong are pretty symmetric.)

My understanding is that the sharpe ratio of the global portfolio is quite similar to the equity portfolio (e.g. see here for data on the period from 1960-2017, finding 0.36 for the global market and 0.37 for equities).

I still do expect the broad market to outperform equities alone, but I don't know where the super-high estimates for the benefits of diversification are coming from, and I expect the effect to be much more modest then the one described in the linked post by Ben Todd. Do you know what's up with the discrepancy? It could be about choice of time periods or some technical detail, but it's kind fo a big discrepancy. (My best guess is an error in the linked post.)

To use leverage, you will probably end up having to pay about 1% on top of short-term interest rates

Not a huge deal, but it seems like the typical overhead is about 0.3%:

• This seems to be the implicit rate I pay if I buy equity futures rather than holding physical equities (a historical survey: http://cdar.berkeley.edu/wp-content/uploads/2016/12/futures-gunther-etal-111616.pdf , though you can also check yourself for a particular future you are considering buying, the main complication is factoring in dividend prices)
• Wei Dai has recently been looking into box spread financing which were around 0.55% for 3 years, 0.3% above the short-term treasury rate.
• If you have a large account, interactive brokers charges benchmark+0.3% interest.

I suspect risk-free + 0.3% is basically the going rate, though I also wouldn't be too surprised if a leveraged ETF could get a slightly better rate.

If you are leveraging as much as described in this post, it seems reasonably important to get at least an OK rate. 1% overhead is large enough that it claws back a significant fraction of the value from leverage (at least if you use more realistic return estimates).

I think it's pretty dangerous to reason "asset X has outperformed recently, so I expect it to outperform in the future." An asset can outperform because it's becoming more expensive, which I think is partly the case here.

This is most obvious in the case of bonds---if 30-year bonds from A are yielding 2%/year and then fall to 1.5%/year over a decade, while 30-year bonds from B are yielding 2%/year and stay at 2%/year, then it will look like the bonds from A are performing about twice as well over the decade. But this is a very bad reason to invest in A. It's anti-inductive not only because of EMH but for the very simple reason that return chasing leads you to buy high and sell low.

This is less straightforward with equities because earnings accounting is (much) less transparent than bond yields, but I think it's a reasonable first pass guess about what's going on (combined with some legitimate update about people becoming more pessimistic about corporate performance/governance/accounting outside of the US). Would be interested in any data contradicting this picture.

I do think that international equities will do worse than US equities after controlling for on-paper earnings. But they have significantly higher on-paper earnings, and I don't really see how to take a bet about which of these effects is larger without getting into way more nitty gritty about exactly what mistake we think which investors are making. If I had to guess I'd bet that US markets are salient to investors in many countries and their recent outperformance has made many people overweight them, so that they will very slightly underperform. But I'd be super interested in good empirical evidence on this front too.

(The RAFI estimates generally look a bit unreasonable to me, and I don't know of an empirical track record or convincing analysis that would make me like them more.)

I personally just hold the market portfolio. So I'm guaranteed to outperform the average of you and Michael Dickens, though I'm not sure which one of you is going to do better than me and which one is going to do worse.

My main point was that in any case what matters are the degree of alignment of the AI systems, and not their consciousness. But I agree with what you are saying.

If our plan for building AI depends on having clarity about our values, then it's important to achieve such clarity before we build AI---whether that's clarity about consciousness, population ethics, what kinds of experience are actually good, how to handle infinities, weird simulation stuff, or whatever else.

I agree consciousness is a big ? in our axiology, though it's not clear if the value you'd lose from saying "only create creatures physiologically identical to humans" is large compared to all the other value we are losing from the other kinds of uncertainty.

I tend to think that in such worlds we are in very deep trouble anyway and won't realize a meaningful amount of value regardless of how well we understand consciousness. So while I may care about them a bit from the perspective of parochial values (like "is Paul happy?") I don't care about them much from the perspective of impartial moral concerns (which is the main perspective where I care about clarifying concepts like consciousness).