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Comment by darawk | Hacker News Reader

Do keep in mind that absolute returns are not the most important factor in investing. What you should care about are risk-adjusted returns of a particular asset, and return stability of your whole portfolio.

You can always use leverage to magnify the returns of any asset class up to whatever level you want. The only limiting factor there is risk and the cost of borrowing.

Before I learned about finance I thought that the purpose of diversification was safety. And it is, in part. But as a consequence of the AM-GM inequality [1], diversification actually increases your long-term returns. A returns stream of 8% every year will have substantially more money than a returns stream with a mean of 8%, that bounces up and down. If you play around with some numbers, you'll quickly see how profoundly important this fact is.

1. https://en.wikipedia.org/wiki/Inequality_of_arithmetic_and_g...

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I'd love to see a primer for leveraged diversification for people at the Bogleheads level. A lot of people are under the impression that a three-fund portfolio is the pinnacle of responsible self-investing, or a target-date retirement fund. But when I dig in I see people regularly make the point that that isn't true diversification, that asset class diversification isn't sufficient, that diversification is about measuring what investments move counter to each other in different macroeconomic environments, that leveraging is good, etc. I want to know more about how to apply all that when managing retirement funds at Fidelity or Vanguard, but I'm never going to work for a quant firm.

Check out portfoliocharts.com

Yes, that's right. What you want to do is maximize your sharpe ratio. You can play around with this python package to get a sense for how it works:

https://github.com/robertmartin8/PyPortfolioOpt

What you should be trying to achieve is a portfolio that earns the exact same return every single year, and you can do that in part by looking at historical covariance of the asset's time series. However, you also want to take a prospective view, and think about which asset classes may become correlated in the future.

There's no universal answer here (in the out of sample case - you can solve it in-sample), however. And another huge, huge factor is tax. Making sure your investments are tax-efficient is extremely important. Nothing will do more to ruin your compounding than taxes. So whatever you do, carefully consider the tax implications of your choices.

A lot of people focus on the tax rate. But what's actually quite a bit more important is the tax frequency. If you pay long term capital gains every two years on your whole portfolio...that's much worse than paying short term capital gains once at the very end (over a long period). What this means is that you want to choose things like passive ETFs, that are not taxed on their internal rebalancing. Even if you were to find a mutual fund that beat that ETF by 1% every year, the tax consequences of that fund would likely make it not worthwhile, before even considering the high fees it would likely charge you.

> What you should be trying to achieve is a portfolio that earns the exact same return every single year

Perhaps this is a dumb question, but wouldn't that mean that you end up with a 100% cash portfolio? After all, that portfolio has exactly the same nominal return every year: 0%.

I would expect that I have to choose a relative weight, to tune the trade-off between maximizing expected returns vs minimizing dispersion of returns.

edit: after reading a bit, it seems that changing this weight would trace out what is called the "efficient frontier".

Sorry, stable returns are not the only consideration. You want them to be as high as you can, while maintaining stability. There is obviously a tradeoff there, and yes, 'efficient frontier' is the term of art for choosing points along this optimal curve.

This is great, thanks. I have looked into maximizing the geometric mean before, similar to Kelly Criteria, but apparently that's a very volatile approach with a long timeframe before you have a high likelihood of approaching that maximization. I'll look more into Sharpe Ratio.

The general Bogle advice is for taxable accounts, pick something like a total us stock market index fund like FSKAX for fidelity. Low expense ratio, but you're right, it still has taxable long term capital gains and reinvestment every so often.

> You can always use leverage to magnify the returns of any asset class up to whatever level you want. The only limiting factor there is risk and the cost of borrowing.

This is false. In order to maintain a constant amount of leverage, you need to buy and sell securities if your leverage isn't unity. With increasing leverage, as security prices increase, you need to buy securities as your position earns a better return than the underlying. Conversely, you need to sell securities as prices fall. Together, this reduces your overall return via volatility drag.

The Kelly Criterion has the math for the absolute max return you can get via levering up assets.

> This is false. In order to maintain a constant amount of leverage, you need to buy and sell securities if your leverage isn't unity. With increasing leverage, as security prices increase, you need to buy securities as your position earns a better return than the underlying. Conversely, you need to sell securities as prices fall. Together, this reduces your overall return via volatility drag.

Ya sure that's true if you want to maintain constant leverage, there are tradeoffs there.

> The Kelly Criterion has the math for the absolute max return you can get via levering up assets.

Not exactly. The Kelly Criterion is the maximum that you should lever, over all the probability-weighted paths the portfolio will take to maximize log(wealth). However, nobody actually uses full Kelly leverage, because of estimation/fit error. One third or so of Kelly leverage is more common.

Diversification only works under specific assumptions, it’s far from a universal benefit.

Low transaction fees being an obvious example. If moving from one asset category to another involved paying high taxes, it’s very rarely worth it.

Ya, there are lots of nuances to consider when rebalancing an existing portfolio. I'm mostly discussing the case of starting fresh.

The arithmetic vs. geometric mean distinction is a good one to note. Since you mention risk-adjusted return, do you favor any particular approaches to optimization? ReSolve makes a pretty strong case for numerical optimization, summarized by this decision tree based on prior beliefs:

https://twitter.com/gestaltu/status/1044977487556595714

I generally prefer using something like scipy.minimize to maximize the expected sharpe ratio with returns de-magnified, which causes the optimization to be closer to a minimum variance portfolio.

> A returns stream of 8% every year will have substantially more money than a returns stream with a mean of 8%, that bounces up and down.

Also why the US is so rich growing at ~2.5% every year without failure vs. e.g. $emerging_economy which can grow at 8.0% on average but with significant volatility

(I'm on mobile so the exact numbers above may vary but the point stands)

That's not entirely true, though. Their mean growth rate is much higher than ours.

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