How standard portfolio theory changes when assets are technologies | Hacker News Reader

How standard portfolio theory changes when assets are technologies

arxiv.org

105 pointsmrleiter43 comments

My eyes glazed over at the vast number of priors introduced in this work. Why should I believe the assumptions hold?

In Machine Learning, the standard expectation of research papers is to empirically demonstrate the increased statistical power of the model over benchmarks, and I wish the authors demonstrated that their model aligns with historical reality.

I attended a talk recently by Aswath Damodaran where he explained that there are two types of investors, most often lying in disjoint sets: 1) number crunchers and 2) story tellers. Perhaps the success of tech companies (e.g. AMZN, GOOG, FB) can be explained in aggregate via the Wright model, but my feeling is that the majority of 'optimal portfolio distortion' these companies caused is mostly idiosyncratic to those specific companies, e.g. the "story tellers" have more information in the long-term behavior of a company. Consequently, aggregate modeling captures statistical correlation rather than causation, which can still make money but is not robust to long tails.

I think number crunching is only useful for short horizon portfolio selection.

> In Machine Learning, the standard expectation of research papers is to empirically demonstrate the increased statistical power of the model over benchmarks, and I wish the authors demonstrated that their model aligns with historical reality.

I went to graduate school in econometrics after taking several undergraduate courses in ML, and I was constantly astounded how paper after paper failed to do this. I don't think you can (or should) claim a result if you can't demonstrate that it works empirically.

Mathematical finance as a field has gone down a deep, dark, weird rabbit hole. The point of papers in the field is rarely to make a statement about how to invest, or how markets work. The point is to do a load of funky maths, showing off how clever you are, and then claim a tenuous link to finance.

If anyone doubts what I'm saying, they should look up the definition of "No free lunch with vanishing risk" [1] and tell me how it relates to the real world.

[1] https://en.wikipedia.org/wiki/No_free_lunch_with_vanishing_r...

Please excuse my total ignorance, but could part of the reason for this be some kind of personal advertising for the financial industry (e.g. "Look at how smart I am, hire me for your quant fund!")?

the buzzword you want is Mathiness

https://en.wikipedia.org/wiki/Mathiness

For a conclusion, it's very inconclusive. :)

"Crucially, we find that the nonlinearity of the problem leads to multiple local optima, so that very different optimal portfolios can exist simultaneously, and the global optimum switches instantaneously between them as parameters change. This means that inside a critical region of parameter space a small change in one of the parameters can lead to a very significant change in the optimal portfolio."

Doesn't that just mean that it's impossible to manage a technology portfolio in a cost efficient way? So the only way to manage a technology portfolio would be to simply try to juggle as many as you can, eliminating them randomly as you are resource constrained?

It means it's very difficult to maintain the global maximum for a technology portfolio. You are at the global maximum, and at the drop of a hat that converts to a local maximum. That could still be pretty good, though. It could still be cost efficient - just not the best that is possible.

> a small change in one of the parameters can lead to a very significant change in the optimal portfolio.

Isn't that the definition of chaotic?

No. This is high sensitivity to parameters. Chaos is ergodic behaviour.

From https://en.wikipedia.org/wiki/Chaos_theory

    Chaos theory is a branch of mathematics focused on the 
    behavior of dynamical systems that are highly sensitive 
    to initial conditions.

Many of the visualizations of chaotic behavior in the wiki don't exhibit ergodic behavior.

Sensitive dependence on parameters ≠︎ sensitive dependence on initial conditions

I'm very much among the (small) camp of people who thinks that standard portfolio theory isn't worth a whole lot even when the assets are stocks. It just fails to describe important features of the data. To me, this ruins the value of work that uses it as a base.

Which important features are missing?

Fat tails, long-term autocorrelation, discontinuities in price changes, divergent variances.

Aside from missing those observable features of the data, the theory is missing much about market agents: herding and contagion, information asymmetries, slow convergence to equilibrium, non-normally distributed errors, heterogeneous strategies and objectives, interaction effects, confirmation bias.

I'm just repeating Taleb, and his mentor Mandelbrot, of course:

https://www.amazon.com/Black-Swan-Improbable-Robustness-Frag...

https://www.amazon.com/Misbehavior-Markets-Fractal-Financial...

Markowitz theory takes the asset means and covariances as 'given', whereas in reality estimating those quantities is extremely difficult.

Essentially, portfolio theory solves the easiest part of the problem, while leaving the hard bits as an exercise for the reader.

A hedge fund manager once told me: "The only free lunch in my business is diversification". Her fund imploded three years later. There is no free lunch and portfolio theory is an inadequate hedge against theta decay and mean reversion.

Diversifying using uncorrelated income streams is a good strategy, generally and there is actual math to show that you cannot significantly reduce risk by diversifying to more than ~20 streams.

Where could one read up more about this math showing you cannot significantly reduce risk by diversifying more than ~20 streams?

Unfortunately, I learned it on the job way back though I will keep an eye out of I see it.

I've also heard of using 30 (not 20) stocks as a sort of rule of thumb for sufficient diversification. I went ahead and looked it up though:

In 1970, Lawrence Fisher and James H. Lorie released "Some Studies of Variability of Returns on Investments In Common Stocks" published in The Journal Of Business on the "reduction of return scattering" as a result of the number of stocks in a portfolio. They found that a randomly created portfolio of 32 stocks could reduce the distribution by 95%, compared to a portfolio of the entire New York Stock Exchange. From this study came the mythical legend that "95% of the benefit of diversification is captured with a 30 stock portfolio."

http://www.investopedia.com/articles/stocks/11/illusion-of-d...

I would really read the rest of that link though, there's some good stuff in there.

This is about minimizing stock idiosyncratic risk, to capture market beta; there are many other asset classes one could put in a portfolio, diversifying the risks of market beta away.

The post said 20 uncorrelated income streams, not random stocks. Random stocks often have high correlations to each other.

Ben Graham and Buffett think diversifying increases risk. How well can you know one girl if your harem has thirty?

Statistical models are just models, not the real world.

Graham and Buffett are investors in the truest sense: they invest in the business, not in the stock. They deal with the managers directly. That is not what most of us do. That is why diversifying in such a situation increases risk: you only have so much mental attention.

No. Graham was a stock market investor. Buffett never bought a company till nearly 20 years into his career. Buffett and Munger believe in focused portfolios when you are investing in stocks, why put 5% into your 20th best idea when you can put 10% in your 10th best idea?

In reality most of us should not buy public equities, we should be in index funds.

Wouldn't that depend on the risk profile of those streams? There was a Bloomberg article a few weeks back showing that, like VC, hedge fund managers underperform the market because they tend to not be invested in the few outliers that are raising the mean.

Imagine hand waving here. This is from memory and there are certainly details missing.

Where can one find those elusive uncorrelated income streams?

Haha, I'd have my own fund if I was that good.

Are there any businesses that are a free lunch though? Most people lose money in finance, like tech startups and every other business I've seen where some of the people are making lots of money. Power laws at work.

You know what's even less conclusive than portfolio theory? Paul Graham essays and everything Steve Blank says.

There is no hedge against excessive leverage. Except of course being too big to fail.

She was playing options?

No. She ran a fund of funds.

you can't find safety in diversifying if it's also loading up on higher layers of fees.

You can't diversify a bad strategy, like selling cheap out of the money puts or picking nickels up in front of a steamroller with lots of leverage.

If you somehow have uncorrelated good strategies it's the best free lunch you'll get.

Heresay: A friend managed a hedge fund for a while. He said most of his peers didn't understand the math (the measures of volatility). Of course, I don't either; but I don't pretend I do.

The measures of volatility are backwards looking, and useless for the Buffetts of the world, who view volatility as opportunity, not risk.

Looking at the special features of technology investments is an interesting idea.

I do think this paper misses an opportunity by failing to model some of the more salient features.

I would be interested to see what the optimal strategy would be if 9/10 investments yielded 0, and 1 out of 100 yielded 100x.

Actually, the model should tune those parameters based on available data.

Now tell me the optimal investment strategy.

Portfolio theory is useless for the rare skilled investors. In fact it's dead wrong. If you are skilled you want to concentrate in your best ideas, and you want high variance to improve your purchase and sale prices.

If you leverage though, you better know portfolio theory math and your risk of ruin.

Nice cite, fun to think about, thanks. Will compare with NPV options based strategy proposed in Design Rules.

Design Rules, Vol. 1: The Power of Modularity http://www.amazon.com/dp/0262024667

1/n

Charts at the bottom on this page here show asset classes and their performance as a portfolio basket relative to the S&P which illustrates some of these points http://54.174.116.134/recommend/datasets/explore-trends.html

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