7 ms·

How standard portfolio theory changes when assets are technologies

105 points by mrleiter 9y ago

erikstarck 9y ago
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."
- tinco 9y ago
  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?
  - AnimalMuppet 9y ago
    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.
- dmichulke 9y ago
  > 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?
  - qubex 9y ago
    No. This is high sensitivity to parameters. Chaos is ergodic behaviour.
    - andreareina 9y ago
      From https://en.wikipedia.org/wiki/Chaos_theory 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.
      - qubex 9y ago
        Sensitive dependence on parameters ≠︎ sensitive dependence on initial conditions
jtraffic 9y ago
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.
- Chris2048 9y ago
  Which important features are missing?
  - jtraffic 9y ago
    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-Fragility/dp/081297381X/ref=sr_1_1?ie=UTF8&qid=1494426362&sr=8-1&keywords=the+black+swan https://www.amazon.com/Black-Swan-Improbable-Robustness-Frag... https://www.amazon.com/Misbehavior-Markets-Fractal-Financial-Turbulence/dp/0465043577/ref=sr_1_1?ie=UTF8&qid=1494426381&sr=8-1&keywords=misbehavior+of+markets https://www.amazon.com/Misbehavior-Markets-Fractal-Financial...
  - soVeryTired 9y ago
    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.
rrggrr 9y ago
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.
- cheez 9y ago
  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.
  - kovek 9y ago
    Where could one read up more about this math showing you cannot significantly reduce risk by diversifying more than ~20 streams?
    - cheez 9y ago
      Unfortunately, I learned it on the job way back though I will keep an eye out of I see it.
    - frgtpsswrdlame 9y ago
      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-diversification.asp 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.
juskrey 9y ago
1/n
iliconvalleys 9y ago
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 http://54.174.116.134/recommend/datasets/explore-trends.html
inputcoffee 9y ago
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.
ericjang 9y ago
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.
- fnbr 9y ago
  > 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.
- soVeryTired 9y ago
  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_risk https://en.wikipedia.org/wiki/No_free_lunch_with_vanishing_r...
specialist 9y ago
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 http://www.amazon.com/dp/0262024667
valuearb 9y ago
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.

105 points by mrleiter 9y ago

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."

tinco 9y ago
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?
- AnimalMuppet 9y ago
  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.
dmichulke 9y ago
> 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?
- qubex 9y ago
  No. This is high sensitivity to parameters. Chaos is ergodic behaviour.
  - andreareina 9y ago
    From https://en.wikipedia.org/wiki/Chaos_theory 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.
    - qubex 9y ago
      Sensitive dependence on parameters ≠︎ sensitive dependence on initial conditions

jtraffic 9y ago

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.

Chris2048 9y ago
Which important features are missing?
- jtraffic 9y ago
  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-Fragility/dp/081297381X/ref=sr_1_1?ie=UTF8&qid=1494426362&sr=8-1&keywords=the+black+swan https://www.amazon.com/Black-Swan-Improbable-Robustness-Frag... https://www.amazon.com/Misbehavior-Markets-Fractal-Financial-Turbulence/dp/0465043577/ref=sr_1_1?ie=UTF8&qid=1494426381&sr=8-1&keywords=misbehavior+of+markets https://www.amazon.com/Misbehavior-Markets-Fractal-Financial...
- soVeryTired 9y ago
  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.

rrggrr 9y ago

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.

cheez 9y ago
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.
- kovek 9y ago
  Where could one read up more about this math showing you cannot significantly reduce risk by diversifying more than ~20 streams?
  - cheez 9y ago
    Unfortunately, I learned it on the job way back though I will keep an eye out of I see it.
  - frgtpsswrdlame 9y ago
    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-diversification.asp 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.

juskrey 9y ago

1/n

iliconvalleys 9y ago

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 http://54.174.116.134/recommend/datasets/explore-trends.html

inputcoffee 9y ago

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.

ericjang 9y ago

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.

fnbr 9y ago
> 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.
soVeryTired 9y ago
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_risk https://en.wikipedia.org/wiki/No_free_lunch_with_vanishing_r...

specialist 9y ago

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 http://www.amazon.com/dp/0262024667

valuearb 9y ago

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.