re: Portfolio Theory Part I...
After reading through all of the comments from last week’s controversial posting I spent quite a bit of time this past week in attempting to better explain both the reasoning behind my accusations as opinions and the point in writing the article. It’s specifically in response towards Mr.Anderson, zacharydavid, and mikesswimn but I want to thank you all for you challenging comments.
Assumption of Risk-Aversion
I’m proposing that economic risk-aversion is one dimensional and that a person who invests in a safer certain sum over a potential higher riskier one also prefers more money to less which incentivizes risk-staking. Thus, not only are their risk-neutral but there risk-seeking investors, like performance-based arbitrageurs in Andrei Scheifer’s: Inefficient Markets? I argue that risk-seeking and loss-aversion can be mutually inclusive. Think about the risk premium, if a Markowitz portfolio is optimized for risk then should it not be constrained in its returns? In other words, this would not be a sufficient condition for risk-seekers (i.e. arbitrageurs) in my opinion and I think that this assumption defines market investment too restrictively.
Implications of Sigma and Risk
Glyn A. Holton’s, Defining Risk is an insightful article on this subject in the Journal of Finance discussing how risk and uncertainty are two different concepts. Risk is a measurable uncertainty (i.e. a known negative outcome) while an un-measurable one is simply called uncertainty (i.e. volatility or variance and that risk is related to objective rather than subjective probabilities, like statisitcs. Markowitz understood this in his model, as he stated,…variance of return is an undesirable thing” and yet he's careful not to say that variance is a proxy for risk as most believe. To the contrary, in his thesis under Footnote 7 he describes these probabilities as “in part subjective” and commented on constructing means and covariances. In other words, I don’t think sigma captures risk entirely and should be treated as uncertainty due to its subjective nature and its misnomer as a proxy for risk.
Historical Price Series of Assets
In my opinion, historical prices don’t reveal much truth about assets in the long-run, why? They are a random price series of Markov Chains in seemingly discernable patterns that emerge from our own inherent psychological biases. Further, David Hume proved that such inductive reasoning (i.e. observations of the past will continue into the future) are deductively invalid and it still holds to this day and any analysis can lead to Ludic and Texas Sharpshooter fallacies. More importantly, the drivers of price fluctuations in the data are lost and so is the context of the volatility. Yet, it seems that everybody is drawing useful conclusions using these methods and that’s because everyone is under the same misguided assumption that price histories contain useful information regarding the future. This leads to a similar outcome like the seeming effectiveness of technical analysis which has empirically been shown to be driven by psychological biases in a cause-and-effect manner.
Single Period Iteration
As far as a one-period iteration is concerned, I think it’s entirely academic. Using a single period to generate variance for past risk-return optimized portfolio is inherent with the problems from historical prices. I propose using an out-sample can provide secondary real-world testing in comparing actual versus modeled portfolio returns and optimizing it over time in an algorithm as mention by zacharydavid However, when forecasting for future returns without addressing cyclicality, serial correlation, and trends within the asset returns or volatility I find it insufficient to have a one-step risk-return adjusted portfolio going forward. Simply put, I think that an n-period model can provide more robust results than a single-period one.
The Misuse of Gaussian Distributions
It seems that at least on this point we’re all in relative agreement, that asset returns aren’t normal. Now I do realize that the Post-Modern Portfolio Theory addresses this as well as the problem of asymmetric risk however, normality is inherent in the assumptions that go into the statistics but yet we know it to not be the case. Then we don’t really have a useful result unless this is addressed and so in estimating portfolio variance, correlation, and asset return data one would would have to undergo an Anderson-Darling test to see if they are indeed normal. Keep in mid that this is no minor issue either as the correct distribution and statistics underlie the entire accuracy of the estimations for volatility and returns.
Bi-Variate Factors and Correlation
The compounding error that I am speaking of is simply the culmination of the issues that I’ve stated above. I will not comment on correlation as I will address in Part II in which Ias well as diversification and a possible alternative strategy.
My Conclusion
First of all, excuse me if I didn’t intially post this clearly as keeping it readable and explaining it well was a difficult challenge. However, the bottom line is these are only my opinions in which I have defended to evoke the community in thinking about MPT given new findings over the last 60 years and the entire point of this article was not for me to reveal some revolutionary portfolio management model but to challenge some of Markowitz's underlying assumptions. With that said I want to thank you for all of your insightful comments!
I take my word back that I look forward to post two. The whole post was a mess.
Are you taking a class on Finance Theory or something? I loathed studying a lot of this stuff but academic literature has obviously gone way beyond most of this. The assumption of risk-aversion is still fair and doesn't preclude the fact that investors seek to optimize portfolios for risk and returns. Single-period models are way old-school and much has been done since which goes beyond that assumption (Monte-Carlo, Black-Scholes...) The rest of the stuff has all been the subject of much econometric research and modeling.
Your initial "proposition" doesn't make much sense, and I'm not sure you just said anything there (i.e. that paragraph is entirely meaningless). Yes: risk-averse, risk-neutral and risk-seeking investors exist. No one argues that.
Like previously noted, Markowitz proposed a relationship between variance of returns and mean of returns. This is empirically untrue.
Again, variance isn't the only factor that defines risk, but it is a factor. Over time the Markowitz portfolio has become known as a relationship between risk and return versus variance and mean, but your nitpicking about risk doesn't add any value to the conversation and certainly says nothing about Markowitz.
This is entirely false. We can demonstrate the out of sample predictive power of momentum even with your misinterpretation of David Hume.
"Drivers of price fluctuations" are present in the data but my not be discernible from noise. This is why we use metrics like Sharpe, which is a basic Signal-To-Noise ratio.
What are you trying to say? I apologize if English isn't your first language, but there isn't a cohesive thought in here.
I think it would serve you much better to do more research into these "opinions" of yours rather than trying to start the conversation. You simply don't know enough yet.
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