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The Role of Investor Selection Bias In Volatility Levels
This article is the second in a series of three articles investigating volatility as "the" measure of risk. To read the first article, "A Thought Exercise: Is Volatility Really an Asset's Risk?", please click here.
In Richard Thaler and Cass Sunstein's Nudge: Improving Decisions About Health, Wealth, and Happiness
In the realm of investments, financial scholars have largely described investors in their models as being essentially the same while retaining varying inherent risk appetites. In a world where more risk is rewarded with more return (an issue I will address in the third article), this makes sense: some people are willing to risk more to make more, and vice versa.
This is where the "Econ" (human as they behave in economic models) vs. "Human" (human as they actually behave) dynamic that Thaler et. al. introduce becomes relevant. The first important difference between the financial model human and the actual human is the tendency to benchmark with assets, leading to a world where payoffs are expressed as relative to a basket of securities such as the S&P 500 (this is exactly how the Motley Fool ranks their participants). In a paradigm where indexing is rampant, perceptions of risk are strongly different than what modern financial theory would lead us to believe.
The second difference is a strong preference for relative wealth: i.e. a level that places one ordinally higher than others. This has been seen in game theory experiments where participants preferred lower absolute payouts that were higher relative to other participant's payouts (i.e. $40 and everyone else getting $20 versus $70 where everyone else gets $80). This further leads to a logarithmic preference scale as you compare the 1st to 2nd, 50th to 51st and 99th to 100th percentiles of wealth. The change in the number of people you are now better off than in the first interval is much higher than the third interval, suggesting that the risk you'd be willing to take in the first instance (i.e. to jump from the 1st percentile to 2nd percentile in terms of wealth) would be much higher than in the third interval.
To change the interval size, and now look at the change from 1st to 75th percentile in relative wealth demonstrates why lottery payouts are so popular, even though from a high level perspective they're effectively like throwing money away (your probability adjusted return is less than the initial capital outlay). They represent the greatest possible delta in relative wealth for the least cost.
High Volatility Stocks: Another Form Of Lottery
This translates to a preference for assets with high volatility, which in conventional terms are seen as the riskiest/most lottery-like. Authors such as Eric Falkenstein have covered this relationship rather extensively, but as it pertains to volatility as a measure of intrinsic risk I would like to go a step further. In our market, investors searching for these lottery-like payouts are going to go in search of assets with already high volatility. In this scenario, volatility is going to beget more volatility, as more lottery seekers pile in. The lottery seeker, by preference for the highest relative wealth delta for the lowest cost, is going to prefer the assets with the highest ordinal ranking in terms of potential payout. This would lead these investors to dramatically favor, say, the 10th decile of assets in terms of volatility over all other assets.
Why is this a problem for volatility's connection to risk? The key is the self-selection going on when picking assets. If the lottery payout seekers had a slope to their preference, this might still plausibly lead to an efficient market where volatility measures intrinsic risk of an asset, as the lottery seekers become more concentrated in higher risk assets. But the preference for the highest risk stock in ordinal rank is going to lead to a disproportionate asset allocation, leading to a breakdown in volatility in its connection with risk.
The final article in this series will serve as an exploration in to the problems with the risk/return correlation
A Thought Exercise: Is Volatility Really An Asset's Risk?
Over the next three articles (this article being one of them), I will be covering why I believe volatility comes up wanting as a proxy for risk.
Throughout a classic education in finance and economics, one core concept that became an assumption of my daily life was that volatility was risk. To a certain degree this intuitively makes sense: if I'm buying an asset, and I have little sense what its value is going to be in an hour or two days from now, I should buckle up because it's going to be one hell of a ride.
In a relatively preset environment, volatility would certainly approximate risk. For example, if we were to live on Mount Kenya as a subsistence farmer, where mean daily fluctuations of temperature equate to 11.5 degrees Celsius (20.7 degrees Fahrenheit), this could surely be seen as one approximation of the risk of being able to generate a successful crop, although another might be seasonal weather fluctuation, such as that seen over a year. Still another would be fluctuation in weather over several years. Thus these three time spans (daily, seasonal and yearly) of weather fluctuation could probably closely approximate your risk of survival (of course there would be others: see bears).
So why might a security's volatility not closely approximate its risk? One answer would be the failure to translate observed volatility to actual volatility, although we would certainly run in to this problem when observing weather. The other problem would come with what this volatility actually represents. In the case of weather, it is the state of our atmosphere, something far beyond our control (although the aggregation of humans is doing a pretty good job: see climate change)
Is An Individual Investor Equivalent to a Subsistence Farmer?
In an asset market, for volatility to approximate "risk of survival" like it does in the natural world, it would have to retain some key characteristics:
The Human Compulsion to Seek Short-Term Patterns When Investing
To read this article in its original format, please click here
One of the details I always comment on when I am reading articles is the inclusion of 'technical analysis' or other types of short-term price prediction based on patterns. It takes a lot of different forms, some as simple as merely looking at charts (i.e. past prices of the stock graphed with time on the x-axis), and others slightly more sophisticated (read: 'mathier'). I have seen citations including Fibonacci retracement, Bollinger Bands, and of course the common 50 day and 200 day moving averages, all interpreted to derive many a different conclusion.
Typical technical analysis mumbo-jumbo
Moving averages can be informative for one's first cold look at a stock: comparing them to the security's current price more or less gives you the market's impression of the company or security. This information can also be generally gleaned from the price relation to 52 week highs and lows and stock analyst buy/sell ratings.
Beyond that, however, I see technical analysis as market tomfoolery. It is an attempt to see patterns in short-term price movements, that depending on which theory you subscribe to, can be more or less random.
The random walk theory is the classic economic perception that because markets are efficient, prices are going to follow a random walk. Here is some analysis that attempts to separate the efficient market theory from the random walk theory. In essence, the idea is that prices are explained by successive random steps in any given direction. The third link above is important because I think it reconciles the fact that a random walk can only coincide with efficient market theory if the random walk is to be short-term noise while eventually leading to the efficient market price. This of course would not support a very rigorous version of the efficient market hypothesis (EMH).
While I subscribe to a weak version of EMH, I do not necessarily believe in the random walk theory, at least in the long term. I do believe that it could explain bubbles and short term market mispricings, but in my opinion these could be better explained with behavioral finance or simply by variance around an 'accurate' price. I find behavioral finance to have more explaining power due to a presumption by a great deal of the statistical analysis in investing that markets are 'cold' and that decisions are being made by efficient automatons and not by humans (Nudge: Improving Decisions About Health, Wealth, and Happiness
provides an excellent framework for understanding the difference, except where I use 'efficient automatons' they use 'econs'). Behavioral finance provides a way of explaining mispricing in the market based on human emotion and the way we perceive.
Does that mean that market participants using statistics have not been successful? Of course not. One of the best success stories I have heard of is the hedge fund Renaissance Technologies, which according to their wikipedia page has averaged a 35% annual return after expenses and as far as I know has never had a losing year. Because hedge funds are such black boxes, it is difficult to understand how Renaissance is truly making money and I am not sure how to address them as a phenomena in the short-term trading sphere. Note: there are also a large number of high-frequency trading (HFT) rigs that use some sort of fundamental or technical indicator, but I have yet to see conclusive evidence that technical trading like this can make money over a longer time period.
The question will always be whether it is not the pattern but rather some fundamental idea being observed through the pattern that is what is making money. Instead of simply finding more complicated mathematical techniques to observe the pattern as it is seen through market prices, perhaps a more effective methodology would be to understand what is causing that event.
On the frontier of simply statistical analysis, Bruce Babcock suggests that over the longer term markets trend after you have looked past short-term noise, and suggests using chaos theory to understand it. This to me seems more plausible than patterns in the short-term, however once again I think it could be better explained by behavioral finance.
Considering the relatively small amount of market data we have to pull from to make statistical assertions lends one to reject a 'patterns for the sake of patterns' investment style. Sample size limitations and a lack of fundamental reasoning for why prices should behave in any given pattern leads me in the end to reject the notions provided by Babcock. While it could be successful as a trading strategy, without any underlying reasoning why prices should adhere to a given pattern might suggest that any given 'trend' he is observing could be better explained and modeled using some other methodology. I am of the persuasion that behavioral finance, while still in its infancy, offers the best methodology for explaining long-term price variance and that the way human emotions interact with capital markets would be the only effective way of attempting to predict future market prices.