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
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