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, one of the most valuable parts of the book is the authors' separation of humans as they behave in economic models and as they behave in real life. TL;DR: quite differently.

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

The Selection Bias in Goldman's Argument Against the Obama Regulation

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The proposed Obama regulations that I'm referring to are the statements that came out today that he would:

"seek to prevent banks that have special access to low-cost Fed funding from operating or investing in hedge funds, private equity funds, or trading purely for their own benefit in a way that’s unrelated to serving customers." [Bloomberg]

While this is sure to be contentious, I think it's important to take a step back and look at what especially discounted Fed funding is intended for. I'm not talking about the funding that the Fed provides during a "business as usual" scenario, but in scenarios such as this recent credit crisis, when the discount window's possible term length was raised to 90 days and interest rates slashed, the goal was presumably to get some emergency liquidity out there to try and unfreeze credit markets and stimulate lending again.

I won't try to quantify the potential for ruin that hedge funds, private equity, and proprietary trading might potentially represent to a bank, although this is certainly possible. If the goal is to stimulate lending, however, having all these components as parts of banks that have the discount window available to them would make it difficult to monitor where these emergency funds might be going once they leave the Fed. While these other activities no doubt have the potential to be economically important, I don't think there would be significant objection that the Fed's primary objective in a crisis, is to funnel funds to firms that are going to use that money to lend and keep credit flowing, might be hindered if these funds are instead going to any number of other activities available to some of the firms that received emergency Fed funding.

This leads to the Goldman comments coming from Chief Financial Officer David Viniar. He argued:

"If people are focused on things that caused, or were real contributors to the crisis, it wasn’t trading...Most trading results were actually pretty good, not just at Goldman Sachs but at most firms and that’s not really where the problems were." [Bloomberg]

Looking at the results of trading from the crisis as a sample of typical trading is a vivid example of selection bias. It seems that Viniar would like us to think that because most trading was profitable during the crisis, it will be profitable in the future and doesn't doesn't pose systemic risk to banks. While on average trading profits might be positive, that says nothing for the skewness and kurtosis of trading profits/losses. By that I mean that proprietary trading could be negatively skewed or with fat tails (positive kurtosis) in the negative end of the distribution.

This is an example of a positively skewed, positive kurtosis, positive mean distribution. While it will be on average positive most of the time, the long negative tail creates the possibility for financial ruin when returns end up in that part of the distribution.

I'm not going to take sides on this issue, since I can see the validity in both. That being said, I think that Vinair's argument regarding proprietary trading is mistaken. For example, while fund managers can on average beat the market by holding a portfolio of the S&P 500 and writing puts (insurance against a fall) on the S&P 500, when it does go bad, it's ruinous. This is the "picking up nickels in front of a steamroller" scenario.

While I don't claim to know the distribution of trading profits or the absolute level of risk these firms are taking on (they might not know either), I can understand why Obama and his administration would want to prevent artificially-lowered interest rates from fueling these types of activities. Especially since it's meant to stimulate lending, allowing firms that have access to the Fed's discount window to engage in hedge funds, private equity and proprietary trading could be a usage of funds not best for unfreezing financial markets.

That being said, Obama needs to be careful when he talks about "curbing excessive risk taking". Lending to small businesses is one of the riskiest types of loan a consumer bank can do, and since stimulating the flow of credit to areas of the economy such as this seems to be an Obama administration priority, curbing risk taking shouldn't be his goal.