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

Is Volatility Getting Cheap Again?

One of the indicators that I like to watch, if for nothing else than for entertainment value, is Barron's Investor Sentiment readings. Last week, depending on which indicator you look at, Bullish consensus ranged from 41.3% to 70%.

One of the questions I constantly want to be asking myself is whether the market is getting complacent, which I would argue is the primary cause of bubbles. I would posit that if the market starts to get too single minded, market efficiency starts to weaken and you start seeing opportunities to take advantage of the follies of other market participants.

Just looking at the way the Dow Industrial Average has been moving (i.e. in terms of scale of the movements), things seem to be quieting down in the market. The standard deviation of daily returns for the Dow Industrial Average has dropped from 2.38 percentage points (from the beginning of 2008 to the end of 2009) to 0.82 percentage points (YTD).

Even when you look at the Dow during a more "pleasant" period of time (mid 2003 to end of 2007), standard deviation of daily returns is 0.74 percentage points, not that much lower than where we are now.

But the key test for whether the market is getting complacent or not is to look at implied volatility. The most common metric for this, the VIX, does so by backing out volatility expectations from S&P 500 put and call options expiring in 30 days (CBOE methodology). When you look at historical VIX levels, the answer to this question is debatable.

Will the Future Be More like 2004 to July 2007 or 1992 to 1999?

These are the two times periods for which there is VIX data that I would call "good" for shareholders. What I was curious about was what the VIX level looked like during these periods.

For 1992 to 1999, you have a geometric mean of 17.03, arithmetic mean of 17.90, and standard deviation of 6.02. For 2004 to July 2007, you have geometric mean of 13.52, arithmetic mean of 13.71 and standard deviation of 2.35 for the VIX.

These are obviously very dramatically different numbers, and the most reasonable explanation for the higher values for the 1992 to 1999 period was the tech boom, and the volatility that that presented. That was a bull market the likes of which was unseen previously, so perhaps an expectation that that will happen again in the near future is foolish. So if you're looking at 2004 to July 2007 as the most likely market climate for the upcoming future, the VIX, which closed at 16.23 today, is still a little bit high.

That being said, 16.23 is the lowest level the VIX has closed at since December 10th, 2007. Depending on how you're feeling about the economy, now might be an interesting time to try and profit off of volatility underpricing.

Trading Strategies

The simplest option would be to buy futures on the VIX, or check out the VXX or VXZ, two ETNs managed by iPath (Barclays).

Another option would be to literally buy options on the S&P 500 to perform a straddle. This would be done by buying a put and call at the same strike price, presumably with the strike price at the current market price. Your hope would be (presuming strike price is market value on day of purchase) that the closing price on the day your option expires would be the strike price plus or minus the sum of the premiums paid for the put and call options.

I've also written another article on volatility: Getting Exposure to the VIX as a Hedge: Is it Conditionally Correlated to S&P 500 Returns? if you're interested in reading it.

Getting Exposure to the VIX as a Hedge: Is it Conditionally Correlated to S&P 500 Returns?

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I've uploaded the PowerPoint I just made for my presentation tomorrow for the Claremont McKenna College Student Investment Fund.

I was looking at the VIX, and whether or not having exposure to it might serve as a better-than-normal hedge for S&P 500 returns. My thought process was built on the assumptions that:

(1) Assets can be conditionally correlated (i.e. different events can result in different correlations between assets)

(2) In hedging against black swan events (statistically insignificant and unpredictable events that can cause financial ruin), the goal would be to ideally find assets that were uncorrelated to the market during sideways or bullish markets but highly-negatively correlated to market returns during market panics and sell offs.

You should read the presentation for my findings (note: the graphs used are from the Barclays prospectus for their VXX and VXZ ETNs and from Standard & Poor's website. I want to make sure I give credit where credit is due). In terms of my looking at the VIX, I tried to break up my time periods either based on significant market events (for example, the Bear Stearns bailout of their Sub Prime funds) or based on market bottoms or tops. It's somewhat of a mixed bag, but I feel like there's evidence, at least based on recent market history, to suggest that this conditional correlation is partially correct.

In terms of looking at what products to gain exposure to the VIX, I looked at Barclays' iPath S&P 500 VIX Short-Term Futures ETN (VXX) and the iPath S&P 500 VIX Mid-Term Futures ETN (VXZ). While the Short-Term VXX has more liquidity and is more highly correlated to the VIX (and this correlation is more statistically significant), based on the way the indices that both funds are based on move (as seen in the graphs from the Barclays' prospectus I mentioned earlier), I feel that mid-term index has offered a better risk-reward payoff since 2005.

I justify this largely by the fact that humans seem to extrapolate market panic in to the future and to be skeptical during the boom times of future performance. While this skepticism might not be evident in the asset markets themselves, I do believe you'd see it in the derivative markets to insure against these positions.

The expense ratio of 0.89% for both funds is a level I believe to be reasonable, especially faced with the impossibility of effectively creating a product like VXX or VXZ on the small scale for retail investors.

From the articles I've read on the two products, the major complaint that I've heard is that the ETNs don't accurately capture the daily changes in the VIX. While I'm sympathetic to these concerns, I think it's important to remember that you're invested in futures based on the VIX and not the VIX itself (which isn't actually possible). To me it's plausible that you'd actually have meta-volatility (i.e. the volatility of the VIX) impacting the pricing of the products. Also, because the products are looking at what the VIX is going to be at in the future, the day to day movements are less significant.

My final conclusion with the PowerPoint is that I would go long the VXZ. I was not able to get actual data for the index that it is priced off of however, so my statement is more based on the chart and my behavioral explanation for the reason it has outperformed the VXX in both the upside and downside.

Exposure to the VIX