Wednesday, November 10, 2010

High Volatility Anomaly Needs More than Lottery Preferences

Last week I noted there are several reasons why people over invest in high volatility stocks: overconfidence, investors chasing extreme performers, winner's curse, cheaper information, alpha discovery, lottery preferences, representativeness bias, and signaling (many of these are related, but slightly different, as where signaling is related to investors chasing extreme performers, but there are different assumptions about what is exogenous). The bottom line is there are many factors 'outside the box' that skew the traditional mean-variance preferences, and researchers such as Baker, Bradley, and Wurgler (2010) and Robert Haugen have pointed out this may underlie the low returns to highly volatile stocks. As highly volatile stocks are risky by any metric--default probability, beta--this creates an anomaly that exists not only within equities, but corporate bonds, currencies, options, everything. This creates a major problem because if an equity premium exists due to 'risk', this risk does not generalize.

A consensus is forming that risk premia exist between asset classes, but not within asset classes due to two confounding effects: risk aversion and the investor preference for highly volatile stocks. This cannot stand as the sole explanation. If there's an equity risk premium between classes like bonds and stocks, but not within bonds and stocks, any investor in broad indices necessarily also holds a lot of the crappy high risk assets without any of the benefits. The benefits listed above work only for picking specific stocks or subsets of stocks.

As many sophisticated and large investors do invest in broad asset index strategies, how can this make sense? I think it is because people are inveterate benchmarkers. If risk is a return relative to what everyone else is doing, the indices are low risk. You can show this using a utility or arbitrage argument, but the idea is pretty simple.

While my argument in this vien has never made it into an academic journal, the idea is bubbling around in piecemeal applications. Abel (1990) first showed that a ‘keeping-up-with-the-Joneses’ utility function--one that defines itself relative to others--the equity risk premium would be smaller than otherwise. Gali (1994), DeMarzo, Kaniel, and Kremer (2004), and Roussanov (2010), all show how relative utility preferences can affect cross-sectional asset pricing, basically lowering the risk premium for highly volatile stocks, if not making it negative. These papers tend to be very qualified and parochial, but that's only because the status quo is too entrenched, so they take baby steps. Yet, a relative status orientation can be efficient for an individual, as modeled by Rayo and Becker (2007) or Pesendorfer (1995). The relative status utility function generates a more accurate description of the world, as people generally prefer to live in societies where everyone earns less but they earn relatively more, than in societies where everyone earns more but they earn relatively less. Adam Smith's seminal Wealth of Nations is as consistent with a utility function based on envy, as he is on one based solely on greed.

The preference for low volatility assets is not directly related to the relative utility preferences. The factors that lead one to highly volatile stocks are pretty independent from utility functions. It's just that the effect of this love for high volatility does not get arbitraged out because it's too risky. Shorting high volatility stocks is risky, and because of benchmarking, merely under weighting highly volatility stocks is risky too.

The bright side is, if you can trade your envy for greed, there's a simple way to create a better portfolio. An investor who prides himself on maximizing return relative to risk, and ignores the 'keeping-up-with-the-Jones' effects, would do well to invest in low volatility equity portfolios that avoid those lottery ticket stocks.


Anonymous said...

In a normal environment, I'd agree with you. However, I'm a poor but confident working guy with limited means trying to turn them into perhaps another year or two of survival for my family down the line in a turbulent, toppy market. I don't have the luxury of being able to sit tight and sip cognac while earning safe and reasonable compound returns on gigantic sums. I don't feel I have the luxury of much time to be patient. I'm trying to squeeze what crumbs I can find out of a dying economy as fast as I can. THOSE are some of the factors that skew me far away from traditional mean-variance preferences. They are the direct consequence and the very high price I have to pay for the failed high risks and unsustainable deficits that others took and ran up all throughout the past generation. I WISH I could take the approach you suggest and resent being put in a position where it won't work for me by all lousy speculators and crooked politicians and I could point fingers and name names if it came down to assigning accountability and culpability.

Ultimately, taking higher risks may not be a good strategy, but it is the only one that offers me the opportunity to achieve my financial goals given these parameters. I don't consider my high-risk investments to be lottery ticket stocks though I'm sure you'd call many that. For the most part, they're intensely researched, intensely managed, outstanding small caps that outperform the S & P by wide margins most of the time because I have no reservations about giving up on losers quickly and moving on to more promising prospects.

My YTD performance of 63% beats the shit out the investment house that's charging me a fee to work full-time earn to earn just 7% YTD on my SEP IRA using a safe approach. It's a very convenient rationalization not to compare one's results to the Jones until clients named Jones start showing up and pointing out that they're cleaning your clock. Why are mutual funds experiencing record multi-year withdrawls? Could poor performance and poor excuses have anything to do with it? You think?

So, I'm confident but NOT OVERCONFIDENT and recognize that
that it's smart and responsible to be hedged with your point of view by my IRA. Quite honestly, it sucks to be so smart. Relative to what I could be earning with that money, I've been screwed to the tune of tens of thousands of dollars. I only stick with it because the videos of the fund managers rationalizing why they should keep being overpaid to underperform the S&P and how difficult it would be to navigate turbulent times without them as if their clientele are complete nimwits provide some of the most humorous moments in my life. So, that's why I'll keep taking "wild" chances with my spare change in my spare time until it doesn't work anymore.

I'm very sorry for the rant, dude. Your article presents you as thoughtful guy and I just thought you might like to hear from a regular guy about what he thinks about some of well-healed, self-serving falderal that's passed off as sound investment advice out there in the blogosphere. No doubt I was wound up from a tough trading day (Chinese caps ARE volatile) and probably misheard or misinterpreted or misunderstood you. You didn't deserve this rant and I apologize and thank you for hearing out my perspective on the purpose and value of investing in lottery ticket stocks in my little corner of the world.

Best of investing to you.

paul b said...

Anonymous, I understand and agree with your frustration with the industry. your observations are spot on. and you motivations for taking "lottery bets" are "understandable." But they are still "sucker bets" and your trading is money going to the industry. there are no free lunches (except low vol portfolios ; )