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Adversity and the Variance Premium

Recently I’ve come to believe that we don’t know nearly as much as we think we do. Specifically the history of markets is nowhere near as big as we often assume. For example, equity options have only been traded in liquid, transparent markets sine the CBOE opened in 1973. S&P 500 futures and options have only been traded since 1982. The VIX didn’t exist until 1990 and wasn’t tradable until 2004. And the average lifetime of a S&P 500 company is only about 20 years. 

This might seem like a decent length of history that we can study and look for patterns in. But I doubt that it is. I think that while there appear to be many thousands of data points, there might only be dozens. Options and volatility wiggle around a lot but their long-term values are related to macro variables such as inflation, monetary policy, commodity prices, interest rates and earnings. And these change on the order of months and years. Even worse, they are all co-dependent.

I think this makes quantitative analysis of historical data much less useful than is commonly thought.But there is something we can rely on: human nature.Humans have been essentially psychologically unchanged for 300,000 years when Homo Sapiens first appeared. This means that any effect that can conclusively be attributed to psychology will effectively have 300,000 years of evidence behind it. This seems to be potentially a much better situation.

The problem with psychological explanations (for anything) is that they are incredibly easy to postulate. As the baseball writer Bill James said, ‘‘Twentieth-century man uses psychology exactly like his ancestors used witchcraft; anything you don’t understand, it’s psychology.’’ The finance media is always using this kind of pop psychology to justify what happened that day. “Traders are exuberant” when the market goes up a lot; “Traders are cautiously optimistic” when it goes up a little etc. I think psychology can be incredibly helpful, but we have to be very careful in applying it. Ideally, we want several psychological biases pointing to one tradable anomaly and we want them to have been tested on a very similar situation to the one we intend to trade.

My new project is that I attempt to formulate linkages between behavioral psychology and volatility.
The most developed idea I have is about regret, the emotion that most dominates my trading. Trading is regret; either that winners weren’t bigger or that losers existed at all.

A paper by Daniel Grosshans and Stefan Zeisberger, “All’s Well That Ends Well? On the Importance of How Returns Are Achieved”, shows that investors don’t only care about returns but also care about exactly how their returns were realized.    

They performed surveys that asked people to imagine that they had six stocks. Three made 10% and three lost 10%. But each of the three had different paths: either, up-down, a linear path, or down up. These are shown stylistically in Figures One and Two.

Figure One: The three different positive return paths.

Figure Two: The three different negative return paths.

For both winners and losers, the participants were happiest when prices first declined then rose. People were even slightly disappointed when stocks rose then fell but were still winners. People are happiest when they feel that they have recovered from adversity, snatching victory from the jaws of defeat. Although this is only survey data I think it captures a general feeling among investors.

I think this directly leads to a new explanation of the variance premium which I'll write up in the next few days.


  1. wow, guess I'm not typical...
    .... for the stylized positive paths i'd much rather have the orange or blue path than the grey path ... after all, i'm always "up" ... even if i gave some back on the orange path i'm always up relative to the start

    how can the gray path be preferable to paths where your results are always positive relative to the starting investment?

    1. First, it is no secret you aren't typical...
      But I don't really have any justification for their results. They did a survey and this is what they found. The evidence is far from overwhelming but it is there. And obviously this was a majority opinion rather than a unanimous one.

    2. I suspect that preference of always being "up" is predicated on viewing this as one trade among many....because then your experience the entire time is one of "which category is this trade in? Look it's a winner! I feel good about my trade." But if it's a one-shot gamble, as I suspect most survey participants would conceive of it, then you are comparing each state to the prior state only.

  2. it would also be interesting to see if one noticed a difference for time series momentum stocks.

    i.e. of the top quintile of time series momentum stocks, (a.k.a. positive momentum stocks) do the ones that have demonstrated a "down then up" pattern subsequently outperform, (or underperform?) the "up then down, but not so down that theyve fallen out of the top quintile" subset of stocks.

    and, of course, inversely vice-versa (wait, is that a double negative?) for the negative time series momentum for the bottom quintile of stocks

    1. yeah, there is definitely some link to momentum. i'm not at all sure what but momentum and reversals always have a link/tension.


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