Are Almost All Investors Biased?

The data suggest, yes almost all are.  But there’s another interpretation, mainly, that people mistakenly apply a rule of thumb (higher risk-higher return) to areas where it doesn’t, and can’t, hold.  Let me explain.

Risk that can be diversified away does not generate returns in theory (see the CAPM ) or practice (see Ang, et al ).  That is, taking more of this risk does not imply a greater average return.  Given the general massive lack of diversification, the only conclusion is that most people think they can pick stocks or funds that will rise more than average. They must be wrong (on average investors are average), but they are the vast majority of investors.  Thus the traditional theory of mean-variance optimization is more prescriptive than descriptive, in that most people are not rational about their forecasts, they are biased upwards in an area of proficiency that seems to be more costly than trivial overestimation of one’s driving ability.  How can this massive delusion be an equilibrium? 

First, the evidence of suboptimal diversification.  From a mean-variance perspective, an optimal portfolio is well diversified, with literally hundreds of stocks underlying a portfolio, most cost efficiently implemented via an ETF or mutual fund.  One may add that diversification into real estate and other countries is optimal, but we can assume that frictions or ‘bounded rationality’ prevent that, and just look at the optimality of a long-only equity portfolio.  As opposed to owning hundreds of stocks, Goetzmann and Kumar (2001) and Polkovnichenko (2004) found the median number about three, not much different than what the Fed reported from a 1967 survey.  So compare an average S&P500 annualized volatility of 15%, with a portfolio of three stocks has an annualized volatility of 22% (assuming an average annualized vol of 34%, and an average correlation of 0.12).  If one is maximizing a Sharpe Ratio, and assuming an equity premium of 6%, an investor maximizing his return over the risk-free rate divided by the standard deviation (the Sharpe Ratio) would need an extra 2.8% return on his picks for this to be rational, so the average investor thinks his stocks return an average of 3% more than the average stock (of course, this is made more complicated by differing transaction costs, the marginal nature of a stock portfolio to one’s wealth, but these other effects are offsetting and the basic logic applies without loss of generality).  Goetzmann and Peles (1997) find that individuals overestimate their own investment performance by an average of 3.4%, so they have biased corroboration of their ability to pick stocks. 

It has been long documented that mutual fund do not outperform passive indices, yet mutual funds that clearly offer less diversification and higher expenses than alternatives like passive S&P500 funds are still a large investment class.  People–retail and professional–clearly think they have some kind of edge, or alpha. 

Now the answer, actually, two answers.  The first is that it is not an equilibrium, as suggested by the continued growth of passive indices as an investment class.  People have been moving away from active management as information about passive indices has grown with experience, and perhaps this growth will only end when informed agents generating above-market returns are the only active traders in the market.  The second answer, the proof I can’t fit in the margins of this blog post (heh), is that risk taking as a general strategy does generate above average returns, but only in domains that are not zero sum.  For example, my investment into a sole-proprietorship is not necessarily zero-sum, I can create value. My investment into a firm via a private-equity placement is not zero-sum because I often receive warrants, options, or rights that are basically an exchange for special financing at the expense of existing shareholders: my investment adds value to the asset, not merely capital, and I capture that value via off-balance sheet contracts. 

When I think of the wealthy people I know, most have built their wealth this way, investing in parochial situations where they captured value via non-straightforward means.  It doesn’t show up in the data–either aggregate stock picking prowess, or the returns to entrepreneurial investment–because there aren’t any good databases with these types of contracts, which are not standardized, and for public equities often not fully documented in the 10-ks and 10-Qs.  Further, people have an incentive to under-report these assets because 1) they would be taxed 2) dissemination would incite the other claim holders who are expropriated and 3) people like to think they generate higher returns through proficient selection, and not from mere better negotiating. The dataset of this type of information does not exist, and it is quite understandable why.  The best empirical support I can give comes from the work of Susan Chaplinsky at Dartmouth, who finds PIPE (Private Investment in Public Equity) investors outperform existing investors by a substantial margin, generating large returns even though the average stock underperforms subsequent to a PIPE offering.  Where are they getting this excess return?  Primarily warrants and rights, because without these PIPE investors would be losing money year after year, while PIPE investors within hedge funds in aggregate make decent returns (ie, you have to add the warrants and rights to have this make sense).  People merely mistakenly apply the risk-reward notion to zero sum arenas, so they mistakenly apply this to areas where it is mathematically impossible, such as me merely buying your existing IBM shares. 

Thus, I posit the theory that risk is compensated by return, but only in areas that are non-zero sum.  When investors merely buy existing claims from each other, they are engaged in overconfidence (see Milgrom-Stokey’s No Trade Theorem ).  People self-select into non-zero sum situations based on their informational advantages and above-average ability, and on average prosper accordingly.  Thus you need not only a high tolerance for risk, but moxie, because it takes energy and negotiating prowess to create and capture these non-standard options from one’s investments.  They are active investments even if the activity is merely in the negotiation of rights. 

While rich people are usually somewhat fortunate, there is an element of skill or ability that suggests it is more than mere tolerance to volatility that is driving their wealth growth rate.  That is, while the CAPM would suggest that the only difference between a large group of investors to outperforms the average is their luck and risk tolerance, I think it is reasonable to think this is not the whole story.  I can’t prove it, but the alternative, that risk is everywhere uncorrelated with risk, is simply too irrational to bear (an assertion in Keynes’ General Theory).   That mere idiosyncratic risk is clearly not compensated is in stark contrast to the behavior of most investors who are massively undiversified, and  even systematic risk appears non-compensated (see Why Risk is Not Related to Returns by yours truly).

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  • Byrne

    Does financial return explain investor behavior, though? It sounds like your unstated premise is that investors are trying to maximize their Sharpe ratio — I think it makes more sense to realize that they’re also maximizing their psychological well-being.

  • Eric

    I actually deviate from the traditional mean-variance utility function in the linked paper on Risk and Return, but in general try to stay in this constraint. If you are suggesting mean-variance-“x” preferences, where people like/dislike some attribute “x” when investing, it would be interesting to document such a characteristic, and then target it, either by marketing to retail that “you won’t pay for our lame attempts to confabulate” or to institutions (e.g.,”short stocks that go green”)

  • Keith Elis

    Thanks for this post.

    You wrote, “As opposed to owning hundreds of stocks, Goetzmann and Kumar (2001) and Polkovnichenko (2004) found the median number about three, not much different than what the Fed reported from a 1967 survey.”

    This is so far from what I would have guessed, I don’t even know what to say. I would have guessed that a huge fraction of those who own stock own it by way of mutual funds in qualified plans — hundreds of stocks.

    The use of online brokerage accounts as a data set in the Geotzmann study may be skewing this result downward. It’s not clear from the abstract where the other study pulled the data. Still, a surprising fact.

  • Kevembuangga

    This may seem off topic but in order to meaningfully participate I would like to know what “overcoming bias” is about, I mean WHICH bias?
    In other words how do you define an truly circumscribe the “no-bias” condition?
    Because if you can’t all this is just another fluffy “philosophical” smalltalk.

  • genetrix

    The statement that well diversified portfolios according to mean-variance optimization consists of hundreds of stocks (besides some portion invested in the riskfree rate) is wrong i guess, its explained by the law of diminishing returns. Most portfolios of professional investors and fund managers only have like 10 or 15 stocks in them and still being on the efficient frontier (Markowitz).

  • eric

    First, as to Goetzmann and Kumar noting only 3 stocks, these were for equity portfolios that seemed to exclude funds. They noted that something like $9k was the average individual mutual fund, and $13k was the average individual equity portfolio. So the equity volatility was in that context, making things tricky.

    As to 15 stocks being sufficient, I think that’s if things are stable and gaussian. In practice, 15 isn’t nearly enough because when it really matters–downturns–correlations rise predictably, so an average correlation of 0.12 based on daily vols is probably off by a factor of two. I find, personally as a portfolio manager, that 100 is necessary to get ‘asymptotic’ volatility for any one country (ie, comparable vol to an index), and that assumes you are not loaded in one industry or some factor (eg, momentum).

  • zzz

    The second answer, the proof I can’t fit in the margins of this blog post (heh), is that risk taking as a general strategy does generate above average returns, but only in domains that are not zero sum.

    Could you clarify what you mean by “domains that are not zero-sum”? If I’m providing an insurance service, is this a “zero-sum domain”?

    Risk-taking should generate excess return unless the risk can be diversified away: clearly this isn’t the case for private-equity placements and other non-standard investments.

    Real estate investment is one domain which is arguably “zero sum” and hard to diversify for most people – at least until recently. Historically, it seems that those investors who were wealthy enough to diversify their investment could earn excess returns.

  • eric

    Well, its a rather inchoate concept in my head, but basically, a non-zero-sum game is where you create rights. When you buy a stock and some warrants that are already trading, you are in a zero-sum game, because you are merely buying what already existed and was priced fairly (on average). So buying listed securities, or passively buying someone’s hot dog stand, are all zero-sum. Buying unlisted securities and negotiating rights to buy more at a fixed price, buying a hot-dog stand but then deciding to sell lemonade as well, that’s non-zero sum. So the extra value can come from expropriation (demanding rights and warrants that dilute existing claim holders–usually because they are desperate) or value creation (providing complimentary services). The key is, you need a lot of capital to be able to demand rights and warrants, so for most investors that’s not feasible. As per providing value no one thought of for existing small operations, that’s more feasible, but again, it’s nontrivial in terms of resources or effort.


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