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).