Why Risk is not Related to Return

By: Eric Falkenstein
Published: February 28, 2007

Hat tip to the CXO Advisory blog for bringing this recent paper to our attention. It’s an interesting addendum to our posting on beta arbitrage last month. As you may recall, Tuomo Vuolteenaho, a Harvard prof moonlighting at ArrowStreet in Boston said that high beta stocks didn’t actually provide the higher returns that CAPM would suggest. As a result, he said, an investor should short high beta stocks and go long low beta stocks.

This paper (written by a mysterious author from a suburb of Minneapolis who is listed in SSRN – a database of academic papers – as having “no affiliation known“) argues that this apparent paradox can be explained by a human desire for relative, as opposed to absolute wealth – what the author calls “relative status”. This is an innovative way to approach the CAPM conundrum since it essentially mixes traditional financial theory with recently topical “happiness” research.

Falkenstein lays out the paradox:

“It is puzzling that risk, when measured directly, is rarely positively correlated with higher average returns. Nevertheless, CAPM remains a pillar of finance curriculums, and most economic models assume a positive variance-return relation adjusted linearly by a positive risk aversion coefficient. Bill Sharpe probably speaks for most economists in saying that in spite of empirical difficulties, ‘it would be irresponsible to assume that [the CAPM] is not true…’”

His explanation is that investors don’t necessarily view higher volatility as being more or less “risky”. Instead, their definition of risk is based on how far they are outside the bounds of what is deemed to be generally acceptable in their peer group.

As a former hedge fund marketer, this makes sense to me. While hedge funds obviously have a higher idiosyncratic risk than most long-only funds, their actual volatility is often much lower than the market’s. So it always amazed me when risk averse investors opted for an equity ETF rather than a diversified fund of hedge funds because the ETF was perceived to be more conservative. My grandfather managed money in the 1950’s when “playing the market” like this was just about the most risk-loving thing an investor could do. So why on earth would investor’s perceive the market portfolio to be less “risky”?

This relativism also revealed itself to me once when I attended a lecture given by former US Labor Secretary Robert Reich on international trade at business school. Reich asked the group of (rational, utility-maximizing) MBA students assembled in front of him whether they would prefer that US producers make $10 billion in a bilateral trade deal while the other nation made $20 billion, or if they would prefer that US producers make $5 billion while the other nation made only $1 billion. Well, you can guess the answer. The majority of students balked at giving up $20 billion to a negotiating counter-part, and opted for a lesser pay-off that was at least going to trump the other nation.

The common thread here is a deep-seated human tendency to value relative status over absolute wealth. The Economist ran a front page story a few months ago on “happiness”. It said that while GDP per capita continues to grow around the world, but “happiness” does not. Notwithstanding valid arguments that researchers often don’t properly define the term, the conclusions are irrefutable: People are happy as long as they have a similar material wealth as their peer group.

Falkenstein argues that this desire to stay close to the pack makes idiosyncratic risk far more undesirable than systematic risk. He describes this self-reinforcing process the following way:

“If people start taking on more of a certain type of asset, these assets become, in this model, less risky. In fact, staying up-to-date on popular investment ideas is not irrational or faddish, but efficient from an individual’s point of view. For example, index funds were initially considered ‘risky’ in the sense that they precluded one from the large gains potentially available to less diversified portfolios.”

“After a generation of experience and growth in popularity, not investing in an index fund is considered the risky choice. This highlights the perhaps underappreciated value of history in finance, in that any new asset class is by definition risky to the early investors in this model. They must have been motivated by expectations of above-average returns, which are objectively measured ex post. Therefore examples of perceived risks that were—with the benefit of hindsight—erroneously optimistic or pessimistic can serve as analogies for understanding risky decisions in our time (are hedge funds risky?).”

Falkenstein even suggests that the desire for relative social status might be a hard-wired biological trait of human beings – developed to ensure successful procreation.

He also says that “enterprise” itself is a form of idiosyncratic risk-taking driven by a desire for relative status (a.k.a. ” getting rich”). Keynes, Falkenstein points out, said “if the animal spirits are dimmed and the spontaneous optimism falters, leaving us to depend on nothing but a mathematical expectation, enterprise will fade and die.”

For an example of such irrational risk taking – guaranteed to fail in the aggregate – look no further than restaurants. How many times have we heard about the abysmal success rate of small restaurants? Yet they continue to flourish.

Better yet, how about mutual funds? While in aggregate, mutual funds produce negative value, our desire to achieve excess relative success always ensures a steady flow of investment (what Falkenstein also describes as “overconfidence”).

If a hedge fund – as we have argued on this website – is really nothing but the residual over- and under-weights relative to a benchmark, then Falkenstein might argue that hedge funds actually have more risk than, say, ETFs, even if both have the same standard deviations).

“A risky investment is a function of an asset’s weighting in their portfolio relative the market, not its objective characteristics. Investing decisions create angst because people are constantly worried that their risk-taking reflects poor judgment.”

This paper is quite interesting. If you have a few hours to kill over the long weekend and want to think about the big picture, it’s highly recommended.

- Alpha Male

Read Full Paper