Monday, August 05, 2013

On the Inverse Correlation between Expected Risk and Return

Imagine a world where expected returns are solely a function of covariances as standard theory implies. Then for assets with specific covariances, the market should give them specific expected returns. People expect risk and return to be positively correlated in this theory.

Instead, Sharpe and Amromin find that people expect volatility and returns to be inversely correlated: when they are bullish they expect low volatility, and when they are bearish they expect high volatility. This is counter to standard theory, which is why it has been in 'working paper' hell for 6 years, because referees find a lot to quibble with when results don't make sense (eg, high vol-low return papers in the 1990s). If you generate a paper like this, it really helps to already have credibility (eg, Fama-French 1992), because otherwise there will be a thousand reasons not to publish it.

On vacation last week I read a great airplane book, You are Not so Smart by blogger David McRaney, which highlights psychological biases in a succinct, interesting way.  He noted the work of  Finucane, Alhakami, Slovic, and Johnson (2000), in a paper entitled The affect heuristic in judgments of risks and benefits. Slovic is the other coauthor of the famous book on behavioral biases, Judgement Under Uncertainty: Heuristics and Biases. They asked a bunch of people about controversial issues like natural gas, food preservatives, and nuclear power.  They divided subjects into groups where some people read only about the risks, while others only read about the benefits of various issues.  Needless to say, those exposed to the risk arguments estimated the risks of these technologies to be higher, and those primed by the benefits judged there to be higher benefits.  However, those who saw the elucidation of risks also judged there to be lower benefits, and those who read about benefits saw lower risks.

Logically, risk and return are separate, but intuitively, we see them as part of a whole, related in a totally antithetical way.  For example, Warren Buffet has famously written that those stocks with the highest return had the lowest risk because such stocks had the largest 'cushion' in their forecast error.  'Low risk' and 'high return' are both good, so they go together in most people's intuition, as do the bad qualities, 'high risk' and 'low return.'

This is part of the 'halo effect', where people see those who are handsome as smarter, because things with good qualities are seen as intrinsically good, so good in each and every way.  Think of a saint with a halo: he was probably good at everything.  Indeed, if you give people positive information on one attribute, they will tend to assume the others attributes are correlated.  Clearly this makes some sense, as I imagine 'fitness' in a person, in terms of their desirable traits, has a general factor the way IQ helps explain language, math and visual-spacial skills, but it has its limits.  This is also why it's hard for people to accept that a lout like Hitler really was nice to dogs and a decent painter, because it seems like that implies you liked his other attributes.

A big theory as to why low volatility stocks outperform high volatility stocks is the Asness, Frazzini and Petersen's Betting Against Beta theory.  I'm more in the 'no risk premium plus delusional lottery ticket demand' camp.  In my view, people buy high beta stocks incidentally because these tend to have characteristics amenable to comforting delusions: big stories, potential for big gains.  In the Betting Against Beta view, people buy high beta stocks because of the higher return implied by this covariance, and their constrained in their allocation to equities by rules of thumb and regulations. I think investors are focused on the return and underestimating the risk, but in any case, buying in spite of it.

The Betting against Beta theory does follow more directly from the Capital Asset Pricing Model than my take, but Sharpe and Amromin, and now I learn, Finucane, Alhakami, Slovic, and Johnson are more on my side.  


E(R) said...

I wonder to what extent this "anomaly" relates to the fact that the standard theory is a one-period model with no ability to handle time. Investment horizons are not fixed, yet risk and return are both functions of time. Plus we never actually know (ex-ante) what the covariance is.

Fish Goldstein said...

The acceptance of behavioral economics opens the door to a new avenue of financial risk research: Let's just ask people what they think! Surveys of actual investors should serve as a pretty good proxy for figuring out expected returns and risk.

In that sense, the reason for the missing risk premium must, at some level, lie in the way real-live investors think and behave. Let's just go ask them...

deniz said...

Hi Eric,

Nice post. You may be interested on our take of how affect is related to risk and return:


Eric Falkenstein said...

Deniz: hey, great link! I never saw that one.

hbkaz said...

One thing the theory ignores, is the incentive structure in the money management industry and the fact that much of the money is managed on a delegated basis. The structure gives rise to excessive risk taking and herding.

Seth said...

Eric you said: .....In my view, people buy high beta stocks incidentally because these tend to have characteristics amenable to comforting delusions: big stories, potential for big gains

That would be fun to test. High Beta stocks should therefore have a greater %move on positive news events and a lower %move on negative events than low beta stocks....That would be fun to run through Lucena Research's QuantDesk event engine.