Tuesday, May 06, 2008

Theories of Everything

Well-documented empirical puzzles are great for science, because they expose opportunities for refinement and extensions. For example, the famous Michelson-Morley experiment showed that the 'aether', was a suspect concept, and Einstein's special relativity, which introduced the idea that the speed of light was constant, could explain this anomaly (and the anomaly implied with Maxwell's equations on a similar point). The heat of the earth was an anomaly, because Lord Kelvin calculated that the Earth was only 20 million years old. This was explained via the discovery of nuclear fission in the earth's core. When Alexander Fleming saw that penicillin spores caused his petri dishes of bacteria to have little dead spots, that was a puzzle.

So in finance, we have a bevy of anomalies, and a bold paper by Xavier Gabaix intends to solve them all in one fell swoop. Specifically, the anomalies:

1 equity premium puzzle (too high)
2 risk-free rate-puzzle (too low)
3 excess volatility puzzle (equity prices are too volatile relative to consumption or dividends)
4 value-growth puzzle (stocks with high price-dividend ratios have abnormally low future returns)
5 yield curve to upward sloping at short end (overnight to 2 years)
6 Fama-Bliss findings that a higher slope of the yield curves predicts higher risk premia on bond returns (steep curve good for stock and bond prices)
7 corporate bond spread puzzle (the spread between Baa corporate and government bond rates are too high)
8 counter cyclical equity premium (lose money in bad times)
9 characteristics vs covariance puzzles (simple numbers such as the price-dividend ratio of stocks predict future returns better that covariances with economic factors)
10 predictability of aggregate stock market returns by price/dividend ratios, and the consumption-asset ratio has explanatory power for future returns
11 high price of deep out-of the money puts, and, last but not least,
12 forward exchange rate premium puzzle (uncovered interest rate parity violated).

OK, what's the trick? Basically, extreme but improbable events, for both inflation and stock market moves. All it takes is to put in a large, one in a hundred year adverse event, and these anomalies are rationalized. Of course, with data of only one hundred years, we often don't realize these events, but that proves nothing. They could happen, and indeed if we look cross sectionally at other countries, they do (eg, Russia, Japan, Poland, Germany).

My criticism of this approach is that it leaves many of the puzzles unaffected. For example, if this explains the equity premium, why is it when you create a synthetic equity position by going long 1.5 beta stocks, and short 0.5 beta stocks, you have a negative expected return? Why does the small chance of large inflation explain the overnight to 2 year yield spread, but not the flatness of the curve from 2 to 30 years? I don't think a solution incompatible with these data is correct.

My own theory, that's been called obvious, wrong, and illegal, is here: risk is not related to return. This is an implication of people investing with respect to 'the market' so every risk taking position (deviation from the market) is like idiosyncratic risk, avoidable, and so unpriced. That's my story, and I'm sticking to it.


J. said...

I for one agree with your theory, your story, but I would not call it illegal (?) but banal. Imporant but banal. I am a very old man, so let me explain myself by way of parable: Once, I spent six months in la Republica Dominicana, living in the house of Rafael Trujillo (dictator from 1930 to 1961), owned by his concubina who rented out rooms to single girls. On Sundays, she dressed them all in white and led them to the Church. I spent my nights in my room in delirium (the suffocating heat, the oversized mosquitoes, those very hot girls in the other rooms) trying to drink enough rum to fall asleep. In those times, Dominican government's income was entirely based on los vicios, that is the lottery monopoly, and the tax on alcohol and tobacco. At night, I wondered, how this could be? Why would anyone, not to speak of a whole nation, engage, no, be obsessed, by an activity "with negative expected returns after transaction costs"? I always fell in feverish stupor before solving the enigma, but the fact is that the Dominican Republic was a financial reality, it paid good salaries, contracted consultants like me and even financed the lovely house of sparkling crushed white coral that daddy Trujillo built as his "casa chica". Bottom line: You can build castles on people's irrational risk taking behaviour. Risk cannot be logically priced.

Tim Worstall said...

"the discovery of nuclear fusion in the earth's core."

Fission....at least I bloody well hope so.

Eric Falkenstein said...

Fusion/fission...good thing I don't work at the plant.