Mervyn King on Piketty and Risk Premia

Several prominent economists have now put pen to paper to review Piketty's "Capital in The Twenty-First Century" (Solow, Summers and Rogoff are three excellent examples, among several more).  However, to my knowledge, only Mervyn King has made the important link between risk premia which, according to modern asset pricing theory, are the biggest driver of returns to capital, and Piketty's r > g.  King points out an important flaw in Piketty's analysis.

The point can be understood as follows.  Asset pricing theory tells us that, because investors are in general risk averse (a genetic trait) and assets are inherently risky, assets are priced to give investors a higher return than risk free investing in a bank account (or, dare I say it, in government bonds).  So, for example, if the risk free rate is 0.5%, then stocks will be priced by market participants to give an expected return of, say, 5%.  This risk premium exists in large part because bad things, like wars and other unforecastable catastrophes (think hurricanes, earthquakes and other unknown global warming related risks) can happen, and stock markets collapse in these scenarios.

The "r" that Piketty uses in his r > g argument is the 5% number.  However, at the same time, Piketty ignores the period from 1910 to 1970 during which major global turmoil occurred and during which the share of wealth of the top 1% dramatically fell.  The reason that r = 5% in the first place is precisely because periods like 1910 to 1970 have happened in the past, and can happen again.  Clearly, it does not make sense to ignore such a period, but including this period significantly weakens Piketty's argument.

Mervyn King's analysis is thoughtful and thoroughly impressive.  At the time of writing, it has just 624 social media "shares" and 215 comments.  I hope that those numbers grow into the thousands.

The Third Moment. Equities vs FX.

Is the skewness of returns bigger in FX or equities?  I guessed equities.  I think that most academics, options traders and other market participants would guess the same.  I finally had time to do the analysis and I found some interesting results.

First, the realised skewness in equities has not been particularly big relative to FX.  The data set from 1980 until 2014 reveals a skewness of -0.6 in US equities, whereas AUD-USD is -0.8 and USD-JPY is -0.44.

Second, and more interesting, that there is any negative skew at all in equities rests heavily on just one observation: 19 October 1987, also known as Black Monday.  If we take this one, single observation out of our sample, the realised skewness of equities drops to just -0.15.  Fascinating.

The charts below contain a full set of results.  The first shows realised skewness by decade across several currencies and equities, all plotted in XXX-USD.  The second chart is the same, but it filters out Black Monday.

Third, the bottom chart shows a positive skewness in USD-CHF (negative in CHF-USD) in the 2010s data set.  That result also lies heavily on one single observation: the SNB's 6 September 2011 intervention to weaken the CHF during the European sovereign debt crisis.  Without this observation, the realised skewness of USD-CHF is close to 0 for the 2010s.

The fact that single observations in data sets spanning several decades can affect our realised skewness statistics so dramatically poses a challenge for options pricing.  A significant proportion of the price of skew in options depends on one of the hardest things for a trader to properly quantify: the conditional probability of an extreme event.

Unforgettable Economics Lessons in Tombstone

Prof John Taylor writes about Tombstone, a Hayek prize winner.

"On every page of Tombstone you see detailed case studies of what Hayek warned about: the pretense of knowledge as political leaders thought they could do away with the family and individual initiative, but ended starving 36 million people to death in the mother of all unintended consequences; the ludicrousness of an economic system which tries to do away with prices to provide information, signals, and incentives, and replaces it command and control; the dangers of repressing freedom and thereby creating a cruel silence which allowed starvation conditions to continue."

While we are a long, long way from China in 1958, when we form our opinions on policies such as energy price caps and rent caps, let us not forget about the importance of the free market price signal, and what can happen when it is completely removed.  See this article by Boris Johnson for a lighter take on the subject.

From Rags to Riches to Rags

In this excellent article, Professors Mark Rank and Thomas Hirschl find that 39% of Americans find themselves in the top 5% of the income distribution at some stage of their lives.  This tells us that income inequality may not be the result of unequal opportunity and that other factors, such as effort, luck and others may be more important.  This is very relevant to the Piketty inspired current debate on inequality and the wealth distribution.