I've got a new job with Pine River, and I want my new colleagues to know I'm not going to blab about anything that comes up, so blogging is now really over. Of course, if you bump into me you can always buy me drinks and try to get me spill the beans (about nonproprietary matters) but I should warn you, I can drink a lot of beer. Best.
Falkenblog
Tuesday, September 24, 2013
Tuesday, September 17, 2013
Historical CBO Budget Projection Highlights Bias
Recently the CBO issued its annual budget projection, and it's pretty benign for the next decade, then climbs at a pretty measured pace.
Yet, note that in the last recession our debt relative to GDP doubled. Given that economists still don't have a good model for predicting business cycles let alone avoiding recessions, we can expect more of them. I think the odds that we elect a modernday Calvin Coolidge next term are much smaller than the odds the deficit will increase dramatically when the next recession hits.
Consider that in 2007, before anyone saw any hint of the 2008 crisis, the debt was actually projected to fall, but we know how that turned out (black are actual historicals). That is, they never anticipate recessions, though we all know they haven't been abolished. I pulled these numbers out of the 2007 'wayback machine' which is a great way to hold large institutions accountable, because for some reason the CBO doesn't keep their historical forecasts on their current site (maybe the NSA can get Google to scrape them away?). Liberals who happen to be economists (eg, Brad DeLong) think the latest objective projections prove we have no budget worries. I guess some people really do think This Time It's Different.
Sunday, September 08, 2013
MSCI Quality Index
I was unaware MSCI had beaten AQR to the punch by producing a boatload of quality indices last spring. These are applied worldwide, so they are necessarily more parsimonious than AQRs...but jeez, these are really barebones:
1) Net Income/Book Equity
2) Debt/Book Equity
3) Earnings volatility over 5 years
Instructively, they Winsorize the data, which everyone should do to financial ratios (ie, truncate extremums). But, book equity in the denominator? Earnings volatility over 5 years? Those seem like bad choices, and AQR's quality index will be superior.
I have a feeling MSCI is a bit confused, as they have another tab noting their 'Risk Premia Indexing', which they note
The riskbegetsreturn model of economics is clearly nonfalsifiable amongst current financial academics and their coterie. They still say interesting things on occasion, so it doesn't render them useless, but it definitely impairs their ability to see and interpret reality.
1) Net Income/Book Equity
2) Debt/Book Equity
3) Earnings volatility over 5 years
Instructively, they Winsorize the data, which everyone should do to financial ratios (ie, truncate extremums). But, book equity in the denominator? Earnings volatility over 5 years? Those seem like bad choices, and AQR's quality index will be superior.
I have a feeling MSCI is a bit confused, as they have another tab noting their 'Risk Premia Indexing', which they note
An accumulating body of empirical research has found positive gross excess returns from exposure to factors (or risk premia) such as Value, Momentum, Low Size (small firms), and Low Volatility stocks. The studies show that these factors historically have improved returntorisk ratios. Today, interest in risk premia (also known as smart beta or alternative beta) has been widespread across the institutional investor community.In other words, risk premia are really return premiums, because predictable returns only come from risk (in theory). But then, they also 'improve returntorisk ratios', because, as we all know, these factors aren't risk in any obvious way, so strangely they all have 'excess return' premia. Indeed, 'value and size were initially thought to be due to distress risk, which would show up only episodically. Alas, 'quality' is basically an metric of antidistress, and this generates a return premium, which MSCI occasionally calls a 'risk premium'...so basically whatever asset outperforms over the next 20 year period will ex post be declared risky.
The riskbegetsreturn model of economics is clearly nonfalsifiable amongst current financial academics and their coterie. They still say interesting things on occasion, so it doesn't render them useless, but it definitely impairs their ability to see and interpret reality.
Wednesday, September 04, 2013
de Botton on Status Anxiety
I find Alain de Botton's approach to philosophy rather refreshing, because one senses his genuine lack of certainty, and appreciation of discovering, in his works. He's interested in applying virtue for daily betterment, and the search for meaning, two very important goals in my life. Interestingly he was insightfully quoted in a NYT review of Sophie Fontanel's selfindulgent book on her selfinduced celibacy, which highlighted his breadth and profundity (de Botton's quip was basically that 'sex is messy, get over it').
Anyway, here's de Botton on status anxiety. He argues that status anxiety is worse than ever because now we believe we are less constrained by our birth, more responsible for our fate. Paul Krugman agrees with this view of life, but like most economists, can't take this to it's ultimate implication, that this this leads to a zero risk premium, which when combined with the various attractions of sexy stocks, leads to high risk assets have lowerthanaverage returns (see my book The Missing Risk Premium).
Anyway, here's de Botton on status anxiety. He argues that status anxiety is worse than ever because now we believe we are less constrained by our birth, more responsible for our fate. Paul Krugman agrees with this view of life, but like most economists, can't take this to it's ultimate implication, that this this leads to a zero risk premium, which when combined with the various attractions of sexy stocks, leads to high risk assets have lowerthanaverage returns (see my book The Missing Risk Premium).
Sunday, September 01, 2013
How to Maximize Lottery Revenue
As a proponent of the idea that people are oriented towards their relative success, not absolute wealth, I think this lottery idea is fiendishly clever. Here's a description from TheWeek of a clever way to capitalize on this instinct:
A salient example is the "Postcode Lottery" in the Netherlands. Weekly it awards a "Street Prize" to one postal code, the Dutch equivalent of a zip code, chosen at random. When a postal code (usually about 25 houses on a street) is drawn, everybody who played the lottery in that code wins about $12,500 or more. Those living there who neglected to buy a ticket win nothing — except the chance to watch their neighbors celebrate.
In a 2003 study, researchers in the Netherlands noted that fear of regret played a significantly larger role in the Postcode Lottery than in a regular lottery. It was not the chance of winning that drove the players to buy tickets, the researchers found, it was the idea that they might be forced to sit on the sidelines contemplating missed opportunity.
The Boring Premium
Todd Mitton and Keith Vorkink from (boring) BYU published Why Do Firms With Diversiﬁcation Discounts Have Higher Expected Returns? Their answer: no skew. People will pay up for lottery tickets, but if you take those dreams away, it becomes an asset that is neglected. They find diversified firms offers less skew, and diversiﬁcation discounts are signiﬁcantly greater when the diversiﬁed ﬁrm offers less
skewness than typical focused ﬁrms in similar business segments. They suggest a
substantial proportion of the excess returns received on discount ﬁrms relative to premium
ﬁrms can be explained by differences in exposure to skewness.
The implication is clear: people pay a premium for volatile stocks that have stories and potential. Conditional upon playing in a risky game, such as equities, there's not a return premium for risk, there's a premium for boring.
The implication is clear: people pay a premium for volatile stocks that have stories and potential. Conditional upon playing in a risky game, such as equities, there's not a return premium for risk, there's a premium for boring.
Sunday, August 25, 2013
AQR's Quality at a Reasonable Price
Our intrepid equity researchers at AQR have come out with a new paper adding to the color on how to pick a strategy given value considerations. In Asness, Frazzini and Pedersen's latest paper, Quality Minus Junk, they first try to create a 'quality' metric, and then try to meld it with value.
Quality is defined very clearly as the composite of 4 factors (each of which is made up of 35 ratios):
They find that
1) Stocks with higher 'quality' have higher market/book ratios (higher price ceteris paribus)
2) A longshort portfolio, where one goes long high quality, short low quality, generates significant, positive excess and total returns
They assert that a valuequality portfolio that tries to balance quality with value has nice properties, and the Sharpe maximizing combination is about 70% quality, 30% value. This is coming from Asness, who is a pretty big value proponent, so I think this is rather telling (value losing it's preeminence!).
Their quality metric has a kitchensink aspect to it, with about 20 ratios that go into those 4 different groupings. I could imagine many people would find this an attractive framework to develop and tweak their own quality metric, substituting for various ratios, or subtle changes to the functional form. Haugen and Baker's (2008) Case Closed, and Zack's Handbook of Investment Anomalies are good places to look for alternative ratios.
I would like to see how this QMJ factor compares to Analytic Investor's Volatile Minus Stable (VMS) factor...they seem similar, though obviously 1) they are negatively correlated and 2) the VMS factor is simply a vol factor, which is just one part of the 'quality' metric.
Lastly, I love the little note at the end:
Quality is defined very clearly as the composite of 4 factors (each of which is made up of 35 ratios):
 Profitability (eg, Net Income/Assets)
 Growth (eg, change in Profitability)
 Safety (eg, volatility, leverage)
 Payout (eg, equity issuance, dividend payout)
They find that
1) Stocks with higher 'quality' have higher market/book ratios (higher price ceteris paribus)
2) A longshort portfolio, where one goes long high quality, short low quality, generates significant, positive excess and total returns
They assert that a valuequality portfolio that tries to balance quality with value has nice properties, and the Sharpe maximizing combination is about 70% quality, 30% value. This is coming from Asness, who is a pretty big value proponent, so I think this is rather telling (value losing it's preeminence!).
Their quality metric has a kitchensink aspect to it, with about 20 ratios that go into those 4 different groupings. I could imagine many people would find this an attractive framework to develop and tweak their own quality metric, substituting for various ratios, or subtle changes to the functional form. Haugen and Baker's (2008) Case Closed, and Zack's Handbook of Investment Anomalies are good places to look for alternative ratios.
I would like to see how this QMJ factor compares to Analytic Investor's Volatile Minus Stable (VMS) factor...they seem similar, though obviously 1) they are negatively correlated and 2) the VMS factor is simply a vol factor, which is just one part of the 'quality' metric.
Lastly, I love the little note at the end:
Our results present an important puzzle for asset pricing: We cannot tie the returns of quality to riskBy construction their returngenerating metric seems patently 'antirisk', as quality implies 'low risk'. The riskbegetsreturn theory obviously has a lot of intuition, because empirically it's counterfactual when not irrelevant. I think if you divided the data described by asset pricing theory into 'puzzles' and 'consistent', it's mainly puzzles.
Economath and the Drake Equation
There were several posts last week on the hypothesis that there's too much emphasis on mathematical modeling in modern economics. Most said yes (Dave Hendersen, Bryan Caplan, Noahpundit, Robin Hanson, The NewYorkTimes), though Krugman said no.
Krugman's experience is very pertinent as his Nobel Prize winning model on increasing returns to scale is a good example of obtuse economodeling: its thesis was known before being the basis of the centuriesold infant industry argument, and after Krugman it was no easier to apply. Consider Detroit, a popular application for regional increasing returns when applied to autos in the early 20th century: what were the key conditions that allowed it enjoy increasing returns to scale in the early 20th century, but then decreasing returns to scale later in the century? He doesn't say.
Krugman responded that his theory changed the debate, because it showedunder certain parameterizationsthat increasing returns to scale can be an argument for lower trade barriers! While true, this is a possibility, not a probability, and those who believe in increasing returns to scale invariably are more inclined to believe in selective tariffs, that is, they don't use Krugman's model to support free trade but rather increased protection. So, it hasn't changed the debate and is counter to his assertion that his New Trade Theory is "probably the main story" in importexport arguments for decreasing trade restrictions; his new model has not changed the debate at all, merely added another obscure reference to the confabulators. Increasing returns to scale remains 1) a fringe argument and 2) used primarily to support trade restrictions, as it was in the 1900s before Krugman's New Trade Theory model.
Krugman is a very smart person, but the fact he can't see this highlights that the greatest lies we tell are the ones we tell ourselves, because he clearly has the capacity to see slight inconsistencies and flaws in others (he's a meticulous advocate against his opponents).
I think a lot of math in econ is like the cargo cult phenomenon, where people see correlations (planes and cargo) and suppose the essence of something is one of those correlations (eg, build models of planes, and cargo will show up). Thus, just as naive people think the essence of a good poem is rhyming, naive economists think that setting up a hypothesis as if one were deriving the Dirac equation or special relativity seems like the essence of a science. Unfortunately, economic equations rarely work out that way.
Consider the Drake equation.
Where
N = the number of civilizations in our galaxy with which communication might be possible
R^{*} = the average number of star formation per year in our galaxy
f_{p} = the fraction of those stars that have planets
n_{p}= The number of planets, per solar system, with an environment suitable for life
etc.
None of the terms can be known, and most cannot even be estimated. As a result, the Drake equation can have any value from a hundred billion to zero. An expression that can imply anything implies nothing. I mean, this formulation is worthy of writing down, but it's very different than the Dirac equation or Newton's laws, even though at some level there's a similarity.
I remember teaching a money and banking course, and a fun way to get the kids introduced to economic models is to show them the BaumolTobin money demand model. This can be derived from some simple assumptions, and applies calculus to the maximization function individuals would apply, generating the equation:
Where
M=money demand
C=cost of withdrawing money
Y=Total income
i=interest rate
All very rigorous and tidy. Yet, it doesn't help predict interest rates, or the size of money aggregates. It's empirically vacuous, because it simply doesn't fit the data.
That's one of the more concrete equations. Most equations are like this one for money demand:
Basically one merely argues what arguments should be in the function and then the derivatives on those arguments. Thus, the first argument is 'permanent income' Y_{p}, and the first derivative here is positive. Yet, the parameters can vary wildly, and may even be endogenous themselves. At the end of the day, atheoretical vectorautoregressions do a better job predicting any of these variables.
Yet, for all the insufficiency of mathematics in creating a good science, sociologists show that an absence of rigor doesn't seem to be any better. I think this highlights there's no delusion greater than the notion that method can make up for lack of common sense. Ultimately, there is no method but to be very intelligent.
Krugman's experience is very pertinent as his Nobel Prize winning model on increasing returns to scale is a good example of obtuse economodeling: its thesis was known before being the basis of the centuriesold infant industry argument, and after Krugman it was no easier to apply. Consider Detroit, a popular application for regional increasing returns when applied to autos in the early 20th century: what were the key conditions that allowed it enjoy increasing returns to scale in the early 20th century, but then decreasing returns to scale later in the century? He doesn't say.
Krugman responded that his theory changed the debate, because it showedunder certain parameterizationsthat increasing returns to scale can be an argument for lower trade barriers! While true, this is a possibility, not a probability, and those who believe in increasing returns to scale invariably are more inclined to believe in selective tariffs, that is, they don't use Krugman's model to support free trade but rather increased protection. So, it hasn't changed the debate and is counter to his assertion that his New Trade Theory is "probably the main story" in importexport arguments for decreasing trade restrictions; his new model has not changed the debate at all, merely added another obscure reference to the confabulators. Increasing returns to scale remains 1) a fringe argument and 2) used primarily to support trade restrictions, as it was in the 1900s before Krugman's New Trade Theory model.
Krugman is a very smart person, but the fact he can't see this highlights that the greatest lies we tell are the ones we tell ourselves, because he clearly has the capacity to see slight inconsistencies and flaws in others (he's a meticulous advocate against his opponents).
I think a lot of math in econ is like the cargo cult phenomenon, where people see correlations (planes and cargo) and suppose the essence of something is one of those correlations (eg, build models of planes, and cargo will show up). Thus, just as naive people think the essence of a good poem is rhyming, naive economists think that setting up a hypothesis as if one were deriving the Dirac equation or special relativity seems like the essence of a science. Unfortunately, economic equations rarely work out that way.
Consider the Drake equation.
Where
N = the number of civilizations in our galaxy with which communication might be possible
R^{*} = the average number of star formation per year in our galaxy
f_{p} = the fraction of those stars that have planets
n_{p}= The number of planets, per solar system, with an environment suitable for life
etc.
None of the terms can be known, and most cannot even be estimated. As a result, the Drake equation can have any value from a hundred billion to zero. An expression that can imply anything implies nothing. I mean, this formulation is worthy of writing down, but it's very different than the Dirac equation or Newton's laws, even though at some level there's a similarity.
I remember teaching a money and banking course, and a fun way to get the kids introduced to economic models is to show them the BaumolTobin money demand model. This can be derived from some simple assumptions, and applies calculus to the maximization function individuals would apply, generating the equation:
Where
M=money demand
C=cost of withdrawing money
Y=Total income
i=interest rate
All very rigorous and tidy. Yet, it doesn't help predict interest rates, or the size of money aggregates. It's empirically vacuous, because it simply doesn't fit the data.
That's one of the more concrete equations. Most equations are like this one for money demand:
Basically one merely argues what arguments should be in the function and then the derivatives on those arguments. Thus, the first argument is 'permanent income' Y_{p}, and the first derivative here is positive. Yet, the parameters can vary wildly, and may even be endogenous themselves. At the end of the day, atheoretical vectorautoregressions do a better job predicting any of these variables.
Yet, for all the insufficiency of mathematics in creating a good science, sociologists show that an absence of rigor doesn't seem to be any better. I think this highlights there's no delusion greater than the notion that method can make up for lack of common sense. Ultimately, there is no method but to be very intelligent.
Tuesday, August 13, 2013
Is The Low Vol Anomaly Really a Skew Effect?
The idea that low volatility stocks have higher returns than high volatility stocks is difficult for economists to digest, because it's so hard to square with standard theory. It brings to mind Dostoyevsky's line "If God is dead, then everything is permitted." Similarly, when one sees their favored theory as being abandoned, it seems like all explanation is lost and chaos reigns. Yet, when a wrong theory is adopted, well, as the everlogical Bertrand Russel used to note, if 1+1=1, everything is both true and untrue. We need a framework to evaluate reality, and it has to be consistent.
Alas, many frameworks are largely untrue, leading to inconsistencies and explanations that are transparently tendentious. The sign of a bad Weltanschauung is that explanations for reality become more and more convoluted, like epicycles in Ptolemaic astronomy. I'll gladly enjoy the hypocrisy of those who don't share my worldview because, as the Detroit bankruptcy has reminded us (eg, its bankruptcy blamed on too much or too little gov't), people might admit tactical errors, but they'll go to their grave with their worldview (see Max Planck).
Consider the recent papers arguing that low volatility is really just a skew effect, in which case their worldview is safe. In the recent Journal of Economic Perspectives, longtime behavioral finance academic Nicholas Barberis wrote a paper on Kahneman and Tversky's prospect theory (that's Nobel prize winning Danny Kahneman, who's unimpeachability seems somewhere around that of Nelson Mandela) It's helpful to note that this insight is 34 years old, because many seem to all think these newfangled behavioural insights are going to revolutionize economics as if they haven't been applied continuously over the past generation.
Barberis goes over his Barberis and Huang (2008) model where prospect theory is used to motivate the hypothesis that a security’s skewness in the distribution of its returns will be priced. A positively skewed security— a security whose return distribution has a right, upper, tail is longer than its left tail—will be overpriced relative to the price it would command in an economy with standard investors. As a result, investors are willing to pay a high price for lotteryticket type stocks.
Barberis references several papers, including Bali, Cakici, and Whitelaw (2011), and Conrad, Dittmar, and Ghysels (here's the 2009 version, though a more recent version was just published in the Journal of Finance). He also finds it relevant to the underperformance of IPOs, the low average return of distressed stocks, of bankrupt stocks, of stocks traded over the counter, and of outofthemoney options (all of these assets have positively skewed returns); the low relative valuations of conglomerates as compared to singlesegment firms (singlesegment firms have more skewed returns); and the lack of diversification in many household portfolios (households may choose to be undiversified in positively skewed stocks so as to give themselves at least a small chance of becoming wealthy).
It seems like an orthogonal way to address these puzzles compared to the constrained rational approach offered by Betting Against Beta, but there's a problem, and it's that the wellknow equity risk premium has a negative skew relative to what's considered less premiumworthy, longterm bonds. That is, equities in general have a lower (ie, more negative) skew than bonds, and this is the most prominent 'risk premium', so it must not be an exception to a rule.
Note that indices have negative skew while individual stocks have positive skew. This is because correlations go up in down markets, and this predictable tendency creates a problem for idiosyncratic skew pricing models. That is, in the CAPM and other asset pricing models, risk factors have prices that are linear in the covariances, otherwise there is arbitrage, the essence of the Arbitrage Pricing Theory: whatever risks are priced, they are based on additive moments, so risk and returns are linear functions. Now we have priced risks that are not just diversifiable, but change sign depending on what else is in the portfolio. If true, there is an implausible level of profit to be had from buying portfolios and selling the constituents.
As an ivy league confabulator Barberis deftly ignores this inconsistency and instead notes that the equity risk premium makes perfect sense given Benartzi and Thaler’s (1995) idea that if you focus only on the net changes in wealth (technically, U(x) vs. U(w+x)), you can get this to work in cumulative prospect theory, because losses hurt more than gains, so one gets paid to take risk in this case.
Alas, there's a limit to how much skew and variance can both be priced in the same universe, where people love positive skew and hate variance. If skew explains most of the volatility anomaly, that implies people can't be globally risk averse because they would like extremum upmoves too much, and these happen proportionally more for volatile stocks. Yet if that's true there's no risk premium of any sort, because people would simply buy single assets or derivatives and have no incentive to mitigate risk via bundling and arbitrage. This has been shown formally by Levy, Post, and van Vliet (2003), but it should be intuitive: skew is positively correlated with volatility for stocks with lognormal returns, so there's a point at which one's love of skew dominates one's fear of volatility. If that point is reached, volatility is always less costly than skew is beneficial. This constrains the size of the skewloving effect to be an order of magnitude less than the risk premium if global risk aversion exists. If global risk aversion does not exist, then the rest of the general framework presented in simply meaningless.
So we have prospect theory explaining the overpricing of high volatility stocks due to skew, the underpricing of equity indices due to 'narrow framing.' One could add that prospect theory is used to explain why people overpay for longshots at the horse track, in that 'decisions weights' applied to payoffs prospect theory are observationally equivalent to overoptimistic probability assessments (see Snowberg and Wolfers (2010)), and that Danny Kahneman is an admirer of Nassim Taleb's Black Swan theory, which argues that small probability events are generally underappreciated. In other words, whatever the probability density function and expected return, it's explained by prospect theory.
Skew also shows up also in the recent publication of Conrad, Dittmar, and Ghysels (2013), who are incredibly meticulous in their analysis of how skew relates to future returns, highlighting what three top researchers over several years can do to data. Yet, they then ignore the elephant in the room, that is, if volatility is negatively priced and skew is positively priced, how do these both exist in equilibrium? It should be hard for these authors to say they don't care, because they are very exhaustive in their analysis, noting at one point:
I'm sure former JoF editor Cam Harvey read this while nodding approvingly throughout (he's referenced every other page, and a big believer that risk explains most everything in finance). While understanding SDFs and their risk premiums won't help you get a job at a hedge fund, it will help you get published and be popular among publishing academics.
I agree that skew is important, as it measures the upside potential that delusional lotteryticket buying investors love, and because of relative wealth preferences, arbitrage is costly and their footprint remains. That's a mathematically consistent story. Skew loving effects can't exist on the same par with variance hating effects in any consistent story about asset returns. Is this important? Consistency can be overdone, but I don't think this is foolish because one tends to see what one believes rather than vice versa, and I think there's more power and predictability in viewing volatility as merely a desirable attribute for delusional investors, as opposed to something that pays you a premium.
Paradoxically, behavioral refinements such as prospect theory are preventing needed outsidethebox adjustments and are used to maintain a defective status quo, one that has been wrong on a profound empirical issue for 50 years (ie, the risk premium). These putative revolutionary insights allow academics to wax eloquent on how their complex paradigm handles subtleties such as any of those 50 behavioral quirks, and outside commentators are pleased to be part of a new vanguard, obliviously marching in basically the same, pointless, confabulating path.
Alas, many frameworks are largely untrue, leading to inconsistencies and explanations that are transparently tendentious. The sign of a bad Weltanschauung is that explanations for reality become more and more convoluted, like epicycles in Ptolemaic astronomy. I'll gladly enjoy the hypocrisy of those who don't share my worldview because, as the Detroit bankruptcy has reminded us (eg, its bankruptcy blamed on too much or too little gov't), people might admit tactical errors, but they'll go to their grave with their worldview (see Max Planck).
Consider the recent papers arguing that low volatility is really just a skew effect, in which case their worldview is safe. In the recent Journal of Economic Perspectives, longtime behavioral finance academic Nicholas Barberis wrote a paper on Kahneman and Tversky's prospect theory (that's Nobel prize winning Danny Kahneman, who's unimpeachability seems somewhere around that of Nelson Mandela) It's helpful to note that this insight is 34 years old, because many seem to all think these newfangled behavioural insights are going to revolutionize economics as if they haven't been applied continuously over the past generation.
Barberis goes over his Barberis and Huang (2008) model where prospect theory is used to motivate the hypothesis that a security’s skewness in the distribution of its returns will be priced. A positively skewed security— a security whose return distribution has a right, upper, tail is longer than its left tail—will be overpriced relative to the price it would command in an economy with standard investors. As a result, investors are willing to pay a high price for lotteryticket type stocks.
Barberis references several papers, including Bali, Cakici, and Whitelaw (2011), and Conrad, Dittmar, and Ghysels (here's the 2009 version, though a more recent version was just published in the Journal of Finance). He also finds it relevant to the underperformance of IPOs, the low average return of distressed stocks, of bankrupt stocks, of stocks traded over the counter, and of outofthemoney options (all of these assets have positively skewed returns); the low relative valuations of conglomerates as compared to singlesegment firms (singlesegment firms have more skewed returns); and the lack of diversification in many household portfolios (households may choose to be undiversified in positively skewed stocks so as to give themselves at least a small chance of becoming wealthy).
It seems like an orthogonal way to address these puzzles compared to the constrained rational approach offered by Betting Against Beta, but there's a problem, and it's that the wellknow equity risk premium has a negative skew relative to what's considered less premiumworthy, longterm bonds. That is, equities in general have a lower (ie, more negative) skew than bonds, and this is the most prominent 'risk premium', so it must not be an exception to a rule.
US Monthly Data 19622013
10year US TBond 
SP500 Index 

AnnRet  7.05%  7.28% 
AnnStdev  6.86%  15.05% 
Skew  61.09%  42.16% 
Note that indices have negative skew while individual stocks have positive skew. This is because correlations go up in down markets, and this predictable tendency creates a problem for idiosyncratic skew pricing models. That is, in the CAPM and other asset pricing models, risk factors have prices that are linear in the covariances, otherwise there is arbitrage, the essence of the Arbitrage Pricing Theory: whatever risks are priced, they are based on additive moments, so risk and returns are linear functions. Now we have priced risks that are not just diversifiable, but change sign depending on what else is in the portfolio. If true, there is an implausible level of profit to be had from buying portfolios and selling the constituents.
As an ivy league confabulator Barberis deftly ignores this inconsistency and instead notes that the equity risk premium makes perfect sense given Benartzi and Thaler’s (1995) idea that if you focus only on the net changes in wealth (technically, U(x) vs. U(w+x)), you can get this to work in cumulative prospect theory, because losses hurt more than gains, so one gets paid to take risk in this case.
Alas, there's a limit to how much skew and variance can both be priced in the same universe, where people love positive skew and hate variance. If skew explains most of the volatility anomaly, that implies people can't be globally risk averse because they would like extremum upmoves too much, and these happen proportionally more for volatile stocks. Yet if that's true there's no risk premium of any sort, because people would simply buy single assets or derivatives and have no incentive to mitigate risk via bundling and arbitrage. This has been shown formally by Levy, Post, and van Vliet (2003), but it should be intuitive: skew is positively correlated with volatility for stocks with lognormal returns, so there's a point at which one's love of skew dominates one's fear of volatility. If that point is reached, volatility is always less costly than skew is beneficial. This constrains the size of the skewloving effect to be an order of magnitude less than the risk premium if global risk aversion exists. If global risk aversion does not exist, then the rest of the general framework presented in simply meaningless.
So we have prospect theory explaining the overpricing of high volatility stocks due to skew, the underpricing of equity indices due to 'narrow framing.' One could add that prospect theory is used to explain why people overpay for longshots at the horse track, in that 'decisions weights' applied to payoffs prospect theory are observationally equivalent to overoptimistic probability assessments (see Snowberg and Wolfers (2010)), and that Danny Kahneman is an admirer of Nassim Taleb's Black Swan theory, which argues that small probability events are generally underappreciated. In other words, whatever the probability density function and expected return, it's explained by prospect theory.
Skew also shows up also in the recent publication of Conrad, Dittmar, and Ghysels (2013), who are incredibly meticulous in their analysis of how skew relates to future returns, highlighting what three top researchers over several years can do to data. Yet, they then ignore the elephant in the room, that is, if volatility is negatively priced and skew is positively priced, how do these both exist in equilibrium? It should be hard for these authors to say they don't care, because they are very exhaustive in their analysis, noting at one point:
We use several methods to estimate [the stochastic discount function] M_{t}(τ) that allow for higher comoments to influence required returns. These methods differ in the details of specific factor proxies, the number of higher comoments allowed, and the construction of the SDF.Alas, as usual in analysis of SDFs, there is no takeaway input one can use to measure risk, no soontobeindispensable tool, just a promise that this has all been vouchsafed against highfalutin theory and so 'it's all good.' Consistency is a good thing, but only in certain dimensions. One of the authors, Dittmar (2002), wrote a very nice paper for the Journal of Finance in 2002 noting that if you restricts a nonlinear pricing kernel to obey the riskaversion needed to ensure that the market portfolio is the optimal portfolio, the explanatory power goes away of higher moments. With all the abstruse checks in this paper, one would think he might want to address that issue, but instead he ignores it.
I'm sure former JoF editor Cam Harvey read this while nodding approvingly throughout (he's referenced every other page, and a big believer that risk explains most everything in finance). While understanding SDFs and their risk premiums won't help you get a job at a hedge fund, it will help you get published and be popular among publishing academics.
I agree that skew is important, as it measures the upside potential that delusional lotteryticket buying investors love, and because of relative wealth preferences, arbitrage is costly and their footprint remains. That's a mathematically consistent story. Skew loving effects can't exist on the same par with variance hating effects in any consistent story about asset returns. Is this important? Consistency can be overdone, but I don't think this is foolish because one tends to see what one believes rather than vice versa, and I think there's more power and predictability in viewing volatility as merely a desirable attribute for delusional investors, as opposed to something that pays you a premium.
Paradoxically, behavioral refinements such as prospect theory are preventing needed outsidethebox adjustments and are used to maintain a defective status quo, one that has been wrong on a profound empirical issue for 50 years (ie, the risk premium). These putative revolutionary insights allow academics to wax eloquent on how their complex paradigm handles subtleties such as any of those 50 behavioral quirks, and outside commentators are pleased to be part of a new vanguard, obliviously marching in basically the same, pointless, confabulating path.
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