DeMuth's Affluent Investor Highlights Hindsight Bias

I received a copy of Phil DeMuth's Affluent Investor, which at around $11 is a bargain. Alas, advice books like these, for the layman, are kind of futile, as good advice is ignored by those who need it precisely because those who need it would never seek it. So, it's best as a gift. If there's a 10% chance they can learn, it's worth $11.

For example, he nicely informs the reader what investment advisers think is wealthy: $100k to $1 million is 'affluent', $1MM to $10MM is 'high net worth', above that is 'ultra high net worth'. From a practical perspective, one should target getting 25 times one's income when one retires, probably a good definition of 'comfortable.'

He makes the interesting point that gambling is fun and savings is hard. But savings, investing, and gambling, are all different shades of grey, and highlights that something may seem the same at one level (not spending) is very different at another (buying Tbills vs. lottery tickets).  Another good point is that some stocks, like utilities, have generated profits and dividends for decades, and some like Facebook are predicated on something unconventional, monetizing something novel. These should be thought of as totally different, yet, these are both 'stocks', and classed the same (FB)

He seems to be plugged in to the big names in finance, and so co-authored several books with Ben Stein, a well-know author and commentator (and son of famous economist Herb Stein), and seems to know the Peter Bernstein crowd (eg, Black, Scholes) pretty well.

Interestingly his book mentions low-beta investing in  a couple of pages, and even includes this blog as charitable reference, which I greatly appreciate. Alas, I don't agree with his portrayal of the low-beta phenomenon.  He promotes an alternative history, one consistent with Frazzini and Pedersen's betting-against-beta theory. The basic idea is that low beta stocks outperform high beta stocks on a risk adjusted (but not absolute) basis, and this is because of borrowing constraints.

DeMuth mentions Myron Scholes, Peter Bernstein, Perry Mehrling and others, in creating his narrative, that these guys were big early believers in the Frazzini and Pedersen model (before these guys were born), but were thwarted by regulation. That is, all the big players knew low beta stocks outperformed since 1969, and activily advocated levering up low-beta stocks. In practice, however, this aggressive leveraging is hardly, if ever, observed, as a result of which the volatility effect can persist, because people are leverage averse. That is, the big players knew about the low volatility investing anomaly all along (just ask them!).

True, Black did show early on why the Security Market Line (SML) is too flat because of borrowing constraints (see Brennan (1971) and Black (1972)) . Facts are important, and Black missed the big one here, which is the SML is flat--not insufficiently upward sloping--but flat (at best). A flat SML doesn't generate a rational reach for high beta that underlies the Frazzini and Pedersen (and Black, Scholes, Mehrling, etc.) model, because you don't prefer the higher returning 1.5 beta stocks if, actually, those stocks don't generate higher returns.

 That is, 1.5 beta stocks don't outperform 1.0 beta stocks, so saying investors prefer them because they have higher returns means their beliefs are irrational. It's like normal form game where everyone is wrong about the other guy. This is general not considered an equilibrium, and so, back in my day, nonpublishable. Times change. I suppose this is the mainstream academic's (eg, Fama, Campbell) favored explanation.

The low volatility (aka low beta) anomaly is not merely that low beta (vol) stocks have higher than expected returns, it's that their returns are higher than average. Just look at the performance of Acadian, Robeco, or Analytic, which have been running low vol funds since 2006ish.

If borrowing constraints were key, we would see a risk premium where they are not applicable, such as futures, but we don't. We also see the opposite in options, where the negative risk premium seems simply related to volatility. Saying this is consistent because investors believe they are amplifying positive returns, while in fact they lose something like 20% per expiration, implies an insane dichotomy between expectations and reality. For this reason I think Frazzini and Pedersen or Scholes are wrong to say this all fits in their theory, because their theory is based on everyone acting on a different model than they assume: maximizing returns personally, while assuming everyone else is maximizing variance-adjusted returns. Usually, the dichotomy is someone thinks everyone else is acting irrational, here, the agents act irrational and assume everyone else is rational.

In sum, I don't think it's a good explanation now, and historically, Scholes or his colleagues didn't ever discuss the low volatility anomaly for 35 years or so, which makes me think it wasn't something they thought was important, relative to their other ideas over that period. For them to now insinuate they documented the low volatility anomaly back in the 1970's is typical post hoc rationalization you find in regular people.

Krugman and Thought Crimes

Paul Krugman highlights his true colors in the NYT today:

You can deny global warming (and may you be punished in the afterlife for doing so — this kind of denial for petty personal or political reasons is an almost inconceivable sin). 

Liberalism clearly hasn't remove the concept of sin, merely changed it. I think that the global warming is a plausible concern, but mainly an overblown pretext for giving more power to governments.

Consider that climate alarmists think that there's an amplification effect of around 3 to our CO2, so that the greenhouse effect of the CO2 is multiplied via its effect on water vapor, etc. This would suggest that the climate is in an equilibrium with positive feedbacks, inconsistent with the millions of years of a habitable planet. Clearly our atmosphere has mainly negative feedbacks, because otherwise we would have slid off to Venus or Hoth many millions of years ago via the 1883 eruption of Krakatoa  or other climate calamities.

Or consider that earth temperature data is measured very imprecisely in prior centuries, often with tree rings. I'm skeptical. Really good data only started about 10 years ago with Argo, where one takes thousands of submersibles and measures the temperature of the sea at various depths. Guess what: no trend.

I think it's reasonable to be a skeptic, and not have any petty or political motive, just sincere doubt.  In any case, I think sins are like vices, and should apply to actions, so even if you did believe in Global Warming, you should look at actions as opposed to 'thoughts'. It's simply more reasonable to judge people on what they do more than what they say, and Gore's airplanes and ethanol program have put more carbon into the atmosphere than anything I might do.

But, liberals don't just want obedience. As Orwell said in his novel 1984:

We are not content with negative obedience, nor even with the most abject submission. When finally you surrender to us, it must be of your own free will...It is intolerable to us that an erroneous thought should exist anywhere in the world, however secret and powerless it may be.

FX Carry Trade is Back

Uncovered interest rate parity suggests that currency returns should relate to interest rates in a pretty straightforward way. For example, the short-term interest rate in American dollars is about 0.25% and the comparable rate in Australia is 3.0%. According to the uncovered interest rate parity, the Australian dollar should depreciate against the American dollar by approximately 2.8%. Put another way, to convince an investor to invest in Australia when its currency depreciates an expected 2.8%, the Australian dollar interest rate would have to be about 2.8% higher than the American dollar interest rate.

On average, however, the high interest rate currencies actually appreciated.  If you borrow in low interest rate countries, invest in high interest rate countries, you simply make more money and no one has found a risk metric that might explain this. It's another example of the failure of the risk premium to appear where it should.  Here's Marty Eichenbaum in a short interview talking about his NBER paper on this subject.

Here I'm simulating the total return to going long the Australian Dollar and Brazilian Real, short the Japanese Yen and Swiss Franc, classic high  and low interest rate economies.

As one can see, this trade took a really big hit in 2008, but rebounded within a year unlike many other assets. However, since then it's been a boring trade. This year, however, it's been going gangbusters,so perhaps we are back to old times.  

Taking Offense is not Righteous

Curiously, a former definition of impoliteness has become a new focal point for all sorts of political and psychological offense.  I remember Miss Manners noting that politeness has two, related, sides: not giving or taking unintentional offense. That's clearly old school. There seems to be a public bounty for perceiving slights, and lots of columnists are full-time commentators noting the latest injustice to their tribe (eg, shocking cover on right). There's a website called MicroAggressions documenting slights felt by people who don't appreciate the guy who opened or failed to open the door for them. Interestingly, the more they talk about things, the more people get upset by people getting upset ad infinitum.

 One of my favorite scientists Michael Gazzaniga writes about a study by Kleck and Strenta (1980)  that showed how our left-brain interpreter is driven to seek explanations for events. In the study the subjects had a scar applied to their face with makeup, which they observed in a mirror. They were told that they were going to have a discussion with another person, and that the experimenter was interested in whether the other person's behavior would be affected by the subject's scar. The subject was instructed to note any behavior that they thought was a reaction to the scar. At the last moment the experimented said he had to moisturize the scar to prevent it from cracking, and then surreptitiously removed the scar.

When shown a video of the other person's facial reaction taken during the discussion, the subjects reported being treated horribly, and noted things like looking away. Their reality was based on two faulty pieces of information: 1) they had a scar and 2) their conversation partner glancing away more than usual. If you give people a good reason to believe someone is biased against them, they will perceive that bias regardless.

Unfortunately, no one talks about that study, but rather the more agreeable stereotype threat research that reinforces the notion that institutional racism powerfully discourages groups like blacks, women, and moms, into performing stereotypically   The idea here is that if you prime subjects to do poorly on a Raven matrices test, they will conform to the stereotype statistically.

A key to good mental health includes the art of not being offended. To do this, you should see that every statement, action and reaction of another human being as the sum result of their total life experience to date, and so it really has very little to do with you. To the extent they are implying you are a knave, fool, or tool, it usually has more to do with them than you, especially in contacts with people one doesn't really know (eg, cops, waiters, teachers).

We are often stand-ins, the chess pieces of life to which others have their own built-in reactions. When we provide no Velcro for it to stick, something changes in the world, and most importantly, you aren't brought down thinking about the implications of some poorly thought-out actions.  Contemplating or correcting those with bad thoughts is like staying up late trying to make sure no one is wrong on the internet. Though it may take a lifetime of practice, a thick skin is truly one of the best kept secrets for living a happy life.

Unfortunately, people today are taught the opposite, to find slights based on whatever angle gives them their greatest insecurity or platform, which somehow will bring justice to the world. It's really a bad meme, counterproductive for the individual and society.  

Is Tampa Pension Fund Manager the Real Deal?

Some managers are above average:

Jay Bowen's stock picking has made the Tampa Firefighters and Police Officers Pension Fund one of the best-performing public pensions in the U.S.... As of Dec. 31, Mr. Bowen's annual returns beat pension giant Calpers—which employs 125 consultants and 1,100 money managers—over three-year, five-year and 10-year spans.  ...The Tampa fund appears to be well funded at about 90%. It uses an unusually high annual investment target and discount rate of 10% to calculate the present value of benefits owed to retirees.

The fact that a particular manager has generated above average returns over the past 10 years is not an anomaly, but rather, a statistical certainty. Given Tampa discounts their liabilities by 10%, implying an expected return of 7% or so, I suspect that statistical logic isn't their strong suit, so they simply see this case in isolation, and infer his return based on what looks to them like a long track record, over ten years.  As the housing bubble showed, you can't argue against someone who has outperformed over the past 10 years, so I'm sure they are going with their rosy assumption, which I bet will fail with a high probability.

This reminds me of a sales pitch a neighbor broker once told me about. He would take his clients to lunch or dinner, and tell them a long, happy tail about an old client of his firm who had simply put away a modest amount in a company they recommended for over 20 years, and by the time she retired, she had tens of millions of dollars and spent most of her time on charity. This fantasy was very appealing because it really happened, as Home Depot was one of those stocks that went up 100 fold over its lifetime. Further, doling out charity is a great way to enjoy high status in your golden years without guilt: it's something the non-rich simply can't do or criticize.

Of course, for every lady like this, there were thousands who didn't do nearly as well, but only a cynic would conclude such cases were impossible.    

Low Vol Makes Comeback in YTD Total Returns

In this year's bull market, low beta portfolios have been doing quite well.  My own Minimum Variance Portfolio, taken using 50 constituents of the SP500, has outperformed the SP500 by just about the same amount as the SPLV ETF (which takes the 100 stocks with the lowest volatility).



It seems that low beta portfolios were insulated against that mini bear market of a couple weeks ago.  

Chavez The Miracle Worker

Though I have not the slightest itch to murder anyone, I do read some obituaries with pleasure. Hugo Chavez was a typical tyrant, and I would surely want to emigrate if I ever found myself in such a country.  Yet, many on the left disagree and point out the trains ran on time.  Salon has an article entitled "Hugo Chavez's economic miracle," and highlights that the official poverty rate fell during his tenure.  I'm skeptical of poverty statistics calculated in countries run by dictators, especially those countries where the murder rate is 4 times that of Mexico.  I guess we probably do not agree on the facts, but I also suspect we have different preferences.


Luckily for them, Chavez is going to be embalmed like his hero Lenin, and I'm glad there's a shrine to people I disagree with so far away from me. I wish one of his Western cheerleaders wouldn't merely praise these guys, but actually move there. That is, if Cuba, Venezuela, China, or Albania is a socialist paradise, then why don't any of these guys actually want to live there.

Why Do Top Income Shares Matter?

From a recent YouTube lecture by UC Berkeley economist Emmanuel Saez, he discusses income inequality. As an introduction he makes the following claim, and it's pretty clear he doesn't find this very controversial:

Inequality matters because people evaluate their economic well-being relative to others, not in absolute terms

He's a pretty conventional, leading academic economist. It's interesting that he can say this as if it's not debatable and move on, because if this is true, many of the fundamental results of economics are simply wrong. For example, there is no risk premium, a theme of my now back ordered book, which discusses why this inconsistency persists.

Yet, I'm pretty much alone in arguing this in finance. In other words, in some fields of economics relative utility is obvious, in others it's applied piecemeal, in others it is not used at all . Such is the science of economics.

Security Market Line in Bull and Bear Markets

Some note that if we are in bull markets, it is better to be in high beta stocks. I would agree that if you know you are in a bull market--that is, you know the stock market will be up at the end of this month--then it is preferable to be in high beta stocks. Yet, implementing this timing rule is not straightforward because even abstracting from the variance drag of high volatility stocks, the dominance of low vs. high beta changes whether you are using contemporaneous or ex ante indicators. That is, it makes a big difference if you use data from today to determine tomorrow's portfolio, or data from tomorrow night.

Low vol, is pretty much like low beta. and betas are actually pretty straightforward to predict. Low beta stocks move lesss than high beta stocks. In up markets, low beta stocks go up less than the average, and much less than the high beta stocks. In down markets, low beta stocks go down less than high beta stocks.  Here's my data on beta portfolios since 1962 using monthly data, using the separation of whether the contemporaneous S&P return that month was up or down. Bottom line: if you know markets are going up, go into high beta stocks.

Now, what about volatility? In above average volatility using the same, ex post, end of month datapoint, one finds that in the tranquil, below average volatility months, markets rise and higher beta stocks dominate; in higher-than-average volatility it's better to be in low beta stocks.

We know that monthly returns are pretty uncorrelated, yet, monthly volatility is highly correlated, and so, perhaps, low volatility periods are better for high volatility stocks?! Alas, no. Looking forward, it goes the other way. That is, using last month's volatily, lower-than-average vol means it's better to be in low volatility, and the opposite in high volatility regimes. 

My Book Out of Print

My book is currently 'out of print' because I'm simply trying to correct some typos, and my publisher does not allow printing while a text is being corrected. I currently have 3 simple syntax correction in the queue (eg, change a comma to a period).  I'll get back this change in 5 business days, and if all goes correctly I'll be up in three weeks. Otherwise, it will take another 3 weeks and we continue. 

If you want to self publish a book that has equations, expect the process to be very difficult. Equations, pictures, and Symbol fonts, are unconventional. For example, on several occasions I've tried to explain what a β is, and it's exasperating; think about getting an inline equation correctly formatted.

They take my changes and send them over to India, and as one can imagine it's a clusterpuck of miscommunication. First, they try to put all the request into a protocol that is completely documented, but alas none of my comments fit into their pre-fit categories, and they generates tons of automated respones that convey no information other than 'we received your comment.' I can't talk to those guys actually making the changes often (I did on my latest round, strangely), so no matter how much I talk to the American sending this off, it's all pretty much irrelevant because 12k miles away, that conversation doesn't count for anything. Most times I receive back my changes and they include changes to other parts of the book I didn't ask for. This is because when they transfer the book to other formats, the gifs or Symbol fonts don't carry over and so look like I want to change the formatting to some incomprehensible giberish known only to me, but also because they compare to a version I sent their prior to the latest one.

Tom Brady Highlights Algorithm Deficiency

The NFL combine is rather interesting, because predicting outcomes based on Moneyball-type inputs is very alluring. For everyone excited by some new statistic, there's another person who notes these don't capture what's most important.  The answer, as usual, is to use both metrics and subjective expert analysis.

An amusing new signal is an athlete's butt, the bigger the better.  Looking at little wrestlers I coach, a protuberant posterior is the best indicator of natural strength for these pre-pubescent kids.  Your gluteus maximus is your largest muscle, so I guess if you are going to focus on one muscle, better to look at that than biceps or triceps.


Tom Brady is one of the better quarterbacks in the NFL, and highlights and interesting modeling issue. He scored as pretty much the worst QB at the NFL combine: 5.3 second 40 yard dash, 24.5 inch vertical leap. If speed is one of your inputs, and your algorithm was a sequence of sorts, you would probably have eliminated Brady as a candidate because he was in the 1st percentile of speed and jumping ability. If your algorithm was more like a linear weighting, he could have compensated in other dimensions.

 In general, I tend to like sequence of filters versus a linear weighting rule, though on large portfolios I find these rarely make a large difference. Yet, knowing that I could miss the equivalent of a Tom Brady in my sequence of sorts, made me rethink this a bit.  Then someone noted that while speed is important in general, a well-specified Quarterback model would give it sufficiently low weight as to not have it in the filter (eg, Joe Montana had poor speed).  That comforted me a bit.

Another thought was, unlike a portfolio, picking a quarterback is like picking a single stock, and for that, perhaps the sequence of filters is not optimal.

Too Many Axioms?

I stumbled upon a website that listed 61 common behavioral biases,  and most of them seemed good to know, unfortunately.  I guess there are so many because we are constantly using heuristics to explain and predict, and of course these heuristics are often applied incorrectly, in the same way we think people from large countries or states far away know each other or get along (eg, I remember when I got to college, and being from Cleveland someone said to me, 'Do you know Joe down the hall? He's from Cincinnati.').  Simple errors, good to rectify. As there are as many different patterns we try to project on little information in life, it's understandable we have so many biases.

In that vein, I was strolling through Barnes and Noble and found this little book, 50 Psychology Classics, for only $7.98. 50 seems like a lot, but luckily this book was only 200 pages, so the author did an admirable job boiling down these big thinkers into some key ideas.  Understanding how we think is pretty important, and we don't have one big drive, rather, many.

While it would be nicer if James, Freud or Jung had it all right in their magnum opuses, it's more probable the best ideas in psychology are from many different thinkers. Here's some good ideas I cribbed from that book:

Alfred Adler: Noted that character involves a balancing the desire for power and that for social togetherness, and that the hardest thing for human beings to do is know themselves, and then to change themselves.

Eric Berne: Humans need social contact more than anything, and we seek it primarily in symbolic emotional strokes. This often breaks down into interactions and games that are repeated, such as going over sports scores. It may seem banal, but it is no less comforting than the soft strokes given to a baby.  We have three selves--the parent, adult, and child. All are necessary, but the adult way best in most cases.

Robert Bolton: Most communication is non-verbal. Learn to listen, mainly by truly wanting to hear what the speaker is saying (then don’t interrupt, encourage elaboration).

Eric DeBono: Creative thinkers use a variety of strategies to think outside the box: generate alternatives, challenge, assumptions, use analogies, find the dominant idea, suspend judgment. A great insight should be obvious after discovered.

Nathanial Branden: Neurosis occurs when we let our feelings dictate our thoughts and actions. It is impossible to be both happy and irrational. Live by reason.

David Burns: Cognitive therapy notes that our thoughts affect our emotions and mood, not the other way around. It isn’t events that dictate your mood, but how you react to events.

Mihaly Csikszentmihaliyi: Creative breakthroughs come after years of hard work and attention to detail. First you need to master a domain, then you can break those rules you understand to create something new.

Erik Erikson: Young people need to really believe in something intensely before they hate it. The real crisis in a person’s life often comes in the late 20’s when they realize they are overcommitted to a path that is ‘not them.’ It’s often too late.

Victor Frankl: The greatest human achievement is not success, but facing an unchangeable fate with courage. The will towards meaning is at least as important as the will to power, and one's meaning differs depending on the issues and opportunities unique to our particular time and talents.

Daniel Gilbert: Humans are the only animals that plan for the future by trying to anticipate, not by instinct, but via mental modelling. We often overestimate how things and money will change our happiness.

Thomas Harris: ‘I’m OK you’re OK’ is like the Christian concept of grace: total acceptance of oneself and others. Successful people assume others are equals from whom they can learn valuable things.

Eric Hoffer: Faith in a holy cause is often a substitute for a lost faith in oneself. People join movements for a sense of belonging, or from a feeling of boredom. When glorious ends justify any means, believers will do horrible things to create their paradise.

William James: We can never have exactly the same thought more than once, because over time we know more, have reacted to it already, know what others now think about that thought, etc.

Abraham Maslow: Instead of trying to create better things, we should try to create societies with more self-actualized people. Such people have a  guilelessness, do things that occasionally are unpopular, work hard at what they are best at, and try to see others in their best light

Jean Piaget: Children seem very social, but actually they are egocentric maniacs, and tend to talk a lot to no one in particular, often performing a monologue on their actions. Only madmen and children say whatever they think, because they think only they matter.

The Spin-Off Anomaly

The straightforward strategy of buying companies that have recently been spun off from their parent has generated very good results.  Here's the performance of the Bloomberg Spin-Off index (BNSPIN Index) since 2003. As you can see, it's pretty good, a 15% annualized return vs a 6% for the S&P500 over that period. Volatility was higher but not extremely so (20% vs. 15%), while the beta was pretty close to 1.0.

Is this a crazy recent phenomenon? No. In 2003 McConnell and Ovtchinikov looked at 311 spinoffs undertaken by 267 parents between January 1965 and December 2000. On average, subsidiaries outperformed their benchmark companies by over 20% over the first three years following the spinoffs, with most of the excess returns within the first 12 months of trading. They found the parent company outperformed as well, but not by a robust amount.

I don't think there's a rational explanation for this. I remember at Moody's when they just spun off from Dunn &Bradstreet, it was really liberating. For years D&B had used the considerable Moody's cashflow to fund their dumb ideas to extend D&B, which really ran the executive board while Moody's made all the money.  It was a classic waste of shareholder money, and so when the spin-off finally happened in 2000, Moody's (MCO) stopped burning its cash and investors reaped the windfall (32% return, annualized, from 2000-present). It's amazing how much money is wasted via such politics, but it's a classic case of a bad incentives and difficult monitoring. 

It makes one wonder about the value potential in Citi (C). If someone could force it to sell itself into pieces, I bet everyone with defensible interests would hit a home run.  Letting a $120B company underperform is really painful to behold. The only people such behemoths serve now are a select bunch of executives and politicians, not shareholders, consumers, or 99.99% of Citi employees.

CitiBank Shows How to Play

Great anecdote on crony capitalism about Jack Lew, the latest Citi employee who will be in charge of a lot of financial regulation:

As for the Citi paycheck, the story is how Wall Street has become a get-rich-turnstile for Democratic political operatives. The terms of Mr. Lew's original employment contract with Citi included a bonus guarantee if he left the bank for a "high level position with the United States government or regulatory body." 

Most companies include incentives for top employees not to leave, but in this case the contract was written to reward Mr. Lew for treating the bank like a revolving door. Citi says it likes to accommodate employees who do public service or work at nonprofits. But the Lew contract was specific about a senior job in the federal government. There would be no special payout if he left to run the Red Cross or the New York state budget office.

Health Care End Game Predictable

Ever notice how quickly the health care debate turns to insurance? It has long seemed to me that this is just a trick to advance redistribution under a different mechanism, because first you conflate insurance with health care, then start regulating in such a way that everyone is treated the same by the insurer regardless of the riskiness of the insured. In such a system, low risk people will try to opt out entirely or form groups that exclude high risk people (say, by having a company of young healthy people form a self-insurance plan).

Brad DeLong notes a professor who sees the end game and then concludes:

Maintaining the pooling equilibrium as health care costs increase is going to be really hard. If it turns out to be impossible--well, then, the ACA system will lurch toward pay-or-play and then single-payer.

Markets break down if low cost people are grouped with high cost people; someone with diabetes will cost more than a healthy person actuarily, and healthy people understand that and try to avoid being in their group. The only way to avoid this is to use force, and so like public schools or postage, have everyone charged the same, and queue the same.

Aristotle had this all explained in his Politics (book 3), where he notes all justice is equality, but the question is really equality of what? Egalitarians want more redistributive equality that generates equal positive rights to goods and services, whereas libertarians want more equality of negative rights, such as our equal right not to be assaulted. I can empathize with the egalitarians, as envy is a fundamental instinct. Yet I think this is not a good objective because it neglects the fact that if you make positive rights equal, then everyone has an incentive to free ride, and this encourages the worst in people. Further, in egalitarian societies like the old Soviet Union or China, it was not as if there was ever euality of positive rights. As H.L.Mencken noted:

The chief difference between free capitalism and State socialism seems to be this: that under the former a man pursues his own advantage openly, frankly and honestly, whereas under the latter he does so hypocritically and under false pretenses.

 I'm not optimistic libertarian preferences will prevail in a direct democracy as opposed to a democratic republic, as more and more republican guards against mob rule are dismantled every generation.

Correlations in Down Markets Aren't That Different

Many people assert that correlations totally break down in down markets.  I created a bunch of portfolios from the Russell 2000 going back to July 1962 using the prior 36 months of data up to 1999, and the prior year's daily data from 1999 onward. I extrapolated backward the bottom market cap, relative to the SP500 index, to get a replica of this grouping back to 1962. This insured I only had real stocks that could be traded.

I then created 5 portfolios, each with 100 stocks.  First, those with the highest and lowest betas. Then, those with the betas nearest 0.5, 1.0, and 1.5.  These are all freely available, without any registration or any work, here.  

Here are the betas in the up and down months.  There's a tendency for betas for low beta stocks do move towards one, but then, high beta stocks move away from one.  In any case, the effect is not huge.

Correlations, which are measures of how linear a relationship is, are higher in down markets, but again, they aren't game changers.  Correlations certainly do not 'go to one', or 'go to zero.' 

A lot of quants have the very a strong opinion on the meaningless of correlations, and I hear from a lot of them via that Black Swan guy's acolytes.  These people are simply letting the perfect be the enemy of the good. Correlations, and betas, vary over time. Yet they are broadly consistent in up and down markets: stocks grouped by prior high betas have higher betas in future up and down markets, while lower beta stocks have lower betas in up and down markets.  It's all relative, but it's very meaningful, and has powerful implications.  You can design a portfolio with lower than average volatility or beta. Sure, you won't create a portfolio that has no basis risk, no downside risk, but that's an absurd objective. 

Gold/SPY Ratio a Puzzler

If Gold and the stock market are both geometric brownian motion, what are the odds of this pattern? It looks like there's a clear trend from when the US closed the gold window in 1971 to 1981 when the monetarist experiment ended, to the end of the internet bubble, then to today.

Gold peaked in 1980, and basically is at a peak again, but it's interesting that this ratio seems stationary. I bet no one thought that was true in 1980, or even 2001.

Facts are important things, and it's not obvious what they are.  Over my life I've seen papers argue gold has a positive, negative, and zero expected return, reflecting what has happened over the past 10 years.

update: Eddy Elfenbein has a theory that seems pretty interesting...basically, when the real interest rate is low, gold is relatively attractive and generates good returns as investors pile in.

Interesting Gender Research

This is the kind of sociological research I find really interesting. Notre Dame Sociologist Elizabeth McClintock did some analysis of gender sex strategies, mentioned by James Taranto at the WSJ:

She made the plausible assumption that the most attractive members of each sex are the ones with the widest range of options, and therefore that their behavior more closely reflects each sex's actual preferences. The corollary is that because less attractive individuals have fewer options, they are under more pressure to compromise and thus their behavior more closely matches the opposite sex's preferences.

So, what did she find?

The better-looking a man is, the more lifetime sexual partners he reports; the better-looking a woman, the fewer. Good-looking men are more likely to have had sex soon after meeting a partner; good-looking women, less likely. Good-looking women are likelier to describe their relationships as "committed"; good-looking men, less likely. 

Very physically attractive women are more likely to form exclusive relationships than to form purely sexual relationships; they are also less likely to have sexual intercourse within the first week of meeting a partner. Presumably, this difference arises because more physically attractive women use their greater power in the partner market to control outcomes within their relationships. For women, the number of sexual partners decreases with increasing physical attractiveness, whereas for men, the number of sexual partners increases with increasing physical attractiveness.

So, when a woman tries to be like a man, or vice versa, it's a low-status move. It's interesting to consider why high status academics recommend such behavior.

Why HFT is Not a Problem

Many people are concerned about the fact that some people can trade more frequently than they can due to having a large infrastructure of high speed computers and connections to various exchanges.  It all seems like regular people can get ripped off, and so some kind of governor is need via transaction taxes, or some limiter on the trade frequency.

This is all unnecessary. If you are concerned about being gamed by high-frequency traders (aka HFT), there's a pretty simple way to avoid this.  Simply trade using Volume Weighted Average Price (VWAP) orders. This order gives you the volume-weighted average price for a period, usually a day, and on InteractiveBrokers it's available pretty cheaply, say for half a cent a share.  Brokers have whittled this fee pretty much down to the exchange fees and spread, taking into account the fact that they trade these things 'algorithmically', so you actually benefit from HFT as they aren't simply and stupidly crossing the market every half hour. Most HFT actually are simply common sense applied to generating a light touch by trying to emulate a market-maker (eg, posting buy orders at the bid) as opposed to something sinister.

Say you decide on Sunday, after doing all sorts of research over the weekend, that you want to buy IBM on Monday. If you are buying less than 1% of ADV, your effect on the price is positive to be sure, but spread out over the day, its too small to front run (ie, it's not sufficiently greater than the spread to be worth buying in the morning and selling at close). 

Widows and orphans can execute VWAP orders now and then benefit from any benefits in a perceived case where trading is simply done at a central auction once a day. Yet with this solution, no one is constrained, no one has to monitor or regulate anyone. The solution exists currently and is available to everyone who wants to avoid HFT.  Real investors shouldn't be day trading, but making long term decisions based on a longer-term analysis of the trends, and in that case, they can trade as if HFT didn't exist without any new rules.  

Olympics Drop Wrestling

OK, here's a conspiracy theory. In 2004 they added women's wrestling along side men's to bring down the brand.  I've been to a lot of youth tournaments in the past several years, and there's perhaps 1 female wrestler for every 100 to 200 male wrestlers in grade school. Many lazy news outlets gave equal space to men's and women's wrestling previews so as not to discriminate, which is like giving Monaco and China the same space in Wikipedia because they are both countries. Yesterday the IOC decided to drop wrestling from the 2020 Olympics, while BMX, handball, pentathlon and trampoline remain.

Wrestling is not just a  sport but a life skill. If you can perform and defend a double leg takedown you have a huge advantage over your average street fighter, because transitioning to a choke that ends the tussle is then pretty straightforward. Then there are the cases where brawlers are basically hugging each other, in which case knowing throws and trips makes this a mismatch: wrestling is skill, you can learn moves that give one a large tactical advantage. Having the confidence from knowing you can physically defend yourself is extremely valuable even if never used.

Further, unlike team sports, in wrestling you have to master the issue of hating to lose but not being fearing it. Young kids cry a lot when they lose in wrestling compared to soccer or baseball. Unlike in team sports, losing is a direct assault on their ego, not merely because it's one-on-one but because the humiliation is not nuanced: some guy just pushed you around like a rag doll. Learning how to cope with unambiguous defeat is an extremely useful life skill that kids today are often sheltered from.

Yet, as wrestling declines, mixed martial arts like the UFC  rises, so the future is not horrible for the gist of my favorite sport.  Further, I never really understood the greco-roman wrestling rules as applied in Olympic matches. Human combat will always be interesting to humans, and  any competitive combat will have some peculiar rules like in wrestling, judo, or boxing, and those sports with the better rules will thrive, though perhaps not in the Olympics.

The Easiest Way to Derive Black-Scholes

Black-Scholes is perhaps the most famous equation in finance.  It was originally derived by Fischer Black and Myron Scholes by using arbitrage to create a partial differential equation, which turned out to be the well-known heat equation from physics.  Solving differential equations is hard, for me anyway (it doesn't come up a lot, so like my French, je sais un peu). Cox and Rubinstein showed how to use a binomial model to prove risk neutrality, and that proof is a lot easier.  From there you can derive the result in a relatively simple way.

So we start with just two assumptions
1) The underlying asset follows a lognormal random walk
2) Arbitrage arguments allow us to use a risk-neural valuation approach (Cox-Rubinstein's proof is easiest here), discounting the expected payoff of the option at expiration by the riskless rate and assuming the underlying's return is the risk free rate

Derivation of Black-Scholes for a European call option c with strike K, discount rate r, on stock S, with time to maturity t, and expectations operator E.

Equation 1: The definition of a call option

Equation 2: End of period stock price as a function of its return by definition, where R is the gross rate of return

Equation 3: rewriting eq(1) in integral form, where h() is the lognormal density function, and labeling S(0) as simply S, (note K and k are the same below, I'm too lazy to change them)

Equation 4: substitute into R an exponential and its normal distribution, where f(u) is the normal density function with a mean of μt=(ln(r)- ½ σ²)t and volatility σ√t

Equation 5: substituting for u now using a change in variables to z we have 

Equation 6: rearranging

Equation 7: substitute (ln(r)- ½ σ²) for μ and factor out e^ln(r)t

Equation 8: multiply the normal density by the exponent

Equation 9: factor exponent

Equation 10: make substitution zhat=z-σ√t

Equation 11: rearrange integral bound

Equation 12: using the fact that 

we can switch and negate the integral bounds

Equation 13: using algebra we then get

Equation 14: rewrite in Normal Cumulative Density notation to get the familiar Black-Scholes equation

where 

QED

Al Gore, Sociologists, Address HFT

Al Gore's latest tome The Future warns us that: 

There are already several reckless practices that should be immediately stopped: the sale of deadly weapons to groups throughout the world; the use of antibiotics as a livestock growth stimulant; drilling for oil in the vulnerable Arctic Ocean; the dominance of stock market trading by supercomputers with algorithms optimized for high-speed, high-frequency trades that create volatility and risk of market disruptions..

As to how the stock market volume hurts the economy, he isn't clear, but his intuition is that 'trading' doesn't add value, and gives the example of the project to trim 3 milliseconds off the internet trip from New York to Chicago, which he says could have been spent on something productive.  Just stop trading, and boom, one could transfer say 50% of the 8% of GDP we currently spend on finance to our inner cities.

Yet, a lot of innovation is an off-shoot of something pretty banal, like porn and VCRs, and I would hate to have all projects need a sign off from some centralized Star Chamber because that would lead to all sorts of corruption. One could say that Al adds dubious value on his various boards and venture investments, as his main value consists of knowing the right regulators and big government contractors, crony capitalism, which is much more destructive than those dreaded limit orders that are often cancelled.  The thought that this guy is a Nobel Peace Price winner, Oscar Nominee and centimillionaire should remind everyone that Life Isn't Fair because he hasn't had an original or courageous thought in his life, as his book presents a caricature of free markets that is obviously indefensible. Only the simplest minds can think that in any great controversy such as that between those believing in more government the other in less, one side is mere folly or cupidity.

It's strange that a lot of people with no real interest or knowledge have very strong opinions on how much assets should trade, even though it doesn't affect them. They hate the idea that someone's getting rich doing something they don't think adds value, though it occurs in a competitive environment. If the average daily volume for a stock was 100% of the shares outstanding, should it optimally be 200%? 50%? I don't think anyone knows, anymore than one knows whether interest rates should be 2% or 5%. The great thing about markets is that while they are often wrong, they correct themselves a lot faster than collectives do, and further, they decentralize decision making. Asset markets don't just produce prices, but they allocate investments to their highest perceived value; when wrong, the owners pay the price, so incentives are aligned.

If you are a dictator the last thing you want to see is your work being second-guessed in real time, you would rather see it evaluated at completion, and never compared to anything. Further, like the Post Office or Medicare, you would like to have no shareholders so you could say you are doing a great job regardless, just point out the services provided to customers without a choice. A stock market on such entities would highlight how inefficient such programs are being run relative to those who would like to run them, and they would have motive, means, and opportunity to follow through.

Unfortunately, such idle rambling is not merely a spectator sport of closet socialists, but PhD students. There's a Howard Zinn-type exegesis of trading in Destructive Destruction? An Ecological Study of High Frequency Trading by some students of Heterodox Economics and Sociology of Financial Markets:

According to heterodox economics the development of thermodynamics brought an end to the dominance of classical physics in economic theory, in particular the dogma of efficient markets hypothesis, and reversal to equilibrium.

Given that the theory of efficient markets wasn't really developed until the 1960's, and Hayek's The Use of Knowledge in Society was written in 1945 I'd say the relation between physics, especially thermodynamics, and this economic theory was pretty independent, though I would agree that every broad economic theory has a vague relation to some physics (optimizing individuals are kind of like the principle of least action).

Anyway, these poor saps figure that it's all based on the 'fourth law of thermodynamics.'

The true novelty of Georgescu-Roegen's formulation lies in his proposal for a fourth law of thermodynamics, where it is not only energy that is subject to decreasing returns, but also matter; friction robs us of available matter

Trading is like friction that simply robs the economy of value.

In as much as it diminishes the risk of trading through higher matching speeds, HFT allows buyers and sellers to reduce their transaction costs considerably.

Like most discussions of risk and return, they suggest there's a risk-return nexus and these firms are merely accessing it, but that metaphor is as misguided as their entropy-flow thesis (not discussed here, but its a vague metaphor these authors think is the key to everything). How does HFT reduce risks, and for whom? I actually think of HFT as simply trying to efficiently parcel orders out of a big trade, and reacting quickly to movements in related securities when providing liquidity. This reduces the risk to retail traders because it gives them greater liquidity because placing a bunch of limit orders at the best bid/ask is like being an electronic market maker.  This allows regular Joe's to trade without moving prices so much, and at more efficient prices. It does not reduce risk for the high frequency trader himself, as this activity generally takes risks because you can't make profits without taking risks in this highly competitive domain. Further, taking intraday positions does not generate a positive return per se, so there's no risk-return relationship merely for taking the position.

As someone against the status quo, I have to say my fellow anti-current-paradigm intellectuals are mostly moon-bat crazy like those above. Clowns to the left of me, but I find myself more broadly sympathetic with the 90% of the jokers to the right such as Cam Harvey, John Campbell, or John Cochrane.  Not that I think they are correct, just that they are much more fruitful to read than those who think there's a fourth law of thermodynamics that's essential to understanding the economy.

Gazzaniga on Preferences

Jonathan Haidt is now a popular speaker, having written two very good books (The Happiness Hypothesis and The Righteous Mind), but his books are really derivative of Michael Gazzaniga, the guy who really pioneered the right/left brain differences by looking at patients who had their corpus collosum.  Gazzaniga's book Who's in Charge is filled with interesting tidbits, and Haidt's especially interested in how our narrating left hemisphere confabulates reasons for beliefs it often doesn't understand, and doesn't know its confabulating: we lie to ourselves all the time because often we don't know it (the most unethical person I have ever known once told me that he never lied, which I knew sounded like trouble, and it was; he was a psychopath). It's the kind of biologically-based psychology that makes one happy to live now because as smart as Aristotle or Schopenhauer were they just couldn't have known this, and so at least in some things I can see more than they could, and I'm grateful for that.

For example, he notes that culture affects genes, and notes that many have noted East Asian culture is more oriented towards harmony, Western towards individual agency.  When shown a sequence of boxes with lines in them,  fMRI sudies show that East Asians looked more at relationships between geometric figures, relative judgments, while Westerners looked more at the absolute sizes from one picture to the next.  They also found that East Asians looked more at the scene of a picture, while Americans looked more at the main items.  This suggests East Asians have an even stronger relative utility preference than Americans, and this could have asset pricing implications in Asia vs. the West.

He also noted studies have found American subjects process social emotions in a particular area of the brain. That is, envy when seeing the rich, or pride in seeing a successful American athlete, or pity when seeing a pathetic looking person, all lit up the medial prefrontal cortex.  These are all related to how we empathize, sympathize, and compare to people. Disgust, meanwhile, lights up different parts of the brain because it is an emotion not related to sociability. This is why he thinks when people find enemy groups disgusting it's the first step to dehumanizing them, which can lead to all sorts of unempathetic behavior common in human history (outgroups were often treated as animals, historically).  More interestingly, greed isn't something that pertains to a specific part of the brain, but envy is.  Envy is a Human Universal, as Donald Brown notes, found in all cultures, where greed is not.  

Acadian Explains Their Paper

I spoke with Malcolm Baker of Acadian who was kind enough to explain what they meant in their latest SSRN low vol paper I mentioned yesterday.  Basically, the main idea was to address the argument that much of the low volatility effect is from industry slants, such as utilities.  To the extent one can parcel out the low vol puzzle into a piece coming from the industry or country vs. firm volatility, one can see that this effect is about 60-40 for firm vs. industry.  So, it's not all an industry or country effect, which is interesting because some people are arguing that it is.  I never argued that, but Dimensional, GMO, and others have, and they are significant players, so it's good to try and settle that issue.

As to allocating things into alphas rather than raw returns, this is because the alphas have much higher significance than raw returns.  That's true, but hardly anyone has intuition for alphas from incorrectly specified models, so all the alphas made about as much sense as telling me how much my house is worth is Zambian kwachas. Statistical significance without intuition has always left me flat, but that's sort of a preference, and I know many academics love J-tests on overidentifying restrictions, and I'm not the only one out there needing convincing.

I think a good way to see the effect they are talking about, is to look at the average annualized monthly returns (ie, monthly returns times 12) for the 1989-2010 period, where data are presorted by industry betas.  The negative relation goes away looking at monthly returns.  That's interesting. But note, there's still a puzzle, because monthly returns should be increasing in beta and they clearly are not. It's not flatter than predicted, its flat.

Now, those were monthly returns, and the higher betas imply higher volatility, and so over the entire sample, the total returns are negatively correlated with the beta, why their figure 1 below has the top quartile betas with loser returns. Is the Security Market Line then, flat, or negative?

 It's kind of a philosophical question as to whether the high beta stocks have lower returns given the total sample return was significantly lower, but their average monthly return was similar.  The trick is whether to think of the total sample return as an estimate, or the average monthly return, because if you do a monte carlo on the monthly returns, the expected total returns will be as equal as those monthly return, even though the expected geometric return is lower via the variance drag on high voaltility portfolios. The trick is, with exponential compounding some histories will have really high returns that will make the average total return much higher than it's geometric return in sample; we haven't seen them, but they are possible. For example, if returns go up or down 50% with equal probability, then with two periods, the average compound return is -7%, but the average total return is zero (total returns of -75%, -25%, -25%, and +225%, average period returns of -50%, -13.4%, -13.4%, and +50%).  If all you saw was up 50% and down 50%, you might think the average return was -13.4%, but that's just one draw from history.

For me, the real evidence is across countries, where in no major economies are highly volatile stocks generating the really high returns that would be consistent with this explanation.  Then again, we only have 20 or so such countries, and maybe we need more.  It's a defensible position, I suppose, but if after 100 years and 20 countries we don't have any examples where the Security Market Line is positive (ie, E(R_i)=R_f+Β_i(R_m-R_f)), I'm thinking it doesn't work that way.

Finally, they do make the rather straightforward assertion that

the incremental value of industry and country selection, even holding stock level risk constant, suggests that the use of a risk model in beta estimation that includes fixed country and industry effects is preferable to simple stock level sorts on beta or volatility.

Now, clearly countries need some separate factor estimation, because it makes a lot of sense theoretically. I'm not so sure that industry risk outside of simple covariances are as helpful to generating a diversified portfolio, as I've seen a lot of overemphasis on industry allocations that hurts overall portfolio variance.

 Like any good recipe, you need a good cook. After all, a good steak is conceptually simple, but most people don't cook a good steak.  The SPLV is the greatest thing for someone in this thread, because while Sturgeon's law implies most refinements will be crap, it's eminently feasible to do better than this and earn your 30 basis points.

Acadian Has New Low Vol Paper

Baker, Bradley, and Taliaferro (2013) have a new paper out that tries decoct the essence of the low risk anomaly with reference to a vague assertion by Respected Dead Economist Paul Samuelson that markets are macro inefficient and micro efficient. Samuelson noted one can arbitrage relative prices via derivatives, long/short portfolios, but if the aggregate market is too high or low, it's basically unarbitragable.  Big bubbles like the housing and internet bubble lasted for longer than anyone anticipated, and those who saw this all coming in early on would surely have lost their capital by the time the end-game rolled around, even though trends were pretty much in place years prior. Fair enough.

Figure 3 from The Low Risk Anomaly: A Decomposition into Micro and Macro Effects

Above is the gist, Figure 3, that the "alpha" from low vol investing is from stock-specific effects, secondly industry or country risk (the do it using either).

Alas, they frame everything in terms of alpha from a CAPM model.  This model basically states that expected returns should increase linearly as beta increases,

E(R_i)=R_f+Β_i(R_m-R_f)

Yet, as they show in their first figure in their paper (not pictured in this post), this model has a sign error, with higher beta stocks have lower returns. That is, if, charitably, the SML is flat, then

E(R_i)=R_m

Then alphas are just inversely related to betas in sample

 α= (1- Β_i)(R_m-R_f)

It's only worse if the returns are negative in beta as they appear to be.  As the equity premium (R_m-R_f) is positive in sample, framing things in terms of alpha is basically framing things in terms of their betas, and so they sort by and then present the resulting betas. It would be much more revealing if they showed raw returns, and showed a cross-tab for returns by industry and firm beta.

Like Frazzini and Pedersen, their theory is based on the premise that the Security Market Line is too flat (thus the alpha for low vol), but it is still positively sloped.  However, they also document the the Security Market Line is negatively sloped: higher beta stocks have lower returns, not just lower-than-CAPM-predicted returns. That's not a minor inconsistency.

Here's where it gets convoluted: in their model, like in Roll (1992) and Frazzini and Pedersen (2010), they have managers reaching for beta to outperform in absolute their benchmark, because they think that higher beta stocks have higher returns.  But then they state that micro selection against the benchark lowers risk because some investors like the alpha in low volatility stocks.  This 'micro' story explains the low vol anomaly  though this sounds more like micro inefficiency to me, as these guys are not just irrational, but bipolar. Meanwhile, as countries/industries aren't good to allocate between, one is stuck in these bad sectors and 1) receive no premium and 2) can't move because of conventions. Methinks they are gilding the product differentiation lily here.

They conclude noting that one should use both industry/country risk and idiosyncratic beta risk to allocate capital, and I agree. I would state it simpler: rank everything by Total Volatility over the past 9 months using daily returns, and don't invest in anything in the top half.  That would include country risk, industry risk, beta risk, and idiosyncratic volatility. If you are a Sharpe ratio maximizing investor, you would be better served simply minimizing the volatility subject to a long-only constraint, but if you are benchmarking, by eliminating the above-average volatility equities you have something with a more moderate beta but without the high-vol detritus that brings down returns and increases portfolio volatility.

While the basic low vol strategy is a commodity, one can easily add 200 basis points of value by relaxing the constraints of size/currency across the globe, but this only works because many investors are constrained in their size/currency equity allocations (eg, large-cap Europe, small cap UK), and this is easy techinically but difficult politically.  One may also add 100 basis points of value via using the right 'risk' metric when choosing low vol, as it's really a 'low risk' story, though this is dangerous and investors should be wary because most people who try this unconsciously overfit the problem and make it worse.

I feel for these guys. On one hand, good approaches are simple.  On the other, if you state it as such, it becomes a commodity that is soon sold at cost.  The dominant solution is to portray a vague convoluted solution that is both deep and powerful.  

Local Paper Discovers Laffer Curve

My local paper is always for more government spending, and higher taxes on 'the rich.' Recently we voted in a Democrat governor and both houses of our state legislature, so we are getting higher taxes as expected. What wasn't expected was higher taxes on newspapers and the business they contract with, so now we have new Tea Party converts. From the StarTribune:

We urge Dayton to reconsider and the Legislature to reject a sales tax on business-to-business services, a tax idea the Star Tribune has long opposed. While expanding the consumption sales tax to a larger share of the economy and reducing its overall rate, as Dayton proposes, is sound tax policy, taxing businesses' service inputs is anything but. ... Consider the impact on one particular industry sector -- one this Editorial Board serves and understands well -- advertising, information and communications. Providers of those services together employ nearly 68,000 Minnesotans. Many of them serve clients outside Minnesota and compete with rivals around the country and the globe.

They assert this has been their position all along, but reading the Strib I don't remember any such argument, though it's a nice attempt to try to present themselves as having a principled stance. Their basic argument is that this will actually reduce revenue because Minnesota businesses, including the Star-Tribune, will shrink as they raise their prices. But they don't state that so explicitly, rather, they allude to it via mentioning competitiveness, and then perfunctorily, that this isn't fair.

 I suppose these liberals think we should just tax rich people for the extra amount, ignoring that rich people can alter their liabilities by moving headquarters, the structure of their various corporations, and lots of other ways. I think the Laffer curve is one of the more powerful ideas in macroeconomics, and also one of the most ridiculed. At the margin, there always appears to be more revenue out there by raising taxes. It reminds me of a famous essay by George Stigler in The Intellectual and the Marketplace arguing that all supply and demand curves were inelastic, which clearly would imply massively suboptimal pricing, but that's the general argument out there.

Relative Status Preferences

Here's a South African on BloggingHeads.tv articulating the theme of my book The Missing Risk Premium, that relative status is a lot more important than absolute wealth: