Utility Functions and the CAPM

A basic concept in classical economics is that given certain plausible assumptions it is possible to define utility functions which measure how desirable economic actors find possible states of the world.  Rational actors will then try to maximize the expected value of their utility function.  For example most people will have an utility function which gives an additional two million dollars less than twice the value of an additional one million dollars.  Hence they will prefer a sure million dollars to a 50% chance of two million dollars as this will maximize the expected value of their utility function.

The Capital Asset Pricing Model (CAPM) uses considerations of this sort to predict that risky assets will sell at a discount to their expected future value (as computed in dollars) and that the amount of the discount will increase as the amount of future uncertainty increases.  As without such discounts investors would prefer to buy only the safest assets.  It follows that risky investments will have greater expected return.  Note risk here is referring to non-diversifiable risk.  Risk particular to individual assets can be essentially eliminated by buying a diversified portfolio of such assets.  However some risks (such that the economy as a whole will do badly) are not particular to individual assets and cannot be eliminated by diversification. 

In the case of stocks it is reasonable to divide the risk (uncertainty in future returns) into two parts.  That due to idiosyncratic factors particular to individual companies and that due to uncertainly about the general future trend of stock prices (as stocks tend to move up and down together).  Stocks vary in how sensitive they are to general market movements.  Some might tend to move up and down twice as much as the market, others only half as much as the market.  The Greek letter beta is conventionally used to denote how sensitive the price of a particular individual stock is to a general change in the level of stock prices normalized so that a stock with a beta of x will tend to move up or down by x% when the general market moves up or down by 1%.  High beta stocks will have more non-diversifiable risk and are predicted by the CAPM to have greater expected returns.

The CAPM is quite elegant mathematically.  However that does not mean it is correct. Eric Falkenstein has extensively criticized it in books and his now dead blog, Falkenblog, which I mentioned earlier this month. Falkenstein's criticism (I don't know to what extent it is original, for the most part it is new to me) comes in two parts.

He claims that empirically high beta stocks have historically performed worse than low beta stocks which is a bit strange if their expected returns were actually higher.  A big part of this seems to be due to the highest beta stocks performing badly with returns otherwise pretty flat with respect to beta.

On the theoretical side he points out the usual utility function framework is inadequate as it neglects the fact that people care about how they are doing relative to others.  So they are going to prefer seeing their stocks go up 20% when the market is up 10% to seeing their stocks go up 20% when the market is up 30% although their personal return is the same in both cases.  To the extent that people care more about relative returns than absolute returns (or as Falkenstein puts it are driven more by envy than by greed) the predictions of the CAPM will be flawed.  For the so called risk free rate of return (often taken to be the interest rate paid on government bonds) is not actually risk free if people care (as they often will)about missing out on a big move upward by the stock market.  The risk free investment for such people will be an index fund which guarantees them the average market return.  Which means in effect that all risk is diversifiable and that there is no reason to anticipate greater expected returns when voluntarily assuming risk by deviating from the market average portfolio. 

Net Neutrality

Vox has an article blaming Congress rather than the FCC for the apparent demise of net neutrality regulations.  In my view this is wrongheaded, according to Vox's own coverage, Congress has given the FCC adequate authority to impose net neutrality regulations.  The FCC simply has to classify broadband internet provision as a "telecommunications service" rather than as an "information service".  This seems more logical and would allow the FCC to enact common carrier regulations.  Instead the FCC has tried to impose common carrier regulations while classifying internet provision as an "information service".  Since this is not allowed by the relevant law the Courts have rejected these attempts. 

Apparently the FCC is reluctant to classify broadband internet as a "telecommunications service" because they fear this would prompt a political backlash from industry groups.  But expecting Congress to be more willing to take political heat than a federal agency seems crazy to me.  The real reason net neutrality is dying is that its advocates haven't mustered enough political support to overcome industry opposition. 

As for my opinions on net neutrality itself, I don't think internet providers should be allowed to discriminate based on content but I am sympathetic to the view that they should be able to charge extra for high bandwidth usage and other behavior which stresses the network.

High Pay

Piketty's book is mostly about increasing inequality in the distribution of capital (and hence in income from capital).  However income from labor is also becoming less equal.  One aspect of this is the emergence of a group of extremely high earners.  Piketty's explanation for this is as follows.  This group largely consists of highly paid top corporate executives.  They are in positions where they can strongly influence their own pay.  This gives them some ability to overpay themselves and the reduction in top marginal income tax rates gives them more incentive to do so.  The natural result is very high rates of pay, well above economic value. 

I agree that top corporate executives in general are currently substantially overpaid.  Piketty's  account certainly seems plausible and is probably part of the explanation.  However it is not the entire story as there are lots of high earners who aren't negotiating their pay with themselves.  Krugman brings this up in his review:

 ... Also, I don’t think Capital in the Twenty-First Century adequately answers the most telling criticism of the executive power hypothesis: the concentration of very high incomes in finance, where performance actually can, after a fashion, be evaluated. I didn’t mention hedge fund managers idly: such people are paid based on their ability to attract clients and achieve investment returns. ...

However I think Krugman is also confused in that it isn't actually any easier to evaluate the performance of hedge fund managers than the performance of corporate executives.  In both cases you can look at how well they have appeared to do in the past but this won't predict their future performance very well.  This is because how well they do is highly dependent on luck and other factors outside their control.  But people tend not to adequately allow for this.

So I think another part of the explanation for unjustified high pay is that employers have a natural tendency to overestimate their ability to predict future performance.  So they are willing to pay more to attract their preferred candidates than is justified by actual differences in expected performance.  As a result it is quite plausible that top corporate executives would be overpaid even if their pay was negotiated with truly independent boards of directors.  Just as hedge fund managers as a group are obviously overpaid even though their clients could readily obtain better expected performance (after fees) in low cost index funds.

Capital in the Twenty-First Century

I recently read "Capital in the Twenty-First Century" by Thomas Piketty (translated by Arthur Goldhammer).  This long (685 pages) 2013 book by a French economics professor has become popular in liberal circles.  However in my opinion it isn't very good.

The book can be summarized as follows.   Around 1900 wealth was large (in terms of years of annual income) and concentrated (unequally distributed) in France and similar nations.  By 1950 wealth was smaller and more evenly distributed but then became to grow larger and more concentrated again.  The author projects further increases in the years ahead, takes for granted that something needs to be done about this and proposes a worldwide tax on capital.

The historical part which traces the distribution of wealth from 1800 or so to the present is of some interest but could have been presented much more concisely.  Piketty concedes that economists in 1900 or 1950 would have been unwise to expect to be able to accurately predict the future distribution of wealth but then undaunted makes his own predictions.  I see little reason to give them much credence.

Piketty's main policy recommendation is a worldwide graduated tax on wealth.  His arguments for this aren't likely to convince anyone not already favorably disposed.  He professes to be concerned about wealth becoming concentrated in a few large inherited fortunes but much less drastic steps would prevent this.  For example requiring large estates be split at least 10 ways (that is no single heir could inherit more than 10%).  This would fairly quickly disperse large fortunes.  As Piketty acknowledges simply abolishing primogeniture has had such an effect.  

In contrast it appears likely that Piketty's wealth tax would not simply cause wealth to be spread more widely but instead would cause wealth to be diverted into consumption which would over time substantially reduce the amount of wealth.  It is unclear why Piketty thinks this is a good idea.  Piketty's predictions rely on the claim that there are few diminishing returns to wealth, that it is possible to productively employ ever increasing amounts of wealth.  So what is the benefit of a poorer society with less wealth available to increase labor productivity?   

Piketty attributes the problems of current (and former) actually existing wealth taxes to difficulties arising from trying to impose such a tax in a single country.  Hence his proposal for a worldwide tax.  But the difficulties could also be attributed to the compromises required to get a wealth tax enacted and these would only increase if you had to get the tax enacted worldwide.

The book seems unfocused and much too long.  Which makes it harder to identify the key points.  Among other things Piketty rambles on about the novels of Austen and Balzac at considerable length.   Which he cites as sources for the claim that around 1800 it was difficult to live a decent life without access to inherited wealth.  Whatever the truth of this it has little relevance to today's conditions where anyone in the top 10% of labor income is doing fine.

Piketty makes some curious claims, for example on page 432 that:

... In the long run, unequal wealth within nations is surely more worrisome than unequal wealth between nations.

This seems debatable to say the least.  But perhaps Piketty is more bothered by the few people who are much richer than he is than by the billions who are much poorer. 

In summary I found this book hard to get through and I don't recommend it.  If you are interested reading a few reviews seems like a less painful way to pick up the main ideas.

User Interfaces

I stopped in a supermarket on my way home Friday night and when I was checking out the clerk erroneously scanned my single item in with the stuff the customer ahead of me was buying. I would have expected this to occur fairly often and be easy to fix but apparently a manager was required and none was immediately available. Meanwhile another line opened up so I was able to switch and complete my purchase but the unfortunate customer ahead of me was still waiting as I left.

This seems like a surprisingly poor design particularly for something as heavily used as supermarket scanners. Of course you need to be careful not to provide options that make it easy for the clerk to steal but I don't see the risk in allowing the clerk to cancel the last item scanned. I suppose it is possible the clerk just didn't know the procedure for fixing the mistake but I got the impression that the problem was they lacked the authority which seems like bad design.

2013 Taxes

This year I got my taxes done a whole day early.  Hopefully things will go better than last year.  My state refunds took months to arrive and then it turned I had made a mistake on my New York return and had to file an amended New Jersey return. 

This year I have already made one mistake.  I realized shortly after submitting my federal return electronically that it was missing a form.  Fortunately this didn't affect the amount of the refund I am due so I just stuck the missing form in the mail to the IRS but it was still aggravating.  I consider this mistake partly TurboTax's fault as it gives you an option to skip things you aren't ready to do yet but then doesn't always remind you in the review phase that you may not be finished.  So you should be careful about starting your return before you have everything you need.

I had some of the same issues with TurboTax as in previous years and noticed another problem.  In the review phase it summarized my effective federal tax rate for 2013 and previous years but computed it incorrectly for 3 out of 4 years.  For 2010 and 2011 it failed to add in the AMT and for 2013 it failed to add in the Obamacare investment income surtax.

I gripe about TurboTax a lot but it really doesn't make much sense to try to do your taxes manually if they are at all complicated.  The Obamacare surtax has just added another layer of pointless complexity.          

Vox and Falkenblog

I have added Vox, where Matthew Yglesias is now writing, to my blog list.  This is Ezra Klein's new venture which he left the Washington Post to start.  Another of their writers is Brad Plumer.

I recently discovered Falkenblog by Eric Falkenstein, a 1994 economics PhD who has held a variety of finance jobs.  I won't be adding this blog to my list as he stopped updating it last September to avoid any conflicts with his latest job.  Also he can come across as a bit of a crank particularly when he moves away from finance to post on things like politics or evolution.  And he has a Yglesias level propensity for typos and other careless errors which can make him hard to understand.  Nevertheless I found some of his finance posts quite interesting and plan to comment further on some of his major themes which include missing risk premiums, low volatility investing and relative utility functions.

Fifth Third Bancorp v. Dudenhoeffer

The Supreme Court heard arguments Wednesday in the case Fifth Third Bancorp v. Dudenheffer.  The case concerns the obligations of the managers (fiduciaries) of a employee stock ownership plan (ESOP) when they have some evidence that the company stock is a bad investment.  The defendants (Fifth Third Bancorp) want a rule that it is presumptively prudent for a ESOP to buy and hold company stock.  This seems sensible to me.  Some (by which I mean one or more) of the Supreme Court Justices seemed concerned about establishing a special rule for ESOPs but I see this as an application of a more general rule that it is presumptively prudent for fiduciaries to obey instructions.  It is common for defined contribution retirement plans to allow participants to direct how their contributions are invested.  Naturally some participants will make better decisions than others but I don't think it is practical (or sensible) to require a fiduciary of such a plan to routinely independently evaluate (and possibly overrule) the participant's instructions.   

There is a complication in the current case in that the negative information was "inside information" which it can be illegal to act on.  The plaintiff's lawyer appeared to be arguing that even if the defendants could not legally act on the information they could nevertheless be liable for failure to act.  The government lawyer appeared to concede that the defendants could not be held liable for obeying the law but were obligated to do everything they could without breaking the law.  Considering the rather unclear state of insider trading law this would put fiduciaries in possession of inside information in a very difficult position.  In particular the government claimed that although you could not legally sell on the basis of inside information you could legally stop buying.  Perhaps this is actually the law (although some Justices noted no lawyer from the SEC had signed off on the government brief) but it makes no logical sense.  As I understand it employees are allowed to participate in stock purchase plans in which a fixed percentage of their pay is regularly used to buy company stock even if this means they are sometimes buying when in possession of favorable inside information.  The idea is they are not buying because of the favorable inside information.  But if you allow them to suspend purchases when in possession of negative inside information this rational disappears.  Now all of their purchases are based in part on inside information, namely that there is no pending undisclosed bad news.  Thus giving them the sort of insider advantage that the prohibition against inside trading is supposed to prevent.