Thursday, May 28, 2015

Trading increases variance

When saving for retirement, most investment advisers recommend holding at any one time a diversified portfolio of stocks and bonds with low management fees (MER). Regular trading is usually not recommended for two good reasons: 1) trading is expensive (transaction fees and bid-ask spreads are lost each time); 2) trading increases your portfolio's variance. Point 2 is not very intuitive and most investors don't realize they are increasing the variance of their nest egg by trading.

To illustrate the increase in variance, let's trade S&P 500 index "shares" and cash from 1/3/1950 to 5/27/2015 (16455 closings = 16454 daily gains). Holding cash for the entire period would result in a nominal gain of 1.0 (eg. no gain). Holding S&P 500 index "shares" for the entire period would result in a nominal gain of 127.6. Holding shares half the time would result in an expected nominal gain of sqrt(127.6) = 11.28.

What happens if we were to hold shares for 8227 consecutive days and cash for 8227 consecutive days (period start chosen at random), as compared to holding shares during randomly chosen 8227 days? See graph.

Again, but only holding shares for one quarter of the days (4113 days shares, 12341 days cash):

Again, but only holding shares for one sixth of the days (2742 days shares, 13712 days cash):

Though the median gain remains similar, the variance of outcomes is higher under daily, monthly and yearly trading regimes. As the second and third plots show, mean reversion is a very long term effect: the increase in variance is only evident at the edges in the last two plots. This demonstrates that markets have a (very) long term tendency to revert to the mean, which is lost when trading often. In practice, this means one should not trade often and should not invest in actively managed funds. It also means holding shares for a very long time is the only way to "fully" compensate for the increased volatility (no surprise here).

Tuesday, April 17, 2012

The sum of its parts

[This is a long post; for those with little time on their hands, the important parts are in red]

The forthcoming university tuition hikes in Quebec have led to an eight week strike by students, putting their semester in jeopardy. Many debates have ensued in the media: I was always under the impression that the electorate did not grasp the workings of society and government, and these debates cemented those impressions.

Student groups proposed increasing taxes on corporate income and capital to fund universities without affecting tuition fees. Some groups even proposed making university education completely free. On the streets of Montreal, one pedestrian in three can be seen wearing a red square, the symbol worn by student protesters.

For a democratic society to operate smoothly, the facts underlying taxation and government service decisions should be well understood by the electorate. Yet this is not the case, even for trivial facts. As an example, ads for lottery products aired on The Buzz (a radio station in Burlington) always end like this: "All lottery profits go to the Vermont Education Fund. Please play responsibly." While it may be true that lottery proceeds are deposited in the Vermont Education Fund (rather than the general tax fund), this does not change the amount of money spent on education. The vast majority of education spending is financed through general taxation, and thus the total amount spent on education remains the same.

Another example is a survey conducted in the United States in which citizens were asked what government services they were benefiting from. Many could not even name a single service, let alone how much that service was worth to them or how much it cost. Yet almost everyone benefits from unemployment insurance and social security. What about law enforcement, infrastructure, parks, water, sewage, education? There are so many to choose from.

Simultaneously debating how to tax and redistribute income, and which services to offer is unnecessarily complicated. For example, students claim that university education subsidies are necessary to be fair to the poor (eg. give the poor equal opportunity). While it is true that helping poor individuals out through redistribution of income is fully justified (both to help them get by and improve their long term prospects), subsiding university education is a very inefficient way to achieve this goal. It should not matter if a poor person chooses to go to university or not, he should receive the same subsidy. Similarly, non-poor university students should not be subsided at all, since that subsidy would be better spent on poorer individuals, might they be university students or not.

To get around the confusion of which services to subsidize, and how to fund each subsidy and service, government activities which deal with money should be split into three independent parts, which do not exchange funds with each other: government managed services, government managed insurance/financing, and redistributive taxation. A fourth part, which does not deal with money directly, is the regulatory aspects of life in society: it has a huge economic impact but is rarely a topic of heated debate amongst the electorate (with the exception of the environment).

Regulatory Aspects of Life in Society
The government should ensure that all drivers have third party insurance, that all individuals save enough to build a minimal nest egg (for a rainy day and retirement), that all individuals have minimum level of health insurance, that all suppliers of consumer products adhere to reasonable level of safety, etc. I could go on and on. Regulatory choices are not trivial and have many economic consequences; however, the electorate is rarely divided on such issues.

Government Managed Services
Most services can be offered by the private sector. However, in some circumstances, government must intervene due to monopolies, externalities and other market failures. Some services can only be provided by the government, such as a the creation of laws and their application, national defense, fundamental research, infrastructure, etc.

These days, governments offer many services, with varying degrees of efficiency. Most of these services would be better handled by the private sector. To decide which government managed services should be improved or dropped, electors need to understand what they are getting and how much it costs them. A first step in doing this is reading through the budget, line by line. Few people do this.

A much better way is having a detailed bill, payable to the government, sent to individuals each month based on the actual services used by that individual. For some services, it is very hard to estimate how much an individual is using, such as law inforcement, election fees, etc. Those items can be simple head taxes. Other items such as renewing a passport, buying a license or other fee-for-service items should be billed based on usage.

Currently, poor individuals don't see that they are paying for subsidies and services: such amounts are net out of the payments they receive. It becomes much clearer that the services are not free if they receive 30K from the government per year, yet have to return 20K in various mandatory services. There would be much more pressure to eliminate some of these services if the electorate knew how much they are costing per month, and that the savings would go to them directly if the services were abolished. Currently they assume that cutting services results in tax cuts for the wealthy, and that they would be worst off overall.

Monthly billing cycles are what all individuals are used to seeing (eg. credit card bill, payments on loans), so they can quantify and compare the savings to other choices they make.

This branch of government should be complete self financed: it should not be financed by taxes at all.

Government Managed Insurance/Financing
In some circumstances, private corporations cannot provide financing or insurance because their borrowing costs are too high; governments can raise taxes to finance shortfalls, giving them lower borrowing costs and allowing them to extend the range of products offered by the private sector. This includes education (financing all but the last few years of education) and counter-cyclical macroeconomic investments (buying distressed assets when markets are panicking). If private insurance markets don't form on their own for some essential types of insurance policies, the government should step in the fill the void as well (such as natural disaster insurance or crop failure insurance).

This branch of government should be completely self financed: it should not be financed by taxes at all. Its income is the result of charging interest on the loans that it makes, and charging premiums for the insurance products it offers.

Redistributive taxation
Given that other government branches must cover their costs without recourse to taxation, they must impose a fee-for-service or a head tax on all citizens. Less fortunate individuals, whatever their predicament, may not be able to afford these fees and other private expenses that they require to get by. A redistributive taxation system is needed to help them.

How to design a fair and efficient redistributive system is quite debatable, whereas the other three branches of government are much less controversial. On the right, hardcore libertarians believe there should be no redistributive taxation at all. On the left, there are two competing positions: zero inequality through tax rates of 100% (eg. complete redistribution supported by coercive labor policies), or tax rates achieving maximum absolute redistribution.

Maximum absolute redistribution is a very interesting proposition, since in dollar terms it helps the poor the most. To achieve this goal, you create a taxation system that splits people into two categories: those who make less than X and those who make more than X per year. Then you set the tax rates of those making more than X in such a way that you get the maximum amount of tax money, which you redistribute in some way to those making less than X. That's it. This can be summarized as "targeting maximum socialism", a bit like the Bank of Canada has a target rate for inflation.

As the tax rate is increased on wealthy individuals, the total tax take from these individuals eventually falls due to the Laffer effect (a combination of tax avoidance, emigration, and preferring leisure over work). Similarly, as subsidies are increased for poorer individuals, the incentive to work is decreased due to the fact that the subsidies will be partly lost as income increases (preferring leisure over work).

There are two ways to increase the total redistribution amount: increase inequality or increase economic output. Fortunately it seems that these days increasing economic output causes inequality to increase, so there won't be many compromises on this front.

How do we increase economic output?
1. By avoiding the emigration of talented individuals
. a) by not taxing them too much
. b) by providing them with career opportunities.
2. By encouraging foreign direct investment (btw, in absence of capital controls, all capital is foreign)
. a) by not taxing corporate income
. b) by not nationalizing foreign owned companies
. c) by eliminating mandatory employer payroll contributions
. d) by eliminating minimum wages
. e) by enshrining these rules in the constitution
3. By reducing regulations and relaxing trade barriers.

Interestingly enough, high income individuals are much more mobile than middle income individuals, especially in a country like Canada (as opposed to North Korea). This means that the tax rate of high income individuals may need to be lower than that of middle income individuals, otherwise they will move to Ireland, and leave with their business, the jobs they created and the associated economic output.

Note 1: Foreign direct investment may seem completely unnecessary, given that the government can issue debt at a lower interest rate than foreign investors, and invest in local businesses directly. While this works in theory, foreign investors have the skills that allow them to select businesses that will thrive over those that will fail. Since the government does not have this expertise, it cannot choose successful businesses, thus ends up losing money despite its cheaper borrowing rate. In less polite terms, foreign capital is smart money, whereas government investments in the private sector is dumb money. Local private capital is somewhere in between. Capital is in large part what distinguishes a successful economy from a stagnating one.

Note 2: subsidizing some university programs may increase future tax revenue, given that the redistributive taxation part of government has an equity stake in high earners future income -- as long as they don't leave the country. I will address this very interesting and complex issue in a another post, as well as the almost as fascinating realm of demographics and health insurance, the three most important roles played by the of government.

Sunday, January 22, 2012

A gaping hole in philantropy (2)

A great TED talk given by winners of the 2011 Google Science Fair shows that high school students can perform useful research if given the chance. These students were persistent and lucky enough to find a researcher who could give them access to a lab. Though it is difficult to know the exact number, a multitude of students must have given up before getting access to research facilities.

It is clearly not cost effective for individual researchers to give access to their lab to research savvy high school students on weekends, but society loses a great deal by not sponsoring these students.

Specialized schools in the fields of sports, ballet, music and theater exist already. Why aren't there any high schools which let teenagers do self-directed research in lieu of classes for half the school day?

Many parents already teach their profession to their children, but giving access to equipment and materials in the workplace is usually not possible. Now that the price of equipment has fallen enough for hobbyists to open labs such as Genspace, why can't specialized schools offer such equipment too?

Thursday, January 12, 2012

Beyond Vouchers

Charter schools and voucher systems are a good first step towards improving the teaching of a state mandated curriculum. However, many market failures remain in such a system. While competition between a few schools offers students choice, the overhead of changing schools or selecting a school which is farther a field makes the market work poorly. Most importantly, student utility (eg. pain and effort to achieve a grade) has very little weight in the selection of teaching methods.

In reality, the operation of schools has little to do with the success of its students: after all managing a building and administrating personnel is a commodity. What matters is the teachers. So why not have charter teachers, all in the same building, rather than charter schools? If there is some overcapacity of teachers, then the worst ones as chosen by the students would end up out of business. This would give students much more choice in the compromise between attaining the highest grades vs. the effort they have to put in.

Knowing how good a teacher is before taking his class is quite difficult for a student, and repeat business is not really possible given that teachers specialize in one subject and grade level. So charter based teachers suffer from some of the same problems as charter schools: by the time students have enough information to choose a teacher, it's too late -- they are already committed.

A solution to this information problem is to force each student to cancel exactly one class per semester at any time prior to the final exam. The worst teacher as judged by the students will be financially penalized for each student that abandons his class. The very worst teachers would abandon teaching altogether.

Whatever system is chosen to improve education, the student's preference for effort vs. grades should be fully internalized.

Wednesday, July 27, 2011

Making leisure pay

The Bixi system in Montreal allows users to rent bicycles at stations all around town. It's popular but expensive: maintaining a Bixi bicycle cost around 3000$ per year, which is heavily subsidized by the city. Some opposition politicians suggest that just buying everyone a regular bicycle would be a cheaper alternative to Bixi, and accomplish the same congestion reduction and environmental goals.

There are often one or two broken bicycles at each Bixi station waiting for repair. Such repairs require paid staff to service the bicycles. The alternate solution would have owners of bicycles repair them on their own time. This is an example of how one method makes use of "work hours" to accomplish a task, whereas the other method makes use of "leisure hours".

While increasing the number of officially worked hours is not popular, making small changes could result in heightened productivity by moving tasks from work hours to leisure hours.

For example, the vast majority of state services provided for individuals could be offered outside of regular work hours. Very often, employees must take time off work to go to a clinic, to renew a passport, etc. Only offering these services on week nights and during weekends would increase productivity of those working in non-government service jobs.

Wednesday, July 20, 2011

Drugs and Drug Policy

I'm currently reading Drugs and Drug Policy. I'm very impressed after two chapters: it's clear, accessible and well balanced. The lesson seems to be that decriminalization of consumption (not production) has little impact on prevalence, whereas retail prices have a huge impact.

I was disappointed to read that the authors do not believe in the legalization of the supply chain while maintaining elevated prices levels. Once the decriminalization of consumption becomes politically feasible, the supply chain of drugs that have a high markup could easily be nationalized.

In Quebec, decent quality alcoholic beverages are distributed exclusively by the government through the SAQ. The SAQ turns a decent profit with markups of two to one, and there is no large scale contraband of wine in Quebec. It should be trivial to run a similar organization for illegal drugs whose markup is significantly greater than two to one.

As an example, cocaine production costs around 1$ per gram; bulk cocaine smuggled across the border costs 20$ per gram, and retail cocaine is sold at 100$ per gram. I'm assuming that given current law enforcement spending, prices are close to as low as they can be to sustain contraband. Nationalized drug prices could be adjusted to prevent the bulk of contraband: in all likelihood that price would in the same order of magnitude as today's retail prices.

Nationalization does not seem to be a compromise at any level.

Tuesday, July 19, 2011

Unconventionnal tools

Economists agree that increasing consumer spending is the most effective way to stimulate an economy out of recession or stagnation. Conventional tools (such as infrastructure spending) are both slow and inefficient. Letting politicians choose how to apply stimulus in recession years is like giving your child a credit card and sending him to Toys R Us. There must be a better way.

Why not give the Fed the responsibility to coordinate direct stimulus in addition to affecting the markets by buying and selling financial instruments? Specifically, the Fed could be given a stimulus fund worth 1% of GDP per year (from general taxation) to be sent to all citizens in the form of monthly cheques when the economy needs to get back on track. Or it could just be trusted to spend the right amount, and possibly need to be recapitalized using general taxation as is the case currently.