It’s not really a practical issue since recent history has shown that not all beneficiaries of land restitution ultimately want to work the land. This is also entirely reasonable given the change of our economy from a primary economy to a secondary and tertiary economy over the last 50 years.

So when I read that the SA Institute of Race Relations states that more land could have been returned to black beneficiaries if money was not offered instead, I just wonder what the point is.

If people are accepting cash rather than land, it may well be because they want the cash rather than the land. Given land, I’m not aware that there is a prohibition on selling that land (which would be a poorer form of property right than they originally had so surely can’t be allowed) so we could end up in the same situation.

The danger for me is that the measures of land restitution could so easily, accurately and misleadingly, refer to the amount of land that has been restituted, or the amount of land currently in the hands of black South Africans, when this is clearly not an accurate measure of what progress has been achieved.

I’m continually disappointed that Moneyweb continues to partner with this distraction.

As I’ve done in the past, I’ve analysed very quickly some of the results of the most recent competition. As background to that, the basic rules are:

1. Put up R20,000 of your own money
2. Trade over three months in currencies, commodities single stock futures and some index trackers.
3. Whoever has the most at the end wins a million rand
4. Everyone keeps what is left of their initial “investment”

So let’s be clear, there are no long-term investment learnings here.

The winner did return 165.5% over 3 months, which is not an impressive performance even though it might look like it.  The point is, given the volatility of the investment universe available for the competition and the encouragement towards rampant risk-taking, it’s entirely pedestrian performance.  It’s very likely an individual’s performance will be good given the wide range of possible outcomes.

Let’s look at some other statistics

These are not performance statistics of which to be proud. They are similar to the losses incurred in prior competitions.

So in short, the competition cost the entrants in total just over a million rand. Losing a million rand is a great way to Make a Million.

Some of the stories around in the news did prompt me to take a look at the South African population pyramids as estimated by Stats SA. Now these figures are extrapolations based on demographic models and the results of the 2001 national census.

As an actuary interested in economic policy I was disappointed with myself that I was surprised by the shape of these pyramids. Some striking messages to say the least.

population pyramid all

The overall population pyramid is relatively typical of developing countries with a significant portion of the population under 15 and a significant majority under 35. The growth rate is clearly already slowing, but a surge of youth, many to poor families with limited prospects for good education is still working its way through our population ranks.

An delegate attending a recent CFA Travelling Conference was muttering something about “the problem with South Africa is that different groups have different growth rates and this causes a problem because some groups already have high unemployment so where will the jobs come from?” Newsflash everyone – more people equates to more consumers as well as more workers. The problem is one of public education that ensures even children born to poor families have great education and gain the skills to be productive. High growth rates make the challenge of ramping up public education to the right level and scale required more difficult, but this is an education issue primarily not a population growth issue.

population pyramid black

I’m including the “black population pyramid” just for completeness.  Given the massive proportion of the population that is black/african, it looks pretty much the same as the overall population pyramid. What is highlighted here, although is also apparent in the total population pyramid, is the sharp decline from the 30-34 band to the 35-39 band. Now, unless there was a sudden spurt of fertility or a sudden decline in infant mortality 40 years ago, this almost certainly reflects HIV/AIDS deaths. Seeing it here as that sharp decline in our most economically productive age group is quite horrifying.

population pyramid indian

The indian/asian pyramid is already in the shrinking stage. As higher incomes and education give rise to lower birth rates, the population shrinks in textbook fashion.

population pyramid white

The white population pyramid is a mix of standard-shrinking (similar to Indian/Asian) and a shocking emigration-bite / brain drain in the 25 to 40 year age bracket. I feel confident saying this is emigration not HIV/AIDS deaths given the low HIV prevalence in the white population.

These emigrated people will generally be the educated, productive, skilled workers (educated with large state subsidies much of the time) and is a big part of the sluggish economic growth in South Africa.

The size and impact of that brain drain has never been as apparent to me as this population pyramid shows.

A MODEL ISN’T REALITY

Any simplified model I can imagine will also therefore not match reality exactly. The closer the model gets to the real world in more scenarios, the better it is.

Not all model parameters are created equal

Part of the approach to getting a model to match reality as closely as possible is calibration. Models will typically have a range of parameters. Some will be well-established and can be set confidently without much debate. Others will have a range of reasonable or possible values based on empirical research or theory. Yet others will be relatively arbitrary or unobservable.

We don’t have to guess these values, even for the unobservable parameters. Through the process of calibration, the outputs of our model can be matched as closely as possible to actual historical values by changing the input parameters. The more certain we are of the parameters a priori the less we vary the parameters to calibrate the model. The parameters with most uncertainty are free to move as much as possible to fit the desired outputs.

During this process, the more structure or relationships that can be specified the better. The danger is that with relatively few data points (typically) and relatively many parameters (again typically) there will be multiple parameter sets that fit the data with possibly only very limited difference in “goodness of fit” for the results. The more information we add to the calibration process (additional raw data, more narrowly constrained parameters based on other research, tighter relationships between parameters) the more likely we are to derive a useful, sensible model that not only fits out calibration data well but also will be useful for predictions of the future or different decisions.

How not to calibrate a model

Scientific American has a naive article outlining “why economic models are always wrong”. I have two major problems with the story:

1. All models are wrong. Some are useful (George Box). “wrongness” isn’t a problem with a model, but lack of usefulness is. The headline demonstrates a starting point poorly informed about the point of economic models.
2. The calibration approach criticised in the article is an extremely poor way to calibrate a model. No serious researcher thinks that is the right way to calibrate a model. So the article merely creates a straw man and then demonstrates how easy it is to knock the argument over.

Calibration and back-testing on separate data sets

The right way to calibrate a model is to separate the data-set into at least two independent subsets. Firstly, the “training set” or portion from which we will calibrate our parameters to get them to match as closely as possible the data. Again, this should make use of all information available and may give rise to several competing models that appear to fit the data similarly well.

The next step is crucial. We back-test the derived models against the second subset of data. This data comes from the same reality (perhaps a different time period) as used to calibrate the model, but the model won’t trivially match the data because none of that data was used to calibrate the model in the first place.

The importance of back-testing

Back-testing is critically important in the model building process, but back-testing against the same data used to calibrate the model is worth than useless (since it takes time and effort and an create a false sense of accuracy or reliability in the model.) Separating the data into two or more subsets is absolutely required, although it has the unfortunate side-effect of reducing the size of the data-set available for calibration.

Yes, it really matters.

A common example of the dangers of bad models fitting data well is with Economic Scenario Generators. These simulate economic scenarios to be used in valuing complex financial securities. If a model is properly calibrated, it will recreate the observable market prices of a wide range of instruments. However, the model could be a black-box neural network, a carefully constructed theoretical model with plausible relationships and constraints, or the proverbial ten thousand (possibly inebriated) monkeys. If all three models are perfectly calibrated to observable market prices, is any of the models inferior to any of the others?

Clearly the answer is yes, but only when it comes to extrapolation. I have far more confidence in the model’s ability to create “market consistent” valuations for instruments that do not have observable prices in the market if I understand how the mechanics of the model make sense on a level other than pure calibration.

Trivial 3 point example

Perfect fit of two models to 3 data points

The example above shows a perfect of a quadratic and cubic model to 3 data points. From this graph, both models appear exactly the same.

However, if we use the model to extrapolate to future time periods, the results are very different. Without additional data to back-test the results on, it’s not possible to tell whether either or any of these models is appropriate, but clearly both can’t be correct.

Extrapolation of the two models shows divergent results

Part of the deal is a “50% loss for private investors”. Which is part true and part nonsense but will be an effective Greek default when enacted / agreed. (I don’t care how “voluntary” it may be, it’s a default and almost all definitions of default include restructuring of debt in any way that isn’t what was originally promised.)

Why is it only partly true? Well it’s not necessarily a “loss” for private investors. The probability of default on Greek bonds has been just about 100% for a while now. This probability of default is derived from market prices for Greek bonds and market spreads on Greek Credit Default Swaps (CDS) and an assumed Loss Given Default or Recovery Rate for investors when the bonds do default. Actual Recovery Rates vary widely, but often analysts plug in the average Recovery Rate over most of this century on unsecured debt which is around 40%.

So if market prices for Greek bonds assumed 100% default probability and a 40% recovery, then a 50% recovery doesn’t sound so bad. The potential downside is that Greece may still (need to) default on these written-down bonds at some point in the next two decades.

So the real question is what will the new probability of default be? Then we will know whether investors “took a loss” and perhaps gain the market’s view on how successful the deal really will be.

It’s worth reading the entire article, but the main message is that we cannot use the dream or story or fairy tale of imminent migration into space and other planets as an excuse not to deal with the very real problems we have on Earth right now. The misconceptions, Hollywood induced and otherwise, about the ease of space travel or even the extent of our current capabilities, are massive.

As with so many things, the stories that fill our society can be very different from the harsh reality.

Teachers can’t do fractions.

For all the complex thoughts on teaching approaches and school feeding schemes and  exam difficulty and class sizes and parental involvement and availability of tertiary education and apprenticeships and any number of other issues, if teachers don’t know their subject education is doomed.

If education is doomed our economy will struggle along for decades. If our economy struggles, income inequality and poverty won’t improve. This is not hard.

“Searchers” were able to find emails more quickly than “filers” in a study by IBM covering 354 email users.  Filers took nearly a minute per email on average, with searchers only take a third of that time.

As an aside, the use of IFRS balance sheet figures for regulatory reporting is also an unusual idea. There is no particular reason to believe that a shareholder financial reporting basis is appropriate as a regulatory measure. It can be, with specific capital rules perhaps, but it’s not automatically so.

Why the 10% of OCR rule for IBNR liabilities is so bad:

1. For very long-tailed business with no or low claims reported in the first year, the IBNR will be massively understated
2. as claims are reported (and before they are paid), the OCR will increase. The IBNR should decrease as the claims have now been reported, but given the 10% rule it will actually increase.
3. The reconciliation of opening to closing IBNR and the comparison of actual vs expected IBNR claims over time is not useful since there are no explicit expectations built into the methodology
4. Clearly the method is not sensitive to risks and delays of product lines or processes.

So what’s better? Well aside from the range of standard but fairly complex techniques (including Ultimate Loss methods, Basic Chain Ladder, Bornhuetter-Fergusson, Average Cost Per Claim and a whole range of stochastic methods) there are better simpler measures.

A starting point, although also very far from ideal, is the current (soon to be changed) South African statutory requirement of 7% of net written premiums. It also isn’t sensitive to different delay patterns and will give poor results if net written premium is growing or shrinking rapidly.

Really, the ideal simplification requires a little more complexity, but as a reward for this effort is a far more robust, more accurate measure that behaves sensibly in a far wider set of scenarios.

For each line of business for each delay year, we use a specified percentage of gross earned premium for the gross IBNR. Reinsurers’ share can be calculated similarly. The information relating to earned premium per line of business going back several years should be trivial to obtain and ensures we get a sensible pattern taking into account the growth in the business, the mix of business as well as change in mix of business. The method works well for start-up, mature or declining books.

The fundamental drawback of not reflecting a particular insurer’s patterns remains, but aside from using actual delay data this is about as good as one can hope for.

Frankly, why more regulators don’t prescribe this method is a mystery. The information is available, it’s trivial to calculate and verify and the results are robust.

Market Risk Premium used in 56 countries in 2011: a survey with 6,014 answers

• Interesting not least because it is a survey of required Equity Risk Premiums (or Market Risk Premiums) rather than expected. The rates are higher than I use, although this is also useful information when attempting to perform a “benchmark” valuation. I still struggle to see how these high estimates tie in with prospective estimates of overall economic growth and market performance, which is an important sense-check on any ERP estimate.

The Equity Premium in 150 Textbooks

• The results show a range from 3% to 10%, and that 51 books use different equity premia in various pages. The 5-year moving average has declined from 8.4% in 1990 to 5.7% in 2008 and 2009. This declining trend has been observed over even longer periods and is one of the common reasons for mis-estimating the ERP. 

Equity Premium: Historical, Expected, Required and Implied

• This work provides a fairly in-depth analysis of the differences between the various definitions of ERP and a comprehensive survey of major sources for estimates of these. In general, the estimates of the Expected ERP over T-bonds (rather than short-dated T-bills) are in line with the range I use of 3% to 5% with several showing values to the lower end of this range.