Fractional Doom

I don’t know what more to say about this:

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.

JPBIBNR – Just Plain Bad Incurred But Not Reported

Nigerian GAAP, soon to be replaced by IFRS at least in the financial services sector, requires IBNR liabilities to be set equal to 10% of the Outstanding Claims Reserve. This is a terrible estimate of IBNR and there really are other, also very simple, better measures available.

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.

Surveys, papers and books on the ERP

Some interesting papers on the ERP:

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

The Equity Premium in 150 Textbooks

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.
The debate certainly isn’t over, but these papers and the referenced papers, research and textbooks are a good starting place to get up to speed.

 

 

 

 

Balanced budgets and present values

Public debt levels and balanced budgets have never been more in the media and the minds of politicians and economists around the world. The question of whether and when a budget should be balanced is fundamental to how governments are reacting to the struggling economy, high unemployment and increasing government borrowing in developed countries around the world.

Much of the conversation ignores some pretty fundamental points about the present value of future taxes and the present value of future payments arising out of current obligations. If a nation’s social security system is not funded or “pay as you go”, one might argue that there is a significant additional liability not being reflected in the national accounts. The size of some of these numbers is sufficiently large to swamp the current conversation about debt levels.

Equally, though, we can’t take into account the present value of all future social security payments for the next hundred years without considering the taxes that will be raised over that same period. This future stream of cash inflows to government treasuries could be considered an asset.

Now the possibility of calculating the present value of cash outflows and inflows and the measurement of these “liabilities” and “assets” doesn’t necessarily mean doing so is the most useful way of understanding the problem. Pension valuations often use “projected unit credit methods” and others of determine an appropriate net liability at a particular point without explicitly considering the future contributions that will be required to fund the liability over time.

The relevance of present values and the budget is fairly well understood when it comes to social security, but the same principles should inform nationalization and privatization debates. Selling a national asset only changes the net position of national finances if the receipts received from the market are higher than the present value of future profits to the treasury from the company.

On the other side, borrowing to finance a productive capital project doesn’t change the net balance sheet position, although it does increase gearing – just like for any organisation.

The point of this slightly rambling post is that budget deficits and the demand to balance budgets are usually based on incredibly short-sighted measurements of national finances. If we don’t consider the impact on economic growth and therefore future tax receipts when making decisions, we are bound to get it wrong more often than right.

Compounding wisdom from a surprising source

I really struggled when Health Minister Aaron Motsoaledi announced (many sources, but here is one) that private healthcare costs have increased by 121% over the last decade.

He continued: “Over the past decade, private hospital costs have increased by 121%, while over the same period, specialist costs have increased by 120%.”

Anyone who measures growth over long periods without using compound annual rates can’t be taken seriously. Abusing numbers for shock value is a sure sign of a weak argument or a lack of appreciation for long-term issues.

121% over nine years (2001 to 2009) equates to an average cumulative annual growth rate of 9.2%. Now medical price inflation of 9.2% is high given inflation over the period and modest real growth in GDP and salaries. But 9.2% tells a very different story to a layperson than 121%. The 9.2% is more useful, more comparable to inflation, more easily able to be understood. 121% is more shocking.

I was really encouraged to read this in a story, quoting Matlala from HASA:

He pointed out that while the green paper said private healthcare costs had increased 121% between 2001 and 2009, this should be contextualised against the backdrop of contributions to public healthcare increasing by more than 100% over the same period.

“Even the price of bread has increased 111% over the decade… We have to face up to the fact that the cost of living has gone up, including healthcare,” Matlala said.

Finally, someone quoted acknowledging that the 121% figure is utterly misleading.

Incidentally, 111% over 9 years is equivalent to an 8.7% annually compounded growth rate, just 0.6% per annum below healthcare cost increases. 

 

The value of spurious precision

From a TimesLive article on looting:

A millionaire’s daughter, Laura Johnson, 19, was remanded in custody when she appeared in court in Bexley near London after being arrested behind the wheel of a car filled with stolen electrical goods and alcohol worth about £5000 (R56385.90).

So the goods were worth about GBP50,000 GBP5,000 (a good round number for an estimate) but worth exactly R56,385.90.  Yes, and 90c.

Accuracy is often important. Precision is sometimes important. Pretending to have either is silly.