Author Archives: David Kirk

About David Kirk

David Kirk is a partner at KPMG running the national actuarial consulting practice. He is an actuary and is the creator of New Business Margin on Revenue. He specialises in risk and capital management, Solvency II and insurance strategy . He also has extensive experience in embedded value reporting, insurance-related IFRS and share option valuation. Apart from his work in South Africa, he has been involved in significant insurance projects in the Middle East and China. David began his career at Tillinghast – Towers Perrin in 2002 where his work experience included embedded value work in life insurance and reinsurance, life insurance appraisal value calculations, stochastic guarantee pricing, and building and reviewing economic scenario generators. He worked in both the London and Cape Town offices, gaining exposure to the insurance markets, products and regulatory environments in South Africa, the UK and Europe. David then headed up the Johannesburg actuarial practice for PricewaterhouseCoopers as a partner with core responsibilities around life insurance, general insurance, financial and risk management and business development. David is an active member of the ASSA’s Life Assurance Committee and Embedded Value subcommittee, chairs the Micro-insurance Committee and chairs the Technical Provisions Task Group as part of the Financial Services Board’s Solvency Assessment and Management (SAM) Project. He has lectured parts of undergraduate and postgraduate courses at the University of Cape Town, the University of Stellenbosch and the Lebanese University. He is an assessor and instructor for the Institute of Actuaries Business Awareness Module. David is a Fellow of the Institute of Actuaries (FIA) and a Fellow of the Actuarial Society of South Africa. He holds a B.Bus.Sci degree in actuarial science and finance from the University of Cape Town, is CFA Charterholder, a Chartered Alternative Investment Analyst (CAIA) and a Certified Professional Risk Manager (PRM).

The virtual irrelevancy of population size to required sample size

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Statistics and sampling are fundamental to almost all of our understanding of the world. The world is too big to measure directly. Measuring representative samples is a way to understand the entire picture.

Popular and academic literature are both full of examples of poor sample selection resulting in flawed conclusions about the population. Some of the most famous examples relied on sampling from telephone books (in the days when phone books still mattered and only relatively wealthy people had telephones) resulting in skewed samples.

This post is not about bias in sample selection but rather the simpler matter of sample sizes.

Population size is usually irrelevant to sample size

I’ve read too often the quote: “Your sample was only 60 people from a population of 100,000.  That’s not statistically relevant.”  Which is of course plain wrong and frustratingly wide-spread.

Required Sample Size is dictated by:

  • How accurate one needs the estimate to be
  • The standard deviation of the population
  • The homogeneity of the population

Only in exceptional circumstances does population size matter at all. To demonstrate this, consider the graph of the standard error of the mean estimate as the sample size increases for a population of 1,000 with a standard deviation of the members of the population of 25.

Standard Error as Sample Size increases for population of 1,000

Standard Error as Sample Size increases for population of 1,000

The standard error drops very quickly at first, then decreases very gradually thereafter even for a large sample of 100. Let’s see how this compares to a larger population of 10,000. Continue reading →

Bacon flavoured Bitcoins

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Bitcoins are an awful idea as a currency. The 21m fixed limitation on bitcoins in a hopefully growing economy requires deflationary prices. Deflationary prices in turn discourage consumption and encourage hoarding. Low consumption and hoarding lead to low economic growth, a decreased velocity of money and more deflation.

But what about Bitcoins as an interesting speculative investment? With prices surges recently some could have made serious money. With the inevitable crash, brave souls may make money shorting Bitcoins. (but “markets can remain irrational longer than you can remain solveny” etc.)

But, the Bitcoin supporters say, if there is a 21m ultimate final supply, won’t increasing demand lead to increasing prices? Won’t this become a type of collectors’ item?

Here we run firmly into the absolute lack of intrinsic value for Bitcoins. Gold is a limited, non-corroding, shiny, vaguely useful in electronics element. It also barely has intrinsic value but at least it is truly unique.

What’s to stop someone investing Bacon Flavoured Bitcoins with a maximum supply of 21m (or any other number). A new version of Bitcoins for when the original or “Classic Bitcoins” are so tightly in demand that there is obviously demand for more of the same or similar. We could also have cheese flavoured, bubble-gum flavoured or, my personal favourite, Dutch Tulip flavoured Bitcoins.

Artificial scarcity is not true scarcity and near substitutes can be created at will.

Bitcoins will not remain above USD100 by end 2013.

Banking failures in South Africa

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South Africa has a pretty rich history of banking failures.  This paper, part of a masters, by Sipho Makhubela, provides an interesting over of banking failures since 1994. I haven’t read the entire paper yet, but Section 4 (starting on page 72) outlines  the background behind banking failures in South Africa and is fascinating reading in its own right.

Summary of Cypriot capital controls

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From a number of sources (CNN, USAToday, FT)

No Eurozone country, since the creation of the Euro, has ever instituted capital controls. It’s not really allowed, except in exceptional circumstances. Which goes to show the value of rules with exceptions for “exceptional circumstances”. Which is to say, not much.

The cost to large depositors

Deposits above 100,000 euros have been frozen at both banks. They could be wiped out entirely at Popular. At Bank of Cyprus, about 40% will be converted into equity.

So that is an absolute bank failure, no two ways about it.

The capital controls

depositors would be able to withdraw no more than €300 in cash each day, said people familiar with the move. Transfers over €5,000 would require permission of the central bank.

Overseas credit card transactions would be limited to €5,000 per month, but unrestricted in Cyprus. And there would be a ban on people taking more than €3,000 of bank notes out of the country per trip.

These rules will expire in 7 days. Oh, unless they’re renewed. Prediction – they will be renewed.

Birdy statistics

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I’m not sure about this fascinating article on birds evolving to avoid cars in the US.

The story is that fewer cliff swallows are being killed on the roads AND those birds killed have longer than average wings. The argument here is that longer wings make for less agility, making the birds more likely to be killed by cars.

So far so good. But then:

The authors of the study found that over a 30 year period, annual cliff swallow roadkill has declined steadily from 20 birds per season in 1984 and 1985 to less than five birds per season during the last five years. Over the same period, traffic volumes remained the constant and the overall bird populations increased.

I am not an ornithologist or evolutionary expert, but I just can’t see how between 20 and 5 birds killed per season will create enough selection pressure to change the wingspan.

The original research summary is far more persuasive than the article. It shows graphs and statistical test results for decreasing average population wing size and increasing average road-kill wing size over time.

The explanation of why the average wingspan for cliff swallows killed be vehicles should increase is left unexplained. It does rather suggest potential measurement or confirmation bias from the research team – once the hypothesis starts looking interesting it would be very easy to unintentionally bias the measurements.  Measuring wingspan accurately to within a few millimetres is fraught with risks of subjective error.

Further, it looks like around 3 data points contribute significantly to the low p values of the tests and I would be very curious to know how robust the results were to removal of these influential points. It looks like the trends might remain, but without anything close to the significant suggested by the original research.

Finally, the clustering of wing measurement points in certain years suggests different levels of care and accuracy in measurement and potential “anchoring and adjustment bias”. It’s very hard to apply the same measurement protocols over 30 years.

So, fascinating research, interesting conclusion, but I’m left somehow unconvinced. It’s a pity the statistics applied weren’t a little more robust and the obvious criticisms weren’t addressed.

 

As Cyprus burns, does South Africa?

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SocGen in worried about South African bonds, government borrowing, budget deficits and the economy as a whole.

“Volcano Eruption” is the phrase they used. That’s not subtle stuff. A few other analysts quoted in the article and more bullish on the Rand and downplay risks for South Africa. I don’t feel that there is much news-flow that indicates an eruption, but I just don’t know what Cyprus Burning does for investor sentiment.