Category Archives: Actuarial and Risk

Binary vs “vanilla” bets and hedging

Nassim Taleb, an author who usually inspires (except in his second book, Black Swans) has co-authored a paper with a long-tailed title “On the Difference between Binary Prediction and True Exposure with Implications for Forecasting Tournaments and Decision Making Research”.

The paper isn’t paygated so check it out – it’s only 6 pages so definitely accessible. Don’t worry about the couple of typos in the paper, bizarre as it may be to find them in a paper that presumably was reviewed, the ideas are still good.

The key idea is that prediction markets usually focus on binary events. Will Person Y win the election? Will China invade Taiwan? These outcomes are relatively easy to predict and circumvent important challenges of extreme outcomes and Taleb’s Black Swans.

A quote from the paper, itself quoting Taleb’s book, Fooled By Randomness, sums up the problem of trying to live in. Binary world when the real world has a wide range of outcomes.

In Fooled by Randomness, the narrator is asked “do you predict that the market is going up or down?” “Up”, he said, with confidence. Then the questioner got angry when he discovered that the narrator was short the market, i.e., would benefit from the market going down. The trader had a difficulty conveying the idea that someone could hold the belief that the market had a higher probability of going up, but that, should it go down, it would go down a lot. So the rational response was to be short.

LAC Seminar 2013 live tweeting complete list

A few people have mentioned that they found my “live blogging” or tweeting of the 2013 LAC Seminar in Cape Town and Joburg useful. I used the hastag #LACseminar2013. I’m repeating all of them here in case they’re useful in a slightly more long-lived medium of my blog. I didn’t cover all the sessions – below is all there is and yes, in reverse order for bizarre reasons I’m not going to go into now.

@23floor: Also, envisaged that product specifications, including commission, must be filed with regulator #LACseminar2013 #microinsurance

@23floor: And yes, a range of market conduct, board composition requirements are envisaged for micro insurance #LACseminar2013 #microinsurance

@23floor: Raw (cleaned and anonymize) data *might* be released publically. I would definitely support this. Data should be open #LACseminar2013

@23floor: PA90 understates mortality on average, but more under for males and only a little over for females #LACseminar2013 Continue reading LAC Seminar 2013 live tweeting complete list

Open mortality data

The Continuous Statistical Investment Committee of the Actuarial Society does fabulous work at gathering industry data and analysing it for broad use and consumption by actuaries and others.

I can only begin to imagine the data horrors of dealing with multiple insurers, multiple sources, multiple different data problems. The analysis they do is critically useful and, in technical terms, helluva interesting. I enjoyed the presentation at both the Cape Town and Johannesburg #LACseminar2013 just because there is such a rich data set and the analysis is fascinating.

I do hope they agree to my suggestion to put the entire, cleaned, anonymised data set available on the web. Different parties will want to analyse the data in different ways; there is simply no way the CSI Committee can perform every analysis and every piece of investigation that everyone might want. Making the data publicly available gives actuaries, students, academics and more the ability to perform their own analysis. And at basically no cost.

The other, slightly more defensive reason, is that mistakes do happen from time to time. I’m very aware of the topical R-R paper that was based on flawed analysis of underlying data. Mistakes happen all the time, and allowing anyone who wants to have access to the data to repeat or disprove calculations and analysis only makes the results more robust.

So, here’s hoping for open access mortality investigation data for all! And here’s thanking the CSI committee (past and current) for everything they have already done.

Why equity matters

Income inequality is a bad thing. It’s a suboptimal scenario. This isn’t something that is debatable. It follows from a few fairly fundamental principles:

  • Wealth demonstrates diminishing marginal returns.  This is evidenced through risk aversity and other empirical studies
  • Happiness does generally increase with wealth, but at a decreasing rate.
  • There’s plenty of evidence that living in an area where others have more money than you makes you unhappy, even if you’d be happy with the exact same amount of money in a neighbourhood where you earned more than average.

In other words, taking money away from the wealthy to give to the poor makes the wealthy less unhappy than it makes the poor happy. More equal incomes will improve over happiness. Although I suspect the action of “taking away from the wealthy” has a certain inherent bias to unhappiness itself.

The virtual irrelevancy of population size to required sample size

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 The virtual irrelevancy of population size to required sample size