### Actuarial Advice, Part II

Now my point in Part I was not to be the latest in a long line of people to point out how foolish the actuarial assumption of equity returns being 10% forever are.

Rather, it is that the rules of the system have produced the behaviour.

If you set things up so that you are given advice where the 'best' thing to do today is purely defined by what happened in the past, you run a lot of risk that the future will be different to the past and hence that the advice will be misleading. One of the pieces of information missing in the old actuarial advice was some measure of the probability of things going sufficiently differently that pension obligations could not be met: perhaps if trustees had had that, they might have invested differently?

In the absence of any theory which we have reason to believe governs the behaviour of a variable, didn't David Hume point out the error of thinking the past behaves like the future? For the financial markets this is even more clearly silly than elsewhere: the global economy is obviously very different now from the one we had in the 80s, let alone the 50s. So why should stock prices follow paths characterised by statistics from long ago? That is not to say that we should not pay any attention to the statistics: just that we should be aware that there is model risk in how we use the past to predict the future, and for the sake of the next generation of pensioners, perhaps that risk should be considered along with all the others involved in running a long term investment portfolio.

When we use mathematics to model the world, as in fitting a return distribution of some financial asset, there is the danger that we use the maths that is convenient rather than the maths that captures the essential features of the problem. In finance, for instance, we are so obsessed with normal distributions that we use them whereever possible. Part of the reason for this is that so much is known about them -- we have a lot of tools to hand. Also, the errors made by using a normal distribution are often small for typical financial applications (especially once we hack in the implied volatility smile). That doesn't mean that the assumption that (log) returns are normally distributed is always good, though.

Phillipe Jorion has a insight into the dangers here in his paper on the fall of LTCM ( then search for Long Term Capital Management): he shows how making an modelling assumption, that correlation is stable and the return distribution is normal, leads to a dramatic understatement of risk. Sometimes, which tool you pick makes a lot of difference, and familiar tools can be the riskiest ones, not least because everyone else is using them too.

This is an education issue: the next generation of mathematical modellers needs to be taught how to model, but also about the dangers of modelling, about the need to look at a problem through the prisms of different models.

Turning back to actuarial advice, we have people trying to model the future using the past but without a theory that explains the dynamics, a system that encourages them to give their best guess with quantifying how wrong that guess might be, and a predilection for using tools that have nice mathematical properties but fail to capture significant features of the real world. Is it any wonder we have a pensions crisis?

There, I managed to talk about actuarial advice without mentioning the Ljung Box statistic once...

Rather, it is that the rules of the system have produced the behaviour.

If you set things up so that you are given advice where the 'best' thing to do today is purely defined by what happened in the past, you run a lot of risk that the future will be different to the past and hence that the advice will be misleading. One of the pieces of information missing in the old actuarial advice was some measure of the probability of things going sufficiently differently that pension obligations could not be met: perhaps if trustees had had that, they might have invested differently?

In the absence of any theory which we have reason to believe governs the behaviour of a variable, didn't David Hume point out the error of thinking the past behaves like the future? For the financial markets this is even more clearly silly than elsewhere: the global economy is obviously very different now from the one we had in the 80s, let alone the 50s. So why should stock prices follow paths characterised by statistics from long ago? That is not to say that we should not pay any attention to the statistics: just that we should be aware that there is model risk in how we use the past to predict the future, and for the sake of the next generation of pensioners, perhaps that risk should be considered along with all the others involved in running a long term investment portfolio.

When we use mathematics to model the world, as in fitting a return distribution of some financial asset, there is the danger that we use the maths that is convenient rather than the maths that captures the essential features of the problem. In finance, for instance, we are so obsessed with normal distributions that we use them whereever possible. Part of the reason for this is that so much is known about them -- we have a lot of tools to hand. Also, the errors made by using a normal distribution are often small for typical financial applications (especially once we hack in the implied volatility smile). That doesn't mean that the assumption that (log) returns are normally distributed is always good, though.

Phillipe Jorion has a insight into the dangers here in his paper on the fall of LTCM ( then search for Long Term Capital Management): he shows how making an modelling assumption, that correlation is stable and the return distribution is normal, leads to a dramatic understatement of risk. Sometimes, which tool you pick makes a lot of difference, and familiar tools can be the riskiest ones, not least because everyone else is using them too.

This is an education issue: the next generation of mathematical modellers needs to be taught how to model, but also about the dangers of modelling, about the need to look at a problem through the prisms of different models.

Turning back to actuarial advice, we have people trying to model the future using the past but without a theory that explains the dynamics, a system that encourages them to give their best guess with quantifying how wrong that guess might be, and a predilection for using tools that have nice mathematical properties but fail to capture significant features of the real world. Is it any wonder we have a pensions crisis?

There, I managed to talk about actuarial advice without mentioning the Ljung Box statistic once...

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