Random Fluctuations Risk

[Sid Dagore]

In Chapter 10 the core reading describes different types of risk associated with mortality - model risk, parameter risk and random fluctuations risk.

This RFR is the risk of actual future experience not corresponding with the model and parameters adopted. The core reading also says that this risk is more likely to arise if the law of large numbers doesn't apply.

What on earth is this risk? It isn't stated in terms of the mean/variance or anything like that!! Also, if one gets a result with a lower probability this isn't a lack of correspondence with the model/parameters; it's just a different manifestation than the average.

So what is going on?

Thanks!

 

[fischer]

If I remember correctly, then April 2008 has a good example to explain this risk. If a company is new then it will not have sufficient data from past experience because the past experience itself will not be enough to base assumptions on.
If the company does base assumptions on this past data then there is a risk that are assumptions may take account of some random fluctuations that may have occurred in the short past experience.

I think it's saying that:
if sample variance = sigma^2/n
where sigma = population variance and n = sample size

then as n increases the sample variance will reduce.

Does this sound like a reasonable explanation?

 

[Sid Dagore]

This doesn't really make sense to me because this should be included under model risk.

Thanks!

 

[fischer]

Model risk is if the model used is not appropriate. For eg using a binomial distribution for mortality instead of a normal distribution (okay not the best example)

Hope this illustrates random fluctuations risks:
Suppose investment returns in the past 12 months were
10%, 10%, -25%, 10%, 10%, ...., 10%

What would be an appropriate estimate of future investment returns?
One approach, take the average including the -25%.
Another approach would be take the average but ignore the -25%. This would be reasonable because the -25% for that month would have been due to a one-off factor (not likely to occur again/ cannot be predicted with any certainty) and not an indicator of future trend in investment return.

Now finally, suppose you had extended this investigation to the last 120 months and if the investment returns were still 10% except that one -25%, it would not make a big difference whether or not you included or ignored the -25% investment return in working out the average as an estimate. The average would still be 10% or close to it.

If this does still not help, then it may be a bit too late to try and understand it. Good luck anyway.